CN109412997B - Improved orthogonal multi-carrier underwater sound mobile communication channel estimation and compensation method - Google Patents

Improved orthogonal multi-carrier underwater sound mobile communication channel estimation and compensation method Download PDF

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CN109412997B
CN109412997B CN201811544844.7A CN201811544844A CN109412997B CN 109412997 B CN109412997 B CN 109412997B CN 201811544844 A CN201811544844 A CN 201811544844A CN 109412997 B CN109412997 B CN 109412997B
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王巍
杨腾
钱斌
毕坤
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SUZHOU SOUNDTECH OCEANIC INSTRUMENT CO Ltd
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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
    • H04L27/2647—Arrangements specific to the receiver only
    • H04L27/2649—Demodulators
    • H04L27/265—Fourier transform demodulators, e.g. fast Fourier transform [FFT] or discrete Fourier transform [DFT] demodulators
    • H—ELECTRICITY
    • H04—ELECTRIC COMMUNICATION TECHNIQUE
    • H04B—TRANSMISSION
    • H04B13/00—Transmission systems characterised by the medium used for transmission, not provided for in groups H04B3/00 - H04B11/00
    • H04B13/02—Transmission systems in which the medium consists of the earth or a large mass of water thereon, e.g. earth telegraphy
    • H—ELECTRICITY
    • H04—ELECTRIC COMMUNICATION TECHNIQUE
    • H04L—TRANSMISSION OF DIGITAL INFORMATION, e.g. TELEGRAPHIC COMMUNICATION
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    • H04L25/02—Details ; arrangements for supplying electrical power along data transmission lines
    • H04L25/0202—Channel estimation
    • H04L25/022—Channel estimation of frequency response
    • H—ELECTRICITY
    • H04—ELECTRIC COMMUNICATION TECHNIQUE
    • H04L—TRANSMISSION OF DIGITAL INFORMATION, e.g. TELEGRAPHIC COMMUNICATION
    • H04L25/00—Baseband systems
    • H04L25/02—Details ; arrangements for supplying electrical power along data transmission lines
    • H04L25/0202—Channel estimation
    • H04L25/024—Channel estimation channel estimation algorithms
    • H04L25/0242—Channel estimation channel estimation algorithms using matrix methods
    • 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
    • H04L27/2647—Arrangements specific to the receiver only
    • H04L27/2655—Synchronisation arrangements
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Abstract

The invention discloses a Doppler estimation and compensation method for detecting sparsity of an orthogonal multi-carrier underwater acoustic mobile communication channel, which aims at the problem caused by limited frequency domain response resolution in a complex multi-path time-varying channel environment, utilizes the principle that the orthogonality of subcarriers of a Doppler distortion signal is not changed, adopts local subcarrier Discrete Fourier Transform (DFT) to extract frequency domain response of pilot subcarriers, calculates channel impulse response and sparsity of signals under different Doppler compensation conditions, selects a compression factor with the maximum channel sparsity to estimate a result and demodulate the signals, and realizes mobile underwater acoustic communication in the complex multi-path time-varying channel environment. The Doppler estimation precision is improved by the method, and the reason is mainly frequency domain resolution precision. The carrier demodulation matrix of the method is generated by utilizing Doppler compression factor calculation, and the Doppler is used for relatively higher resolution of the carrier matrix for demodulating each subcarrier, so that the Doppler compensation effect is better.

Description

Improved orthogonal multi-carrier underwater sound mobile communication channel estimation and compensation method
Technical Field
The method relates to the research of OFDM mobile communication under the complex multipath time-varying channel environment, in particular to an improved channel sparsity detection Doppler estimation method, which is provided for solving the problem that the Doppler distortion estimation effect of an Orthogonal Frequency Division Multiplexing (OFDM) underwater mobile communication channel sparsity detection Doppler estimation method based on Frequency domain variable sampling is poor under the fast time-varying multipath channel environment, and is applied to the field of underwater mobile communication.
