CN104079518A - Polarity diversity reception device and method based on SOQPSK-TG signal - Google Patents

Polarity diversity reception device and method based on SOQPSK-TG signal Download PDF

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CN104079518A
CN104079518A CN201410348436.XA CN201410348436A CN104079518A CN 104079518 A CN104079518 A CN 104079518A CN 201410348436 A CN201410348436 A CN 201410348436A CN 104079518 A CN104079518 A CN 104079518A
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soqpsk
signal
fpga
polarizations
phase
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CN104079518B (en
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王旭东
樊涛
陈雨
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Nanjing University of Aeronautics and Astronautics
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Nanjing University of Aeronautics and Astronautics
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Abstract

The invention discloses a polarity diversity reception method based on an SOQPSK-TG signal. The method comprises the following steps: adopting two ADCs to transfer a received levogyration polarity signal and a received dextrorotation polarity signal into digital signals respectively; adopting an automatic gain control loop to enable the two digital signals to be constant in amplitude or in a threshold value section; tracking frequency difference and phase difference of the two gained digital signals through a difference module loop to fulfill same frequency and phase locking of the two digital signals; adopting maximal-ratio combining to obtain average SNR gain; tracking Doppler frequency shift to conduct carrier recovery; conducting position timing clock recovery; tracking clock phase shift and frequency shift between a receiver and a transmitter. The invention further discloses an SOQPSK-TG signal modulation and polarity diversity reception device based on FPGA. The modulation and reception device utilizes the characteristics of constant envelope and high spectral efficiency of the SOQPSK-TG to meet modern satellite communication demand; the polarity diversity reception technology is introduced to avoid deep zero point influence; system performance is improved.

Description

SOQPSK-TG polarizations diversity receiving device and method thereof based on FPGA
Technical field
The present invention relates to technical field of satellite communication, relate in particular to a kind of SOQPSK-TG polarizations diversity receiving device and method thereof based on FPGA.
Background technology
The channel of satellite communication system has power and Bandwidth-Constrained and non-linear feature, therefore must be in ensureing enough power, adopt as far as possible the modulation system of high bandwidth efficiency (referring to " Beidas B F, Cioni S, De Bie U, et al.Continuous phase modulation for broadband satellite communications:design and trade-offs[J] .International Journal of Satellite Communications and Networking, 2013, 31 (5): 249-262 " and " Maral G, Bousquet M.Satellite communications systems:systems, techniques and technology[M] .5th edition.California:John Wiley & Sons, 2011 ").
Traditional BPSK (Binary Phase Shift Keying, binary phase shift keying), QPSK (Quadrature Phase Shift Keying, Quadrature Phase Shift Keying) etc. modulation system there is permanent envelope, the feature that power efficiency is high, but secondary lobe is higher, spectral leakage is larger, easily produce spread spectrum (referring to " Kim P S, Oh D G.Modulation and demodulation method for satellite communication using widespread signal-to-noise ratio (snr): U.S.Patent Application13/754, 436[P] .2013-1-30 ", " Kim T H, Kim P S, Shin M S, et al.Method and system for effective adaptive coding and modulation in satellite communication system:U.S.Patent8, 179, 778[P] .2012-5-15 ", " Jokhakar Jignesh D, Sripati U, Kulkarni M.Performance of QPSK modulation for FSO geo-synchronous satellite communication link under atmospheric turbulence[C] // 2013Annual International Conference on Emerging Research Areas (AICERA)-2013International Conference on Microelectronics, Communications and Renewable Energy (ICMiCR) .Piscataway:IEEE, 2013:1-5 " and " Long W, Gengxin Z, Dongming B, et al.Algorithm for modulation recognition of satellite communication signals based on phase statistic[C] // 2011International Conference on Computer Science and Service System (CSSS) .Piscataway:IEEE, 2011:1047-1050 ").
CPM (Continuous phase modulation, Continuous Phase Modulation) be in Modern Communication System the normal a kind of constant enveloped modulation technology adopting (referring to " Graell i Amat A, Abdel Nour C, Douillard C.Serially concatenated continuous phase modulation for satellite communications[J] .IEEE Transactions on Wireless Communications, 2009, 8 (6): 3260-3269 " and " Perotti A, Benedetto S, Remlein P.Spectrally efficient multiuser continuous-phase modulation systems[C] // 2010IEEE International Conference on Communications.New York:IEEE, 2010:1-5 "), as MSK, the modulation systems such as GMSK all make moderate progress (referring to " Sacchi C in the availability of frequency spectrum, Rossi T, Ruggieri M, et al.Efficient waveform design for high-bit-rate W-band satellite transmissions[J] .IEEE Transactions on Aerospace and Electronic Systems, 2011, 47 (2): 974-995 " and " Seshardi R, Eroz M, Lee L.Improved continuous phase modulation for satellite communications:European Patent EP2385662[P] .2011-11-9 ").
SOQPSK (Shaped Offset Quadrature Phase Shift Keying, shaping offset quadrature phase-shift-keying) be that a kind of improved CPM is (referring to " Umashankar B, Aswathy S, NNSSRK P, et al.SOQPSK – A Spectrally Efficient Modulation Scheme for Aeronautical Telemetry Applications[J] .International Journal of Engineering Science and Innovative Technology (IJESIT), 2013, 2 (2): 383-388 "), its partial response form SOQPSK-TG (Shaped Offset Quadrature Phase Shift Keying-Telemetry Group, shaping offset quadrature phase-shift-keying-remote measurement group), obtain application in aerial remote reconnaissance field (referring to " Williams I E, Saquib M.Linear Frequency Domain Equalization of SOQPSK-TG for Wideband Aeronautical Telemetry Channels[J] .IEEE Transactions on Aerospace and Electronic Systems, 2013, 49 (1): 640-647 ").OQPSK (Offset Quadrature Phase Shift Keying-Telemetry Group, offset quadrature phase-shift-keying) is expressed as CPM form by it, forms filtering with level and smooth pulse, has permanent envelope, narrow bandwidth characteristic.
