EP2880876A1 - Dispositifs et procédés utilisant la transformation hermétique pour émettre et recevoir des signaux utilisant ofdm - Google Patents

Dispositifs et procédés utilisant la transformation hermétique pour émettre et recevoir des signaux utilisant ofdm

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Publication number
EP2880876A1
EP2880876A1 EP13824997.4A EP13824997A EP2880876A1 EP 2880876 A1 EP2880876 A1 EP 2880876A1 EP 13824997 A EP13824997 A EP 13824997A EP 2880876 A1 EP2880876 A1 EP 2880876A1
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European Patent Office
Prior art keywords
signal
array
transform
noise
hermetic transform
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EP13824997.4A
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German (de)
English (en)
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EP2880876A4 (fr
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Harvey C. Woodsum
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Priority claimed from US13/788,556 external-priority patent/US8948718B2/en
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    • H—ELECTRICITY
    • H04—ELECTRIC COMMUNICATION TECHNIQUE
    • H04L—TRANSMISSION OF DIGITAL INFORMATION, e.g. TELEGRAPHIC COMMUNICATION
    • H04L27/00—Modulated-carrier systems
    • H04L27/26—Systems using multi-frequency codes
    • H04L27/2601—Multicarrier modulation systems
    • H04L27/2626—Arrangements specific to the transmitter only
    • H04L27/2627—Modulators
    • H—ELECTRICITY
    • H04—ELECTRIC COMMUNICATION TECHNIQUE
    • H04L—TRANSMISSION OF DIGITAL INFORMATION, e.g. TELEGRAPHIC COMMUNICATION
    • H04L27/00—Modulated-carrier systems
    • H04L27/26—Systems using multi-frequency codes
    • H04L27/2601—Multicarrier modulation systems
    • H04L27/2626—Arrangements specific to the transmitter only
    • H04L27/2627—Modulators
    • H04L27/2639—Modulators using other transforms, e.g. discrete cosine transforms, Orthogonal Time Frequency and Space [OTFS] or hermetic transforms
    • H—ELECTRICITY
    • H04—ELECTRIC COMMUNICATION TECHNIQUE
    • H04L—TRANSMISSION OF DIGITAL INFORMATION, e.g. TELEGRAPHIC COMMUNICATION
    • H04L27/00—Modulated-carrier systems
    • H04L27/32—Carrier systems characterised by combinations of two or more of the types covered by groups H04L27/02, H04L27/10, H04L27/18 or H04L27/26
    • H04L27/34—Amplitude- and phase-modulated carrier systems, e.g. quadrature-amplitude modulated carrier systems

Definitions

  • This disclosure deals with systems and methods using a Hermetic Transform, as well as related transforms, for applications such as directional or non-directional reception and/or transmission of signals, which use of phased-array devices and systems a d / or waveforms that utilize Hermetic ' Transforms to create and decipher a plurality of modulated sub-carrier tones used in data transmission.
  • the Hermetic Transform (and related transforms) can be designed using an array manifold, effectively a complex calibration response vectors from the array in question to signal arrivals from different directions, whether developed from a mathematical model or from collected data, arranged in a particular fashion.
  • the transform can be utilized for receiver and/or transmit beams to provide narrower main-lobes than classical methods would typically allow. Further background about the Hermetic Transform can be found in U.S. Patent No. 8,064,408, incorporated herein by reference in its entirety and for all purposes.
  • Orthogonal frequency- division multiplexing is a method of encoding digital data on multiple sub-carrier frequencies, where the sub-carriers are selected so as to be non-interfering (orthogonal).
  • OFDM and OFDMA have been adopted for wideband digital communication, both wireless over copper wires, used in applications such as digital television and audio broadcasting, DSL broadband internet access, wireless networks, such as 802.11 and in 4G mobile
  • Irs traditional OFDM a number of closely spaced orthogonal sub-carrier signals are used to carry data.
  • the data is divided into several parallel data streams or channels, one for each sub-carrier.
  • Each sub-carrier is modulated with a conventional modulation scheme (such as quadrature amplitude modulation (QAM), or phase-shift keying, (PSK) at a low symbol rate, maintaining total data rates similar to conventional single- carrier modulation schemes in the same bandwidth.
  • QAM quadrature amplitude modulation
  • PSK phase-shift keying
  • the low symbol rate makes the use of a guard interval between symbols affordable, making it possible to eliminate intersymbol interference (IS!) and utilize echoes and time-spreading from multipath propagation in order to achieve diversity gain, for signal-to-noise ratio improvement.
