TWI730284B - Receiving method, receiving device, transmission method, transmission device, transmission and reception system - Google Patents

Abstract

One aspect of the receiving method of the received signal includes an estimating step, which refers to a parameter space with a co-dimension 2 irreplaceable displacement to estimate the time shift and the frequency shift represented by the received signal.

Description

Receiving method, receiving device, transmitting method, transmitting device, transmitting and receiving

The present invention relates to a receiving method, a receiving device, a transmitting method, a transmitting device, and a transmitting and receiving system.

At present, there have been many researches and developments on communication system technology and its related technologies, and the present inventors have conducted research and development on transmission and reception systems using time division methods and frequency division methods (for example, the following patent documents 1- 6. Non-Patent Document 1-32).

[Prior Technical Literature]

[Patent Literature]

[Patent Document 1] Japanese "JP 2016-189500" gazette

[Patent Document 2] International Publication "WO2012/153732 A1"

[Patent Document 3] International Publication "WO2014/034664 A1"

[Patent Document 4] International Publication "WO2013/183722 A1"

[Patent Document 5] Japanese "JP 2016-189501" gazette

[Patent Document 6] Japanese "JP 2016-189502" gazette

[Patent Document 7] Japanese "JP 2013-251902" gazette

[Patent Document 8] Japanese "JP 2012-170083" gazette

[Non-Patent Literature]

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[Non-Patent Document 2] D. Gabor, "Lectures on communication theory", in Technical Report., No., 238. Research Laboratoty of Electronics, Massachusettes Institute of technology Cambribge, 1-48, 1952.

[Non-Patent Document 3] L.W. Couch, II, Digital and Analog Communication Systems, 8th Ed.," Pearson, 2013.

[Non-Patent Document 4] G.B.Folland, Harmonic Analysis in Phase Space, Annals of Mathematics Studies Princeton Univ. Press, 1989.

[Non-Patent Document 5] Howe,R. On the role of the Heisenberg groups in harmonic analysis," Bulltein of the American Mathematical Society, 3-2,821-840 (1980)

[Non-Patent Document 6] Rosenberg, J. A selective history of the Stone-von Neumann theorem, Contemporary Mathematics, 365. American Mathematical Society (2004)

[Non-Patent Document 7] I. Daubechies, Time-frequency localization operators: a geometric phase space approach," IEEE Trans. Information Theory, 34-4,605-612,1988.

[Non-Patent Document 8] I. Daubechies, The wavelet transform, time-frequency localization and signal analysis," IEEE Trans.Information Theory, 36-5,961-1005, 1990.

[Non-Patent Document 9] B. Le. Floch, M. Alard & C. Berrou, "coded OFDM: Coded Orthgonal Frequency Division Multiplex," Proc. of IEEE, 83-6, 982-996, 1995.

[Non-Patent Document 10] P. Siohan, C. Sciclet, & N. Lacaille, "OFDM/OQAM: Analysis and Design of OFDM/ OQAM Systems, based on Filterbank Theory," IEEE, Trans. Sig.50-5, 1170 -1183, May, 2002.

[Non-Patent Document 11] Sciclet, C., Siohan, P. & Pinchon, D. Perfect reconstruction conditions and design of oversampled DFT-based transmultiplexers, EURASIP J. on Applied Signal Processing, 2006, Article ID 15756,1-14, 2006.

[Non-Patent Document 12] B.F. Boroujeny, "OFDM Versus Filter Bank Multicarrier," IEEE Signal Processing Magazine, 28-3, 92-112, 2011.

[Non-Patent Document 13] P.P.Vaidyanathan, "Multirate Systems and Filter Banks," Prentice-Hall, 1993.

[Non-Patent Document 14] J. Ville, ”Th′eorie et application de la notion de signal analytique,” C′ables et transmission, no.2, pp.61-74.1948. (J.Ville: ”Theory and Applications of the notion of complex signal", translated from the French by I.Stein, T-92,8-1-58,USAir Force Project Rand, 1958)

[Non-Patent Document 15] P.M. Woodward, Probability and Information Theory, with Applications to Radar, Pergamon Press, New York, 1953.

[Non-Patent Literature 16] C.H. Wilcox, "The synthesis problem for radar ambiguity function," MRC Technical Report, No. 157, pp.1-46. Mathematics Reaearch Center, U.S. Army, Univ. Wisconsin, Madison, 1960.

[Non-Patent Document 17] L. Auslander and R. Tolimieri, "Radar Ambiguity Functions and Group Theory, SIAM J. Math. Anal., 16-3, 577-601, 1985.

[Non-Patent Document 18] C.W. Helstrom, Elements of Signal Detection and Estimation," PTR Prentice-Hall, 1995.

[Non-Patent Document 19] N. Levanson and E. Mozeson, "Radar Signals," Wiley interscience, 2004.

[Non-Patent Literature 20] Sakurai, J. J. Modern quantum mechanics, S. F. Tuan editor, Rev. ed., Addison-Wesley Pub. Comp. 1994.

[Non-Patent Document 21] J. von Neumann, The Geometry of Operators, vol. II (Ann. Math. Studies, no. 22), 1950.

[Non-Patent Document 22] Youla, D. C Generalized image restoration by the method of alternating orthogonal projections, IEEE Trans. Circuits and Systems, CAS-25-9, 694-702, 1978.

[Non-Patent Document 23] Stark, H., Cahana, D. & Webb, H. Restoration of arbitrary finiteenergy optical objects from limited spatial and spectral information, J.Opt.Soc.Amer., 71-6,635-642, 1981.

[Non-Patent Document 24] Kohda, T., Jitsumatsu, Y. & Aihara, K. Separability of time-frequency synchronization, Proc.Int.Radar Symp., 964-969,2013.

[Non-Patent Document 25] T. Kohda, Y. Jitsumatsu, and K. Aihara, “Gabor division/spread spectrum system is separable in time and frequency synchronization,” Proc. VTC 2013 Fall, 1-5,2013.

[Non-Patent Document 26] Y. Jitsumatsu, T. Kohda, and K. Aihara, “Spread Spectrum-based Cooperative and individual time-frequency synchronization,” Proc.(ISWCS), 1-5,2013.

[Non-Patent Document 27]Jitsumatsu, Y., Kohda, T., & Aihara, K. Delay-Doppler space divisionbased multiple-access solves multiple-target detection, Jonnsson, M., et al, (eds.) MACOM2013, LNCS8310 , Springer, 39-53, 2013.

[Non-Patent Literature 28] T. Kohda, Y. Jitsumatsu, and K. Aihara, ”Recovering noncoherent MPSK signal with unknown delay and Doppler using its ambiguity function,” 4th International workshop on recent Advanced in Access Network, (RABAN2013), 251 -256, 2013.

[Non-Patent Document 29] T. Kohda, Y. Jitsumatsu and K. Aihara “Phase-tuned layers with multiple 2D SS codes realize 16PSK communication,” 2014 2014 IEEE Wireless Commun. Networking Conference, WCNC 2014,469-474 (2014) .

[Non-Patent Document 30] Jitsumatsu, Y. & Kohda, T. Digital phase updating loop and delay-Doppler space division multiplexing for higher order MPSK, Jonnsson, M., et al, (eds.) MACOM2014, LNCS8715, Springer,1 -15, 2014.

[Non-Patent Document 31] T. Kohda, Y. Jitsumatsu, and K. Aihara, “Frequency-division spread spectrum makes frequency synchronisation easy,” Proc. IEEE Globecom 2012, 3952-3958, 2012.

[Non-Patent Document 32] T. Kohda, Y. Jitsumatsu, and K. Aihara, “Frequency synchronisation using SS technique,” Proc. The ninth Int. Sympo. on Wireless Communication Systems, 855-859, 2012.

[Non-Patent Document 33] J.F. Daughman, "Two-dimensional analysis of cortical receptive field profiles," Vision Research, 20, 846-856, 1980.

[Non-Patent Document 34] J. F. Daughman, “Image analysis by local 2-D spectral signatures,” J. Opt. Soc. Amer. (A), 2, p. P74, 1985.

[Non-Patent Document 35] J. F. Daughman, "Complete Discrete 2-D Gabor Transform by Neural Networks for Image Analysis and Compression," IEEE Trans. Acoustics, Speech and Signal Processing, 36-7, 1169-1179, 1988.

[Non-Patent Document 36] Movella, Javier R. "Tutorial on Gabor filters". Archived from on 2009-04-19, Retrieved 2008-05-14.

[Non-Patent Document 37] Hans G. Feichtinger and Thomas Strohmer: Gabor Analysis and Algorithms, Birkhauser, 1998.

[Non-Patent Document 38] Jones, J. P. and Palmer, L. A. "An evaluation of the two-dimensional gabor filter model of simple receptive fields in cat striate cortex". J. Neurophysiol. 58(6): 1233-1258. 1987.

[Non-Patent Document 39] Tai Sing Lee, “Image representation using 2d Gabor wavelets,” IEEE Trans. on pattern analysis and machine intelligence, 18-10, 1-13, 1996.

[Non-Patent Document 40] W. D. Montgomery "Optical applications of von Neumann's alternating projection theorem," Optics Letters, 7-1, 1-3, 1982.

[Non-Patent Document 41] W. D. Montgomery "Restoration of images processing a finite Fourier series," Optics Letters, 7-2, 54-56, 1982.

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[Summary of the invention]

At present, the inventors of the present case, based on the related research on the theoretical aspects of communication technology, have achieved that they must focus on the inherent non-replaceability of the displacement operators on the Time Frequency Plane (TFP, also simply referred to as TFP). .

The state of the present invention is based on the above-mentioned known technology, and aims to realize a high-efficiency receiving method, receiving device, transmission method, transmission device, and transmission receiving system.

In order to solve the above-mentioned problems, the state of the present invention is a receiving method of a received signal, which includes: an estimation step, which refers to a parameter space with an irreplaceable displacement of Codimension 2 to estimate what the received signal represents的 time shift and frequency shift.

In addition, in order to solve the above-mentioned problems, the aspect of the present invention is a receiving device for receiving signals, which includes: an estimating unit that estimates the time represented by the received signal by referring to a parameter space with a co-dimension 2 irreplaceable displacement Displacement and frequency displacement.

In addition, in order to solve the above-mentioned problems, the aspect of the present invention is a signal transmission method, which includes: a displacement step, which refers to a parameter space with a co-dimension 2 irreplaceable displacement, so that the time of the signal of the transmission object is Frequency shift.

In addition, in order to solve the above-mentioned problems, the aspect of the present invention is a signal transmission device, which includes: a displacement part, which refers to a parameter space with a co-dimensional 2 irreplaceable displacement, so that the time of the signal of the transmission object is Frequency shift.

In addition, in order to solve the above-mentioned problems, the aspect of the present invention is a receiving method for receiving image signals, which includes: an estimation step, which refers to the parameter space to estimate the spatial displacement and spatial frequency represented by the received image signal Displacement; and the above-mentioned spatial displacement and spatial frequency displacement system each has more than 2 dimensions.

In addition, in order to solve the above-mentioned problems, the aspect of the present invention is a transmission method for transmitting image signals, which includes: a displacement step, which refers to the parameter space to shift the space and frequency of the image signal of the transmission object; and The spatial displacement and the frequency displacement system each have two or more dimensions.

According to the above configuration, a highly efficient receiving method, receiving device, transmitting method, transmitting device, and transmitting and receiving system can be realized.

1.1a: Transmitting and receiving device

100, 100a: conveyor

101: Data acquisition unit for transmission

102, 102a: Transmission signal generating unit

103: Transmission Department

110: Displacement embedded part

200, 200a: receiving device

201: Receiving Department

202, 202a: Displacement estimation and received data extraction unit (estimation unit)

203: Received data analysis department

S101~S103, S102a: steps

S201~S203, S202a: steps

[Figure 1] shows the three segmentation methods of TFP in the implementation type. (a) is Time Division (TD, Time Division); (b) is Frequency Division (FD, Frequency Division); (c) is Gabor Division (GD, Gabor Division) as shown in [Non-Patent Document 1]. Among them, the solid line in (a) represents the division of the time width T of the information data; the dotted line represents the fine division based on the time division phase code (TD-PC, TD-Phase code, phase code also known as PC). The thick dotted line in (b) represents the information data The division of bandwidth F; the thin dashed line represents the fine division based on frequency division phase code (FD-PC, FD-phase code).

[Figure 2] is a diagram schematically showing the irreplaceability of the time-frequency shift in the implementation type. The non-substitutability lies _{in the relational expression T τ,0 ‧T 0,ν} =e ^-i2πτν T _0,ν T _τ,0 about the product of displacement operators (the left side corresponds to the triangle label in the figure, and the right side corresponds to the square in the figure Among them, it appears as phase distortion (PD) e- ^i2πτν . The circle symbol ○ in the figure indicates the Symmetrical Time-Frequency Shift Operator (TFSO)

[Non-Patent Document 26].

[Figure 3] (a) shows the Gabor function and its related information configured at the chip level on the TFP in the implementation type. In particular, (a-0) is the Gabor function g _{mm ′} (t) and its Fourier transform (FT) G _{mm ′} (f) showing the chip level arranged on the TFP. (a-1) Display the real and imaginary parts of the TD-template (time division template _{) that adds g mm '} (t) to frequency division phase encoding (FD-PC) X ' _{m '; (a-2} ) Shows the real and imaginary parts of the FD-template (frequency division template) _{that G mm '} (f) is emphasized and added by the time division phase encoding (TD-PC) X _m. (b) is NN' cross correlation function (CCF) on TFP, TD-CCF value of N'column sum and FD-CCF value of N row sum. (c) According to the Alternating Projection Theorem (APT, Alternating Projection Theorem), the upper orthogonality of the time limited time space (TL-TD, time limited time domain) and the band limited frequency domain (BL-FD, band limited frequency domain) Estimated value of projection

The interactive update process and the convergence value t _d , f _D.

[Figure 4] is a schematic diagram of the synthesis filter bank (SFB _{) of the TD feature mark (sig n} ature) v[k] of formulas (25) and (67) generated in the implementation type, wherein the above formula has TD-PC of X _m, FD-PC's X _'m' and the number m 'of the TD-template

[Figure 5] shows the FD signature of formulas (25) and (67)

[Math 5] V [ l ]

A schematic view of the SFB, having the above formula wherein X _m TD-PC's, FD-PC's X _'m' and the number m 'of the TD template

[Figure 6] shows the TD-Complex Envelope (TD-CE, TD-Complex Envelope) that produces formulas (27) and (71)

[Math 7] ψ [ k ]

Schematic diagram of the SFB in which the above formula has complex data as the implementation form of the input signal

[Figure 7] shows the FD-Complex Envelope (FD-CE, TD-Complex Envelope) that produces formulas (27) and (71)

[Math 9] Ψ[ l ]

Schematic diagram of the SFB in which the above formula has complex data as the implementation form of the input signal

[Figure 8] It shows the complex data of the implementation type of the equipment

A schematic diagram of the analysis filter bank (AFB, Analysis Filter Bank) of the TD correlator array for decoding.

[Figure 9] It shows the complex data of the equipment with the implementation type

A schematic diagram of the AFB of the FD correlator array for decoding.

[Figure 10] (a) is a schematic diagram showing the implementation of the TD correlator array; (c) is a schematic diagram showing the analysis filter bank (AFB) of the FD correlator array; (b) is a schematic diagram showing the von based Neumann's APT will interactively update the maximum likelihood estimates of the two arrays.

[Figure 11] is a diagram schematically showing von Neumann's Alternating Projection Theorem (APT) in the implementation mode. In the figure, TL-TD (time limited time domain, limited time space) and BL-FD (band limited frequency domain, limited bandwidth frequency space) respectively represent two partial spaces of the Hilbert space (Hilbert space). In addition, the partial space TL-TD means LΔt-(or T _S )-Time-limited (TL) space. Partial space BL-FD means L△f-(or F _S )-band-limited (BL) space. In the figure, the arrows indicate the orthogonal projections of each part of the space upward, and the CCF numbers that provide the maximum likelihood estimation value and the maximum likelihood value are measured.

[Figure 12] shows the implementation type

[Math 12] M

-PSK is a block diagram of the structure of a transmitter (encoder) that can communicate and perform high-speed and high-precision distance measurement.

[Figure 13] shows the implementation type

[Math 13] M

-PSK is a block diagram of the structure of a receiver synchronizer (decoder) that can communicate and perform high-speed and high-precision distance measurement.

[Figure 14] is a diagram schematically showing an example of the distribution of the real part of the CCF in the main channel (MC, Main channel) delay τ -Doppler displacement ν space of the implementation type.

[Figure 15] is a diagram schematically showing an example distribution of the size of the real part of the CCF in the τ - ν space when the artificial channel (AC, Artificlal Channel) of the implementation type is overlapped on the main channel (MC).

[Figure 16] is a diagram showing that the signal in the parameter space with irreplaceable AC displacement in dimension 2 of the implementation type is used for TFP division. In the time/frequency plane TFP S division (Gabor division) (S ⁽⁰⁾ , S ⁽¹⁾ , S ⁽²⁾ , S ⁽³⁾ ) plane orthogonal to the signal (time width T _S , bandwidth F _{S) time/frequency plane} On the axis of, the non-replaceable displacement of AC is displayed

Scale, and the two-dimensional PC code corresponding to the TFP segmentation

[Math 15] χ ^{( i )} .

[Figure 17] is a diagram showing that the signal in the parameter space with irreplaceable AC displacement of dimension 2 of the implementation type is used for TFP division. In response to the non-replaceable displacement of AC, TFP is shifted to TFP of AC0, TFP of AC1, TFP of AC2, and TFP of AC3, respectively.

[Figure 18] is a block diagram showing a configuration example of the transmission and reception system of the first embodiment.

[Figure 19] is a flow chart showing the flow of data transmission and reception processing using the transmission and reception system of Embodiment 1.

[FIG. 20] is a block diagram showing a configuration example of the transmission and reception system of the first embodiment.

[Fig. 21] is a flowchart showing the flow of data transmission and reception processing using the transmission and reception system of Embodiment 1.

[Form to implement invention]

[Embodiment 1]

The following describes the transmission and reception system in this embodiment with reference to the drawings. The following first describes the theoretical aspects and specific configuration examples of the transmission and reception system in this embodiment. After that, it corresponds to the content recorded in the scope of the patent application.

In addition, the patent documents and non-patent documents in the following description are incorporated herein by reference.

In addition, the patent documents and non-patent documents cited in the following description are cited only from the viewpoint that they have some relevance to the content described in this specification. Therefore, the citing of these documents does not affect the patentability of the invention described in this specification.

<<Summary of the theory: communication using the non-replaceability of the two operators of time delay and frequency shift (Subtitle: High-precision ranging transmission signal design and its receiver design)>>

In order to _{efficiently transmit data of the time width T S} and the frequency width F _S, it is a difficult problem to synchronize the multiple communication methods that divide the time (TD) and the frequency space (FD). _{Even the radar problem of delay (delay) t d} and Doppler (Doppler) f _D estimated from the reflected signal of the transmitted radio wave is still in an unresolved state. The root of this is the same as the position and movement operator of quantum mechanics [Non-Patent Document 4], which is the phase distortion (PD) derived from the Time-Frequency Shift Operator (TFSO).