On the other hand, in satellite communication, multipath effect extensively exists, satellite is high relative to ground station's speed, rotate fast, the elevation angle is low, cause receiving signal fadeout serious, violent rise and fall (referring to " Loyka S; Tellambuira C; Kouki A; et al.Comments on " new method of performance analysis for diversity reception with correlated Rayleigh-fading signals " [J] .IEEE Transactions on Vehicular Technology; 2003,52 (3): 725-726 ").Diversity reception is (referring to " Jingjing S, ANZAI D, Jianqing W.Channel Modeling and Performance Analysis of Diversity Reception for Implant UWB Wireless Link[J] .IEICE Transactions on Communications, 2012, 95 (10): 3197-3205 " and " Han D, Liu Y, Zhang K, et al.Theoretical and experimental research on diversity reception technology in NLOS UV communication system[J] .Optics Express, 2012, 20 (14): 15833-15842 ") can effectively improve this type of decline.Based on the diversity reception of traditional modulation, there is abundant research at home and abroad.As phase-locked in the dicyclo based on FM modulation system and three ring lock phase polarization diversity reception techniques (referring to " east of a river. the phase-locked polarization diversity receiver of novel dicyclo [J]. remote measuring and controlling; 1995; 16 (5): 52-65 " and " snow three is protected. a kind of polarization diversity reception programme [J] of practicality. and telecom technology; 1996; 36 (4): 1-4 "), be analog phase-locked look due to what adopt, stability and reliability are poor; The phase-locked polarization diversity of Digital Dual-loop based on BPSK receive (referring to " and Chen Zhu. the research [D] of Digital Diverse Receiver. University Of Chongqing, 2006 "), its spectral characteristic is not good, can not meet the demand of Modern Satellite communication.Receive system for the tradition of SOQPSK modulation system and also have comparatively ripe technological achievement (referring to " Hosseini E, Perrins E.FPGA implementation of a coherent SOQPSK-TG demodulator[C] //MILCOM2011-2011IEEE Military Communications Conference.Piscataway:IEEE, 2011:471-476 " and " Kumaraswamy B, Perrins E.Simplified2-State Detectors for SOQPSK[C] //IEEE Military Communications Conference.New York:IEEE, 2007:1272-1278 "), but error performance can sharply worsen in the time that signal exists deep fading.
Therefore, need to provide the signal diversifying method of reseptance in a kind of new satellite communication, to overcome the signal fadeout problem in satellite communication.
Summary of the invention
The technical problem to be solved in the present invention is, in prior art, fail effectively to overcome the signal fadeout problem in satellite communication in order to solve, need by SOQPSK modulation signal is adopted to the reception of double polarization, the complementary folding of two passages, a kind of SOQPSK-TG polarizations diversity receiving device and method thereof based on FPGA is provided, to can utilize the permanent envelope, high spectrum utilization feature of SOQPSK-TG to meet Modern Satellite communication requirement, and introduce polarization diversity reception technique, overcome tradition and receive the dark impact at zero point that system exists, improve systematic function.
In order to solve above technical problem, the invention provides SOQPSK-TG polarizations diversity receiving device and method thereof based on FPGA.
According to an aspect of the present invention, a kind of SOQPSK-TG polarizations diversity receiving device based on FPGA is provided, comprise SOQPSK-TG signal modulation module and polarization diversity receiver module, wherein: polarization diversity receiver module comprises: as the module one of automatic gain control loop; As the module two of differential mode ring; The module three merging as high specific; As the module four of common mode loop; As the module five of Timing Synchronization ring.
Further, described modulation module is used for carrying out: at the inner binary sequence that generates of FPGA, be to carry out precoding after nonreturn to zero code sequence by sequence mapping, this symbol pulses integration after pulse shaping filtering obtains phase-modulated information, utilize sine and cosine look-up table to obtain base band homophase and quadrature component, finally can obtain SOQPSK-TG signal by quadrature modulation.
Further, described polarization diversity receiver module one is for carrying out: the two ways of digital signals after analog to digital converter ADC conversion is carried out to automatic gain control in FPGA inside, utilize the special multiplier of FPGA inside to realize signal gain.
Further; described polarization diversity receiver module two is for carrying out: the signal after two-way gain is carried out with homophase locking frequently in FPGA; utilize the IP kernel in FPGA hardware to produce two local oscillators; calculate by the phase discriminator of differential mode ring frequency deviation, the skew that two paths of signals exists, the phase place of simultaneously controlling two oscillators is pushed into two paths of signals with frequency homophase.
Further, described polarization diversity receiver module three is for carrying out: to being weighted merging with the two paths of signals after frequency homophase in FPGA, weight coefficient is provided by the gain coefficient of automatic gain control module, utilizes adder, multiplier, the divider of FPGA inside to realize weighting merging.
Further, described polarization diversity receiver module four-function is in carrying out: the signal after being combined carries out carrier wave recovery in FPGA, utilize IP kernel to produce local oscillator, calculated frequency and the phase error of local oscillator and signal carrier by the phase discriminator of inphase quadrature ring, realize carrier track with this error control local oscillator phase place.
Further, described polarization diversity receiver module five is for carrying out: the baseband signal after carrier wave is recovered is carried out bit timing clock recovery in FPGA, utilize the d type flip flop of FPGA inside to form FIFO, to preserve the value in symbol transition moment and sampled point moment, calculate position error, realize location clock compensation.
According to another aspect of the present invention, provide a kind of polarization diversity method of reseptance of SOQPSK-TG signal, comprised the steps: to adopt two-way analog to digital converter ADC respectively the left-handed polarization of reception and right-hand polarization signal to be converted to two ways of digital signals; Utilize automatic gain control loop to make two ways of digital signals constant amplitude or in threshold interval, to realize level normalization; Follow the tracks of the frequency difference of the two ways of digital signals after gain and differ by differential mode ring, to complete the same frequency homophase locking of two ways of digital signals; To adopting high specific merge algorithm with the digital signal after homophase locking frequently, to obtain average signal-to-noise ratio gain; The digital signal obtaining after average signal-to-noise ratio gain is followed the tracks of to Doppler frequency shift, to carry out carrier wave recovery; Digital signal after carrier wave is recovered is carried out bit timing clock recovery, the clock phase shift and the frequency displacement that between track receiver and transmitter, exist.
Further, described tracking Doppler frequency shift carry out carrier wave recover adopt with the following method: the common mode loop of utilizing inphase quadrature ring algorithm.
Further, described bit timing clock recovery is adopted with the following method: Timing Synchronization loop.SOQPSK-TG polarizations diversity receiving device and method thereof based on FPGA provided by the invention, to can utilize the permanent envelope, high spectrum utilization feature of SOQPSK-TG to meet Modern Satellite communication requirement, and introduce polarization diversity reception technique, overcome tradition and receive the dark impact at zero point that system exists, improve systematic function.Further, SOQPSK-TG polarizations diversity receiving device based on FPGA provided by the invention and method thereof have been filled up the blank of prior art, and SOQPSK-TG modulation system is introduced to satellite communication system, have obtained good result.