  • IS intersymbol interference
  • IFFT Inverse Fast Fourier Transform
  • I-waveform real-part or Q-waveform and imaginary-part or I- waveform components of the signal.
  • IFFT Inverse Fast Fourier Transform
  • These real and imaginary parts are impressed onto cosine and sine waveforms (sub-carriers) and summed to provide a real signal for transmission, which in the case of an application such as Wi-Fi (for example, 802.1 in) is mixed onto a radio -frequency carrier, e.g. at 2.4 or 5.8 GHz.
  • Demodulation is accomplished in an inverse fashion of the modulation, using a Fast-Fourier Transform.
  • Another limitation of OFDM is the required spacing to achieve orthogonality between sub-carriers using FFT/IFFT. Two factors would improve the data-rate of OFDM, one being the reduction of noise
  • Systems and methods are described for using the Hermetic Transform for OFDM and OFDMA for transmitting and receiving signals by replacing a FFT and IFFT with the Hermetic Transform and inverse Hermetic Transform.
  • the systems and methods include receiving a serial signal, dividing the signal into multiple parallel paths, performing an inverse Hermetic Transform to produce real and imaginary part signals, converting the real and imaginary signals to analog signals, upconverting the signals, and transmitting as RF signals.
  • the receive method is substantially performed in reverse.
  • the transmitting process can include a noise conditioning matrix.
  • FIGS. 1-4 are block diagrams of processing steps performed according to methods described herein.
  • FIGS. 5-8 are plots showing results from systems and methods described herein.
  • FIGS. 9- 14 are block diagrams and plots showing use in detecting a jammer.
  • FIGS. 15 and 16 shown the typical OFDM transmission and reception with IFFT and FFT.
  • FIGS. 17 and 18 illustrate comparisons in an OFDM application.
  • a conventional approach utilized is based on a spatial matched filter.
  • the spatial matched filter forms a beam in a given direction, characterized by a set of direction cosines ( , ⁇ ,-, ⁇ ), by multiplying each array element signal channel ⁇ V j ⁇ by the complex conjugate of the expected response from the given 'look direction", and summing the result.
  • vector fields e.g., electromagnetic waves
  • scalar fields e.g., electro-magnetic wave fields
  • indices related to vectors components and polarization are suppressed in the treatment, below, i.e., the fields of the received signal(s) are treated as scalar (field indices suppressed).
  • the sum is over the set of receiving N receiving elements in order to form a single beam in the desired look direction.
  • the "G” term is a gain term used to normalize beam amplitude appropriately.
  • the matched-filter beam-former above is known to be optimum in terms of signal to noise ratio under the stated circumstances, and (2) for an array with more closely spaced elements, the ambient noise signals received by the array elements become spatially correlated and therefore more 'signal-like' in terms of the processing approach that one might contemplate.
  • the condition L- ⁇ 72 represents sampling at the spatial Nyquist Rate, the minimum spatial sampling that will avoid spatial aliasing, which would produce unwanted grating lobes, i.e., strong responses in unwanted directions away from the beam look- direction.
  • the beam response of such an array to a given wave-vector has a beam shape that roughly conforms to the expression ⁇ ⁇ ⁇ 1 where ⁇ corresponds to the beam ambiguity (main lobe width) in wave-vector space, and ⁇ . corresponds to the array dimension.
  • ⁇ corresponds to the beam ambiguity (main lobe width) in wave-vector space
  • ⁇ corresponds to the array dimension.
  • the ruie-of-thumb for beam-width in radians ⁇ is given by:
  • ⁇ ⁇ / D
  • ⁇ the acoustic wavelength.
  • the spatial filters (beams) that are formed essentially produce a significant response to signal arrivals only within a range of ⁇ in angle around a chosen look direction.
  • the actual response of the beam-former in the case of a linear array corresponds to the familiar patterns known from diffraction theory, and the above formula is sometimes referred to as the diffraction limit on resolution. This rule of thumb is a well- known type of uncertainty principle, taken for granted by system designers, often without regard to the underlying assumptions on which the result rests.
  • the rule of thumb extends to a two-dimensional, rectangular, planar array, with dimensions D x and D y , the angular "beam- widths" of the beam-former response, ⁇ ⁇ and AQ y , correspond to the x and y dimensions in comparison to the signal wave-length:
  • the use of beam-forming is analogous to the use of filtering in the frequency domain to reject noise which is either spread out across a broad band or which is located at a frequency not corresponding to that of the signal (for example, use of FFT processing to detect narrow-band, sinusoidal signals in the presence of noise ).