Or

The ranging problem is the estimation problem of two unknown parameters contained in the PD of the TFSO that cannot be replaced. Therefore, it is impossible to use the signal detection and parameter estimation theory based on the Weyl-Heisenberg Group (WHG, Weyl-Heisenberg Group). Achieve high accuracy and high speed. The following five points are summarized as a summary of the description in this manual.

(Summary 1)

The first part is that in the design of transmission and reception, the TD signal and the FD signal are the same as the object. In addition, the pair of time-frequency symmetrical properties (TFSP, time-frequency symmetrical property) is satisfied. The symmetrical TFSO is an operator that displays the address information of the multiplexed signal based on the irreplaceability of time delay and frequency shift (refer to formulas (39), (44), (51)) , (56)).

(Summary 2)

The second part is the time. Frequency-shifted Gaussian Chip function (Gabor function), using cycle N, N'TD-PC, FD-PC (phase code) modulation, that is, TD-BPSK and FD-BPSK (Binary phase shift Keying, two-dimensional phase shift keying), is useful for the M value detection method of parameter maximum likelihood estimation.

In the past, the two types of PCs were called "two-dimensional diffusion notation", and there were many misuses of expanded explanatory terms. However, this specification explains that the two-dimensional phase shift key (BPSK) has the following advantages and disadvantages that have not been discovered so far.

Modulated TD- and FD- broadband (broadband) spatial signals (also known as signature) complex packet (CE) (Equation (27)) in the PD generated by the PC, as N types (type)- 3 (or type-1) TD template CE (formula (29)) (or formula (49)) (each support set (support) is T _s × L△f, L△t×F _s ), N'type-4 (or type-2) FD template CE (formula (33)) (or formula (54)) (each support is L△t×F _s , T _s ×L△f ) Is automatically embedded, so the hypothesis detection of template detection can be TD, FD (formula (30), proposition 4 and formula (35), proposition 5).

(Summary 3)

Different from the usual maximum likelihood method where the phase information is not effectively used, the third part is: type-3 (or type-1) TD-CE template, type-4 (or type-2) FD -The four precise formulas of TD-CCF and FD-CCF of CE template matching, in addition to the ambiguity function (AF, ambiguity function), also include TD-PC, FD-PC modulation with time width △t and bandwidth △f Discretization L=(△t△f) ^-1 point twiddle factor (twiddle factor)

Moreover, in the above-mentioned precise formula, among the sums of discrete Fourier transform (DFT, Discrete Fourier Transform) and inverse Discrete Fourier Transform (IDFT) type of W, the non-substitutable PD is regarded as the sum of W The power appears, and the result is that the exact formula appears as a product of three elements (Lemma 2 formula (41), Lemma 4 formula (45), and formulas (52), (57)). Therefore, according to the method described in this embodiment, high-speed calculation with a digital signal processor (DSP) can be ensured.

(Summary 4)

The fourth part is about the convergence of the phase-updating loop (PUL) defined and introduced in Patent Document 1, based on Youla [Non-Patent Document 22]'s signal recovery method and provides proof.

First, as part of the signal space of the Hilbert space, import and define T _s- (or L△t-) time-limited TD space E ₃ (or E ₁ ), F _s- (or L△f-) limited bandwidth (Band-Limited) FD space E ₄ (or E ₂ ). Then, based on N, N'TD-CCF and FD-CCF arrays, the orthogonal projection operator (PO, projection Operator) of these spaces upwards; T _s -(or L△t-) Time-limited operator P ₃ (or P ₁ ); and F _s -(or L△f- _{) The four POs of the frequency-limited operator P 4} (or P ₂ ) are given by formulas (62)-(64) To define.

Next, will replace the projection theorem (APT, Alternative Projection Theorem) [Non-Patent Document 21] interactive projection operator (APTO)

[Math 19] P ₃ F ^{-1, d} P ₄ F ^d (or P ₄ F ^d P ₃ F ^{-1, d} ) ( F ^d , F ^{-1, d} is DFT, IDFT)

Defined from the viewpoint of the present invention. Next, use as the estimated value

The updated equation (59) of the maximum likelihood estimate (MLE) of the communication path attenuation constant Aei κ as a function of

The updated formulas (60) and (61) of APTO are used for maximum likelihood estimation in the convergence space of APTO (support of TD-CE template, FD-CE template and its product set, that is, for chip address(p, p') The time width L△t and the frequency width L△f in the rectangular space) have t _d , f _{D to} perform its maximum likelihood estimation to prove the estimated value

Is the accuracy of L△t×L△f, and proves that the calculation amount is

[Math 23] O ( NN' )

And was replaced with

[Math 24] O ( N + N' ).

That is to say, this APTO is: extract a certain space of time-frequency plane (TFP, time-frequency plane), and filter-out other parts (LO, localization operator), which is Alternatives to risky filters commonly used in DSP.

Due to the reason that the Nyquist condition was not met in the previous communication, it can be known that the Gaussian function that has never been used plays an essential role based on other superior properties.

If PUL uses time PT _s and bandwidth P'F _s , the necessary resource and data level address (address)

, It is an exploratory method that does not limit the existence range of _{t d} , f _D. Therefore, it is shown that the combination of a transmitter equipped with a two-dimensional PC modulation signal with TD-Gauss function and FD-Gauss function, and a receiver with PUL installed on TD-CCF and FD-CCF arrays can achieve high A communication system for accurate and high-speed signal recovery, high-precision and high-speed parameter estimation. In other words, by using the above configuration, the template shift of the communication system that utilizes the non-replaceability is suggested.

In the fifth part, the department provides a system that synchronizes and gives super high

[Math 26] M

-PSK encoding and decoding.

[Math 27] M

-The PSK communication system can be used as a vehicle-mounted radar capable of simultaneous ranging and data communication. Because high-end

[Math 28] M

-PSK signal

Transmission, under the influence of various phase noises, it is difficult to phase

, So from the effective use of frequency resources (

[Math 31] log ₂ M -bit

From the point of view of transmission, although this is important, it is difficult to achieve.

To solve this problem, as in the lower part of Figure 12 (the block between Switch 1-1 and Switch 1-2), 1) Decompose the "message k" into

Next, 2) The parameter plane of time delay and Doppler shift (referred to as target space) is equally disjoint division (disjoint division) as

[Math 33]

And each is assigned a 2-dimensional PC (TD-PC, FD-PC) (here,

); and with the first

A 2D PC modulates the pulse wave of the chip, and this

-Code multiplexing.

Next, 3) Delay the time of the center point of the partial plane corresponding to the j-th target space in the obtained signature signal

Doppler shift

The amount (will

It is called the shift of the artificial channel (AC, Artificlal Channel); 4) Transmit and use the shifted signature modulation

[Math 40] M ₀

-PSK signal

After the signal. result,

-The signature after displacement is

[Math 43] ( k _d , l _D )

(Called the shift of the main channel (MC, Main Channel)) receives the double shift on the propagation path. Use the following steps to obtain the necessary estimated received CE for the correlation function (CCF) related to the received CE signal. As shown in the middle part of Figure 13 (block connected to Switch2-1), 1’) will estimate the value

Decompose into

2’)以第

2')

A 2D PC modulates the pulse wave of the chip; 3’) shifts its signal to the first

AC

的量; 4’) Use the obtained signal to make the presumption

Of

[Math 50] M ₀

-PSK signal

The modulated signal becomes the presumed receiving CE.

N, N'array type TD-CCF, the maximum variable system of the real part of FD-CCF is the chip address ( ρ ', ρ ) and data address

The determined CCF number and presumptive code

. First of all, based on the decision that will be attached

Kind of 2D PC Number

Data address

Phase compensation term

The two kinds of CCF real part maximized PUL, and as shown in the lower part of Figure 13 (connected to the block of Switch2-2), use

[Math 58] ( k _d , l _D )

And variables

Of the maximum likelihood estimate

[Math 60] k ^* = j ^* M ₀ + j ^* '

, Decode k maximum likelihood.

This department will be low-level

[Math 61] M ₀

-ary PSK-based encoding and decoding system, with

Kind of non-replaceable AC-shift-multiple super high

[Math 63] M

-ary PSK system. That is, this is in

Among the non-replaceable shift ACs, the cascade is connected to the AC determined by "message k"

[Math 65] ( k _d , l _D )

The MC output of, the synchronizer (range finder) for parameter estimation and the decoder of k are both used as a system. Therefore, the multiplex method based on non-replaceable AC-shift-encoding and decoding is a template shift used by PD in communication. also,

[Math 66] M

-The computational complexity of PSK decoding is based on the computational complexity of synchronization and ranging (N+N')

Times.

<<Theoretical details, as well as specific examples of the structure of the communication system>>

The following describes the detailed content of the theoretical aspects of the communication system in this embodiment, and the specific configuration examples of the communication system.

<1. Background>

An important subject of communication is the design of a communication method that effectively utilizes frequency resources [Non-Patent Document 1]. Orthogonal Frequency (OFDM, Orthogonal Frequency) is a communication method that divides time space (TD) and frequency space (FD) (refer to Figure 1), and multiplexes data of time width Ts and bandwidth Fs (refer to Figure 1) Division Multiplex), the system has the disadvantage of destroying orthogonality _{based on delay t d} or Doppler f _D.

In addition, Figure 1 shows the three segmentation methods of TFP. (a) display time division (TD, time division); (b) display frequency division (FD, Frequency Division); (c) display GD (Gabor Division, Gabor division) [Non-Patent Document 1]. The solid line in (a) represents the division of the time width T of the information data, and the dotted line represents the fine division based on the TD-Phase code (PC). The thick dashed line in (b) represents the division of the bandwidth F of the information data, and the thin dashed line represents the fine division based on the FD-Phase code (PC).

In addition, before communicating via a _{communication path with t d} and f _D , the earliest procedure is synchronization processing. However, the accompanying work is the PD (phase distortion) of the time and frequency shift operation (TFSO (time-frequency shift operator)) of the two shift operations required for multiplexing.

, Will follow the PD of the communication path

It happens, so synchronization is not easy. Even the radar problem of estimating t _d and f _D from reflection [Non-Patent Document 15] has not yet been able to find an effective solution.

First of all, the inventors used t _d and f _D to encode the TD signal that satisfies TFSP (refer to Figure 2) [Non-Patent Documents 24, 26] and the FD signal of Fourier Transform (FT) with the phase encoding of TD and FD. (PC, phase code) to perform modulation to generate TD-signature and FD-signature.

In addition, FIG. 2 is a schematic diagram schematically showing the irreplaceability of time-frequency shift. The non-substitutability lies _{in the relational expression T τ,0 ‧T 0,ν} =e ^-i2πτν T _0,ν T _τ,0 about the product of the displacement operators (the left side is the triangle label in the corresponding figure, and the right side is the corresponding figure In the square symbol), it appears as a phase distortion (PD, Phase Distortion) e- ^i2πτν . The mark ○ in the figure indicates the symmetrical time-frequency operator (TFSO, Symmetrical Time-Frequency Shift Operator)

[Non-Patent Document 26].

Next, since the PC-based PD is embedded in the signature as a template, the ambiguity function (AF, ambiguity function) type [Non-Patent Document 15] TD-CCF and FD-CCF used to detect TD-template and FD-template are defined Array (refer to Figure 3a).

Next, detect the parameter value that sets the real part of the CCF to the largest value, and the largest CCF number that achieves the largest value. _{Therefore, it is known that the non-information estimation method of t d} , f _D that interactively updates the parameter values (refer to Figures 3b and 3c) is the solution to the radar problem ([Non-Patent Document 27]-[Non-Patent Document 32] and patent Literature 1-6).

In addition, FIG. 3(a) shows the Gabor function of the chip level configured on the TFP and related information. In particular, (a-0) represents the Gabor function g _{mm ' (t) of the chip level arranged on the TFP and G mm '} (f) of the Fourier transform (FT); (a-1) means that g _{mm '} (t ) to (FD-PC, FD-Phase code) X 'm' for the addition of increased TD-template of the real part, imaginary part. (a-2) is the real part and imaginary part of the FD-template in _{which G mm '} (f) is (TD-PC, TD-Phase code) X _{m and is added.} (b) is the NN' cross-correlation function (CCF, Cross Correlation Function) on the TFP and the TD-CCF value of N'column sums and the FD-CCF value of N row sums. (c) is the estimated value of the upward orthogonal projection of the limited time space TL-TD and the limited bandwidth frequency space BL-FD based on the Alternating Projection Theorem (APT)

The interactive update process and the convergence value t _d , f _D.

_{Estimating the ranging problem of delay t d} and Doppler f _D from the reflected signal is the estimation problem of two unknown parameters included in the non-replaceable PD from the time and frequency shift operators. Therefore, its category is signal detection and parameter estimation based on WHG (Weyl-Heisenberg Group) detection. However, with some exceptions [Non-Patent Document 17], many radar researchers rely on the presumption that ignores irreplaceability, and therefore have not succeeded in increasing the accuracy of ranging. On the other hand, the invention described in this specification is based on the present inventor’s cognitive basis: for wireless communications including radar problems, in particular, this irreplaceability is the focus of improving efficiency. In addition, the Wavelet paper [Non-Patent Document 8] is based on a Gabor function that is shifted in time and frequency with respect to the function f(t) [Non-Patent Document 1]

And unfold

The coefficient a _{m,m '} is the central issue. In addition, in 5G, after 5G (after 5G) OFDM/OQAM or Filter Bank Multicarrier (FBMC, Filter Bank Multicarrier) [Non-Patent Documents 9,10,12], a _{m, m '} is used to transmit information The design of the function g(t) in which the intersymbol interference (ISI, intersymbol interference) and the interchannel interference (ICI) of the multiplexed signal f(t) are zero is not orthogonal to the non-orthogonality of _{g mm ' (t)} Solve as the subject.

In addition, in wireless communication, although time and frequency offsets (time, frequency deviation) tolerance are necessary for synchronization, there are few attempts to reveal the estimation of _{t d} and f _D. In addition, many communication researchers believe that PD _{with time and frequency shifts mτ 0} , m ' ν _{0 for signal multiplexing}

It can be ignored. However, due to the group-theoretic nature of the time/frequency shift of WHG, the PD of the communication path

PD of the continued displacement

Other PDs with multi-carrier

It also happens at the same time, so the mechanism is not simple.

The following three topics lurking in the radar problem should be dealt with at the beginning. In addition, the conventional radar transmission signal is a linear frequency modulation continuous wave (LFM-CW, Linear FM Continuous Wave) using a chirp signal, or the recently proposed short-time pulse for phase modulation Compressed radar or its multi-carrier version (Non-Patent Document 19).

(Question 1)

As the first issue, although radar is originally a _{problem with two unknown variables, t d} and f _D , many receivers want to express the negative correlation coefficient of 2 variables between the time τ displacement and the frequency ν displacement as an aliasing function (AF, Ambiguity Function). , And can perform, for example, the peak search of the absolute value of AF, or the specific use of AF based on the chirp signal. More than 2 functions should be used for 2 unknown problems.

(Question 2)

As a second problem, the radar problem can be exemplified by PD based on non-substitutable time and frequency shifts like the position and movement operators of quantum mechanics.

Or based on the time width T _p ; or the PD of the pulse train of the chirp of the frequency shift width F _p

. In addition, even if the data of the time width T _s and the bandwidth space F _{s are transmitted on the TFP through the communication path with t d} or f _D without overlap (refer to Figure 1), it will continue

And there is PD

. Although most researchers ignore this PD, the existence of PD is a common problem with the real-value received signal of the information data.

(Topic 3)

Although the third topic is related to the second topic, it is difficult to observe the mechanism of PD occurrence. That is to say, in the space of communication or radar, the time shift operator or the frequency shift operator are usually defined as

, Since M(v)S(u)=e ^-i2πuv S(u)M(v), the irreplaceability of M(v) and S(u) is taken as the two on the shoulders of ^{PD e -i2 π uv index} The product of this displacement is presented faithfully. The solution to the high-precision ranging or synchronization method is focused on this point. The processing of PD e ^{-i2 π uv} (hereinafter referred to as TFSP (refer to Equations 4 and 24, Fig. 2)) is an important subject of investigation in this specification.

<2. Time. Frequency symmetry time. Frequency shift operator>

The typical reflected signal is provided as

, But ψ (t) is a complex value signal of CE called pulse wave, and

[Math 84] A , t _d ,Ω, φ ,Ω-Ω _r =2 π f _D

They are the displacement of the amplitude, arrival time, carrier frequency, carrier phase, and carrier frequency, which is the displacement (Doppler displacement) _{from the reference frequency Ω r} = 2πf _r. For simplicity, let Ω _r =0 temporarily. To

[Math 85] F [． ]

To represent the Fourier Transform (FT, Fourier Transform), and the

[Math 86] Ψ( f ) = F [ ψ ( t )]

As the FT of ψ (t), the FT of _re (t; t _d ,f _D ) is

. _{Thereto, r e (t; t d} , f D) and _{R e (f; t d,} f D) of the pair (pair) in about t _d, f _D and asymmetric. The product of the unknowns t _d and f _D only appears on the PD of the TD function.

However, the slightly revised formula [Non-Patent Documents 24,26]

, Provided as for the TD function x(t) and its FD function

[Math 89] X ( f ) = F [ x ( t )]

, In terms of t _d , f _D , the definition formula of the symmetric time-frequency shift operator that satisfies the Symmetrical Time-Frequency Shift Operator (Symmetrical TFSO, Symmetrical Time-Frequency Shift Operators) (refer to Figure 2)

And the identity between the two shift operators, giving [the property of symmetric TFSO 1]

[Math 91]

. Compared with the commonly used time shift operator S(-t _d )x(t)=x(tt _d ) or the frequency shift operator

It is different, although the half shift of the TD signal x(t) of formula (4)

Or the half shift of FD signal x(f)

, Which is used in the theory of signal time-frequency performance

Or with

In contrast, only a slight correction can be observed, but this is the expression method that the radar signal or the phase information of the received signal like formulas (39) and (44) can be completely tracked by TD and FD.

The TFSO of formula (4) is the same as Canonical Commutative Relations (also known as CCR) [Non-Patent Documents 4 and 6] of von Neumann of quantum mechanics, so it is called "von Neumann's TFSO" hereinafter. If the well-known Heisenberg (Non-Patent Documents 4, 5) is related to the so-called uncertainty principle

If it corresponds to the time-frequency shift operator [T _τ,0 ,T _0,ν ] of the communication, we can get

, Therefore the limits of classical mechanics [Non-Patent Document 20]

Corresponding to communication without distortion/distortion conditions

. however,

Planck constant

And the commutator in quantum mechanics.

In addition, by TFSO’s chain rule:

Derived [Properties of symmetrical TFSO (symmetrical TFSO) 2]

Where, formula (7) is an example of the first formula of formula (9).