The aspect that the present invention is additional and advantage in the following description part provide, and these will become obviously from the following description, or recognize by practice of the present invention.
Brief description of the drawings
Fig. 1 shows the SOQPSK-TG signal modulation block diagram according to the SOQPSK-TG polarizations diversity receiving method based on FPGA of technical solution of the present invention;
Fig. 2 shows according to the SOQPSK-TG of the SOQPSK-TG polarizations diversity receiving method based on FPGA of technical solution of the present invention and the schematic diagram of 3 kinds of conventional phase-coded signal power spectral density comparative results;
Fig. 3 shows according to the SOQPSK-TG polarization diversity of the SOQPSK-TG polarizations diversity receiving method based on FPGA of technical solution of the present invention and receives block diagram;
Fig. 4 shows according to the automatic gain control loop of the SOQPSK-TG polarizations diversity receiving method based on FPGA of technical solution of the present invention and realizes block diagram;
Fig. 5 shows according to the differential mode ring of the SOQPSK-TG polarizations diversity receiving method based on FPGA of technical solution of the present invention and realizes block diagram;
Fig. 6 shows according to the common mode loop of the SOQPSK-TG polarizations diversity receiving method based on FPGA of technical solution of the present invention and realizes block diagram;
Fig. 7 shows according to the Timing Synchronization ring of the SOQPSK-TG polarizations diversity receiving method based on FPGA of technical solution of the present invention and realizes block diagram;
Fig. 8 shows according to the oscillogram of the rectangular pulse of the SOQPSK-TG polarizations diversity receiving method based on FPGA of technical solution of the present invention and matched filtering output thereof;
Fig. 9 shows according to the schematic diagram of the two-way input signal of the SOQPSK-TG polarizations diversity receiving method based on FPGA of technical solution of the present invention;
Figure 10 shows according to the schematic diagram of the automatic gain control loop output signal of the SOQPSK-TG polarizations diversity receiving method based on FPGA of technical solution of the present invention;
Figure 11 shows according to the differential mode ring Phase Tracking curve chart of the SOQPSK-TG polarizations diversity receiving method based on FPGA of technical solution of the present invention;
Figure 12 shows according to the differential mode ring frequency-tracking curve chart of the SOQPSK-TG polarizations diversity receiving method based on FPGA of technical solution of the present invention;
Figure 13 shows according to the common mode loop Phase Tracking curve chart of the SOQPSK-TG polarizations diversity receiving method based on FPGA of technical solution of the present invention;
Figure 14 shows according to the common mode loop frequency-tracking curve chart of the SOQPSK-TG polarizations diversity receiving method based on FPGA of technical solution of the present invention;
Figure 15 shows according to the wave amplitude schematic diagram of the left and right road input of the SOQPSK-TG polarizations diversity receiving method based on FPGA of technical solution of the present invention and high specific merging output signal;
Figure 16 shows according to the homophase of the SOQPSK-TG polarizations diversity receiving method based on FPGA of technical solution of the present invention, the wave amplitude schematic diagram of quadrature component matched filtering demodulation output signal;
Figure 17 shows according to the characteristic curve of error code figure of the SOQPSK-TG polarizations diversity receiving method based on FPGA of technical solution of the present invention;
Figure 18 shows according to the schematic flow sheet of the SOQPSK-TG polarizations diversity receiving method based on FPGA of technical solution of the present invention;
Figure 19 shows according to the total system schematic diagram of the SOQPSK-TG polarizations diversity receiving device based on FPGA of technical solution of the present invention;
Figure 20 shows according to each loop measured waveform figure of the design software Signal-tap II of the SOQPSK-TG polarizations diversity receiving device based on FPGA of technical solution of the present invention;
Figure 21 shows according to the demodulation result measured waveform figure of the design software Signal-tap II of the SOQPSK-TG polarizations diversity receiving device based on FPGA of technical solution of the present invention.
Embodiment
Describe embodiments of the present invention below in detail, the example of described execution mode is shown in the drawings, and wherein same or similar label represents same or similar element or has the element of identical or similar functions from start to finish.Be exemplary below by the execution mode being described with reference to the drawings, only for explaining the present invention, and can not be interpreted as limitation of the present invention.
Unless those skilled in the art of the present technique are appreciated that specially statement, singulative used herein " ", " one ", " described " and " being somebody's turn to do " also can comprise plural form.Should be further understood that, the wording using in specification of the present invention " comprises " and refers to and have described feature, integer, step, operation, element and/or assembly, exists or adds one or more other features, integer, step, operation, element, assembly and/or their group but do not get rid of.Should be appreciated that, when we claim element to be " connected " or " coupling " when another element, it can be directly connected or coupled to other elements, or also can have intermediary element.In addition, " connection " used herein or " coupling " can comprise wireless connections or couple.Wording "and/or" used herein comprises arbitrary unit of listing item and all combinations that one or more is associated.
Those skilled in the art of the present technique are appreciated that unless otherwise defined, all terms used herein (comprising technical term and scientific terminology) have with the present invention under the identical meaning of the general understanding of those of ordinary skill in field.Should also be understood that such as those terms that define in general dictionary and should be understood to have the meaning consistent with meaning in the context of prior art, unless and definition as here, can not explain by idealized or too formal implication.
Below in conjunction with accompanying drawing, the specific embodiment of the present invention is described further.
[SOQPSK-TG signal modulation principle]
SOQPSK-TG signal can be represented by the form of CPM on the basis of OQPSK:
Wherein E is energy per bit, and T is bit period, f 0for carrier frequency, for initial phase, phase place for carry information:
Wherein h is modulation index, and value of the present invention is 0.5, α ifor ternary code metasequence 1,0,1}, f (t) is phase place shaping function:
f ( t ) = 0 t < 0 &Integral; 0 t g ( &tau; ) d&tau; 0 &le; t < LT 1 / 2 t &GreaterEqual; LT - - - ( 3 )
L is partial response length, and g (t) is frequency shaping function.For OQPSK signal, g (t) is δ (t) function; For total regression form SOQPSK-MIL signal, L=1, g (t) is the rectangular pulse of a symbol width; The present invention adopts partial response form SOQPSK-TG signal, gets L=8, and its frequency shaping function is:
g ( t ) = A cos ( &pi;&rho;Bt 2 T ) 1 - 4 ( &rho;Bt 2 T ) 2 &times; sin ( &pi;Bt 2 T ) &pi;Bt 2 T &times; &omega; ( t ) - - - ( 4 )
A is constant, and its value will make g (t) meet (3) formula, and ω (t) is window function, is defined as:
&omega; ( t ) = 1 0 &le; | t 2 T | < T 1 1 2 + 1 2 cos [ &pi; T 2 ( t 2 T - T 1 ) ] T 1 &le; | t 2 T | &le; T 1 + T 2 0 T 1 + T 2 < | t 2 T | - - - ( 5 )
The present invention chooses ρ=0.7, B=1.25, T 1=1.5, T 2=0.5.