  • the array area can be divided into cells that are half- wavelength in each dimension if there are N such cells, the isotropic noise gain is on the order of 10 logio( ) in decibels (dB), The smaller the array (in units of w avelength), the smaller the spatial processing gain.
  • H the Hermetic Transform
  • the "#” symbol represents the pseudo-inverse of the bracketed quantity (Gelb notation), and "superscript H” indicates the Hermitian Conjugate of the quantity.
  • the pseudo-inverse is based on the Singular Value Decomposition (SVD) of the target matrix, with any singular values having magnitude less than a pre-set threshold set to zero so that the pseudo-inverse operates only over the subspace corresponding to significant singular vectors, i.e. those with significant smgular value magnitudes.
  • Singular Value Decomposition Singular Value Decomposition
  • data is used directly in the construction of the Hermetic Transform.
  • the present invention can also be made to work with other representations, for time snapshots from an N-element array can be transformed using a linear transformation which combines elements to create fewer or greater numbers of signal vector components.
  • data from an 8-element array arranged around a circle can be combined into omni, sine, and cosine pattern channels, as is common in direction finding applications.
  • Such arrays can be beam-form.
  • a linear array of four elements can be transformed using an FFT of arbitrary size with zero-padding to form signal vectors of arbitrarily large size.
  • a wave-vector power spectrum (Power Spectral Density or PSD) can be used to determine a direction of arrival (DOA) to signal sources (emitters).
  • the wave-vector PSD is essentially signal arrival power as a function of DOA (wave-vector).
  • the methods involved are analogous to PSD methods involving DFT/FFT techniques for time series, with the contradistinction that Hermetic Transforms are utilized instead. Examples of such time series techniques are the Blaekman-Tukey and Periodogram PSD approaches. Peaks in the PSD imply arrivals from specific direction.
  • the determination of arrival angle using PSD is termed radio direction finding, or just "direction finding" (RDF/DP).
  • ⁇ 0033 ⁇ There are several direct methods for obtaining the wave-vector PSD. As shown in FIG. 1, one method involves forming beams first by applying the Hermetic Transform to element data vectors, and then processing data from each beam to obtain the PSD from the various beam time-series. Referring to FIG. 2, another method includes applying beam- forming first, and then time averaging the modulus squared from the complex time series of each beam. Referring to FIG.
  • another method utilizes a Hermetic Transform derived from an array manifold produced from a set of vectors formed from signal covariance m atrices (each MxM for an M-element array) reshaped into column vectors (dimension NT x 1), arranged in columns, with each column corresponding to a given DOA for the manifold.
  • this transform is applied to the similarly re-shaped covariance matrix from a single arrival or from set of incoherent (uiicorrelated) arrivals, a wave-vector PSD estimate is produced. Peaks in the PSD produced from any of the above methods correspond to DF estimates of directiorts-of-arrival for signals arriving at the array.
  • the Hermetic Transform has at least a pseudo-inverse (#), so that filtering in the wave-vector (beam-space) domain can be accomplished using the following steps.
  • FIG. 4 is a block diagram of an exemplary implementation that further includes a noise conditioning step.
  • Each "snap-shot" vector is an Nxl column vector for an N-element array.
  • the Hermetic Transform has dimension MxN for N - DOAs in the array manifold.
  • the result has dimension Nxl (column vector) in 'beam-space".
  • an elemental filter matrix can be designed to place one null in a particular direction (the p-th DOA) would use a A matrix which is the modified identity matrix.
  • the identity matrix has all ones on the diagonal and zeroes elsewhere.
  • one of the diagonal elements (element in the p-th row, p-th column) is set to zero.
  • the resulting filter matrix can be raised to a power (Rth power) in order to control the strength of the null.
  • This matrix offers the analogous function of placing a "zero" into the spatial transfer function.
  • an elemental filter matrix can be constructed to emphasize signals only in one direction (the p-th DOA) by starting with a A matrix that is all zeros, except for the element in the p-th row and p-th column, the value of which is set to unity.
  • the resulting filter matrix (M x M) can be raised to a power (Rth) in order to control the strength of what amounts to a "pole" (beam) or "zero" (null) in the spatial transfer function.
  • the matrices can also be normalized, for example by dividing by the trace of the matrix in order to control numerical precision problems.
  • Such elemental matrices can be multiplied / cascaded to create shaping of the array response to signal arrivals from particular directions.