Background
The available bandwidth resources in the underwater acoustic communication are very limited, and the OFDM technology with high spectrum utilization rate and good multipath propagation resistance becomes a hot spot of the underwater acoustic high-data rate communication in recent years. However, OFDM is sensitive to doppler frequency offset, and particularly in underwater acoustic communication with relatively low sound velocity, the factors such as carrier asynchronism caused by relative motion between communication carriers and crystal oscillator offset of receiving and transmitting systems all bring about large doppler frequency offset, which severely restricts the application of OFDM in mobile underwater acoustic communication.
In the prior art, an OFDM underwater acoustic mobile communication Doppler estimation method combining frequency domain variable sampling and channel sparsity detection is adopted, Doppler distortion signal frequency domain response analysis is realized through a Fast Fourier Transform (FFT) algorithm, a good effect is obtained in a sea trial test, but the algorithm is limited by the problem that the frequency domain response resolution of the high-order FFT algorithm is limited, and the application effect is poor in a complex multipath time-varying channel environment.
Because the Doppler compensation matrix of the Doppler estimation and compensation method in the prior art is obtained through high-order FFT conversion, and the frequency domain resolution is fixed, the demodulation process of different subcarriers can be regarded as that carrier vectors between the frequency offsets of the different subcarriers are searched in the carrier demodulation matrix generated by the high-order FFT, and the information carried by the subcarriers is subjected to integral demodulation respectively.
Disclosure of Invention
The method aims to provide an improved orthogonal multi-carrier underwater acoustic mobile communication channel estimation and compensation method, aims at solving the problem caused by limited frequency domain response resolution under the complex multi-path time-varying channel environment, utilizes the principle that the orthogonality of the sub-carriers of a Doppler distortion signal is not changed, adopts the Discrete Fourier Transform (DFT) of local sub-carriers to extract the frequency domain response of the pilot sub-carriers, calculates the channel impulse response and the sparsity of the signal under different Doppler compensation conditions, selects the compression factor with the largest channel sparsity to estimate the result and demodulate the signal, and realizes the mobile underwater acoustic communication under the complex multi-path time-varying channel environment.
The scheme of the invention is suitable for the Doppler estimation of the channel sparsity detection signal in the complex multipath time-varying channel environment, and has better precision.
The scheme of the invention is as follows:
an improved orthogonal multi-carrier underwater sound mobile communication channel estimation and compensation method comprises the following steps:
A. a receiving end receives a Doppler distortion signal;
B. calculating a frequency domain response of the received Doppler distortion signal;
C. doppler compression factor estimated through p-1 th OFDM symbol
Figure GDA0002896184860000023
Construction of a received Signal yp(n) matrix samples for doppler demodulation of pilot subcarriers in (n);
D. matching the frequency domain response in the step B with the matrix sample in the step C to obtain a received signal yp(n) the data subcarrier demodulation matrix;
E. d, demodulating the received signal y according to the matched data subcarrier in the step Dp(n) performing DFT demodulation to obtain transmission data of the p-th OFDM symbol, and estimating the Doppler compression factor lambda of the p-th OFDM symbolpAnd C, returning to the step C to construct a matrix sample of the Doppler demodulation of the pilot subcarriers of the next sequence.
Further, the step C includes the steps of:
C1. the matrix sample is gammaM×Ns＝[Λ-M Λ-M+1 … Λm … ΛM-1 ΛM]Wherein Ns is the length of comb-shaped pilot vector s adopted by the signal sending end, and gammaM×NsElement in matrix ΛmExpressed in a Doppler compensation factor of
Figure GDA0002896184860000021
A pilot frequency subcarrier orthogonal demodulation matrix generated by a time receiving end, wherein delta lambda is a search wavelength, and m is the mth search sample in a Doppler search range matrix; definition of γ ═ γ0,γ1,…,γNs-1]For a set of sub-carriers in the OFDM band position carrying a comb pilot vector s, the matrix ΛmCan be expressed as:
Figure GDA0002896184860000022
wherein N ismTo make the Doppler compensation factor be lambdamThe time-demodulation carrier continues to sample the number of points, β ═ j2 π Δ fn.