The difference of SOQPSK-TG signal and common CP M is that its glossary of symbols is that { 1,0,1} carries out precoding: by binary system list entries b to ternary sequence before modulating i{ 1,0} is mapped as non-return-to-zero (NonReturn to Zero, NRZ) code to ∈.Sequence α i{ 1,1} is converted to ternary sequence u to ∈ i∈ 1,0,1}, its transformation rule is as follows:
u i = ( - 1 ) i + 1 &alpha; i - 1 ( &alpha; i - &alpha; i - 2 ) 2 - - - ( 6 )
Fig. 1 shows the SOQPSK-TG signal modulation block diagram according to the SOQPSK-TG polarizations diversity receiving method based on FPGA of technical solution of the present invention.Its FPGA realizes block diagram as shown in Figure 1, binary sequence carries out precoding after being mapped as NRZ code sequence, again by gained information interpolation, after pulse shaping filtering, integration obtains phase-modulated information, utilize sine and cosine look-up table to obtain base band homophase and quadrature component, finally can obtain SOQPSK-TG signal by quadrature modulation.
Fig. 2 shows according to the SOQPSK-TG of the SOQPSK-TG polarizations diversity receiving method based on FPGA of technical solution of the present invention and the schematic diagram of 3 kinds of conventional phase-coded signal power spectral density comparative results.As shown in Figure 2, SOQPSK-TG and BPSK, QPSK, the general comparison of GMSK signal power, wherein simulation parameter: sample rate is f s=1, carrier wave f 0=1/8, bit rate f b=1/64.Due to the relative traditional BP SK of SOQPSK-TG modulation system, QPSK modulation system eliminated carrier phase ± pi/2 or ± jumping phenomenon of π; With respect to GMSK modulation mode, carrier phase not only can change continuously in ± pi/2, can also remain unchanged.Therefore as can be seen from the figure SOQPSK-TG modulation system power spectral density is more compact, and the speed of roll-offing is fast, and the availability of frequency spectrum is high, therefore can meet the requirement of current satellite communication field to spectral performance.Because it has permanent envelope trait, amplifier nonlinearity is little on its demodulation impact again, and therefore power utilization is high, meets the requirement of satellite to low-power consumption.
[polarization diversity of SOQPSK-TG signal receives]
Satellite received signal after Gaussian channel transmission can be expressed as:
The decline that k in formula (t) is change at random, τ is timing phase skew, and μ is timing frequency skew, and θ is carrier phase, f dfor Doppler frequency shift, n (t) is receiving terminal Gaussian noise.
Fig. 3 shows according to the SOQPSK-TG polarization diversity of the SOQPSK-TG polarizations diversity receiving method based on FPGA of technical solution of the present invention and receives block diagram.The polarization diversity receiving system entire block diagram of the present invention's design as shown in Figure 3; first by ADC, the two-way polarized signal (left-handed polarization, right-hand polarization) receiving is converted to digital signal; then pass through automatic gain control loop (Automatic Gain Control; AGC), differential mode ring (Differential Model Loop; DML), high specific merges (Maximum Ratio Combining; MRC), common mode loop, Timing Synchronization loop, obtain restituted signal:
1, automatic gain control loop
Fig. 4 shows according to the automatic gain control loop of the SOQPSK-TG polarizations diversity receiving method based on FPGA of technical solution of the present invention and realizes block diagram.Its FPGA realizes block diagram as shown in Figure 4, satellite communication channel decline makes the envelope that receives signal can produce fluctuating, changes in amplitude can differ tens decibels, MRC algorithm, carrier recovery algorithm and the clock recovery algorithm that the present invention provides all requires the two paths of signals amplitude of input to keep invariable, and visible AGC is most important in system.Therefore need to regulate by AGC the gain that receives signal, make receiver output voltage constant or substantially constant, improve systematic function.
Its Mathematical Modeling is as follows:
A(n+1)=A(n)+β[R-|A(n)x(n)|] (8)
The adjusting gain that A in formula (n) is AGC, R is gain threshold, β is gain step size.Signal A (n) x (n) through current time gain A (n) gained makes comparisons with thresholding R, can increase the gain A (n+1) in next moment if be less than thresholding, if be in like manner greater than thresholding and reduce the gain in next moment, output signal is maintained near thresholding substantially.Gain step size β is less, and amplitude convergence is slower, and capture time is longer, and error is less, and wave distortion is less; Otherwise β is larger, restrain sooner, capture time is shorter, and error is larger.
2, differential mode ring
Fig. 5 shows according to the differential mode ring of the SOQPSK-TG polarizations diversity receiving method based on FPGA of technical solution of the present invention and realizes block diagram.Its FPGA realizes block diagram as shown in Figure 5, reach the two paths of signals of receiver due to phase place or certain phase deviation and the frequency shift (FS) of the inconsistent meeting introducing of local frequency, and MRC algorithm could merge after requiring two paths of signals with frequency, homophase in weighting, obtain gain, therefore must complete the same frequency homophase processing of two paths of signals.Two paths of signals is divided into two-way by phase discriminator by the error signal of gained after down-conversion, low-pass filtering (LPF), by adjusting numerically-controlled oscillator (Numerical Controlled Oscillator with contrary polarity after loop filter (LF), NCO), two paths of signals is pulled on same public frequency with contrary direction, realizes the same frequency homophase locking of two paths of signals.