The more important property of symmetrical TFSO (symmetrical TFSO) is that the product td and f _{D of} the unknowns are symmetrical on the PD of the TD and FD functions due to the symmetry of the TD and FD signals. Therefore, as described later, it has multiple signals The address information plays an important role in the estimation of PD visualization parameters. For example, in wireless communications [Non-Patent Documents 9, 10], OFDM signals

As the central topic. However, the coefficient a _m,n represents the complex number data that should be transmitted, and x(t) is a time waveform function. The OFDM signal can be expressed as

Therefore, if the distortion-free/distortion condition τ ₀ ν ₀ =1 (refer to Equation 8) is satisfied, ^{PDe iπnτ0mν0} will not affect regardless of the sign of _{a mn.} However, if there is a deviation τ ' = τ ₀ +ε _τ ,ν ' = ν ₀ +ε _ν ,

[Math 107]

Will follow the PD of the communication path of _{t d} and f _D

Occurs, so we have to deal with the signal that contains the phase-distorted PD

. In the conventional non-overlapping method of signals on TFP as in formula (10), as in [Non-Patent Documents 1, 2, 9, 10, 12] and formula (12), PD is caused by the group-theoretic nature

Therefore, the output of the receiver is weakened by various PDs, which leads to the important synchronization degradation in digital communication [Non-Patent Document 3]. Nevertheless, the design of the time function x(t) to reduce intersymbol interference (ISI) and interchannel interference (ICI) is still a central issue. This observation is the starting point of this manual.

<3. Likelihood function and CCF>

Radar theory is based on the textbooks of Woodward [Non-Patent Document 15], which discusses the analysis and design of radar optimization systems, or Helstrom [Non-Patent Document 18], which is a general study of signal detection and inference.

As noted by Aulander and Tolimieri in [Non-Patent Document 17] Wilcox's [Non-Patent Document 16], it must be noted that these do not consider irreplaceability.

However, the basis of radar theory lies in the following signal detection and parameter estimation theory.

<3.1 Signal Detection>

After the reflected signal reaches the receiver, since the reflected signal will be mixed in the noise, the decision of the reflected signal is bound to become uncertain.

Consider the signal detection problem: "Whether a certain form of signal s(t) in Gaussian noise n(t) arrives at a predetermined time". By observation time

Based on the receiver input w(t) measured in, two hypothetical tests of the receiver are performed:

H ₀ , "No signal", that is, w(t)=n(t)

H ₁ , "there is a signal", that is, w(t)=s(t)+n(t)

If the measured value w _k = w(t _k ) can be obtained at the time t=t _k in the observation time, the n specimens w _k are assumed to be H _i , i=0, 1 has a binding density function ( joint probability density function) i.e. (pdf) p _i (w) of the random variable. In the receiver, the observer's optimal decision is made according to the likelihood ratio Λ(w)=p ₁ (w)/p ₀ (w), w=(w ₁ ,...,w _{n ).}

First, a decision level for the observer in Λ ₀ Λ (w) <Λ ₀ is selected H _0; in Λ (w)> selected when H ₁ Λ _0.

The radar signal is expressed as

[Math 112]

[Patent Documents 15, 18]. However, ψ(t) is a complex-valued signal called "complex envelope (CE)", and Ω=2 π f _c is the carrier frequency. The spectrum of s(t) is

, _{There are narrow peaks near f c} and -f _c . When the bandwidth ratio Ω is smaller, the signal is called narrowband (NB, narrowband) or quasi-harmonic.

Input the receiver

Assume NB, and assume its CE

[Math 115] ψ _w [ k ]

It can be measured by a modulator.

Has a covariance function

NB signal under static NB white Gaussian noise

The best detector has a logarithm of likelihood function (LLF, logarithm of likelihood functional) [Non-Patent Document 18, p.106]

. However, N ₀ represents the one-sided spectral density of the white noise, and g and d ² represent the statistics of the likelihood function LFΛ[ψ _w (t)] and the signal-to-noise ratio (SNR). ).

<3.2 Parameter estimation>

The principle of hypothesis testing can also be applied to multiple hypothesis testing. If one of the M signals is transmitted by the transmitter, the receiver will determine which of the M signals is in the observation time (0, T). That is, assuming that _{the receiver input under H k} "signal S _k (t) has been transmitted" is

. However, ψ _k (t) represents the NB CE, and f _k represents the carrier,

[Math 120] φ _k

It represents _{the phase of s k} (t), and n(t) represents random noise.

The receiver selects one of M hypotheses based on the measured value of the input w(t). For n measurement values w _1, ..., w _n, the p _k (w) to assume a prior probability of pdf ζ _k H _k H _k is set under the hypothesis. For simplification, when ζ _k =M ^-1 , the orthogonality of the signal s _{k (t)}

As the premise (Ei is the i-th signal energy), taking all k≠j as the object, when Λ _k (w)> Λ _j (w), the receiver H _{k is selected} .

The unknown parameters of the signal are set as θ ₁ ,..., θ _m , and these are expressed as the frequency spectrum θ=(θ ₁ ,...,θ _{m) in the m-bit parameter space θ.} The radar reflection signal is expressed as

. However, Ae ^{i κ} is an attenuation constant, and A, t _d , f _c , κ, f _D are amplitude, arrival time, carrier frequency, phase, and Doppler shift. The unknown parameter of the reflected signal is θ=(A,κ,t _d ,f _D ).

when

, And when the noise is _{white with spectral density N 0} , LLF [Non-Patent Document 18, p.251] is

By variable conversion

(Here

(Representing the imaginary part) can get the maximum likelihood estimate (MLE, maximum likelihood estimate) of A, κ with θ ' = (t _d , f _{D) ML estimated value (MLE)}

. Therefore, the remaining part of the MLE of the unknown parameter θ 'only requires

The maximum parameter value is sufficient [Non-Patent Document 18, p.251]. Therefore, the receiver can focus on the estimation of θ'. MLEθ 'may be closer to constitute a match for the Doppler shift

One of the set of values is the signal of the object

Derived from the filter bank. But W _D is the maximum f _D. However, it is practically impossible to investigate statistics based on the configuration of the parallel NB filter. This is the biggest reason for decomposing the unknown two-variable problem into two unknown one-variable problems.

Rewrite formula (15) and its FT

. however,

Is "von Neumann's TFSO" with t _d and f _D,

[Math 133] ψ ( t ), φ ₀

Is the CE and phase to be designed (details omitted),

In order to shift (modulate) the complex value signal CE of the base bandwidth with the reference frequency f _{r into a signal of the passband space signal.}

In order to grasp _{the correct position on the TFP of (t d} , f _D ), use the TD-phase code (PC) of period N and the FD-phase code (PC) of period N'to specify the 2-bit format on the TFP (2-D lattice)

On the location. However, T _c = T _s /N, F _c = F _s /N', T _s and F _s are the chip pulse interval, chip (sub) carrier frequency interval, data signal time width, and data signal bandwidth. Divide the parameter space θ′ of (t _d , f _{D) into data addresses (address)}

NN’ rectangular spaces

[Math 137]

To H _{m, m 'represents} a hypothesis "θ' in the space

among".

However, the NN' hypotheses can be decomposed into as follows: the N'hypotheses of f _{D of the presumed TD signal s echo} (t; A,κ,t _d ,f _D ), and the presumed FD signal S _echo (f; a, κ, t _d, hypothesis f _D) t _d of the N '.

Considering the premise that the signals s _k (t; θ ' ) are orthogonal to each other, CEψ _k (t) and phase _{in the hypothesis H k of formula (14)}

[Math 139] φ _k

The kth NB reflection signal

. If the noise is a _{white Gaussian with a spectral density N 0} , its LLF is [Non-Patent Document 18, p129, p.251]

[Math 141]

. Taking a certain decision level r ₀ as the object, if it meets

If the integer of is k=k ₀ , the receiver determines that the K-th signal has arrived. If all g _k is _{below r 0} , the receiver determines that there is no signal. This is the ML receiver. Therefore, the design of orthogonal signals is important. Equation (18) expresses _{the method of maximizing |g k} (θ ' )| (one is the maximization of the integrated function, the other is the phase e ^iκ of the compensation carrier and the phase of the signal

). However, in general, the phase factor is due to

[Math 144] CE ψ _k ( t )

The redefinition was absorbed. In addition, generally, g _k (θ ' ) is not simply evaluated but |g _k (θ ' )|. This method will eliminate the phase information. Woodward [Non-Patent Document 15] uses Ville [Non-Patent Document 14] in radar analysis, which is called an ambiguity function (AF), a two-dimensional CCF

[Math 145]

. The WHG-based non-permutable and group-theoretic properties of the function of elapsed time and frequency shift appear in the phase function of formula (9). In addition, [the nature of symmetrical TFSO 3] is based on the TD signal z(t) and

[Math 146] FT Z ( f ) = F [ z ( t )]

For the object, the inner product IP between the time/frequency displacement functions of TD and FD is

. however,

Is the TD-IP between r(t) and s(t),

Department said

[Math 150] R ( f ) = F [ r ( t )]

versus

[Math 151] S ( f ) = F [ s ( t )]

FD-IP between.

Equation (19) is the maximum when the real parts of i) TD-IP and FD-IP are t ₂ =t ₁ and f ₂ =f ₁ , and at this time, the maximum value of AF is also reached. ii) If the items around IP are regarded as transmitting/receiving signals, the received signal comes from an irreplaceable PD, which means that the PD of a well-designed receiver can be used to compensate. Formula (19) teaches that the phase of the modulated signal is as important as the "phasor" (Non-Patent Document 18) of the alternating voltage and current of electricity; and the two quantities t _d and f _D always appear于PD. This part is different from the usual method of matched filter (matched filter) which depends on TD. In order to realize the _{big step of (t d} , f _D )-estimation method in TD and FD based on WHG, it is an important part of this manual. The backbone of the company. By designing a signal with a phase term that is easy to track, the transmitter and receiver can achieve effective use of phase.

Gabor [Non-Patent Document 1] points out the importance of the Gaussian function to achieve the lower limit of the uncertainty relationship between time and frequency for signal analysis on TFP, and gives the time and frequency performance of the following function f as follows.

. The set of Gabor Gaussian functions g _m,n (t) is localized on TFP. However, this base is not orthogonal, nor is it a frame [Non-Patent Document 7]. In addition, many communication researchers do not use Gaussian functions that do not satisfy the Nyquist condition. However, in the (t _d , f _D )-estimation method of this specification, several good properties of the Gaussian function play an important role.

<4. Signature and template of TD- and FD->

TD-PC (phase code), that is, spreading spectrum [Non-Patent Document 3], realizes code-division multiple access (CDMA, code-division multiple access). To make CE

[Math 153] ψ ( t )

To meet TFSP, its FTΨ(f) also undergoes phase modulation. In addition, the transmission signal s(t) is modulated by the independent pulse symbol c(t) and the transmission signal m(t) to become s(t)=m(t)c(t). Each user can use a wide-band space at the same time by assigning a symbol that is orthogonal to the signal.

Below, as

Instead of the continuous time signal indicated by

Represents the discrete-time signal. The TD signal s(t) is sampled at intervals of Δt, and the discrete FD signal is defined by L-point Discrete Fourier Transform (DFT). In other words, the frequency interval of adjacent bins of FD is Δf=1/(LΔt).

(fraction

The carry)).

For the above [Math 156] and

(fraction

Carry)) discrete variables and the orthogonality of the chip pulse, if set

And set

[Math 161] T _c = M △ t , F _c = M' △ f

, Then the twiddle factor of the L-point is defined as

The following defines 7 types of discrete time and discrete frequency signals.

{-1,1}^N為週期N的TD-PC；而X'=(X'0,...,X' _N'-1)

{-1,1}^N' 為週期N’的FD-PC，即χ=(X,X')。 . However, X=(X ₀ ,...,X _N-1 )

{-1,1} ^N is the TD-PC with period N; and X ' = (X ' 0,...,X ' _{N ' -1} )

{-1,1} ^{N 'cycle} N' of FD-PC, ie χ = (X, X ') .

For the continuous-time chip pulse g(t) with support[-L△t/2,L△t/2][that is, the time width L△t], a delay (D/2)△t,D can be obtained =L-1,L=(△t△f) ^-1 =MM ' [Non-Patent Document 10], and the causal discrete time L△t-time limited (TL, time limited) chip pulse g[k]

Also, support[-L△f/2,L△f/2], that is, L△f-limited bandwidth (BL, band-limited) chip pulse G[1 ], can be derived from the DFT of g[k]

In addition, for chip pulse g[k] (or G[L] pulse interval Tc=M△t (or F _c = M ' △f)), the support time width L△t (or frequency The interference from M'/2 (or M/2) chip pulses on the left and right sides of the width L△f). Since the guard interval is not used, this is the biggest difference from the conventional method.

Discrete time TD-signature v[k; χ] and its FD-signature defined by the next formula

TD-template of type-3 in which the next formula is embedded

FD-template with type-4

. however,

versus

Is the discrete version of von Neumann's TD and FD's TFSO in formula (4)

TD-signature v[k; χ ] is TD-templates containing N'

, On the other hand, due to the FD-signature

[Math 173] V [ l ; χ ]

Contains N FD-templates

Therefore, the CCF between the signature and the embedded template has a large value by using the PC. TD-template

Rectangular support with T _s ×L△f on TFP; FD-template

It is a rectangular support of L△t×F _s. Link TFSO

(Or

) Is applicable to formula (22), then we can know that TD-signature and FD-signature

It is completely symmetrical. Obtained with [mathematical formula 180] CE ψ [k; χ ] and carrier frequency

The radar TD-signal s[k: χ ] and the FD-signal S[l; χ ] of the FT are

CE and DFT of radar TD-signal

Can design TD-signal, FD-signal

[Math 184] s [ k ; χ ], S [ l ; χ ].

In this system _{, the signatures of time width T s} =NM△t and carrier interval F _s =N'M'△f

[Math 185] υ [ k ; χ ]

(or

[Math 186] V [ l ; χ ]

) Superimpose PP' binary sequences without overlap. however,

Is a grid with TFP

Data address on

(0,PT_s)與Doppler The data mark. That is, in the radar system, in order to explore the delay t _{d whose range is not known beforehand}

(0,PT _s ) and Doppler

, And prepare the time width and bandwidth of _{PT s} × P ' F _s. On the other hand, the number of P‧P's in the transmission data communication

[Math 191] M -value data

, which is

Here, it is assumed that it has been transmitted via

The communication path s[k;χ]. At this point, with

The received TD-signal is expressed as

. however,

[Math 196] ψ _r [ k ]

Is the CE of the signal component of the received signal, and η [k] and ξ [k] are the interference component and Gaussian noise. FD-signal and DFT

[Math 197] R [ l ; χ , A , κ , θ' ^{, d} ] = F ^d [ r [ k ; χ , A , κ , θ' ^{, d} ]]

The details of is omitted here. Although accompanied by irreplaceable modulation/demodulation PD

It can be ^absorbed by redefining e iκ, but as described later, it should be compensated by the relevant receiver. Such TD and FD receive signals provide the observed value w and its DFT W in the receiver.

Independent and identically distributed (i.i.d, independent and identically distributed) TD-PC and FD-PC are the necessary independent N'TD-templates using M-type detection methods

[Math 199]

And N FD-templates

. The PC has two functions (signal chaos and PD generation from TFSO). Fortunately, PD itself is a good indicator for parameter estimation in the sense of providing easy traceability. This represents the advantages and disadvantages of importing into a PC. In fact, the bandwidth of the phase modulation system is N times larger than that of the classical radar system, and it is multi-carrier, that is, FD-PC requires N'times more than sub-carriers. The bandwidth.

<5. TD-, FD-signal detection and estimation based on M hypothetical detection>

So far, the CE with formula (27) is detected

[Math 201] ψ [ k ; χ ]

(Or have

[Math 202] Ψ[ l ; χ ]

The radar signal of formula (26)

[Math 203] s [ k ; χ ]

(Or

[Math 204] S [ l ; χ ]

) And the preparations for the application of M-type hypothesis testing are complete.

_{Next, consider the NN'hypothetical H mm '} strategy selected by the receiver and related to formula (17). This part only needs to find the parameter θ' ^,d that maximizes the LLF of TD (or FD) (or its associated CCF). In the beginning, the grid with TFP

Address

Receiving TD-template CE

The problem of detection began to be considered. however,

, And FD-PC TD-template of chip address (chip address) ρ ′ (refer to formula (22))

And

Is the presumed integer value of k _d,

[Math 211] l _μ

Presumption

[Math 212] l _D

The control uses an integer value. This CE is embedded in equation (27) (refer to equation (28)

[Math 213] ψ _r [ k ]

) The presumed receiving CE of ψ[k; χ]

Medium (refer to Figure 3a-1). However, using the relation

. Equation (29) is as shown in the next section. CE includes various intentional phases from PD. Will

Complementary CE

Expressed as

. Since formula (22) and formula (27) can use N’ TD-template

, So the receiver uses N’ CE

To determine which of the N'LLFs is the largest (refer to Figure 3b).

i) TD discrete-time signal detection, and Doppler-shift-ML estimating problem: Based on N _T th random variable w = (w [0], ..., w [N T -1]) of the receiver selects two Hypothesis

. however,

[Math 222] ψ _w [ k ]

Is the observed value at time k

[Math 223]

NB CE,

[Math 224] ψ _n [ k ]

Gaussian noise

NB CE, while

[Math 226] N _T =[ T /△ t ]≫1

Is the number of samples at the observation time (0, T). Assume that the signal component of H1 is

equal. N’ CE

To wait for energy, in

In the sense of using pseudo-orthogonal as the premise, the following results are obtained.

Proposition 4:

Observations under Gaussian noise based on spectral density N ₀ w=(w[0],...,w[N ₁ -1])

The detection and presumption of the

The log likelihood of each is [Non-Patent Document 18]

. however,

For a certain decision level r ₀ , the integer value satisfying the following formula is

. however,

In formula (31)

The MLE ^{based on Ae -iκ} in formula (16)

Compensated version. At this time, the receiver determines that the grid on the TFP has been received

Address on

The CE. If all

When all values are below r ₀ , the receiver determines that there is no signal. therefore

For the provided

[Math 243]

Below

[Math 244] l _μ

MLE. In addition,

To accompany TFSO

The phase function.

Next, based on the DFT of the observed value w

, Transfer to the problem of signal detection and delay estimation in FD. Consider having a lattice

Address

Receiving FD-template CE

[Math 250]

Detection problem. however,

And

FD-template of TD PC (phase-coded) with chip address (chip address) ρ (refer to formula (22)). This CE is embedded in the DFT of equation (27)

[Math 253] Ψ[ l ; χ ]

Receiving FD-CE

Medium (refer to Figure 3a-2). however,

for

[Math 256] l _D

The estimated integer value of k _σ is the _{integer value for the estimated control of k d} , and the relational expression is used

[Math 257]

. Will

Complementary set

Expressed as

From formulas (22) and (27), N FD-templates can be used

, So use FD-CE with N receivers

, To determine which of the N LLFs is the largest (refer to Figure 3b).

ii) Signal detection and delay-ML estimation problem in FD: Based on the observation value W=(W[0],...,W[N _T -1]), the receiver chooses the following two assumptions in FD

[Math 263]

. however,

For having NB CE

[Math 265] ψ _w [ k ]

The DFT of the observation value w[k];

For having NB CE

[Math 267] ψ _n [ k ]

DFT of noise n[k], and

Is the number of samples in bandwidth B. For simplicity, set N _B =N _T.