Further, the step D includes the steps of:
D1. using ΛmFor the p-th OFDM symbol ypDemodulation is performed to obtain a compression factor of lambda at the Doppler compensationmTime-pilot subcarrier frequency domain response vector
Figure GDA0002896184860000031
Wherein (·)HRepresenting a conjugate transpose.
At this time, the channel impulse response estimation value
Figure GDA0002896184860000032
Can be calculated to obtain:
Figure GDA0002896184860000033
D2. constructing an overcomplete dictionary psi consisting of a plurality of atoms phi, and estimating a channel estimation result by using a matching pursuit sparse channel estimation technology
Figure GDA0002896184860000034
Carrying out matching estimation to obtain a weighted vector Wm,p。
Figure GDA0002896184860000035
To Wm,pAnd (3) carrying out normalization treatment:
Figure GDA0002896184860000036
D3. according to formula (5) searching
Figure GDA0002896184860000037
Corresponding when sparsity is maximum
Figure GDA0002896184860000038
Calculating Doppler compression factor
Figure GDA0002896184860000039
Figure GDA00028961848600000310
M is the matrix search range boundary,
Figure GDA00028961848600000311
for the best match within the search range, subscript p is for the p-th OFDM symbol;
using lambdapAnd constructing a data subcarrier demodulation matrix.
By adopting the technical scheme, the method has the following technical effects:
compared with a Doppler compensation matrix transformed by high-order FFT in the prior art, the Doppler estimation accuracy is improved due to the fact that frequency domain resolution accuracy is improved by means of DFT mediation. The carrier demodulation matrix of the method is generated by utilizing Doppler compression factor calculation, and the Doppler is used for relatively higher resolution of the carrier matrix for demodulating each subcarrier, so that the Doppler compensation effect is better.
The frequency domain response of the pilot frequency sub-carrier is extracted by adopting the Discrete Fourier Transform (DFT), the calculation amount of the DFT is reduced, the channel impulse response and the sparsity of the signal under different Doppler compensation conditions are calculated, the compression factor with the largest channel sparsity is selected to estimate the result demodulation signal, and the mobile underwater acoustic communication under the complex multipath time-varying channel environment is realized.
Drawings
FIG. 1 is a flow chart of a time-varying Doppler tracking and fast compensation method.
Fig. 2 is a graph of simulated channel observation history.
Fig. 3 simulates the channel impulse response.
Figure 4 doppler tracking effect comparison.
Figure 5 shows the comparison of the Doppler estimation effect under different signal-to-noise ratio conditions.
FIG. 6 radial velocity between two vessels.
Fig. 7 shows the constellation diagram after the demodulation of the 1 st frame signal (comparison method).
Fig. 8 shows the constellation diagram after the demodulation of the 1 st frame signal (the method).
Fig. 9 communication algorithm bit error rate comparison.
Detailed Description
The technical solutions in the embodiments of the present invention will be clearly and completely described below with reference to the drawings in the embodiments of the present invention, and it is obvious that the described embodiments are only a part of the embodiments of the present invention, and not all of the embodiments. All other embodiments, which can be derived by a person skilled in the art from the embodiments given herein without making any creative effort, shall fall within the protection scope of the present invention.
The method is described in more detail below with reference to the accompanying drawings and the embodiments.
1. Time-varying doppler identification principle
The frequency domain impulse response of a time-varying underwater acoustic channel containing a Doppler factor is modeled as follows:
Figure GDA0002896184860000041
wherein,
Figure GDA0002896184860000042
λland τlRespectively representing the Doppler factor and the fixed time delay, C, of the signal samples propagated on the ith pathlIs the magnitude of the amplitude of the ith path. The transmitted OFDM signal may be represented as:
Figure GDA0002896184860000043
t represents the symbol duration of one OFDM, K is the number of subcarriers, and Δ f is the subcarrier spacing. The transmission of the receiving end signal via the above channel can be expressed as:
Figure GDA0002896184860000044
where v (t) is Gaussian additive noise.