The differential mode ring algorithm model of SOQPSK-TG signal is derived as follows, and the two paths of signals of establishing after AGC is respectively:
U L(k)=a(k)cos(ω ikT si)-b(k)sin(ω ikT si) (9)
U R(k)=a(k)cos(ω i′kT si′)-b(k)sin(ω i′kT si′) (10)
Orthogonal and the in-phase component that a in formula (k), b (k) they are base band symbol, T sfor the sampling period, ω i, θ iwei Zuo road signal angular frequency and initial phase, ω i', θ i' be right wing signal angular frequency and initial phase, Ze Zuo road phase iikT s+ θ i, right wing phase i'=ω i' kT s+ θ i'.If ω o, ω o' and θ o, θ o' be respectively local oscillator angular frequency and the phase place of left and right road NCO, Ze Zuo road NCO phase ookT s+ θ o, right wing NCO phase o'=ω o' kT s+ θ o'.
Make ω lio, ω ri'-ω o', θ lio, θ ri'-θ o', after down-conversion and low-pass filtering, can obtain:
Left road I component:
U LI(k)=a(k)cos(ω LkT sL)-b(k)sin(ω LkT sL) (11)
Left road Q component:
U LQ(k)=b(k)cos(ω LkT sL)+a(k)sin(ω LkT sL) (12)
Right wing I component:
U RI(k)=a(k)cos(ω RkT sR)-b(k)sin(ω RkT sR) (13)
Right wing Q component:
U LQ(k)=b(k)cos(ω RkT sR)+a(k)sin(ω RkT sR) (14)
Bring formula (11), (12), (13), (14) into phase discriminator output U d(k), can obtain:
U d(k)=U LQ·U RI-U LI·U RQ
=[a 2(k)+b 2(k)]·sin[(ω LR)kT sLR] (15)
Make A=a 2(k)+b 2(k), Δ φ=(ω lr) kT s+ θ lr, Δ φ llkT s+ θ lio, Δ φ rrkT s+ θ ri'-φ o', Δ φ=Δ φ l-Δ φ r=(φ ii')-(φ oo').
Now U d(k)=Asin (Δ φ), sin in the time that Δ φ is very little (Δ φ) ≈ Δ φ, A is constant.Therefore gained phase error is the once linear function of Δ φ, phase error signal after loop filter is level and smooth by make-φ of NCO FREQUENCY CONTROL word generator o'=φ o:
U d(k)≈A·Δφ=A·(Δφ L-Δφ R)
=A·((φ ii′)+2φ o′) (16)
Wherein φ o' be the phase place of differential mode ring compensation, A is phase detector gain, φ when the leading right wing of Dang Zuo road phase place o' be negative value, vice versa, makes so gradually two paths of signals reach with frequency homophase.
3, high specific merges
Conventional polarization diversity receives merging mode three kinds: equal gain combining, selection merge, high specific merges, the present invention adopts the high specific merge algorithm of diversity gain the best, its principle is that the weight coefficient obtaining by AGC is weighted merging to two paths of signals, make signal to noise ratio obtain larger weights compared with great mono-tunnel, the smaller Yi of noise road obtains less weights.If s ofor merging output signal voltage, α ifor each branch road weight coefficient, s ifor each branch input signal voltage, N is branch road number.Suppose that each branch road noise is irrelevant, therefore merge output noise power should be each branch road input noise power sum, can merge output signal-to-noise ratio γ o:
&gamma; o = s o 2 2 n o 2 = [ 1 2 &Sigma; i = 1 N &alpha; i s i ] 2 &Sigma; i = 1 N &alpha; i 2 n i 2 = [ 1 2 &Sigma; i = 1 N &alpha; i n i s i 2 n i 2 ] 2 &Sigma; i = 1 N &alpha; i 2 n i 2 - - - ( 17 )
Can be obtained by Schwartz inequality:
[ 1 2 &Sigma; i = 1 N &alpha; i n i s i 2 n i 2 ] 2 &le; 1 2 ( &Sigma; i = 1 N &alpha; i 2 n i 2 ) ( &Sigma; i = 1 N s i 2 n i 2 ) - - - ( 18 )
Bringing formula (17) into formula (18) can obtain:
s o 2 2 n o 2 &le; &Sigma; i = 1 N s i 2 2 n i 2 - - - ( 19 )
Be each branch road signal to noise ratio sum by the maximum of the known high specific merge algorithm of formula (19) output signal-to-noise ratio.Formula (18) is got the condition that equal sign need be satisfied:
s 1 a 1 n 1 2 = s 2 a 2 n 2 2 = . . . . . . = s N a N n N 2 - - - ( 20 )
And if only if when each tributary signal voltage equates with the ratio of weighted noise power, and output reaches maximum, and this time diversity gain is:
p &OverBar; ( n ) = N - - - ( 21 )
The present invention discusses the system of N=2, after two paths of signals is by the AGC and DML that above analyzed, has reached with frequency homophase and constant amplitude, i.e. K ls l=K rs r, S l, S rfor the left and right road of receiving terminal input signal, K l, K rfor the gain of AGC gained, weight coefficient C l, C rneed to meet following two conditions:
C L + C R = 1 , C L C R = S L 2 S R 2 = K R 2 K L 2 - - - ( 22 )
Suppose that it is N that two paths of signals noise power equates l=N r=N i, can be obtained the ratio of combined signal amplitude and noise amplitude by formula (22):
S N o = C L &CenterDot; K L &CenterDot; S L + C R &CenterDot; K R &CenterDot; S R ( C L &CenterDot; K L &CenterDot; N L ) 2 + ( C R &CenterDot; K R &CenterDot; N R ) 2 = C R &CenterDot; K R &CenterDot; S L S R &CenterDot; S L + C R &CenterDot; K R &CenterDot; S R ( C R &CenterDot; K R &CenterDot; S L S R &CenterDot; N i ) 2 + ( C R &CenterDot; K R &CenterDot; N i ) 2 = C R &CenterDot; K R &CenterDot; S L 2 + C R &CenterDot; K R &CenterDot; S R 2 N i &CenterDot; ( C R &CenterDot; K R &CenterDot; S L ) 2 + ( C R &CenterDot; K R &CenterDot; S R ) 2 = S L 2 + S R 2 N i - - - ( 23 )
Known in the time that receiving terminal two-way input signal equates by formula (23), signal to noise ratio can obtain theoretical maximum gain 3dB; In the time that two paths of signals amplitude differs greatly, synthetic signal to noise ratio also can approach the signal to noise ratio on amplitude great mono-tunnel.Obtained the weight coefficient on left and right road by formula (22):
C L = K R 2 K L 2 + K R 2 , C R = K L 2 K L 2 + K R 2 - - - ( 24 )
4, common mode loop
Fig. 6 shows according to the common mode loop of the SOQPSK-TG polarizations diversity receiving method based on FPGA of technical solution of the present invention and realizes block diagram.The high-speed motion on the relative ground of satellite can make signal carrier produce Doppler frequency component, and this just requires receiver to have stronger frequency displacement capture ability, faster synchronizing speed and higher synchronization accuracy.The present invention adopts inphase quadrature ring algorithm to recover carrier wave, and its FPGA realizes block diagram as shown in Figure 6:
If the signal s (k) after high specific merges is:
s(k)=a(k)cos[(ω c±ω d)kT s1]
-b(k)sin[(ω c±ω d)kT s1] (25)
ω in formula dfor the angular frequency deviation that Doppler effect produces, θ 1for initial phase.Signal obtains after orthogonal mixing, low-pass filtering are removed high fdrequency component:
U I(k)=a(k)cos[(ω c±ω do)kT s1o]
-b(k)sin[(ω c±ω do)kT s1o] (26)
U Q(k)=b(k)cos[(ω c±ω do)kT s1o]
+a(k)sin[(ω c±ω do)kT s1o] (27)
Make Δ φ=(ω c± ω do) kT s+ θ 1o, by U i, U qsend into phase discriminator, phase discriminator is based on hard decision algorithm herein.In the time that Δ φ is very little, cos (Δ φ) ≈ 1, sin (Δ φ) ≈ 0, can obtain phase detector error U d(k):
U d(k)=U Q(k)·sgn[U I(k)]-U I(k)·sgn[U Q(k)]
=[b(k)cos(Δφ)+a(k)sin(Δφ)]·sgn[a(k)]
-[a(k)cos(Δφ)-b(k)sin(Δφ)]·sgn[b(k)] (28)
=[|a(k)|+|b(k)|]sin(Δφ)≈[|a(k)|+|b(k)|]Δφ
For QPSK, | a (k) |+| b (k) | perseverance is 2, and for SOQPSK-TG, | a (k) |+| b (k) | be the value of approximate constant, error amount is controlled NCO and is eliminated gradually frequency displacement after loop filter is level and smooth, reaches carrier synchronization.Now I, Q road output is respectively sgn[a (k)], sgn[b (k)], this two-way value is sent into Timing Synchronization loop and carries out clock recovery.
5, Timing Synchronization ring
Fig. 7 shows according to the Timing Synchronization ring of the SOQPSK-TG polarizations diversity receiving method based on FPGA of technical solution of the present invention and realizes block diagram.Its FPGA realizes block diagram as shown in Figure 7, because the clock of Receiver And Transmitter all can exist certain phase deviation and frequency shift (FS), along with building up of skew will produce error code, has a strong impact on systematic function.The present invention adopts the algorithm of door sooner or later based on self-synchronizing method, is applicable to the system of high power sample rate, can "ball-park" estimate clock skew, and the hardware that is easy to simple for structure is realized.
Fig. 8 shows according to the oscillogram of the rectangular pulse of the SOQPSK-TG polarizations diversity receiving method based on FPGA of technical solution of the present invention and matched filtering output thereof.To utilize the symmetry of signal after matched filter to carry out bit timing synchronous for a door algorithm sooner or later, as shown in Figure 8:
Signal optimum sampling moment after matched filter is t=nT, but due to noise, clock skew may cause sampling cannot be in the maximum moment of code element signal to noise ratio.In the time that transition value t=nT-τ and the sample value in t '=nT+ τ moment equate, the optimum sampling moment is just at the center time point of two sampling instants.If there is sampling late, the difference of adjacent transition value can be detected, by feedback loop control sampling clock, as the same while occurring early to sample.Based on this principle, utilize adjacent two symbol transition values whether to equate, add amplitude and this information of polarity of optimum sampling point, make τ=T/2, can derive the model of Timing Error Detector:
e ( n ) = u I ( n + &tau; ( n ) ) [ u I ( n + 1 2 + &tau; ( n ) ) - u I ( n - 1 2 + &tau; ( n - 1 ) ) ] + u Q ( n + &tau; ( n ) ) [ u Q ( n + 1 2 + &tau; ( n ) ) - u Q ( n - 1 2 + &tau; ( n - 1 ) ) ] - - - ( 29 )
τ in formula (n) is the sampling clock of compensation, represent the transition value of n+1 and n code element, represent the transition value of n and n-1 code element.Can obtain NCO by formula (29) is output as:
τ(n+1)=τ(n)+γ·e(n) (30)
In formula, γ is step parameter.Due to the modulation feature of SOQPSK-TG, Q road component is symbol period T of I road component delay relatively bsampling.Finally obtain final restituted signal by parallel-serial conversion strange, even road.
[test result]
Test condition: signal intermediate frequency f 0=32MHz, carrier wave f after down-conversion r=f l=4MHz, sample rate f s=128MHz, each cycle sampling number N c=32, each symbol sample points N s=64, code element number Num=800, receiving signal is sinusoidal fluctuating envelope, and fluctuating scope is 20dB, and two-way input signal frequency difference Δ f=2.56KHz, differs Δ φ=π/4, Doppler frequency shift f d=6.4KHz, noise is narrowband Gaussian noise, signal to noise ratio snr=15dB, each go-and-return test result is as follows:
Above-mentioned test result shows, automatic gain control loop can good constant incoming level, as shown in Fig. 9,10; Differential mode ring, common mode loop can accurately be followed the tracks of two-way input signal frequency difference, be differed and Doppler frequency shift, as shown in Figure 11-14; High specific merges module and can make the poor Yi of signal to noise ratio road be compensated, as shown in figure 15; Last demodulation result as shown in figure 16, under maximum rises and falls as 20dB condition, has realized correct demodulation by diversity reception.By further verifying that the present invention is carried algorithm performance, Figure 17 has provided the performance comparison result of diversity reception SOQPSK-TG satellite communication system and traditional BP SK satellite communication system.
Comparing result shows, polarization diversity SOQPSK-TG transmission system is obviously better than traditional BP SK system, rises and falls as under 20dB condition in maximum, can obtain 5 to 10dB average signal-to-noise ratios gains.
Through making rational planning for, well-designed, this new receive mode is achieved in the large-scale F PGA chip of monolithic ALTERA company, and has carried out testing authentication on development board.