  • the matrix multiplication operations do not necessarily commute, therefore different permutations of filtering orders itsing the same set of fil ter matrices can produce significan tly different results.
  • One of the interesting results obtained using the above approach is that there can be more nulls placed in the response pattern than the conventional limit of (N -1) independent nulls for an array with N elements.
  • FIG. 5 shows five nulls in an otherwise omnidirectional pattern at a single frequency, which was accomplished with a 4-element array.
  • the curves show a cumulative probability of detection for signal arrivals and noise only arrivals versus detection threshold when conventional beam-forming is applied to 1000 Hz signal having a -6 dB signal to noise ratio at each element of the 18-element array.
  • the curves tests show the corresponding results for the case of Hermetic Transform beam forming of the same array.
  • the increase in detection performance resulting from the application of the Hermetic Transform beam forming process, as observed in the simulation experiment, corresponds to an extra spatial gain of approximately 12 dB in signal to noise ratio. Curves are shown in the provisional application.
  • a visible graphic representation of the improvement in detection performance for the case described above is shown in the provisional application.
  • Two plots are shown, which represent a plot of energy vs. time at the output of the conventional, phased-array beam forming process and the Hermetic Transform beam forming Process.
  • the x-axis is bearing (direction of arrival), the y-axis is time, as an ensemble of time records are presented, and the energy of each beam (bearing) is represented by intensity and pseudo-color.
  • Visual detection of a signal in this representation is accomplished by observing differences in the intensity and color of the data being presented relative to the surrounding ambient background.
  • the conventional plot shows no differentiation between signal and isotropic noise, while the Hermetic Transform plot shows a band of energy at a particular bearing, corresponding to the direction of the signal arrival.
  • the signal arrival is at -6dB (array element ) signal-to-noise ratio (SNR).
  • SNR signal-to-noise ratio
  • FIG 6 indicates a rectilinear representation of the beam-pattern of a 7- element array having a single plane-wave arrival which is observed in the presence of significant internal noise ( ⁇ -10 dB signal to internal noise ratio).
  • the array length is 0.67 lambda .
  • FIGS. 1-4 are block diagrams of systems described elsewhere herein, and each includes a noise conditioning step before the Hermetic Transform.
  • DMI Direct Matrix Inverse
  • a beam ⁇ ( Q m ) in the direction of 9 m can be formed using DMI using the signal reference vectors V( Q m ) as previously described and the inverse of the interference covariance matrix R n r , ' according to the expression
  • the first term on the right-hand-side ( HS) of the above equation is the spatial matched filter to the arriving signal; the second term is a spatial "pre-whitener" of the interfering background.
  • the interference covariance matrix is formed from the time a v eraged outer product of the Hermitian Conj ugate (complex conjugate transpose) of the received data vector with the received data vector for the case where noise/interference only is present.
  • the DMI technique can be effective.
  • the present method applies similar mathematical reasoning to that used to derive the DMI to develop a different approach, a beam-forming transform which is fixed for a given array configuration and signal frequency, and which is not dependent on the specific noise interference and thus need not be data-adaptive.
  • FIG. 7 provides an example produced using a MATLABTM 1 analysis/simulation.
  • the simulated array- is a one-dimensional, linear array with eleven (11) receiving elements, with the array being one wavelength (lambda) in length.
  • the elements are ideal point elements with no appreciable aperture.
  • the curve shown with one broad main peak is the amplitude pattern of the broadside beam generated with conventional Discrete-Fourier Transform processing.
  • the pattern with a sharper main peak was generated using the Discrete Hermetic Transferal.
  • the points correspond to the pattern generated using the technique of the present invention, the MSG beam.
  • DHT Discrete Hermetic Transform
  • MSG Transform MSG Transform
  • FIG. 8 A typical result involving the increase of resolution from adding additional physical elements for an arra of a fixed physical dimension (aperture size) is shown in FIG. 8.
  • the black curve in the plot indicates a beam which is approximately this extent
  • the minimum number of elements needed to satisfy the spatial Nyquist criterion is 3 (half- wavelength spacing).
  • results are shown for patterns corresponding to conventional, 5 elements, 7 elements, and 21 elements, each of the latter three curves corresponding to different degrees of spatial oversampling, and sharing an increasingly and successively narrow main peak.
  • the 21 -element pattern corresponds to 10-times oversampling relative to the Nyquist sampling criterion for the mmimum sampling required to avoid grating lobes (spatial aliasing). It can be seen from the plot that the beam-width becomes smaller as the number of elements increases, however, at some point, a minimum beam width is reached. In this case, the baseline Hermetic Transform Algorithm reaches a minimum width of 14 degrees, approximately 1 ⁇ 4 of the con v entional beam width.