Δ λ is the Doppler search step, fk,mThe demodulated carrier frequency generated under the mth search step compensation condition is as follows:
fk,m＝fk(1+m×Δλ) (5)
considering that the remote communication is carried out under the condition of shallow sea area, the incidence angles of all the multipath are close, the Doppler of all the multipath is approximately equal, and at the moment, the following steps are carried out:
Figure GDA0002896184860000051
where σ (k, m) is additive Gaussian noise v (t) at fk,mA noise component on the frequency domain subchannel. Substituting equation (4) into the above equation gives:
Figure GDA0002896184860000052
substituting equation (3) into equation (7)
Figure GDA0002896184860000053
Where σ' (k, m) is the k-th subcarrier at a Doppler compensation factor of λmWhen the modulation is carried out under the condition, the self carrier offset and other N-1 sub-carriers cause intersymbol interference.
Therefore, when the Doppler compensation factor is λmTime, frequency domain response estimation result of k sub-channel
Figure GDA0002896184860000054
Can be expressed as:
Figure GDA0002896184860000055
if and only if
Figure GDA0002896184860000061
In time, there are:
Figure GDA0002896184860000062
when the channel is responding
Figure GDA0002896184860000063
Can be expressed as:
Figure GDA0002896184860000064
wherein
Figure GDA0002896184860000065
The channel impulse response is under the static condition of both ends of the communication end.
2. Matching pursuit sparse channel estimation method
The idea of the sparse channel estimation method by matching pursuit is to design an overcomplete dictionary psi consisting of a plurality of atoms phi and to estimate the result of the sparse channel
Figure GDA0002896184860000066
In the process of iterative decomposition, a sum is screened from psi
Figure GDA0002896184860000067
Matched atoms, then from
Figure GDA0002896184860000068
And psi, removing the influence of the atom, obtaining the residual error of the channel, and continuing to select the atom matched with the residual error of the channel in the rest atoms until the termination condition of the method is satisfied. And finally, reconstructing a sparse channel by using the selected atoms and observation vectors thereof.
Let Ψ be an overcomplete dictionary, consisting of atoms Φ. The dictionary Ψ is an L × N dimensional matrix corresponding to N subcarriers in the overcomplete dictionary Ψ, where L is the number of atoms Φ in the overcomplete dictionary Ψ.
Figure GDA0002896184860000069
Is the atom vector, ω, selected from the dictionary Ψ for the first matchjIs a weighting factor. The channel is then mapped by the following method flow
Figure GDA00028961848600000610
Matching:
step 1: initializing to obtain residual signal
Figure GDA00028961848600000611
Step 2: finding the residual signal R in the dictionary ΨHAtom phi with largest inner productlAnd calculating a weighting factor omega thereofj。
Figure GDA00028961848600000612
Figure GDA0002896184860000071
And step 3: updating the weighting factor storage vector Wl＝[Wl-1,ωl]And atom philLocation vector S in dictionaryl＝{Sl-1,sl}。
And 4, step 4: updating residual errors
Figure GDA00028961848600000710
Figure GDA0002896184860000072
Repeating the steps 2-4 until
Figure GDA0002896184860000073
Is sufficiently decomposed. System for controlling a power supply
Figure GDA0002896184860000074
Matched channel frequency domain response vector
Figure GDA0002896184860000075
Can be expressed as:
Figure GDA0002896184860000076
where L' is the maximum number of iterations. Equation (15) since W contains the weighting coefficients for all atoms in the dictionary Ψ, ω is the case and only if l ∈ SlThe value is not 0 or much larger than 0.