CE with formula (33)

First

The signal spectrum of the template of the number, and

Is CE with formula (34)

Complementary signal spectrum. Assuming the signal component of H ' _{1, and}

the same. N CE

Is equal to energy, and is based on

As the premise of pseudo-orthogonal in the sense of, the following results are obtained.

Proposition 5: Observations in white Gaussian noise based on spectral density N ₀

[Math 277] W =( W [0],..., W [ N _T -1]), W [ l ] = F ^d [ w [ k ]]

To proceed

The detection and the presumption of the

The log-likelihood function of number LLF is expressed as

. however,

And a decision level for r _'0, and set ρ = ρ ₀

[Math 282]

Is an integer satisfying the following formula

. At this time, if the receiver determines the TFP grid

Address

Signal arrives, and all

Under all words r _'0, the receiver determines that no signal.

For the provided

MLE below k _d. In addition,

Based on TFSO

Of

The phase function of the FD version.

<6. TD-CCF, FD-CCF for parameter estimation>

<6.1 TD-CCF, FD-CCF>

Observations

NB, and suppose its CE

[Math 293] ψ _w [ k ]

The real and imaginary parts of can be measured separately [Non-Patent Documents 18, 3].

In order to detect the signal

[Math 294]

(Or

), and use each of the associated CCFs defined below (refer to Figure 3b).

And, in order to get instead of having formula (31)

Of

(Or with formula (36)

Of

) Time and frequency symmetric statistics, and use the following defined CCFs (refer to Figure 3b).

Lemma 1: When the two assumptions of formula (30) H ₀ , CE of _{H 1}

[Math 300] ψ _n [ k ]

Assuming Gaussian noise, CCF

Established. Only <‧,‧> _d,k is the space of discrete time function

In the inner product (IP, inner product). Therefore (input CE as a receiver

[Math 303] ψ _w [ k ; χ ]

Instead of), will have an attenuation constant

Receiving CE

(That is, the receiving CE of equation (28)

[Math 306] ψ _r [ k ; χ ]

Signal component), and the address of formula (29)

Presumption in TD-template CE

The CCF (called type-3 correlator) between the NB matched filters reflected by the impulse

Define. Here, as a substitute for the notation X ' _{ρ '} , X in the formula (29), the one with Y ' _{ρ '} , Y is used

After a little calculation, we know that this CCF can be expressed as

Unfortunately, AF θ _gg (τ,ν),Θ _GG (ν,-τ) generally have multiple sidelobes. However, the Gaussian chip pulse wave g(t) has the variable separability and exponential function type attenuation characteristics of τ and ν with respect to its AF

[Math 312]

, Bring a brand-new answer to the presumptive question. Here

. because

If it becomes a large value, when N,N'≫1, the first and second variables of θ _{gg [‧,‧] must be reduced.} In other words, the formula (39)

Items can be completely ignored. This property of Gaussian function is to maximize

The decision of l _μ played a key role.

In order to evaluate the cubic sum of the PC related to the power PD of the twiddle factor (twiddle factor) W, an IDFT-type sum

, Angle brackets

[Math 318]

And parentheses (a) _{m '} (convenient notation is _{defined by (a) m '} = W ^{-am '} ) to mark the mark, DFT-type and

Also with

Of the pair to make the mark on the mark, if the mark is used

, Then Lemma 2: The address of the type-3 receiver is

, If Y=X,Y ' =X ' , CCF is expressed as

[Math 323]

Therefore, in order to make

Becomes a big value,

It must be established. However, 5 of the 6 terms of the second twiddle factor of formula (39) change the arrangement

, The remaining one moves to the first twiddle factor. On the other hand, in FD, if Lemma 3: the two assumptions of formula (35) H ' ₀ , H ' ₁

[Math 327] N [ l ]

If it is Gaussian noise, then

Established. However, <‧,‧> _d,l is the space of the FD-function of discrete frequency

IP.

(As FD-CE

[Math 330] Ψ _W [ l ; χ ]

Instead of) will have an attenuation constant

Receiving FD-CE

, Which means receiving CE

[Math 333] ψ _r [ k ]

FT of the signal component of, and the address of formula (33)

[Math 334]

Presumption in FD-template CE

CCF (called type-4 correlator) between the complex impulse responses of the NB matched filter (matched filter) to

Define. This CCF is expressed as

Similarly, in order to make

Becomes a large value because it can be assumed

[Math 339]

, So when N,N’≫1, formula (44) can be completely ignored

All items. If we sort the three terms of the Twiddle factor and evaluate the cubic sum of the PC, then Lemma4: Type-4 related receivers have

Address (address), and if Y=X, Y ' =X ' , then CCF is expressed as

Therefore, in order to make

To become a large value and must

[Math 344]

However, 5 of the six items in the second twiddle factor of formula (44) change the arrangement and change

The remaining one is moved to the first twiddle factor of formula (44), and using the variable separability of Gaussian function, formula (45) can be obtained. Formulas (41) and (45) indicate

versus

on

[Math 348] k _d , l _D

Complete symmetry.

will

versus

If the functions of TD-PC and FD-PC of CP (complementary pair, [Non-Patent Document 27]) are exchanged, we can get

and

The group (called the original pair (OP, original pair) [Non-Patent Documents 24, 30]) is as follows.

[OP’s TD-CCF, FD-CCF:] v[k; χ ] and

[Math 353] V [ l ; χ ] can be other decomposition

. However, TD-template

And FD-template

for

. will

Defined by the following formula. If it will have a grid

Address

Set to have TD-template

Presumptive reception of TD-CE

, You can get the CCF called type-1 correlator

, And can be expressed as

Set Y=X,Y ' =X ' , except

Except for items, all

Can be ignored, so you can get

However, 5 of the 6 items of the second twiddle factor of formula (51) change the arrangement and become

, And if the remaining one is moved to the first twiddle factor, the variable separability of AF using Gaussian function can be obtained by formula (52).

Then, if the

A lattice defined by the following formula

[Math 370]

Address

FD-template

The presumption of receiving FD-CE is set as

, Then get the FD correlator called type-2 correlator

並可得到

And get

[Math 375]

If Y=X,Y ' =X ' , when ignoring but satisfying "

of

All the items in ", you can get

. However, 5 of the 6 items of the second twiddle factor of formula (56) change the arrangement

, And if the remaining one is moved to the first twiddle factor, formula (57) can be obtained.

<6.2 PUL and von Neumann's APT>

About Lemma 2

Or Lemma 4

, If it is possible to obtain the correct estimated value of the accuracy of the time width L△t or the bandwidth L△f of all chip pulses

Then, two CCFs

, Including each in

Interference component

For filter removal, you do not need to use conventional sensitive filters to remove

recovery. This part is fundamentally different from the digital signal processing used in previous communications. The estimated value of the two sets of correlators

A simple method of updating has the following procedure called phase-updating loop (PUL, phase-updating loop), which is completely different from the conventional "phase-locked loop" used for synchronization of communication in the past.

[MLE with attenuation constant update PUL algorithm]

will

and

Set as the complementary pair (CP, com-plementary pair) of the type-3 and type-4 correlator arrays, and set

and

Set as the original pair (OP, original pair) of the type-1 and type-2 correlator arrays respectively. For simplicity, set the PUL algorithm until it converges.

. As the estimated value of discretization of the s-step of (t _d , f _D ) among the parameters θ ′

And as formula (16)

Instead of using each

Attenuation constant

S-step MLE

defined as

Pairs of integer values (pair)

The update is defined as

will

Respectively set to

. But the initial value

Department can be freely selected. For example, it can be set to

. Taking chip pulse g[k], G[l] time width L△t and bandwidth L△f as the object, if

If yes, then (s+1)-step ends. The estimated value obtained is MLE, and the two correlators are ML receivers.

The recovery of distorted signals is an important area of signal processing. Youla [Non-Patent Document 22] provides answers to recovery problems. Using Youla's method and notation, it can be seen how the convergence of the PUL algorithm depends on von Neumann's APT [Non-Patent Document 21].

Consider the inner product (IP, inner product)

(Or

), and norm (norm)

(Or

) Is a Hilbert space formed by a continuous discrete time function (or a discrete frequency function) with square additivity

[Math 410] H

. Set ε to

[Math 411] H

Any closed linear manifold (CLM, closed linear manifold) in. According to the projection theorem [Non-Patent Document 22], if ε ' and ε " are orthogonal to each other

[Math 412] H

ε為具有特定性地分解f=g+h,g

ε',h

ε"。惟，g,h指的是f之ε',ε"往上的投影，標記為g=Pf，h=Qf。P為ε'往上的投影運算子(PO,projection operator)，Q=I-P為ε"的往上的PO，I為恆等運算子。 Part of the space, then any f

ε is a specific decomposition f=g+h,g

ε ' ,h

ε " . However, g, h refers to the upward projection of f of ε' , ε " , marked as g=Pf, h=Qf. P is ε 'upward projection operator (PO, projection operator), Q = IP is ε "up to the PO, I is the identity operator.

Set ε ₁ (or ε ₃ ) to L△t- (or T _s -) time limited (TL, time limited) signal

A collection composed of all of. On the other hand, the signal of L△f- (or F _s -) is limited to the bandwidth (BL, band limited)

The set consisting of all of is set as ε ₂ (or ε ₄ ).

It is CLM [Non-Patent Document 22].

Set P _i to

The projection operator of the upward projection, set Q _i =IP _i as the orthogonal complement of _{ε i}

ε具有特定地分解 The projection operator for the upward projection. CCF plays the role of PO in the following sense. In other words, for any signal r and s, the signal r

ε has a specific decomposition

. however,

[Math 419] s ^⊥

Is the orthogonal space of S. Correlation coefficient

Think of it as a projection operator that projects r on top of ε'.

The complementary pair (CP, complementary pair) of the type-3 and type-4 correlators and the original pair (OP, original pair) of the type-1 and type-2 correlators are the orthogonal projection operators of the following formula (PO).

[Math 421]

. however,

Respectively

Orthogonal complement.

Using the alternative projection theorem (APT, Alternative projection theorem) (refer to Figure 11), the following results can be obtained. In addition, according to APT [Non-Patent Document 21, p.55, theorem 13.7], when E and F are each CLM ε in Hilbert space,

[Math 424] F

When the projection operator is upward, the sequence of operators E, FE, EFE, FEFE,... has a limit G. In addition, the sequence F, EF, FEF,... also has a limit G. In addition, G is

[Math 425] εF

The upward projection operator (no need for symmetry condition EF=FE).

[Theorem: Convergence Theorem of PUL Algorithm] (Refer to Figure 3c): Regarding the estimated value of s-step with formula (60)

(Or formula (61))

And, also has the s-step estimated value of formula (60)

(Or with formula (61)) (ρ,k _σ ) (or (ρ ' ,k _σ )), considering its related argmax-calculus. The four POs including the maximum likelihood estimates TD and FD of the (s+1)-step determined by the argmax-algorithm are marked as simplified symbols as

and

. The PUL algorithm converges.

[prove]:

Take CP's PO pair (T _s -TL-PO P ₃ ,F _s -BL-PO P ₄ ) (OP's PO pair (L△t-TL-PO P ₁ ,L△f-BL-PO P ₂ )) Two different recursive formulas can be obtained in the order of application. In addition, if you replace TD-PC X with FD-PC X', that is, the subscript (3,4)(1,2), OP and CP are the same, so only the proof of CP is provided.

First, provide

[Math 431] ψ

Recovery algorithm. If

,then

[Math 433] ψ = F ^-1,d P ₄ F ^d ψ

, So you can get

[Math. 434] g ₁ = P ₃ ψ = P ₃ F ^-1,d P ₄ F ^d ψ = ψ - Q ₃ F ^-1,d P ₄ F ^d ψ

And

[Math 435] ψ

Satisfy the operator equation

[Math 436] A ₁ ψ = g ₁ , A ₁ = I - Q ₃ F ^{-1, d} P ₄ F ^d

, So the equation

[Math 437] ψ = g ₁ + Q ₃ F ^-1,d P ₄ F ^d ψ

Provide the following TD recursive formula [Non-Patent Documents 22,23]

. According to APT

[Math 439] lim _{i →∞} ( Q ₃ F ^-1,d P ₄ F ^d ) ⁱ ( ψ ₀ - ψ )

for

[Math 440] ( ψ ₀ - ψ )

CLM ε _c = ⊥ε ₃ ∩ε ₄ upward PO. ε _c contains only functions that are equal to zero [Non-Patent Document 22, p.699] [Non-Patent Document 23, p.637], which is

[Math 441] lim _{i →∞} ψ _i = ψ .

This part is one of the main results of Youla [Non-Patent Document 22]. So combined with PO

[Math 442] P ₃ F ^-1,d P ₄ F ^d

Grid space

Chip and data address (address)

The L△t×L△f rectangular area (CE

Support and

The product collection of support):

[Math 447][(( p -1) N + ρ -△ a' ) T _c ,(( ρ -1) N + ρ +△ b' ) T _c ]×[(( p' -1) N ' + ρ'- △ a ) F _c ,(( p' -1) N' + ρ' +△ b ) F _c ]

Extract and filter to remove the remaining TFP. However, △a, △b, △a ' and △b ' are integers satisfying △a+△b=M,△a ' +△b ' =M '. Such a PO pair is called a localization operator in phase space (or TFP in time and frequency space) [Non-Patent Document 7]. Since CE ψ [k] can perform signal recovery, the parameters k _d and

[Math 448] l _D

The accuracy of L△t and L△f can be estimated. Different from the general precise TL (or BL) operator [Non-Patent Document 23], TL-PO P ₃ (or BL-PO P ₄ ) modulates the phase of N TD-Gauss chip pulses g[k] (or N'phase modulated FD-Gauss chip pulse

[Math 449] G [ l ]

) Is a time-frequency shift, and the superimposed signal is defined as a template without setting a guard interval (guard interval).

ε ₃的話 Conversely, in FD, if Ψ

ε ₃ words

[Math 450] Ψ = F ^d P ₃ F ^-1,d Ψ

and

[Math 451] g ₂ = P ₄ Ψ = P ₄ F ^d P ₃ F ^-1,d Ψ=Ψ- Q ₄ F ^d P ₃ F ^-1,d Ψ

Established. In other words, Ψ satisfies the operator formula [Non-Patent Document 23]

[Math 452] A ₂ Ψ = g ₂ , A ₂ = I - Q ₄ F ^d P ₃ F ^-1,d

, So the recursive formula of FD can be obtained

. According to APT

[Math 454] lim _{i →∞} ( Q ₄ F ^d P ₃ F ^-1,d ) ⁱ (Ψ ₀ -Ψ)

CLM for (Ψ ₀ -Ψ)

[Math 455]

PO of upwards. This CLM is only a zero function, so lim _i→∞ Ψ _i =Ψ.

Because of FD CE

[Math 456] Ψ[ l ]

Is restored, so the parameters can be estimated

[Math 457] k _d , l _D

It is the accuracy of L△t and L△f.

[Math 458] P ₄ F ^d P ₃ F ^-1,d

Put another localization operator, the grid space

Of the chip and data addresses on the

The rectangular area of L△t×L△f (TD-CE

Rectangular support with FD-CE

[Math 462]

And its product set:

[Math 463][(( p -1) N + ρ -△ a' ) T _c ,(( p -1) N + ρ +△ b' ) T _c ]×[(( p' -1) N ' + ρ'- △ a ) F _c ,(( p' -1) N' + ρ' +△ b ) F _c ])

Extract and filter to remove the remaining part. (The proof ends).

<7. Twinned FBMC>

<7.1 SFB: Signature Transmitter and Radar Signal Transmitter>

Provide TD-signature v[k; χ] and FD-signature that generate formula (25)

[Math 464] V [ l ; χ ]

Multi-carrier filter bank (FBMC, multi-carrier filter bank). By repeatedly executing TD-PC X _{m of} cycle N, the sample point -∞,...,-T _c ,0,T _c ,...,∞ at time t generates an infinite sequence, and on the other hand, it executes repeatedly period N 'of FD-PC _{X' m} ', the frequency f of the sampling points _{-∞, ..., - f c,} 0, f c, ..., ∞ infinite sequence.

Proposition 6:

V[k; χ] in formula (25) and

[Math 465] V [ l ; χ ]

It can be rewritten as the following formula respectively.

[Math 466]

but,

Modulation filter defined by

. In addition, Vaidyanathan [Non-Patent Document 13] defines three types of multi-rate filters with filter coefficients h[‧] for input x[k] and output y[n]: reduction ratio Decimation filter of M _f:

Interpolation filter with expansion rate L _f:

, And the decimation filter of the _{reduction rate M f} /L _f:

[prove]

The TD-signature v[k; χ] (or FD

[Math 472] V [ l ; χ ]

) Is N'(or N) sub-bands and the magnification rate M (or M'), each m'th sub-band (or mth sub-band) can be regarded as FD- PC _X'm' (or TD-PC X _m ) is a signal obtained from the output of the synthesis filter bank (SFB, synthesis filter bank) [10,12] of phase modulation. In fact,

Is the input signal, and if

Is the (m,m’)th sub-band filter of the SFB, then output

[Math 475] υ [ k ; χ ] (or V [ l ; χ ])

Is formula (67). (The proof ends).

In addition, if the notation lcm[M,N ' ]=M ₀ N ' =MN ' ₀ , lcm[M ' ,N]=M ' ₀ N=M ' N ₀ (Non-Patent Documents [13], [10] , [11]), by introducing _{M 0 N ', M' 0} N polyphase components (polyphase component)

[Math 476]

To define each polyphase filter (Vaidyanathan [13] Type 1 polyphase)

. In addition, lm = lcm [M, N ' ], g d = gcd [M, N'], satisfies _{lm = MN '0 = N'} M 0 of the respective N _'0, M ₀ is present, on the other hand, by the The identity lm‧g _d =M‧N' shows that M=g _d ‧M ₀ , N ' =g _d N ' ₀ holds.

Therefore, the SFB of the signature v[k], V[l] shown in Fig. 4 and Fig. 5 with two-bit TD-PC and FD-PC phase modulation can be obtained.

In addition, Fig. 4 shows SFB, which generates X _m and X ' _{m '} with TD-PC and FD-PC, and the m'th TD template

The synthesis filter bank (SFB, Synthesys Filter Bank) of TD signature v[k] in formulas (25) and (67).