  • a general interpolation matrix can be formed by taking an appropriate linear combination of the individual interpolation matrices, each of which maps a P-element output that the array would see for a particular direction ( ⁇ k) into a Q-element array output for the identical direction ( ⁇ k) -
  • the i-th interpolation matrix weighting coefficient C ⁇ is determined according to the wave-number spectrum content of the original signal in the i direction.
  • One approach is to map the input signal array vector onto the B directions using the Hermetic Transform and add together the interpolated arrays for each direction weighted by the component of signal in each direction.
  • Another approach is to pre-fiiter the signal using a beam transform, then apply the predetermined spatial filter response as a set of weighting coefficients.
  • Prior Patent No. 8,064,408 focuses more on receiving.
  • a modified version of the above approach can be applied to transmit arrays. Beginning with a standard expression of the electric field (E) from an array excited with a specified current density, Js as seen below, one can design a set of current densities for the set of antenna elements in the array in order
  • pre ious re suit corresponds to standard
  • the F is the transmit Greens Function matrix
  • the ⁇ H term corresponds to the excitations obtained by reciprocity from the array receiving response manifold, i.e., the complex conjugate excitations
  • the weight matrix W is used in the transformation of the conjugate excitations to produce a set of excitations which produce the response p.
  • the improved transmit directivity which results from this approach is illustrated by the beam pattern shown in the provisional application calculation below.
  • the array is a 24-element circular array of dipole antennas (or monopoles) over a perfect ground plane with an array diameter of one quarter wavelength.
  • the conventional equivalent is
  • One pattern is in decibels (dB) while the other pattern is power.
  • processing can be done with any form of suitable processor, whether implemented in hardware or software, in application-specific circuitry, or special purpose computing. Any software programs that are used can be implemented in tangible media, such as solid state memory or disc-based memory.
  • the forms of processing can generally be considered to be "logic,” which can include such hardware or software of combined hardware-software, implementations.
  • the computing can be done on a standalone processor, groups of processors, or o ther devices, which can be coupled to memory (such as solid state or disc-based) for showing input and output data, and provide output, e.g., via screens or printers.
  • the Hermetic Transform can be used to create elemental spatial filters which contain a single direction of signal rejection (nulling) (analogous to a "zero" in the transfer function of a conventional digital filter) or a single direction of signal enhancement
  • each elemental transform is a complex, 4x4 matrix (4-rows, 4 columns).
  • One elemental "pole” and one elemental "zero” were created for each of the look directions in the manifold (for this study, there are 36 look directions spaced 10 degrees apart, therefore 72 elemental transforms). This process can he accomplished offline to create a set of 4x4 matrices, each of which satisfies a particular specification (rejection or enhancement of signals from one direction.)
  • FIG. 10 indicates an off-line procedure for making more general spatial transforms.
  • the current genetic algorithm uses a set of the original 72 transform matrices plus all possible sums and products of pairs of these transforms.
  • the genetic algorithm guarantees a reasonable solution without the combinatorial explosion associated with a search of all possible solutions.
  • an array model is applied to four-channel data from both a given communications signal ("COMM”) and interference/jammer signal (“JAM”) and summed, then added to simulated internal system noise.
  • the internal noise is set so that the signal to internal noise ratio is +20dB.
  • the jammer signal strength is arbitrary.
  • Two test points are set up to measure the result of the nulling. A best set of onini-weights is derived as described above, and appl ied to the four channels at Test Point "in” (prior to applying the nulling matrix), and to the output of the nulling step to create Test Point "out”.
  • the genetic algorithm supplies a plot of the desired spatial response which can be compared to the desired / specified spatial pattern.
  • a pattern was derived as a prediction of the genetic algorithm, based on calibration from noiseless 10-bit LFSR / MSK signals used as the COMM signal (below).
  • the pattern is measured in decibels (dB) from the pattern minimum, located at the null of the pattern.
  • the desired (ideal) pattern is shown with a sharp wedge pattern.
  • the depth of null as shown is approximately 70 dB.
  • the jammer data is chosen as 1 1-bit LFSR/MSK which occupies the same spectrum as the signal.
  • the combined signal is matched filtered (replica correlated) at both the "in” Test Point and “out” Test Point, using both the signal replica and the jam signal replica, in order to determine the signal gain and the jammer gain through the process.