Total system schematic diagram is as Figure 19, and transmitter module produces two-way SOQPSK-TG modulation signal, by two-way digital to analog converter DAC, the digital signal of two-way SOQPSK-TG modulation is converted to analog signal.The signal that two-way analog to digital converter ADC produces by SMA cable sampling transmitter module, the polarization diversity receiver module in recycling chip carries out demodulation to signal.Data are mutual by JTAG mouth and PC.
The Signal-tap II oscillogram of Figure 20,21 for receiver module in FPGA is surveyed.In Figure 20, the first via, the second road waveform are the sampled signal of two-way analog to digital converter ADC, all have decline in amplitude; Three, Si road waveform is respectively the output of two paths of signals after automatic gain control, the substantially constant of the signal amplitude after output; Five, Liu road waveform is respectively two paths of signals and completes the output signal after locking with frequency homophase through differential mode ring; Qi road waveform is the output signal after two paths of signals high specific merges; Eight, Jiu road waveform is respectively the homophase after the common mode loop reinsertion of carrier, orthogonal demodulated baseband signal.In Figure 21, first, second road waveform is the Phase Tracking value of differential mode ring two paths of signals local oscillator, and polarity is contrary, and two paths of signals is pushed into frequency homophase; Third Road waveform is the Phase Tracking value of common mode loop local oscillator, follows the tracks of carrier doppler frequency displacement and phase error; Si road waveform is the binary message sending; Wu road waveform is the binary message after demodulation, can recover the binary message of transmission after certain time-delay.
More than showing, is attainable according to the SOQPSK-TG polarizations diversity receiving device based on FPGA and the method thereof of technical solution of the present invention.
According to an aspect of the present invention, a kind of SOQPSK-TG polarizations diversity receiving device based on FPGA is provided, comprise SOQPSK-TG signal modulation module and polarization diversity receiver module, wherein: polarization diversity receiver module further comprises the following functional structure connecting successively: as the module one of automatic gain control loop; As the module two of differential mode ring; The module three merging as high specific; As the module four of common mode loop; As the module five of Timing Synchronization ring.
Further, described modulation module is used for carrying out: at the inner binary sequence that generates of FPGA, be to carry out precoding after nonreturn to zero code sequence by sequence mapping, this symbol pulses integration after pulse shaping filtering obtains phase-modulated information, utilize sine and cosine look-up table to obtain base band homophase and quadrature component, finally can obtain SOQPSK-TG signal by quadrature modulation.
Further, described polarization diversity receiver module one is for carrying out: the two ways of digital signals after analog to digital converter ADC conversion is carried out to automatic gain control in FPGA inside, utilize the special multiplier of FPGA inside to realize signal gain.
Further; described polarization diversity receiver module two is for carrying out: the signal after two-way gain is carried out with homophase locking frequently in FPGA; utilize the IP kernel in FPGA hardware to produce two local oscillators; calculated frequency difference that two paths of signals exists, differed by the phase discriminator of differential mode ring, the phase place of simultaneously controlling two oscillators is pushed into two paths of signals with homophase frequently.
Further, described polarization diversity receiver module three is for carrying out: to being weighted merging with the two paths of signals after frequency homophase in FPGA, weight coefficient is provided by the gain coefficient of automatic gain control module, utilizes adder, multiplier, the divider of FPGA inside to realize weighting merging.
Further, described polarization diversity receiver module four-function is in carrying out: the signal after being combined carries out carrier wave recovery in FPGA, utilize IP kernel to produce local oscillator, calculated frequency and the phase error of local oscillator and signal carrier by the phase discriminator of inphase quadrature ring, realize carrier track with this error control local oscillator phase place.
Further, described polarization diversity receiver module five is for carrying out: the baseband signal after carrier wave is recovered is carried out bit timing clock recovery in FPGA, utilize the d type flip flop of FPGA inside to form FIFO, to preserve the value in symbol transition moment and sampled point moment, calculate position error, realize location clock compensation.
Figure 18 shows according to the schematic flow sheet of the SOQPSK-TG polarizations diversity receiving method based on FPGA of technical solution of the present invention.According to another aspect of the present invention, a kind of SOQPSK-TG polarizations diversity receiving method based on FPGA is provided, has comprised the steps: to adopt two-way analog to digital converter ADC respectively the left-handed polarization of reception and right-hand polarization signal to be converted to two ways of digital signals; Utilize automatic gain control loop algorithm to make two ways of digital signals constant amplitude or in threshold interval, to realize level normalization; Frequency difference by the two ways of digital signals after differential mode ring algorithm keeps track gain and differing, to complete the same frequency homophase locking of two ways of digital signals; To adopting high specific merge algorithm with the digital signal after homophase locking frequently, to obtain average signal-to-noise ratio gain; The digital signal obtaining after average signal-to-noise ratio gain is followed the tracks of to Doppler frequency shift, to carry out carrier wave recovery; Digital signal after carrier wave is recovered is carried out bit timing clock recovery, the clock phase shift and the frequency displacement that between track receiver and transmitter, exist.
Further, described tracking Doppler frequency shift carry out carrier wave recover adopt with the following method: the common mode loop of utilizing inphase quadrature ring algorithm.
Further, described bit timing clock recovery is adopted with the following method: Timing Synchronization loop.
[design brief summary]
The present invention adopts polarization diversity reception technique to carry out coherent demodulation to SOQPSK-TG signal, and the EP2S180F1020C3 chip in the advanced FPGA device Stratix II of application ALTERA company series carries out hardware programming design.For ease of the test new reception system of carrying, give the modulation scheme of SOQPSK-TG signal and FPGA thereof and realize, employing Continuous Phase Modulation technology, make to transmit there is permanent envelope, the speed of roll-offing is fast, frequency efficiency is high characteristic.Polarization diversity receiving demodulation scheme: (1) adopts two-way ADC that the two-way polarized signal (left-handed polarization, right-hand polarization) receiving is converted to digital signal; (2) utilize automatic gain control loop to make two paths of signals constant amplitude or substantially constant, realize level normalization; (3) differential mode ring is followed the tracks of the frequency difference of the two ways of digital signals after two-way gain and is differed, and completes the same frequency homophase locking of two paths of signals; (4) adopt the best high specific merge algorithm of diversity gain to obtain average signal-to-noise ratio gain; (5) common mode loop is followed the tracks of Doppler frequency shift, carries out carrier wave recovery; (6) Timing Synchronization loop carries out bit timing clock recovery, the clock phase shift and the frequency displacement that between track receiver and transmitter, exist.