In addition, FIG. 5 shows SFB, which generates X _m and X ' _{m '} with TD-PC and FD-PC, and the m'th TD template

FD signature of formulas (25) and (67)

[Math 480] V [ l ].

On the other hand, formula (27) provides

[Math 481] ψ [ k ; χ ]

and

[Math 482] Ψ[ l ; χ ]

SFB.

Proposition 7:

CE ψ[k; χ] and

[Math 483] Ψ[ l ; χ ]

It can be described as follows.

however,

It is a modulation filter defined by the following equation.

[Proof] Formula (71) has the following meaning.

(Or

).

If the above [Math 487] (or [Math 488]) is the input signal, and

(or

) Is the (q,q’))th sub-band filter of the SFB, then

[Math 491] TD-CE ψ [ k ; χ ]

(Or FD-CE

[Math 492] Ψ[ l ; χ ]

) There are PP' sub-bands, and each sub-band has an SFB output with a magnification rate of NM (or N'M').

Therefore, the SFB of the transmission signal embedded in the information data of Figs. 6 and 7 can be obtained. There is no signature generation process shown in Figures 4 and 5 in the general SFB. The situation of N=N ' =1 in Figures 6 and 7 corresponds to the general SFB. In addition, if using the modulated filter (MF, modulated filter) characteristics of data transmission

, Each polyphase filter (Type 1 polyphase of Vaidyanathan [Non-Patent Document 13])

Get defined. However, P ' ₀ , P ₀ are integers satisfying P ' ₀ MN=lem[P ' ,MN], P ₀ MN=lem[P,MN]. (The proof ends).

In addition, Figure 6 shows SFB, which generates complex-valued data

TD-CE (TD-complex Envelope) which is the formula (27) of the input signal

[Math 496] ψ [ k ].

In addition, Figure 7 shows SFB, which generates complex-valued data

FD-complex envelope (FD-CE, FD-complex Envelope) of formula (27) for the input signal

[Math 498] Ψ[ l ] .

<7.2 AFB: Receiver and Decoder>

PD that includes non-replaceable modulation and demodulation other than the attenuation constant Ae ^{i κ}

The received signal of formula (28)

[Math 500] r [ k ; X , A , κ , θ' ^{, d} ]

(Or its FT

[Math 501] R [ l ; X , A , κ , θ' ^{, d} ]

) (Abbreviated as

[Math 502] r [ k ], R [ l ]).

Presumption template TD-CE of the above received signal [Math 500] and formula (29)

[Math 503]

(Or the presumption template FD-CE of formula (33)

) Between the type-3 (or type-4) CCF, set them to

However, PD

(Or

) Is r(k) (refer to formula (28), formula (38)

) (Or

[Math 509] R [ l ]

(Refer to formula (28) and formula (43)

)) Modulation and demodulation of signal components PD

Compensation items.

The TD- (or FD-) analysis filter bank (AFB, analysis filter bank) [Non-Patent Documents 10, 12] can be obtained as follows.

Proposition 8:

The CCFs of Type-3 and Type-4 are

. However, D=L-1,

Modulation filters of TD- and FD-AFB respectively

. In addition, when N=N'=1, it corresponds to a general AFB [Non-Patent Documents 10, 11].

Send PxP’s

[Math 515] M -value symbol

After that, it is evaluated for presumption

The address of the correlator array (address)

(P-th bandwidth space, p'-th time) output value.

[prove]:

The AFB has P sub-bands (or P’ sub-bands) with a reduction rate of NM (or N’M’) in each sub-band.

(Or, the first

If the input signal of the sub-band of the formula (75) (or formula (76)) is phase modulation to receive the TD-signal

(Or FD-signal)

), we can know the following two facts: the symmetry of the TD signal [Non-Patent Document 10]:

(Refer to formula (21)).

(ii) The nature of the FD signal inherited by the symmetry of the TD signal

Look, the filter coefficient

(Or

) Can be said to be formula (77). (The proof ends).

In addition, filter characteristics when using formula (77) with the AFB _{P '0 MN, P 0 M'N} ' th polyphase component (polyphase components)

, Then N’ and N polyphase filters (Vaidyanathan [Non-Patent Document 13] Type 2 polyphase)

Is defined, and the AFB in Figures 8 and 9 is obtained. If N=N'=1, N ₀ =N' ₀ =1, it corresponds to the general AFB.

The binary symbols of TD-AFB (or FD-AFB) are

(Or

) To define.

however,

Has MLE value

(Refer to equation (59)) MLE ^{of the attenuation constant Ae i κ.} The SFB of FIGS. 4-7, which are symmetrical to TD and FD, and the pair of TD-AFB and FD-AFB of FIGS. 8 and 9 are called "twinned-FBMC (twinned FBMC)".

In addition, Figure 8 shows the analysis filter bank (AFB, analysis filter bank), which is equipped with a complex value data

Decoded TD correlator array.

In addition, Figure 9 shows AFB, which is equipped with a complex value data

The decoded FD correlator array.

In addition, in Figure 8, Figure 9

and

, Respectively corresponding to the above

and

After installing the PUL algorithm as the interface of TD-AFB and FD-AFB as shown in Figure 10, the time-varying, adaptive AFB obtained is a parameter estimator for radar and PUL algorithm for other communication systems After the convergence of the synchronizer. In addition, this is based on complex CCF values for data communication systems

and

of

Decoder. In addition, the filters defined by formula (68), formula (72), and formula (77) of this FBMC can all be polyphase filters (called Vaidyanathan's type 1- or type 2-polyphase [non-patent Document 13]) to achieve, the detailed content is omitted here.

In addition, Fig. 10(a) shows the correlator array of TD, (c) shows the analysis filter bank (AFB, analysis filter bank) of the FD correlator array, and (b) schematically shows the two methods according to von Neumann's APT. Interactive update of the maximum likelihood estimate of the array.

<8. Other examples of communication that utilizes the non-replaceability of time and frequency displacement>

In the radar problem, which is a typical example of communication that uses non-replaceability, it is about _{TFSO with the delay t d} and Doppler shift f _D of the communication path as the parameters

, And the estimated value of delay and Doppler shift (shift) required by the receiver

TFSO

It can be seen that the prior half-shifts of transmitting and receiving TD and FD signals are useful in estimating the parameters of _{t d} and f _D. In this section, two and three specific examples of communication that make use of irreplaceability are listed.

The single goal for simplification has been discussed earlier. It is easy to extend to and fro several goals. For example, by using equation (32), equation (37) determines the level of r _0, r _'0, the search target can be detected in the plurality of target space. In addition,

<8.1 Multiple target detection based on CDMT>

For example, divide the target search space Θ'=[0,T)×[0,F) into four:

[Math 544] R ₁ =[0, T /2)×[0, F /2), R ₂ =[0, T /2)×[ F /2, F ), R ₃ =[ T /2 , T )×[0, F /2), R ₄ =[ T /2, T )×[ F /2, F ) , allocate TD-PC and FD-PC to each space,

[Math 545] X ={X,X ' }, y ={Y,Y ' }, Z ={Z,Z ' }, W ={W,W ' }

, And the two-dimensional PC

[Math 546] X , y , Z , W

The chip address (address) is expressed as

. In addition, set the signature to

. Only χ ⁽¹⁾ , χ ⁽²⁾ , χ ⁽³⁾ , χ ⁽⁴⁾ correspond to

[Math 549] X , y , Z , W

. The CE of the radar signal is

, Used to detect multiple targets (target).

Delay, Doppler, attenuation constant through N _path double-diffusion channels (doubly dispersive chanel)

The signal component of the received signal of the communication path is

. On the other hand, in the receiver, the TD-CE and FD-CE of formula (33)

vio two-dimensional PC χ (or

[Math 554] y

) Into formula (29), and the type-3 and type-4 of formula (38) and formula (43)

Of

[Math 556] l _μ , k _σ

The movable range of are set to

(or

) Maximum likelihood estimation for target retrieval.

The target retrieval in other parts of the space is also the same. This is to imitate the code division multiple access (CDMA, Code division multiple access) thinking that uses a two-dimensional PC to perform multiple target retrieval, so it is called Code Division Multiple Target (CDMT).

Among the numerical simulation results of N=N ' =64 and N _path =4, the result of applying the PUL algorithm is that under the condition of SNR above 5dB, 3 or 4 targets can be successfully detected with an 80% probability.

<8.2 Embedded artificial non-replaceable displacement based on delay-Doppler Space Division Multiplexing (dD-SDM, delay-Doppler Space Division Multiplexing) ultra-high multi-phase shift keying (MPSK, multiple phase shift keying)>

The use of PUL's proof of convergence has realized the important role of the partial space of the Hilbert space, the T _s -TL TD space, and the orthogonal projection operator P of the _{F s -BL TD space. 3.} Formula (38) of P ₄ , TD-CCF, FD-CCF of formula (43)

, Which refers to the TFSO pair that generates transmission and reception signals among various TFSOs based on non-replaceable communication.

(Or

) Is the essence.

The reason is that there are unknowns in these

[Math 562] ( l _D , k _d )

Maximum likelihood

Control parameters for search

[Math 564] ( l _μ , k _σ )

One of them. Modulated and demodulated TFSO

Or based on data, chip address (address)

TFSO for the parameter

It has nothing to do with any of these.

On the other hand, with

The designated TD-CCF, FD-CCF pair

The output of (Equations (41), (45)) contains information data of various PD types

Appeared in the Xianfang.

This part means that as long as the aforementioned multiple target detection method is used,

[Math 571]

The parameter value of the artificial parameter as the phase term

(For simplicity, set the attenuation constant as

) Is available. In view of the above, the transmission and reception system of this embodiment specifically uses N _path TFSO pairs for transmitting and receiving signals, as well as TD-CCF and FD-CCF pairs.

Non-replaceable communication, using embedded parameter values

TD-template and FD-template of the N _{path pair of the received signal.} Manually embed the PUL in this situation into the irreplaceable displacement of the received signal

[Math 576] ( k _{d, i} , l _{D, i} )

In the sense of recovering with the receiver, it is slightly different from the general PUL. In addition, in the non-patent literature [25, 30], although the transmitter and receiver The parameter update of is called "active PUL (active PUL)"; but because PUL cannot be applied to the update of the transmitter on the condition of the proof of convergence, in this manual, a known non-replaceable displacement is embedded in the transmitter

, And use its displacement in the receiver to estimate the maximum likelihood. This is an application example of general PUL.

Using a plurality of independent two-dimensional PC CDMT, in

[Math 578] M -ary

Phase shift keying (PSK, phase shift keying) data

The data communication is valid. Each phase compensation item

The phase tuned layer (PTL, phase tuned layer) placed in front of the input part of the N’, N array type TD-CCF and FD-CCF is equivalent to: the TD-CCF, FD-CCF pair

Of the output (Equations (41), (45))

[Math 582]

, Respectively replace to each

Compensation of the phase, and the calculation of the maximum likelihood estimation as a substitute for the PUL of formula (60)

The two variables, the variables used by the PTL

[Math 585] l , l'

Corrected to the additional three variables

. Thereby, the phase variation of the complex output with the maximum likelihood becomes a distribution similar to the Gaussian distribution of mean zero.

In the transmission and reception system of this implementation type, N=N ' =16 can be obtained,

[Math 587] M =8,16,

Good numerical simulation of SNR 30dB. However, when

[Math 588] M =16

At this time, side lobes are generated on the left and right sides of the distributed main lobe, which causes decoding errors. Therefore, only from the perspective of decoding errors using pure phase compensation, only

[Math 589] M = 8

For better.

Next, as the transmission and reception system of this embodiment, in order to perform

For data communication, the parameter space Θ′ of the delay-dpppler used for data communication is equally divided into

A two-dimensional PC

Allocate to each part of the space. In addition, because of the artificial displacement

[Math 593] ( k _{d, i} , l _{D, i} )

, The system is considered to be located near the center point of its i-th partial space, so it exemplifies the implementation of delay-Doppler space division muliplex (dDSDM, delay-Doppler space division muliplex) non-replaceable communication The dDSDM system sets the phase compensation items of TD-CCF and FD-CCF PTL with 8-PSK as the basic unit as

. In this case, for

The PTL and the four-variable calculus of its maximum likelihood estimation are respectively

. Therefore, the transmission and reception system in this embodiment has a total of

CCF. The decoding results of 128PSK and 256PSK using 16, 32 2-bit PCs are available. However, because this system inherently imposes _{the discrimination accuracy of the phase W M} , this will not lead to super high

[Math 598] M

-PSK encoding and decoding improvements.

Below, while synchronizing,

[Math 599] M

-PSK encoding and decoding system; and for both synchronization and ranging

[Math 600] M

-ary PSK-encoder and decoder, described with reference to Figures 12-17.

First, Figure 12 shows

[Math 601] M

-PSK is a block diagram of the structure of a transmitter (encoder) that can communicate and perform high-speed and high-precision distance measurement.

During synchronization and distance measurement (Switches 1-1 and 1-2 in Figure 12 are connected to the state) and

[Math 602] M

-In the case of PSK data communication (the state where switches 1-1 and 1-2 in Fig. 12 are connected), switch between the transmitter and the receiver. When the input data

for

[Math 604] M

-In PSK (in other words, a state with data communication), the switches shown in each figure are switched to the lower route.

In the following, firstly, description will be given to each block in the block diagram of the transmitter in FIG. 12. In Figure 12, the input at the left end is

, In the synchronization and ranging mode with the switch 1-1 and switch 1-2 connected to the upper side shown in Figure 12, the transmitter performs

. On the other hand, in the state where the switch 1-1 and the switch 1-2 shown in FIG. 12 are connected to the lower side (in other words, the state with data communication), the transmitter performs chip waveform input

. Then, in the box of "k's encoder", starting from 0th-AC,

th-AC is arranged side by side, with multiple black dots in the middle such as

General vertical configuration. Here, each black dot is only represented by omitting each AC.

The encoder of this embodiment switches the switches 1-3 and 1-4 on the left and right sides of the box of "encoder of k" according to the value of j in the box of "encoder of k". After that, perform on the downstream side in the box of "k's encoder"

Modulation, and coded into

After that, go to the top and bottom of the switch 1-2 of the transmitter to obtain each transmission

[Math 612] TD-CEψ[ k ]/ FD-CE Ψ[ l ]

And each transmission

[Math 613] TD-CEψ ^AC [ k ]/FD-CEψ ^AC [ l ]

. In the encoder of this embodiment,

[Math 614] l _c

After modulation, after

[Math 615] ( k _d , l _D )

-MC, and increase noise (nosie), after passing

[Math 616] l _c

Demodulate and get the receiving CE.

The above is the description of each block shown in FIG. 12.

Because high-end

[Math 617] M

-PSK data

Transmission, under the influence of phase noise, phase

It’s difficult to distinguish between, so first, in the middle block of the k coder (the part enclosed by the realization in the lower right of Fig. 12), it is coded into

, And consider low-level

[Math 621] M ₀

-PSK data

Transmission. on the other hand,

The transmission system uses the synchronization and ranging method of this patent, which can make the time shift and frequency shift correctly restored. Therefore, the parameter plane Θ of time delay and Doppler shift is equally disjoint division (disjoint division) as

Part of the plane Θ ^{(i) is} assigned a 2-dimensional PC χ ⁽ⁱ⁾ (refer to Fig. 17). If the chip waveform is

2D BPSK modulation, then this

Multiplexing. Furthermore, it is assumed that passing this signal is equivalent to the artificial channel (AC, Artificial Channel) of the time shift and frequency shift of the center point of ^{Θ (i).} Therefore, starting from 0th-AC, in

Select the AC corresponding to j in th-AC, and set the

get on

[Math 629] M ₀

-PSK modulation. This system becomes the transmission CE, after

[Math 630] l _c

Modulated and sent to the main channel (MC, Main Channel)

[Math 631] ( k _d , l _D )

-MC. after

[Math 632] l _c

It demodulates and imposes noise and becomes the receiving CE.

Next, each block shown in FIG. 13 will be described.

Figure 13 series display

[Math 633] M

-PSK is a block diagram of the structure of a receiver synchronizer (decoder) that can communicate and perform high-speed and high-precision distance measurement.

In the state where the switch 2-1 shown in Figure 13 is connected to the upper side, the receiver performs

. On the other hand, in the state where the switch 2-1 is connected to the lower side (in other words, the state with data communication), first of all, in the block of "k's encoder", the decoding becomes

And will go through

The following signal is input into the box on the left. This block is from 0th-AC to

th-AC, AC are arranged side by side, and there are multiple black dots in the middle, such as

General vertical configuration. Here, each black dot is only represented by omitting each AC.

The encoder of this embodiment corresponds to the box of "k's encoder"

And switch the switch 2-3 and switch 2-4 on the left and right sides, and then proceed to the left

The demodulation and input to the lower block correlator (COR) together with the receiving CE on the left end.

Among them, "COR" in Figure 13 refers to Correlator. The large box (ρ ', ρ ) on the right side of "COR" in Figure 13 is the result of the selection

[Math 641] ( k _d , l _D )

,Ae ^{i κ} -maximum likelihood estimation and

Recover and decode the block of k. With switch 2-2 connected to the upper side, the receiver performs

In the state where the switch 2-2 is connected to the lower side (in other words, the state with data communication), the receiver performs

Processing.

The above is the description of each block shown in FIG. 13.

Consider performing 2-dimensional PC χ 2-dimensional BPSK demodulation of the chip waveform on the receiving CE. In the receiver, the switch 2-1 is connected to the lower side in the mode with data communication, the chip waveform will pass the estimated value of j

2D PC

The signal obtained by the 2D BPSK demodulation is inputted from 0th-AC to

selected in th-AC

th-AC, and in this output signal,

get on

[Math 650] M ₀

-PSK demodulation. In the final part of the parameter estimation box (that is, the box that can be input into "COR" output), for

On each of the four variables

Calculate argmax and perform PUL

[Math 653] ( k _d , l _D )

-Maximum likelihood estimation (the convergence value of PUL is

).

Here, although the maximum likelihood estimation is common when the switch 2-2 is connected to the upper side and the switch 2-2 is connected to the lower side, the decoder performs

Recovery, and in the data communication mode with switch 2-2 connected to the lower side, perform

-Decoding of k caused by the maximum likelihood estimate

[Math 657] k ^* = j ^* M ₀ + j' ^,*

. Moreover, even in the general synchronization and ranging mode (the switch state above), the data

Low-level

[Math 659] M ₀

-PSK adjustable and demodulated (e.g.

[Math 660] M ₀ =8

).

Figure 14 is a diagram schematically showing an example of the distribution of the size of the real part of the CCF on the space of the delay τ-Doppler displacement ν of the main channel (MC, Main channel) of the implementation type.

In synchronization and ranging mode, the main lobe is located at

[Math 661] ( k _d , l _D )

, And can be differentiated from other side lobes. In addition, the wavy line shows background noise.

FIG. 15 is a diagram schematically showing an example distribution of the size of the real part of the CCF in the τ-ν space when the artificial channel (AC, Artificial Channel) of the implementation type is overlapped on the main channel (MC, Main Channel).