  • the outputs of the matched filters (replica coiTelators) are converted to power (magnitude squared of the complex data).
  • the signal-to-jammer gain is the signal gain minus the jammer gain.
  • the results are compiled in dB.
  • the replica correlator is known to be the optimal processor for the case where the noise is white and Gaussian; if this were not the case a noise pre-whitener would be employed to achieve maximum SNR.
  • the HPMV simulation verifies the null value, but shows a jammer gain which moves with the signal, this being attributed to non-zero correlation between the 10-bit LFSR signal for the COMM signal and the 1 1 -bit LFSR signal for the JAM. An adjustment to that simulation is being made to correct this issue. Another artifact that results from this correlation is the appearance of S/J gain varying with jammer power. Since the process is linear (the null transform is a simple 4x4 matrix multiply) the gain should be a constant. The jammer gain showing dependence on signal position and also showing dependence on jammer power is proof of artifacts in the prior simulation results.
  • the Hermetic Transform can also be used to create a novel form of OFDM. If each subcarrier replica for one symbol frame is defined as is S(f; n) (for the moment treated as a complex I&Q waveform), where n is the time index and f is the frequency of the sub- carrier, a signal matrix can be formed:
  • ⁇ [ S(f 0 ; n) Sftjn) ; .. 8( ⁇ ( ⁇ - ⁇ ) ; n)] where n corresponds to the row index and f corresponds to the frequency index.
  • Hermetic Transform H is defined in terms of the minimum norm solution to the equation:
  • H ⁇ H w as described in US Patent 8,064,408. Note that the result is a transform which when applied to the signal, produces orthogonality in a minimum norm / least- squares sense.
  • the inverse of the Hermetic Transform is taken to be the pseudo-inverse of the Hermetic Transform.
  • FIGS. 15 and 16 show OFDM transmit and receive systems.
  • a serial signal is divided into multiple parallel paths, each of which is modulated and provided to an inverse FFT, Thereafter, the output is provided to RF circuitry for transmission.
  • the receive side is essentially just a reverse of the transmit side to recover the signal.
  • the Hermetic version of the OFDM system replaces FFT and IFFT with the Hermetic Transform and inverse Hermetic Transform, respectively, as discussed in detail above and in the incorporated patent.
  • fOOSSj In practical application, a noise conditioning matrix as shown and described in conjunction with FIGS. 1 -4 can be used to condition the data, embedding this matrix multiply into the actual transform (no such conditioning on the inverse transform is needed).
  • Channel gains can be made in decoding individual amplitudes for QAM demodulations by multiplying the decoded amplitudes obtained by the inverse of a diagonal matrix formed by the application of the Hermetic Transform to the sum of the sub-carrier reference data.
  • H-QFDM Hermetic transform OFDM
  • the frequency resolution is higher than with an FFT, thus reducing noise in each sub -carrier signal demodulation (increase of S N in the channel capacity formula) and by a consequent ability to stack sub-carriers closer together than with traditional FFT-based OFDM while maintaining orthogonality in a wide sense.
  • Examples of demodulated symbol constellations for identical circumstances of Phase Shift Modulations on a set of sub-camers are shown in FIG. 17 to illustrate the superior performance of the H-OFDM.
  • Constellations for OPSK (8-phase Modulation) are shown in FIG. 18.
  • the 'fuzziness' and cluster size indicates the effects of noise and inter-symbol interference, which is clearly much less for the case of the H-OFDM.
  • An estimated 4-10 fold improvement could be realized in terms of signal data rate for a given bandwidth, due to SNR improvement, closer sub-carrier spacing, and higher keying (chip) rate.

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Abstract

La présente invention porte sur des systèmes et des procédés utilisant une transformation hermétique et une transformation hermétique inverse pour émettre et recevoir un signal OFDM par remplacement d'une FFT et d'une IFFT par la transformation hermétique et la transformation hermétique inverse.
EP13824997.4A 2012-08-02 2013-08-02 Dispositifs et procédés utilisant la transformation hermétique pour émettre et recevoir des signaux utilisant ofdm Withdrawn EP2880876A4 (fr)

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US201261678716P 2012-08-02 2012-08-02
US13/788,556 US8948718B2 (en) 2012-03-07 2013-03-07 Devices and methods using the Hermetic Transform
PCT/US2013/053422 WO2014022771A1 (fr) 2012-08-02 2013-08-02 Dispositifs et procédés utilisant la transformation hermétique pour émettre et recevoir des signaux utilisant ofdm

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