The feature such as non-linear and circumstance complication for satellite communication power limited, Bandwidth-Constrained, power amplifier, the present invention utilizes the permanent envelope, high spectrum utilization feature of SOQPSK-TG to meet Modern Satellite communication requirement, and introduce polarization diversity reception technique, overcome tradition and receive the dark impact at zero point that system exists, improve systematic function.By utilizing the programmable parallel organization of the high-performance FPGA of ALTERA company device, and the unique texture of inner DSP module, complete efficient multiply device, design realizes at a high speed, reliable, stable Vanguard satellite receiving system.SOQPSK-TG polarizations diversity receiving device based on FPGA provided by the invention and method thereof have been filled up the blank of prior art, and SOQPSK-TG modulation system is introduced to satellite communication system, have obtained good result.
Those skilled in the art of the present technique be appreciated that step in the various operations discussed in the present invention, method, flow process, measure, scheme can by alternately, change, combination or delete.Further, have other steps in the various operations discussed in the present invention, method, flow process, measure, scheme also can by alternately, change, reset, decompose, combination or delete.Further, of the prior art have with the present invention in step in disclosed various operations, method, flow process, measure, scheme also can by alternately, change, reset, decompose, combination or delete.
The above is only part execution mode of the present invention; it should be pointed out that for those skilled in the art, under the premise without departing from the principles of the invention; can also make some improvements and modifications, these improvements and modifications also should be considered as protection scope of the present invention.

Claims (10)

1. the SOQPSK-TG polarizations diversity receiving device based on FPGA, is characterized in that, comprises SOQPSK-TG signal modulation module and polarization diversity receiver module,
Wherein: polarization diversity receiver module further comprises the following functional structure connecting successively:
As the module one of automatic gain control loop;
As the module two of differential mode ring;
The module three merging as high specific;
As the module four of common mode loop;
As the module five of Timing Synchronization ring.
2. the SOQPSK-TG polarizations diversity receiving device based on FPGA according to claim 1, is characterized in that, described modulation module is used for carrying out:
At the inner binary sequence that generates of FPGA, be to carry out precoding after nonreturn to zero code sequence by sequence mapping, this symbol pulses integration after pulse shaping filtering obtains phase-modulated information, utilize sine and cosine look-up table to obtain base band homophase and quadrature component, finally can obtain SOQPSK-TG signal by quadrature modulation.
3. the SOQPSK-TG polarizations diversity receiving device based on FPGA according to claim 1, is characterized in that, described polarization diversity receiver module one is for carrying out:
Two ways of digital signals after analog to digital converter ADC conversion is carried out to automatic gain control in FPGA inside, utilize the special multiplier of FPGA inside to realize signal gain.
4. the SOQPSK-TG polarizations diversity receiving device based on FPGA according to claim 1, is characterized in that, described polarization diversity receiver module two is for carrying out:
Signal after two-way gain is carried out with homophase locking frequently in FPGA; utilize the IP kernel in FPGA hardware to produce two local oscillators; calculated frequency difference that two paths of signals exists, differed by the phase discriminator of differential mode ring, the phase place of simultaneously controlling two oscillators is pushed into two paths of signals with homophase frequently.
5. the SOQPSK-TG polarizations diversity receiving device based on FPGA according to claim 1, is characterized in that, described polarization diversity receiver module three is for carrying out:
To being weighted merging with the two paths of signals after frequency homophase in FPGA, weight coefficient is provided by the gain coefficient of automatic gain control module, utilizes adder, multiplier, the divider of FPGA inside to realize weighting merging.
6. the SOQPSK-TG polarizations diversity receiving device based on FPGA according to claim 1, is characterized in that, described polarization diversity receiver module four-function is in carrying out:
Signal after being combined carries out carrier wave recovery in FPGA, utilizes IP kernel to produce local oscillator, is calculated frequency and the phase error of local oscillator and signal carrier by the phase discriminator of inphase quadrature ring, realizes carrier track with this error control local oscillator phase place.
7. the SOQPSK-TG polarizations diversity receiving device based on FPGA according to claim 1, is characterized in that, described polarization diversity receiver module five is for carrying out:
Baseband signal after carrier wave is recovered is carried out bit timing clock recovery in FPGA, utilizes the d type flip flop of FPGA inside to form FIFO, to preserve the value in symbol transition moment and sampled point moment, calculates position error, realizes location clock compensation.
8. a polarization diversity method of reseptance for SOQPSK-TG signal, is characterized in that, comprises the steps:
Adopt two-way analog to digital converter ADC respectively the left-handed polarization of reception and right-hand polarization signal to be converted to two ways of digital signals;
Utilize automatic gain control loop algorithm to make two ways of digital signals constant amplitude or in threshold interval, to realize level normalization;
Frequency difference by the two ways of digital signals after differential mode ring algorithm keeps track gain and differing, to complete the same frequency homophase locking of two ways of digital signals;
To adopting high specific merge algorithm with the digital signal after homophase locking frequently, to obtain average signal-to-noise ratio gain;
The digital signal obtaining after average signal-to-noise ratio gain is followed the tracks of to Doppler frequency shift, to carry out carrier wave recovery;
Digital signal after carrier wave is recovered is carried out bit timing clock recovery, the clock phase shift and the frequency displacement that between track receiver and transmitter, exist.
9. SOQPSK-TG polarizations diversity receiving method according to claim 8, is characterized in that, described tracking Doppler frequency shift carries out carrier wave and recovers to adopt with the following method: the common mode loop of utilizing inphase quadrature ring algorithm.
10. SOQPSK-TG polarizations diversity receiving method according to claim 8, is characterized in that, described bit timing clock recovery is adopted with the following method: Timing Synchronization loop.
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CN105356993B (en) * 2015-10-18 2018-10-23 中国电子科技集团公司第十研究所 The channel time delay control method of PCM/FM polarizations synthesis
CN105356993A (en) * 2015-10-18 2016-02-24 中国电子科技集团公司第十研究所 Channel time delay control method for pulse code modulation or frequency modulation (PCM/FM) signal polarization synthesis
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CN108964748A (en) * 2018-08-21 2018-12-07 中国科学院空间应用工程与技术中心 A kind of clock recovery method under maximum Doppler frequency shift
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CN111896917A (en) * 2020-07-30 2020-11-06 北京融为科技有限公司 Left-handed and right-handed signal polarization synthesis method
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