Show a distribution, which is before MC, use

[Math 662] M

-The size distribution of the real part of the CCF when the three artificial channels (AC) imported by the coding of the message K of the PSK signal are cascaded. Although MC is still located

[Math 663] ( k _d , l _D )

, But when AC overlaps, MC+AC0, MC+AC1, and MC+AC2 are located at

. Although the amounts of time shift and frequency shift become additive, the PD system propagates along with the group-theoretic nature. In order to obtain a distribution diagram like Figure 15, as disclosed in this specification, it is necessary to maximize the maximum likelihood of the real part of the CCF by performing a strict evaluation of PD while maximizing the real part of the CCF. The number of variables of the value is increased and correctly estimated. In addition, the types and numbers of the added variables j and j'are respectively

FIG. 16 shows a diagram of using the signal of the parameter space with irreplaceable AC displacement of the additional dimension 2 of the implementation type for TFP division (because it is a parameter space, the performance of the "co-dimension" is used).

In Fig. 16, in the time/frequency plane TFP S division (Gabor division) (S ⁽⁰⁾ , S ⁽¹⁾ , S ⁽²⁾ , S ⁽³ _{) of the signal (time width T S} , bandwidth F _{S) in the time/frequency plane} ⁾ ) On the axis orthogonal to the plane, the non-replaceable displacement of AC is displayed

Of the scale.

FIG. 17 also shows a diagram of using the signal of the parameter space with irreplaceable AC displacement of dimension 2 of the implementation type to perform TFP division.

As shown in Figure 17, according to the non-replaceable displacement of AC, TFP is shifted to TFP of AC0, TFP of AC1, TFP of AC2, and TFP of AC3, respectively. In addition, the signal S system can interact with

[Math 667] ( k _d , l _D )

The unit plane of the MC target space (target space)

[Math 668][0, T _s )×[0, F _s )

Equal sign. In other words, the target is located at the data address (address)

In the case of part of the plane [(p-1)T _s ,pT _s )×[(p'-1)F _s ,p'F _s ) of the nearby target space, it becomes necessary to determine the address

[Math 670]

, So in any case (it has nothing to do with whether there is data communication), accept

As the maximum variable of the real part of the two CCFs in Figure 13.

As described above, in the transmitter receiver of FIGS. 12 and 13, the upper and lower systems can be switched.

In Fig. 12 and Fig. 13, the system in which switches 1-1, 1-2, 2-1, and 2-2 are connected to the upper side is the system disclosed in Patent Document 6, and these open relations are connected to the lower side based on the impossibility A multiplexing method that replaces AC-shift-encoding and decoding.

In this way, Fig. 12 and Fig. 13 show diagrams with obvious differences and novelty from the traditional system.

In the transmission and reception system of this embodiment, the multi-value phase modulation (

[Math 672] M

-ary PSK)

In order to efficiently embed the "message k" in the above transmission signal in the transmission of the data signal, relative to the integer

, Prepare the TD phase modulation coding (TD-PC) of period N for the two-dimensional phase shift key (BPSK)

FD phase modulation coding with period N’ (FD-PC)

The combination

group. Parameter plane of time delay and Doppler shift

[Math 678]Θ=[0, T _max )×[- F _max /2, F _max /2)

And the signal TFP S=(0,T _s )×(0,F _s ) is equally divided into

Part of the plane, each as

. (T _s =NM△t,F _s =N'M'△f is the data symbol

The time, bandwidth and T _max , F _max are the time delay to be detected, the maximum value of Doppler shift, T _s , _{integer multiples of F s} P, P'). △t,△f are the quantization widths.

Next, decompose the message k into

, And will

And the rest of it is coded into

. In order to transmit the code (j,j'), first, apply ^{the TD- which uses 2-dimensional PC X (i)} to modulate the chip pulse with time T _c =M△t and bandwidth F _c =M'△f. signature, FD-signature, _{shifted at (T s} ,F _s ) level

-signature-multiplexing. Second, suppose its multiplexed signal passes through the center of a ^{plane with partial parameters Θ (j):}

The displacement of the artificial channel (AC). In order to simulate this, the fourth shift operator

It has an effect on TD-signature and FD-signature signals. Third, in the received signal, the

[Math 688] M ₀

-ary data signal

Modulate

. Mark this signal on TFP

The superimposed signal without overlapping of (P/P') is used to transmit TD-CE and FD-CE (refer to Figure 12).

[Math 692] M ₀

-ary data communication TD-signal CE and its DFT system as a substitute for formula (27)

[Math 693]

And decided. among them,

[Math 694] υ[ k ; X ^{( i )} ], V [ l ; X ^{( i )} ]

Department of TD-signature and FD-signature

(Refer to formula (25)). Here,

It means that the part of the plane shown in Figure 16 and Figure 17 is accompanied by the movable range of the chip address (m, m') (the corresponding part of the address of S).

, And compared with N, N'in the synchronization method and ranging, in data communication, because the time, frequency plane and target plane of the signal are divided by PC coding, in order to obtain accuracy,

Times. Please refer to Figure 12 and Figure 13 (Up and down switches with data communication, corresponding to the synchronization method and data communication during distance measurement).

In equation (87), and after the signature will be modulated through ν i-th two-dimensional ^{PC X (i) [k;} χ (i)] ( or

[Math 699] V [ l ; X ^{( i )} ]

),get on

-(χ ⁽ⁱ⁾ & signature)-The signal after multiplexing, through

[Math 701] M

-ary data

The displacement corresponding to the k code (j, j')

AC, and carry

[Math 704] M ₀

-ary data

CE of the message

(Or DFT

) Is the new transmission TD-CE (or FD-CE).

among them,

It is a real number with a size of 1 (refer to the conveyor in Fig. 12).

In the receiving system, for the decoding of k, the estimated value

Presumptive coding

And the corresponding displacement

Shift operator after AC

Presumption

PD compensation (refer to the transmitter in Figure 13). Specifically, the type-3 and type-4 correlators using the displacement of AC are used as a substitute for formulas (38) and (43), and two variables j, j'and the maximum variable corresponding to them are added.

,

. In the above two correlation functions, in formula (87) to transmit the CE signal, the operator

[Math 716]

It is a 2-dimensional PC operator for inserting parameter estimation

and

[Math 718] ( k _d , l _D )

Operator of the master channel (MC)

Between (refer to Figure 12). On the receiving side of the other party, the formulas (89) and (90)

[Math 720] M

-ary PSK

Kind of

Use the AC operator to push the AC

(or

), is inserted

[Math 725] ( k _d , l _D )

Presumed MC operator

(or

) And the 2-dimensional PC operator

Between (refer to Figure 13).

Figure 12 and Figure 13

[Math 729] M

-PSK can communicate and can carry out high-speed and high-precision distance measurement transmitter and encoder/decoder, which is the time delay, Doppler displacement, and the parameter plane Θ of dimension 2, which is different An implementation example of delay-Doppler space division multiplexing (dD-SDM) (Non-Patent Document 30, Patent Document 6) after the division of the intersection. This department serves as

[Math 730] M

-Replacement of PSK data k, and transmit encoding

, And because the signal passes through the time shift of the ^{Θ (j) center}

And frequency shift

Therefore, the generated PD detection (refer to Figures 14 and 15) decodes j, j'. In order to detect j on the receiving side, a PC χ ^{(i) of} a different i is used on the transmitting side to perform 2-dimensional BPSK, and so on

Multiplex and enter this into

th-AC, and in its output signal, carry on

[Math 736]

of

[Math 737] M ₀

-PSK demodulation.

because

Have

Kind, so

PC with AC and 2D BPSK

Department necessary. On the receiving side, quadruple multiplexing is performed on the TFP using the chip wave to detect the embedded template. Use presumption

th-AC selection, proceed

[Math 743] ( k _d , l _D )

The maximum likelihood estimation. for

[Math 744] M ₀

-PSK communication, use

This kind of non-replaceable displacement AC insertion produces multiplexing to achieve high-level

[Math 746] M

-PSK communication.

This dD-SDM is a multiple communication method that utilizes the parameter space of non-replaceable displacement of co-dimension 2. This is because the axis orthogonal to TFP (equaled with the unit part plane of the target plane) in the sign plane of [0, T _s )×[0, T _{s] has a non-replaceable displacement axis as AC} The time and frequency space (Time-Frequency Space: TFS) (refer to Figure 16 and Figure 17) after 3-dimensionalization (using AC displacement stratification), so it is compared with the TDMA and FDMA system of the TFP division of the conventional signal For different methods. APT-based PUL system basic technology that guarantees high-speed and high-precision estimation of parameters. In addition, since the AC system with irreplaceable displacement can be replaced by various propagation lines, it can be expected to be applied to optical communication where ultra-high-order PSK communication is desired.

In Non-Patent Document 30 and Patent Document 6, the

[Math 747]

The problem of multiple target detection as CDMT (Code-Division Multiple Targets) (Non-Patent Document 27), using N ^path 's 2-dimensional PC and

The product of the two phase rotation factors of the shift operation

The generated phase compensation is used for target detection. Because this system essentially forces the distinction of very small phase quantities

Method, so it produces for the big

The decoding error of phase noise has its limits. Also, because I don’t use

[Math 752] ( k _d , l _D )

-MC operator

And its compensation displacement

, While proceeding

[Math 755] M

-ary decoding, so it is not a problem of multiple target detection after double displacement of MC, nor is it a guarantee of convergence of parameter estimation. In order to solve this problem, two related functions are redefined in this manual

, And perform correct PD evaluation and compensation based on various displacement operators. Among them, the aforementioned receiving unit is used to convert the formula (87) of the two correlation functions contained in formulas (89) and (90)

(or

)of

decoding. Embedded in the receiving part (refer to Figure 12)

The calculation system of PD compensation is very complicated. However, although the detailed calculation process is omitted, it is used for high-level

[Math 761] M

-ary PSK decoding related functions, which are used

2D PC

, So the following variables are replaced:

(Replacement on the receiving side: with

, To generate a large number of phase terms, and to maximize the maximum likelihood estimation parameters of the real part of the correlation function from 2 variables

(or

) Expand into 4 variables

(or

)) (Refer to Figure 13. Among them,

(or

)). In the generalized form of formulas (39) and (44), each is

[Math 772]

. among them,

. also,

Part of the signal plane

The movable range of the attached chip address n, n', namely

. The confusion function (AF) of formulas (91) and (92) θ _gg [‧], Θ _GG [‧] g, G in the case of Gaussian function are exponentially decreasing functions; and, because of mutual exclusion of chip address division

and

Is the center of Θ ^(j) _{, so the data address (pq)MN 1} , (p'-q')M'N 1'p'≠q' of _{(p'-q')M'N 1} 'can be ignored for the first variable and the second variable of AF. Item p≠q and chip address

, So only p'=q', p=q and

Items of

[Math 781]

middle

And be able to specify

This system divides Θ disjointly and uses 2-dimensional PC χ ^{(i) to} convert the modulated signal

-Multiple, more challenging AC that generates PD

Parallelization, which is the biggest reason for the signal to pass through that AC. also,

The specific department can use

[Math 787] M ₀

-ary phase compensation

To achieve (refer to Figure 12 and Figure 13).

The above two correlation functions are decoding methods that are resistant to phase noise, which use independent 2D PCs

, And by coding based on the use of k

And its presumptive code

-Dependent non-displaceable displacement

-The maximum likelihood estimation of the PUL of the AC PD, so that the minimum discrimination of the phase is used as

In progress

[Math 794] M

-Before the data communication of ary PSK, the establishment of synchronization (synchronization capture, synchronization maintenance) and ranging are effective. However, in real communication, to pass

[Math 795] ( k _d , l _D )

The above two related functions are necessary for the communication of the MC as a prerequisite. The two functions are synchronously captured and kept synchronously in the upper switch state of Fig. 12 and Fig. 13, and in the lower switch state of Fig. 12 and Fig. 13, make

[Math 796] M

-Parallelization of encoding and decoding of ary PSK is possible. In other words, the above two correlation functions act as a rangefinder with time delay and Doppler displacement relative to the radar, and they are relative to

[Math 797] M

-ary data wireless communication (lower switch state in Fig. 12 and Fig. 13), which operates as a time delay/Doppler shift synchronizer and encoder/decoder, which does not require amplitude modulation for multi-value phase modulation and demodulation. 2D PC

As an implementation example of a secret key wireless secret communication system, it may be provided for secret data communication, vehicle-mounted radar and data communication systems that can measure distances.

Different from the conventional method, the reason why "message" is not applied to the amplitude is (1) the ^{estimating with time of the attenuation constant Ae i κ} of the communication path; (2) the simplification of the decoder, etc. Correct PD evaluation, compensation, and PD utilization are the ultra-high-end communication methods used as frequency resources

[Math 799] M

The realization of -ary communication becomes easy. Also, because using

A 2-dimensional PC, so also

Multi-communication becomes possible.

<8.3 Signal processing using multi-dimensional non-replaceability>

Daughman put the Gabor function

Expansion into 2 dimensions [Non-Patent Documents 33,34]. As a pre-preparation, follow Howe [Non-Patent Document 5] and import the

Two shift operators

. Among them, ν‧t shows the inner product. Then, if for

Import scalar product

, Then the collection

Department becomes

The unitary operation group on the

(Call H the Heisenberg group of degree n) associative laws

Established. Also, if you import

[Math 811]

And using Fourier transform, the unified performance of the two H

[Math 812] ρ , ρ ￮ r

between,

The relationship is established (Howe ('80)).

Daughman [Non-Patent Document 35] is defined as the space variable of the two-dimensional space domain (SD, space domain) having the same form as the following equation

[Math 814] x=( x , y )

The complex Gabor elementary function (complex Gabor elementary function) g(x) and 2 are the spatial frequency of the spatial frequency domain (FD, frequency domain)

[Math 815] u=( u ,υ)

2-D Fourier Transform (FT)

[Non-Patent Documents 35,36]

[Math 817]

The 2-D Gabor filter family. In addition, the P-system DC component becomes the initial phase of zero.

[Math 818] ( x - x ₀ ) _r , ( y - y ₀ ) _r

Rotating the elliptical Gaussian clockwise by θ

. SD function g(x), FD function

The system is completely symmetrical, and in each displacement

[Math 821] x ₀ =( x ₀ , y ₀ ), u ₀ =( u ₀ ,υ ₀ )

The position of contains the 2-D Gaussian envelope that becomes the Peak; in addition, it provides 2 moments of momentum

Uncertainty relationship between [Non-Patent Documents 35,36]

. (The equation system can be achieved by the 2-D Gabor filter family of equation (97).) Also,

It is called modulation and scale parameter.

Under the condition of formula (99), in image processing, simultaneous representation of space/spatial frequency with the best resolution (image representation is a 4-dimensional expanded version of the sound spectrum (spectrogram)) is important.

For the performance of a given 2-D signal I[x] (for example, an image on a 256×256 pixel (pixel), that is, ^{a vector in (256) 2} = 65536 dimensional vector space), consider the selected group Set of 2-D vectors of I[x]

The best performance produced by the projection on the screen. [Non-Patent Document 35] The system leads to the linear sum

The error energy of ∥I[x]-H[x]∥ ^{2 is} reduced to the minimized expansion coefficient

decision. In Daughman, because it is found that for non-orthogonal systems

The gradient method of a _i becomes a sparse matrix problem of n×n (in the above example, n=65536), and its execution system is impractical. Therefore, someone proposed a neural network-based method . In addition, various methods for image analysis such as edge detection and feature extraction have also been proposed [Non-Patent Documents 37, 38, 39].

In this patent, because (100) is a 2D Gauss function _{with spatial/spatial frequency shift (x 0i} , u _0i)

The generated 2D Gabor expansion, in order to imitate the signal processing method based on the one-dimensional non-permutable operation in the previous chapter, and to examine the FD performance of SD performance (100) symmetrically, using 2-D of I[x], H[x] Fourier transform

, And consider the SD-FD performance of the image

. Consider the image as the element of the partial space ε,ε’ of Hilbert space

, The error

Minimize, and perform orthogonal projection operators of SD and FD for each n groups

Produced by

Direct decomposition

. Template collection

The choice is important. For example, change

As each (L ₁ △x×L ₂ △y)-space-restricted Gauss function and (L ₁ △u×L ₂ △v)-spatial bandwidth-restricted Gauss function, then

It is an orthogonal projection (OP, orthogonal projection) on part of each Hilbert space. Two-dimensional von Neumann APT can be applied to two OPs. As the interactive projection of the APT from the two OPs, because it can guide the localization operator

, Therefore

. This system extracts the peak-address (x _0i ,u _0i ) in the SD-FD space of 2x2 dimensions

Part of the area, and filter-out the signal from other areas. This signal regeneration method is completely different from the conventional method and utilizes 2-dimensional non-replaceability signal processing. among them,

system

Orthogonal space. Also, at this time, it is different from Howe's shift operator formula (93), for SD and FD signals

Symmetry, if you use half displacement

2D von Neumann's SD, FD symmetrical space-space frequency shift operator (SFSO, symmetrical space-space frequency shift operator)

, Then the 2-D Gabor function _{of peak-address (x 0i} ,u _0i ) in the SD-FD space of 2x2 dimensions

and

system

. Consider DFT. Space coordinates

[Math 852] x=( x , y )

The sampling interval of is (M, N), and relative to the spatial variable

SD function

, Spatial frequency

[Math 855] u=( u ,υ)

Sampling interval

[Math 856]△ u =1/( L ₁ △ x ),△υ=1/( L ₂ △ y )

Discretized spatial frequency

FD function

, The department uses the function with SD

Twiddle factor

[Math 860]

2D DFT

[Math 861] F ^(2),d [． ],IDFT F ^-1,(2),d [． ]

Relationship

To decide.

Therefore, the SD function

(Or FD function

) Support system

[Math 865] L ₁ △ x × L ₂ △ y

(or

[Math 866] L ₁ △ u × L ₂ △υ

).

The interval of peak-address x _{0i in} SD space is taken as (Mx△x,My△y), and the _{interval of peak-address u 0i} in FD space is taken as

[Math 867] ( M _u △ u , M _υ △υ)

, And if normalization conditions are required

[Math 868] M _x △ x × M _u △ u = M _u △ y × M _υ △υ=1

, You get

[Math 869] L ₁ = M _x M _u , L ₂ = M _y M _υ

. Also, if also will

Space shift, frequency shift

Discretization, the two-dimensional version of von Neumann's discrete TFSO is used as the two-dimensional symmetrical spatial displacement and spatial frequency displacement operator symmetrical SFSO of the following formula

And be defined. For image processing, the calculation method based on this is effective. The reason is that with the two shift operators of formula (108), because the half shift

The phase term is embedded in each SD and FD signal

, So in the inner product of formula (102), we can effectively extract

. In addition, an image analysis system with time variation can be considered as a target of signal processing using 3D non-substitutability.

<9 Features of the invention described in this specification>

The high-precision estimation method of time delay and Doppler shift constructed in this manual is only an example of a multi-element communication system that makes use of irreplaceability. This is the paper [Non-Patent Document 2] following the 1946 paper [Non-Patent Document 1] of Gabor, the ancestor of communication theory. A specific example of "Substitutional Multiple Communication".

With the superposition of signals on TFP, in the current situation where the understanding of the time and frequency displacement of the signal is not progressing, we look forward to the realization of a communication system that utilizes the non-replaceability.

The communication system proposed in this specification that utilizes the time and frequency shift of the non-replaceable communication system has at least the following viewpoints.

(Viewpoint 1)

The time/frequency symmetrical shift operator (Symmetrical TFSO) (Equation 4, 24) defined and imported in Patent Document 1 and references [Non-Patent Documents 26, 27, 30] is: (i) With its half shift, Parameter estimation visualizes important displacement as PD of TD and FD; (ii) Modulation and demodulation accompanied by irreplaceable PD

The occurrence of is obvious and easy to know; (iii) PD assessment with irreplaceability can be regressed to the twiddle factor

The PD compensation method has the characteristics of easy formation and so on.

(Viewpoint 2)

TD-PC, FD-PC modulation (2-bit BPSK) is a conventional communication technology. By understanding it as a way of calculating time and frequency displacement, each TD-PC, FD-PC modulated wideband space In the transmission signal, PC-based PDs are embedded as TD-template and FD-template.

(Viewpoint 3)

As a traditional method for effective use of frequency resources, the time and frequency shift calculations used in the superposition of signals on TFP without overlap cause data-level PD. This PD is an important element of parameter estimation.

(Viewpoint 4)

The TD- and FD-likelihood functions of TD-template and FD-template, which are necessary for the M detection methods for parameter estimation, guide each TD-CCF and FD-CCF array. TD-CCF and FD-CCF define part of the Hilbert space TL-TD space, and the upper PO P ₃ , P ₄ (or P ₁ , P ₂ ) of the BL-FD space, provided The applicable framework of APT.

(Viewpoint 5)

Represents the combined operator of the PO pairs of the interactive projection of APT

[Math 878] P ₃ F ^-1,d P ₄ F ^d

(Or

[Math 879] P ₄ F ^d P ₃ F ^-1,d

) Based on the reason that the Nyquist condition is not satisfied, the AF variable separability or exponential function type attenuation characteristics based on the Gaussian function that is not used in communication becomes a local selection operator that locally selects a specific part of TFP (localization operator). As a result, the TD-CCF and FD-CCF arrays are high-quality receivers.

The above-mentioned viewpoints are novel viewpoints disclosed after publication in patent documents and non-patent documents, and the main points of the invention described in this specification can also be expressed as follows.

(Point 1)

Symmetrical TFSO based on time/frequency symmetry (Equations 4, 24) provides non-replaceable operations on the TFP for multiple communications that utilize the two non-replaceable properties of time delay and frequency shift , The accompanying PD evaluation method and PD compensation method algorithm and its theoretical basis.

(Point 2)

The likelihood functions constituting TD and FD are used to realize signal restoration or parameter maximum likelihood estimation based on the maximum likelihood correlator.

(Point 3)

Classical binary phase modulation (BPSK) triggers PD based on its irreplaceability, which is an important key to parameter estimation or signal recovery.

(Point 4)

The non-replaceable PD that occurs with the non-overlapping superposition of the signal on the TFP or modulation and demodulation that belongs to the traditional method of communication is effective for data-level signal detection.

(Point 5)

The CCF of the TD (or the CCF of the FD) that these PDs are fully compensated is defined as two indispensable parts of the APT Hilbert space of von Neumann (time-limited time space, limited frequency (Wide space) orthogonal projection operator up.

(Point 6)

The combined operator of the orthogonal projection operators of TD and FD becomes the local selection operator on TFP, which plays the role of the sensitive filter of the conventional DSP.

(Point 7)

In image signal performance, Gabor expansion (100) with a 2-dimensional Gabor function (97) with excellent signal separation on a 2×2 space/spatial frequency plane (SFP, Space-Frequency plane) is widely used. However, in the prior art, the 2-dimensional space/frequency shift operator included in the Gabor function is the same as the non-replaceable time/frequency shift operator of the 1-dimensional signal, and no attention is paid to the difference from the non-replaceable displacement. Generation of phase distortion. By the orthogonal projection operator on the SD area limitation function of Hilbert space and the FD bandwidth limitation function

Direct decomposition of (102), solve the problem of simultaneous representation of the space/spatial frequency of the image that symmetrically process SD and FD signals (101), define the symmetrical space/frequency shift operator SFSO of SD and FD (105) The two-dimensional Gabor function (106) and the discrete version of symmetrical SFSO (108), guide the localization operator (103), and provide a theoretical framework for image processing methods, which are based on von Neumann's APT The irreplaceability of image expression and image restoration.

<<Configuration example 1 of transmission and reception system>>

Hereinafter, the first configuration example of the transmission and reception system based on the above-mentioned theoretical aspect will be described with reference to the drawings.

FIG. 18 is a block diagram showing a configuration example of the transmission and reception system 1 in this configuration example. As shown in FIG. 18, the communication system 1 has a transmitting device 100 and a receiving device 200. The transmitting and receiving system 1 can be used as a radar, or as a communication system other than radar (for example, a transmitting and receiving system mainly for transmitting and receiving data of audio data or image data).

<Transport Device 100>

In the above description, the transmission device 100 regards the items described as a device that actually executes the actions of the "transporter".

For example, as shown in FIG. 18, the transmission device 100 includes a transmission data acquisition unit 101, a transmission signal generation unit 102, and a transmission unit 103.

(Transmission data acquisition unit 101)

The transmission data acquisition unit 101 acquires the data of the transmission and reception target. When the transmission and reception system 1 is used as a data transmission and reception system, the data to be transmitted may be a content obtained by digitizing at least any one of, for example, audio data, image data, and text data, or it may be Other data.

In addition, when the transmission and reception system 1 is used as a radar, the data to be transmitted may also be a pulse wave for radar.

(Transmission signal generator 102)

The transmission signal generation unit 102 uses the transmission target data acquired by the transmission data acquisition unit 101 as an object, and performs transmission signal generation processing, thereby generating a transmission signal.

As an example of the transmission signal generating unit 102, it is configured to have at least one of the SFBs shown in FIGS. 4-7.

As far as the example of the transmission signal processing is concerned, for example, the PC (phase code) of TD- and FD- with the above-mentioned period N, N'is used, that is, TD, FD-Binary phase-shift key (BPSK, Binary phase-shift) keying) and so on.

As the transmission signal generated by the transmission signal generating unit 102, for example, the above-mentioned

. In addition, as a specific process based on the transmission signal generating unit 102, the processes described in <4. TD-, FD-signature, and template> can be cited.

In addition, the transmission signal generating unit 102 can also be used as a configuration for performing the various processes described in the above-mentioned <7.1 SFB: Signature Transmission Receiver and Radar Signal Transmitter>. In addition, the transmission signal generating unit 102 can also be used as an ultra-high multi-phase shift based on delay-Doppler Space Division Multiplexing (dD-SDM, delay-Doppler Space Division Multiplexing) that performs the above-mentioned <8.2 embedded artificial non-replaceable shift Key (MPSK, multiple phase shift keying)> The configuration of each process described in.

(Transport Department 103)

The transmission unit 103 transmits the transmission signal generated by the transmission signal generation unit 102.

<Receiving Device 200>

The receiving device 200 is a device that actually executes the items described as the operation of the "receiver" in the above description.

As an example, as shown in FIG. 18, the receiving device 200 has a receiving unit 201, a displacement estimation and received data extraction unit 202, and a received data output unit 203.

(Receiving part 201)

The receiving unit 201 receives the signal transmitted by the transmitting device 100. As an example of the message received by the receiving unit 201, it can be as described above

[Math 882] TD, FD receiving signal: r [ k : X ], R [ l : X ],.

(Displacement estimation and received data extraction unit 202)

The displacement estimation and received data extraction unit 202 (or simply the estimation unit) performs displacement estimation processing on the signal received by the receiving unit 201, and extracts the received data.

As an example of the displacement estimation and received data extraction unit 202, it can be constituted by at least any one having AFB as shown in FIGS. 8-10.

The displacement estimation and received data extraction unit 202 is executed in, for example, the aforementioned <5. TD-, FD-signal detection and estimation based on M types of hypothesis detection> and <6. TD-CCF, FD-CCF for parameter estimation> Description of each processing.

In addition, the displacement estimation and received data extraction unit 202 may also be configured to execute each process described in the aforementioned <7.2 AFB: Receiver and Decoder>. In addition, the transmission signal generating unit 102 can also be used as an ultra-high multi-phase shift based on delay-Doppler Space Division Multiplexing (dD-SDM, delay-Doppler Space Division Multiplexing) that performs the above-mentioned <8.2 embedded artificial non-replaceable shift Key (MPSK, multiple phase shift keying)> The configuration of each process described in.

Therefore, the displacement estimation and received data extraction unit 202 is a receiving method of the received signal (refer to FIG. 13), and it executes: the estimation step, which refers to the parameter space of the non-permutable displacement with the co-dimension 2 (refer to FIG. 17), Estimate the time shift and frequency shift represented by the received signal (refer to Fig. 13 and formulas (38), (43), and formulas (89), (90) corresponding to the upper and lower connections of switches 2-1 and 2-2 in the same figure )).

In addition, the transmission signal generation unit 102 executes: a displacement step, which refers to a parameter space with a co-dimension 2 of non-replaceable displacement to shift the time and frequency of the signal of the transmission target (refer to FIG. 12 and corresponding to the switch 1- in the same figure). The formulas (25), (27), and formulas (88), (87) for the upper and lower connections of 1,1-2).

In addition, the above-mentioned non-replaceable displacement parameter space with a co-dimension of 2 uses a third axis showing time displacement and frequency displacement to display the plane opened by the first axis showing time and the second axis showing frequency, 3 Dimension the resulting space (refer to Figure 17).

Also, the above

[Math 883] ( k _d , l _D )

-MC itself is also the same as AC. It is a parameter plane of co-dimension 2 and a parameter plane accompanied by a displacement operation on the time/frequency signal plane TFP. It is necessary to distinguish the "displacement plane" from the TFP of time t and frequency f (refer to FIG. 16). In addition to the four arithmetic operations, differentiation, integration, etc. performed on the signal variables t, f, the phase-related non-replaceable displacement operations (see the third axis in Figure 17) are considered special.

In addition, the following contents will be added in conjunction with Patent Documents 6 to 8.

a) When it is necessary to modulate/demodulate

(Or its discrete version

) And PD e ^{i κ of the} attenuation constant Ae ^{i κ} are all captured and merged. This is because, due to the group-theoretic nature of the displacement, each PD is propagated non-independently, so it is not an accurate PD compensation. In the process of updating the estimated values of time shift and frequency shift, it is necessary to pay attention to the linkage with these PD compensations (simultaneous parallel processing: formula 59).

b) The time displacement/frequency displacement system of this patent refers to the parameter space variable of the remaining dimension 2 of the time/frequency variable. These non-replaceable displacement calculations cause correlation functions (phase distortion). On the other hand, the time deviation and frequency deviation in communication are the "offset" of the period and carrier frequency.

(1) The time deviation and frequency deviation estimated in Patent Documents 7 and 8, and the time/frequency deviation in the communication method of the OFDM method of Patent Document 7 are the fluctuations in the time width of each pulse waveform and the carrier frequency, and correspond to The time displacement t _d and frequency displacement f _{D of} this patent. Because the two patent documents ignore _{the irreplaceability between t d} and f _D , they can be understood as a general synchronization capture/synchronization maintenance method.

(2) Because "intentional" displacement and deviation are easily mixed, in this specification, "deviation" is not used but the expression of "half displacement of the shoulder of exponential function (half of the conventional non-replaceable displacement)" is used. . In addition, a feature of the invention described in this specification is that the transmission signal includes a "phase function after a half-shift in advance" and can be used as a compensation method that takes into account the group-theoretic nature of time/frequency shifts that are irreplaceable. which performed.

c) The preamble used for channel estimation in Patent Document 8 is a time zone template signal after acceptance. It cannot be said to be a frequency zone signal. It is not based on non-replacement, but a general channel estimation method.

(1) Compared with the PUL algorithm of Patent Document 6, 1) Define the Hilbert space ε _i to which various templates belong, 1≦i≦4, as a partial space of the signal space of the Hilbert space; 2) Set the above-mentioned first N' A correlation function (type 3- or type 1-CCF) is the orthogonal projection operator P ₃ (or _{ε 1 ) on the Hilbert space ε 3} (or ε 1) of the NM△t (or L△t)-TL-TD function P ₁ ), and the above-mentioned second N correlation function (type 4- or type 2-CCF) is the Hilbert space ε ₄ (or ε ₂ ) Orthogonal projection operator on P ₄ (or P ₂ ); 3) Use TFP for two-dimensional template matching (template-matching), local selection operator LO's alternative projection theorem operator (APTO, Alternative Projection Theorem Operator) ^{_{) P 3 F -1.d P 4 F}} d ( or ^{_{P 4 F d P 3 F -1}} , d) update process, based on the convergence function (von Neumann in the combined set of two APT Hilbert space: F ^{- 1d} , F ^d is IDFT, DFT); 4) clarify that the combined set of TL-TD function and BL-FD function is an empty set, that is, the zero function (Youla theorem), etc., and it is proved that the PUL system provides non-correlation The number of function types is N, the product of N'is proportional to N‧N' but proportional to the sum of N+N'. The calculation complexity is accurate to the time width L△t and bandwidth L△f of the Gauss chip pulse. Estimated value of displacement and frequency displacement (L=(△t△f) ^-1 =MM').

(2) The channel estimation minimum mean square error (MMSE, Miminum mean square error) algorithm of Patent Document 8 is based on the Bayes rule of 2-parameter estimation, so the computational complexity becomes the product (N‧N'). On the other hand, although the likelihood function in this specification is related to the Bayes rule, it is composed of N'likelihood functions estimated by time shift and N likelihood functions estimated by frequency shift, and each is in TL- TD space and BL-FD space perform maximum likelihood estimation interactively, so the computational complexity becomes the sum (N+N'). This is a parameter estimation method completely different from the method in Literature 3.

In addition, the displacement estimation and received data extraction unit 202, as described in the formula (84) and the use-related description, as an example, executes the estimation step, which is the time displacement and frequency displacement represented by the received signal, and the above estimation Step system use: the first shift operator

, Which represents the estimated value of time shift and frequency shift; the second shift operator

, Which represents the estimated value of time displacement and frequency displacement; to estimate the time displacement and frequency displacement indicated by the above-mentioned received signal.

The above presumption step is to use: the first shift operator

, The second shift operator

, The third shift operator

Or its dual frequency (Dual Frequency)

And the fourth shift operator

Or its coupled frequency

, To estimate the time shift and frequency shift represented by the received signal; and, the first shift operator system represents the estimated value of the time shift, the frequency shift and the phase term of the half shift of the estimated time shift; The second displacement operator system represents the estimated value of time displacement, frequency displacement, and the phase term of half of the estimated frequency displacement; the third displacement operator system represents the time displacement of the estimated object and the observed value of frequency displacement of the estimated object And the phase term of the half of the estimated time displacement; and the fourth displacement operation sub-system represents the phase term of the estimated value of the time displacement, the frequency displacement, and the half of the estimated time displacement.

The phase function of the transmitted time signal includes: the phase quantity of the half displacement with respect to 1 of the time or half of the displacement of the plural displacement parameters. In addition, the phase function of the transmitted frequency signal includes the phase amount of half displacement with respect to 1 of the frequency or half of the displacement of the plural displacement parameters.

According to the receiving device 200 configured as described above, a highly efficient receiving device can be realized. As an example, when the receiving device 200 is configured as a radar receiving device, a high-speed receiving device can be realized.

In addition, the above-mentioned estimating steps performed by the displacement estimation and received data extraction unit 202 are as described in formula (84) and related descriptions. As an example, refer to the first correlation function expressed by the first displacement operator

, And the second correlation function represented by the second shift operator

, To estimate the time shift and frequency shift represented by the received signal.

In addition, as described above, the first correlation function described above is expressed as

, The second correlation function above, expressed as

[Math 897]

In the above estimation step, the first correlation function expressed by the first shift operator, the third shift operator, and the fourth shift operator is referred to

, And refer to the second correlation function represented by the second shift operator, the third shift operator, and the fourth shift operator

, To estimate the time shift and frequency shift represented by the received signal.

In this way, the above-mentioned first correlation function (refer to formula (89)) and second correlation function (refer to formula (90)) include: the modulation of the modulation frequency f _c and the impossibility of the time shift t _{d in the demodulation.} Phase distortion of displacement calculation

[Math 900]

Or its discrete version

; And the phase distortion e ^{iκ during transmission} .

In addition, the displacement estimation and received data extraction unit 202 uses the formulas (60), (61) and related descriptions to describe the estimated axis of the time displacement and the estimated value of the frequency displacement.

or

Update processing to

Decided

, Set it to

To deal with it.

In this way, displacement estimation and estimation processing executed by the received data extraction unit 202 are performed.

The above-mentioned estimation processing includes an interactive update step in which the update step of the estimated value of frequency shift and the update step of the estimated value of time shift are alternately repeated. In addition, the update procedure of the estimated value of the frequency shift refers to the first correlation function

(Or formula (89)), find

, And by setting its value to

, To update the estimated value of frequency shift.

In addition, the update procedure of the estimated value of the time shift refers to the second correlation function

(Or formula (90)), find

, And by setting its value to

, To update the estimated value of the time shift.

Furthermore, in the above estimation step, as described above, the maximum likelihood estimation of the frequency shift based on the likelihood function of the N'TD-template signal detection and the time shift of the likelihood function of the N FD-template signal detection Maximum likelihood estimation is used to estimate the time shift and frequency shift represented by the received signal.

In addition, in the above-mentioned maximum likelihood estimation, referring to the correlation function of formula (89)

And the correlation function of formula (90)

, Each of which is applicable as the right side of the first formula of formula (60)

[Math 915]

And the second type

Substitution, and in the argmax calculus,

It has also become the object of maximum likelihood estimation.

Also, in the above-mentioned maximum likelihood estimation, the receiving device is

[Math 918] M -ary

Under communication, part of the encoder through k

Receive

[Math 920] TD-CEψ ^AC [ k ]/FD-CEψ ^AC [ l ]

The receiving department.

In this way, the receiving device of this embodiment is a receiving device that receives a signal, and it includes an estimating unit that refers to a parameter space with a co-dimension 2 that cannot be replaced with a displacement to estimate the time shift and frequency represented by the received signal Displacement.

In addition, in the above-mentioned maximum likelihood estimation, the TD-CE and FD-CE in formula (87) (or (27)) (here, due to the switch 1-1, 1-2 of the transmitter in Figure 12) The upper and lower levels of multiplexing are different, so the corresponding formula is quoted), the TD-signature and FD-signature of the formula (88) (or (25)) on the right are multiplexed, and the two signatures themselves can also be Gaussian functions by using Or its FD function is obtained by multiplexing 2D PC modulation. also,

[Math 921] M -ary

Communication transmission TD-CE, FD-CE are as shown in formula (87), TD-signature, FD-signature are mutually independent 2-dimensional PC sets

The resulting multiple and the code corresponding to its k

Of

The displacement calculation corresponding to the displacement

Have an effect.

In this way, the transmission method of this embodiment is a transmission signal transmission method, which includes: a displacement step, which refers to a parameter space with a co-dimension 2 irreplaceable displacement to shift the time and frequency of the signal of the transmission object.

Moreover, in the above-mentioned maximum likelihood estimation, Yu passed

[Math 926] M -ary

Part of the encoder of k under communication

Receive

[Math 928] TD-CEψ ^AC [ k ]/FD-CEψ ^AC [ l ]

In the case of the correlation function with the estimated reception template (formula (89)) (the first and second terms on the right are the transmitted signal and the estimated signal template respectively), the sum Σ in formulas (87)-(90) represents The "multiplexing = no overlap superposition" can be simulated using various shift operators. In the process of generating the transmission signal shown in FIG. 12, various multiplexing are performed. In formulas (87)-(88), for each TD-, FD-chip pulse wave usage cycle

2D PC modulation

The multiplexed, generate signature; and use the obtained signature for data multiplexed data level shift, define and transmit TD-CE, FD-CE. In addition, in simple addition without displacement, because the template cannot be detected, it is natural to understand the following: the displacement operator is indispensable; and the PD associated with the displacement calculation is for template detection, and compensation should be paid at the same time. Clues for correct PD distortion evaluation.

Also, on the right side of equation (89), apply PD with modulation/demodulation

, The encoding of k

of

的PD compensation.

In this way, in the above displacement step, the time pulse waveform is modulated by the time phase code of period N, and then the time pulse waveform after the time phase code modulation is modulated by the frequency of period N' The regional phase code modulation is multi-carrier, and then the transmission signal is generated.

In addition, in the transmission device of this embodiment, in the state where the switches 1-1 and 1-2 in FIG. 12 are connected, the TD-signature, FD after the multiplexed data is multiplexed. -signature pass the code of k

[Math 934]

corresponding

, And get

[Math 936] TD-CE ψ ^AC [ k ], FD-CE Ψ ^AC [ l ]

. Among them, the aforementioned multiplexing is to perform the time pulse waveform with period N time phase code modulation, and then the time pulse waveform after the above-mentioned time phase code modulation is modulated by the frequency region phase code modulation of period N'. Multi-carrier and so on.

In addition, in the state where the switches 2-1 and 2-2 in Fig. 13 are connected to the bottom, the real part of the correlation function of formulas (89) and (90) is maximized with respect to four variables

Argmax calculus, and based on PUL, use

Convergence value of the account update is carried out

The restoration of and the decoding of k.

In addition, the expansion of the image signal specified by the following various configurations is as described in section 8.3, which is based on a one-dimensional signal that uses a half-shift that is accompanied by a non-substitution between spatial/spatial frequency shifts. Towards a natural expansion of the 2-dimensional signal (refer to formulas (102)-(108)).

(Expanded composition towards image signal 1)

A receiving method for receiving an image signal, which includes: an estimation step, which refers to a parameter space to estimate the spatial displacement and the spatial frequency displacement represented by the received image signal; and the above-mentioned spatial displacement and the spatial frequency displacement system each has More than 2 dimensions.

(Expanded structure toward image signal 2)

In the above estimation step, refer to the two-dimensional symmetrical spatial displacement and spatial frequency displacement operators

versus

, To estimate the spatial displacement and spatial frequency displacement.

(Expanded composition towards image signal 3)

A transmission method for transmitting an image signal, which includes: a displacement step, which refers to a parameter space to shift the space and frequency of the image signal of the transmission object; and the displacement of the space and the frequency of the displacement system each have 2 or more Dimension.

(Expanded composition toward image signal 4)

In the above displacement step, refer to the two-dimensional symmetrical spatial displacement and spatial frequency displacement operator

and

, To shift the space and frequency.

(Received data output unit 203)

The received data output unit 203 outputs the received data extracted by the displacement estimation and received data extraction unit 202.

<Flow of Transmission and Reception>

FIG. 19 is a flowchart showing the flow of data transmission and reception processing using the transmission and reception system 1.

(S101)

First, in step S101, the transmission data acquisition unit 101 acquires transmission and reception data. The specific description based on the data acquisition unit 101 for transmission is as described above.

(S102)

Next, in step S102, the transmission signal generating unit 102 generates a transmission signal. The specific processing by the transmission signal generating unit 102 is as described above.

(S103)

Next, in step S103, the transmission unit 103 transmits the transmission signal. The specific processing by the transmission unit 103 is as described above.

(S201)

Next, in step S201, the receiving unit 201 receives the signal transmitted by the transmitting unit 103. The details based on the receiving unit 201 are as described above.

(S202)

Next, in step S202, the displacement estimation and received data extraction unit 202 performs displacement estimation processing and extracts received data. The specific processing based on the displacement estimation and received data extraction unit 202 is as described above.

(S203)

Next, in step S203, the received data output unit 203 outputs the received data extracted by the displacement estimation and received data extraction unit 202. The specific processing based on the received data output unit 203 is as described above.

<<Communication system configuration example 2>>

Hereinafter, the first configuration example of the communication system based on the above-mentioned theoretical aspect will be described with reference to the drawings.

FIG. 20 is a block diagram showing a configuration example of the transmission and reception system 1a in this configuration example. As shown in FIG. 20, the communication system 1a includes a transmitting device 100a and a receiving device 200a. The transmitting and receiving system 1a can be the same as the aforementioned transmitting and receiving system 1 and can be used as a radar or as a communication system other than radar (for example, a transmitting and receiving system mainly used for transmitting and receiving data of audio data or image data). In addition, the same reference numerals are given to the components that have already been described, and the description thereof is omitted.

<Transfer device 100a>

As described above, the transmission device 100a is a device that actually executes the recorded items as the operation of the "transporter".

As one example, as shown in FIG. 20, the transmission device 100a has a transmission data acquisition unit 101, a transmission signal generation unit 102a, and a transmission unit 103.

(Transmission signal generator 102a)

The transmission signal generating unit 102a is based on the configuration of the transmission signal generating unit 102 in the configuration example 1, plus a displacement embedding unit 110.

The displacement embedding part 110, as mentioned after the formula (84), generates embedded parameter values

The transmission signal.

Therefore, the transmission signal generating unit 102a uses: 1 or multiple displacement parameters related to time, and 1 or multiple displacement parameters related to frequency

, To shift the time and frequency of the signal of the transmission object.

<Receiving Device 200a>

In the above description, the receiving device 200a will be a device that actually executes the recorded items as the action of the "receiver".

As an example, as shown in FIG. 20, the receiving device 200a has a receiving unit 201, a displacement estimation and received data extraction unit 202a, and a received data output unit 203.

(Displacement estimation and received data extraction unit 202a)

An example of the displacement estimation and reception data extraction unit 202a has the same configuration as the displacement estimation and reception extraction unit 202 in the configuration example 1.

<Flow of transmission and reception>

FIG. 21 is a flowchart showing the flow of data transmission and reception processing using the transmission and reception system 1a. The parts of steps S101, S103, S201, and S203 are omitted here because they are the same as the description of FIG. 19.

(S102a)

In step S102a, the transmission signal generating unit 102a generates a transmission signal. The specific processing based on the transmission signal generating unit 102a is as described above.

(S202a)

In step S202, the displacement estimation and received data extraction unit 202a performs displacement estimation processing and extracts received data at the same time. The specific processing based on the displacement estimation and received data extraction unit 202a is as described above.

<<Communication System Configuration Example 3>>

The transmission and reception system described with reference to FIGS. 18 to 21 can be configured to perform the steps described in <8.3 Signal Processing Using Multi-Dimensional Non-replaceability>.

As an example, as explained in <8.3 Signal Processing Using Multi-Dimensional Irreplaceability>, the receiving device 200 executes: an estimation step, which refers to the parameter space to estimate the spatial displacement represented by the received image signal and Spatial frequency displacement; In addition, the above-mentioned spatial displacement and spatial frequency displacement systems each have two or more dimensions.

Also, as explained in <8.3 Signal Processing Using Multi-Dimensional Non-substitutability>, as an example, in the above estimation step, reference is made to the spatial displacement and spatial frequency displacement operators that express two-dimensional symmetry.

And the operator that expresses the irreplaceability between the spatial frequency shifts

, To estimate the spatial displacement and spatial frequency displacement.

Similarly, the transmission method of this configuration example is the transmission method of the transmission signal, which includes: a displacement step, which refers to the parameter space, and converts the space and frequency position of the image signal of the transmission object. Shift, and use two operators representing the phase term of half of the space displacement (or the phase term of the space and frequency shift and the half of the space frequency shift); also, the above-mentioned spatial displacement and frequency shift The lines each have more than 2 dimensions.

In the above displacement step, refer to the two-dimensional symmetrical spatial displacement and spatial frequency displacement operator

and

, Shift the space and frequency.

[Software-based embodiment]

The control blocks of the transmission device 100, 100a, and the reception device 200, 200a (especially the transmission signal generating unit 102, 102a, the displacement estimation and reception data extraction unit 202, 202a) can be formed by forming an integrated circuit (IC chip ) Logic circuit (hardware) realization; it can also be realized by software.

In the latter case, the transmitting devices 100, 100a and the receiving devices 200, 200a are equipped with computers, which execute software that implements each function, that is, program commands. This computer has, for example, more than one processor, and a storage medium that can be read by the computer storing the above-mentioned program. In addition, in the above-mentioned computer, the processor reads the program from the storage medium and executes it, thereby achieving the object of the invention. As an example of this processing, a central processing unit (CPU) can be used. As an example of the storage medium, "non-transitory tangible media" can be used, such as read-only memory (ROM, Read Only Memory), tapes, disks, cards, semiconductor memory, programmable logic circuits, etc. In addition, it may further have a random access memory (RAM, Random Access Memory) etc. to expand the program. In addition, the program can also be supplied to the computer through any transmission medium (communication network or broadcast wave) that can transmit the program. In addition, the same aspect of the present invention can also be realized as a form of a data signal embedded in a carrier wave, and the carrier wave is realized by electronically transmitting the aforementioned program.

In addition, computer program products that execute the functions of the transmitting devices 100, 100a and the receiving devices 200, 200a are also included in the scope of the present invention. The computer program product loads at least one "program provided via any transmission medium" through at least one computer, and causes the computer to execute at least one program command. In this way, the processor of the computer equipped with at least one of the above-mentioned processors performs corresponding processing in response to the program commands. In this way, the functions of the transmission devices 100, 100a, and 200, 200a are realized. This computer program product executes the steps of the transmission process (transmission method) and the reception process (reception method) by at least one computer loaded with the program.

The above-mentioned implementations of the present invention are not limited, but various changes can be made to the content shown in the scope of the patent. The technical means disclosed in different implementations can be appropriately combined to form various implementations, which are also included in the present invention. The technical content of the invention. In addition, the combination of various technical methods disclosed in each implementation type can form new technical features.

[Industrial Utilization]

The present invention is preferably used in wireless transmission and reception systems, radar systems, and the like.

1: Transmitting and receiving device

100: Conveyor

101: Data acquisition unit for transmission

102: Transmission signal generator

103: Transmission Department

200: receiving device

201: Receiving Department

202: Displacement estimation and received data extraction unit

203: Received data analysis department

Claims (16)

A receiving method of a received signal, which includes: an estimation step, which refers to a parameter space with an irreplaceable displacement of co-dimension 2 to estimate the time shift and frequency shift represented by the received signal; and, in the above estimation step, The operator is used to estimate the time displacement and the frequency displacement represented by the received signal, and the aforementioned operator includes a half displacement of a symmetrical displacement with respect to time and frequency. The receiving method according to claim 1, wherein the parameter space with the non-replaceable displacement of the co-dimension 2 is displayed by displaying the third axis of time displacement and frequency displacement, so that the first axis of display time and the display frequency The space obtained by the 3-dimensionalization of the plane opened by the second axis of. The receiving method according to claim 1 or 2, wherein the above-mentioned estimating step uses the first shift operator

, The second shift operator

, The third shift operator

Or its dual frequency (Dual Frequency) [Math 4]

And the fourth shift operator

Or its coupled frequency

, To estimate the time shift and frequency shift represented by the received signal; and, the first shift operator system represents the estimated value of the time shift, the frequency shift and the phase term of the half shift of the estimated time shift; The second displacement operator system represents the estimated value of time displacement, frequency displacement, and the phase term of half of the estimated frequency displacement; the third displacement operator system represents the time displacement of the estimated object and the observed value of frequency displacement of the estimated object And the phase term of the half-and-half of the estimated time shift; and the above-mentioned fourth shift operation sub-system represents the phase term of the time-shift, the estimated value of the frequency shift and the half-and-half of the estimated time shift; where the superscript f represents Fourier transform; the superscript d system represents the discrete version of the operator;

Is the estimated value of Puller displacement in a given capital

ML k _d of the estimated integer; k represents a time shift lines _D; k are diagrams M - integer value of information data transmission phase modulating communication should, and k

{0,1,..., M -1}, this system can be decomposed into integer parts

And fractional part

; Among them, j and j'are integers representing the integer part and the fractional part; M ₀ < M and M are integers representing the multi-valued number of phase modulation communication methods; l _μ is the control of the estimated Doppler shift l _D Use integer values;

Is the estimated value of displacement at a given time

The ML estimated integer value of l _D below; k _σ represents the integer value used for control of the estimated time shift k _d. The receiving method according to claim 3, wherein, in the estimating step, it refers to the first correlation function and the second correlation function to estimate the time shift and the frequency shift represented by the received signal; and, the first The correlation function is represented by the first displacement operator, the third displacement operator, and the fourth displacement operator; the second correlation function uses the second displacement operator, the third displacement operator, and the fourth displacement operator. To represent. The receiving method according to claim 4, wherein the first correlation function and the second correlation function include: modulation of the modulation frequency f _c and phase distortion associated with non-permutation calculation of the time shift t _{d in the demodulation}

Or its discrete version

; And the phase distortion e ^{iκ during transmission} ; where W is the Fourier transform operator (rotation factor) of discrete time and frequency, which is the Fourier transform of continuous time and frequency by using each sample width △ t , △ f The continuous time variable t and the continuous frequency variable f of the exponent of the calculus e ^{- j 2π ft are sampled; and the discrete frequency variable system}

；K _D system discrete time displacement

; L _c is the discrete carrier frequency

. The receiving method according to claim 4, wherein the estimation step includes: an interactive update step, which alternately repeats the update step of the estimated value of the frequency shift and the update step of the estimated value of the time shift; and, the above-mentioned frequency The step of updating the estimated value of displacement refers to the first correlation function to update the estimated value of frequency displacement; and the step of updating the estimated value of time displacement refers to the second correlation function to update the estimated value of time displacement. The receiving method according to claim 1 or 2, wherein, in the above estimation step, the maximum likelihood estimation of the frequency shift based on the likelihood function of the N'TD-template signal detection and the N FD-template signal detection The maximum likelihood estimation of the time shift of the likelihood function of, to estimate the time shift and frequency shift represented by the above-mentioned received signal. A receiving device for receiving a signal, which includes: an estimating part, which refers to a parameter space with an irreplaceable displacement of co-dimension 2 to estimate what the received signal represents Time shift and frequency shift; In addition, in the above-mentioned estimating unit, an operator including half of the estimated time shift and a half shift operator including half of the estimated frequency shift are used to estimate the time indicated by the received signal Displacement and frequency displacement. A method of transmitting a signal, which includes: a displacement step, which refers to a parameter space with a co-dimension 2 of non-replaceable displacement to shift the time and frequency of the signal of the transmission object; and, in the above-mentioned displacement step, based on The half displacement of the symmetrical displacement of time and frequency shifts the time and frequency of the signal of the transmission object. The transmission method according to claim 9, wherein, in the above-mentioned shifting step, the time pulse waveform is subjected to a time phase code modulation of period N, and the time pulse wave modulated by the above-mentioned time phase code The waveform is subjected to phase encoding modulation in the frequency region of period N'to be multi-carrier, thereby generating a transmission signal. A transmission device for transmitting a signal, comprising: a displacement part, which refers to a parameter space with a co-dimension 2 of non-replaceable displacement to shift the time and frequency of the signal of the transmission target; and, in the displacement part, based on The half displacement of the symmetrical displacement of time and frequency shifts the time and frequency of the signal of the transmission object. A transmitting and receiving system including a transmitting device and a receiving device, characterized in that: the transmitting device includes a displacement part, which refers to a parameter space with a co-dimension 2 irreplaceable displacement to shift the time and frequency of the signal of the transmission object, And in the above-mentioned displacement part, the half displacement based on the symmetrical displacement with respect to time and frequency The above-mentioned receiving device includes an estimating unit, which refers to a parameter space with a co-dimension 2 irreplaceable displacement to estimate the time displacement and frequency displacement represented by the received signal, In addition, in the estimation section, an operator including a half displacement of half the estimated time displacement and an operator including a half displacement of half the estimated frequency displacement are used to estimate the time displacement and frequency displacement indicated by the received signal. A receiving method for receiving an image signal, which includes: an estimation step, which refers to a parameter space of irreplaceable displacement to estimate the spatial displacement and the spatial frequency displacement represented by the received image signal; and the above-mentioned spatial displacement and spatial frequency The displacement systems each have 2 or more dimensions; and, in the above estimation step, operators are used to estimate the spatial displacement and spatial frequency displacement represented by the image signal, and the aforementioned operator systems include symmetrical displacements with respect to space and spatial frequency. The half displacement. The receiving method according to claim 13, wherein in the above estimation step, the two-dimensional symmetrical spatial displacement and spatial frequency displacement operators are referred to

versus

, To estimate the spatial displacement and spatial frequency displacement; among them, the superscript f represents the Fourier transform; the superscript d represents the discrete version of the operator;

Is the spatial displacement;

The system represents the spatial frequency displacement. A transmission method for transmitting an image signal, which includes: a displacement step, which refers to the parameter space of the non-replaceable displacement to shift the space and frequency of the image signal of the transmission object; and the displacement of the space and the frequency of the displacement are respectively It has more than 2 dimensions, and in the above-mentioned displacement step, the space and spatial frequency of the image signal of the transmission object are displaced based on the amount of half displacement of the symmetrical displacement with respect to the space and the spatial frequency. The transmission method according to claim 15, wherein, in the displacement step, the two-dimensional symmetrical spatial displacement and spatial frequency displacement operators are referred to

And its coupling frequency

, To shift the space and frequency; among them, the superscript f represents the Fourier transform; the superscript d represents the discrete version of the operator;

Is the spatial displacement;

The system represents the spatial frequency displacement.

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