3. The method is described in more detail below in connection with method flow diagram 1 of the method.
Assume that the signal transmitting end uses a comb pilot vector s with length Ns. Definition of γ ═ γ0,γ1,…,γNs-1]For the set of sub-carriers carrying comb-shaped pilot vectors s at OFDM frequency band positions, modulating the pilot vectors s into time domain signals x (t) by using sub-carriers of OFDM symbols at gamma set positions andinto channel H. Suppose x (t) is a signal sample x which reaches a receiving end through each propagation path when remotely propagating in a complex multipath time-varying channel environmentl(t) the Doppler distortions are approximately uniform.
Step 1: firstly, the Doppler compression factor is obtained according to the estimation of the p-1 OFDM symbol
Figure GDA0002896184860000077
Construction of a received Signal ypMatrix gamma for pilot subcarrier doppler demodulation in (n)M×Ns＝[Λ-M Λ-M+1 … Λm … ΛM-1 ΛM]，γM×NsElement in matrix ΛmExpressed in a Doppler compensation factor of
Figure GDA0002896184860000078
Orthogonal demodulation matrix of pilot frequency sub-carrier generated by time receiving end, matrix lambdamCan be expressed as:
Figure GDA0002896184860000079
wherein N ismTo make the Doppler compensation factor be lambdamThe time-demodulation carrier continues to sample the number of points, β ═ j2 π Δ fn.
Step 2: using ΛmFor the p-th OFDM symbol ypDemodulation is performed to obtain a compression factor of lambda at the Doppler compensationmTime-pilot subcarrier frequency domain response vector
Figure GDA0002896184860000081
Wherein (·)HRepresenting a conjugate transpose.
At this time, the channel impulse response estimation value
Figure GDA0002896184860000082
Can be calculated to obtain:
Figure GDA0002896184860000083
and step 3: constructing an overcomplete dictionary psi consisting of a plurality of atoms phi, and estimating a channel estimation result by using a matching pursuit sparse channel estimation technology
Figure GDA0002896184860000084
Carrying out matching estimation to obtain a weighted vector Wm,p。
Figure GDA0002896184860000085
To Wm,pAnd (3) carrying out normalization treatment:
Figure GDA0002896184860000086
and 4, step 4: according to formula (20) searching
Figure GDA0002896184860000087
Corresponding when sparsity is maximum
Figure GDA0002896184860000088
Calculating Doppler compression factor
Figure GDA00028961848600000810
Figure GDA0002896184860000089
Using lambdapConstructing a data sub-carrier demodulation matrix for the received signal yp(n) the transmission data of the p-th OFDM symbol can be obtained by DFT demodulation.
The Doppler estimation precision is improved by the method, and the reason is mainly frequency domain resolution precision. The carrier demodulation matrix of the method is generated by utilizing Doppler compression factor calculation, and the Doppler is used for relatively higher resolution of the carrier matrix for demodulating each subcarrier, so that the Doppler compensation effect is better.
Because the frequency domain response of the pilot frequency sub-carrier is extracted by adopting the Discrete Fourier Transform (DFT), the calculation amount of the DFT is reduced, the channel impulse response and the sparsity of the signal under different Doppler compensation conditions are calculated, the compression factor with the largest channel sparsity is selected to estimate the result demodulation signal, and the mobile underwater acoustic communication under the complex multipath time-varying channel environment is realized.
4. Description of simulation experiment
In order to verify the feasibility and reliability of the method, the Matlab software is used for carrying out Monte Carlo simulation on the method. The channels used in the simulation are shown in fig. 2; during channel measurement, the transmitting transducer is located 5m underwater, and the receiving hydrophone is located 10m underwater; the horizontal distance between the transmitting end and the receiving end is 6500m, and the average sea depth is 150 m.
Table 1 gives the main parameters used by the OFDM communication system in simulation. Each frame of the simulation signal contains 5 symbols, the signal has no Doppler change within the duration of one OFDM symbol during simulation, and the relative speed change between adjacent OFDM symbols is not more than 0.3 m/s. When communication is simulated, the Doppler search step length delta lambda is 10-4The maximum doppler search range M is 5.
TABLE 1 OFDM System Primary parameters
Figure GDA0002896184860000091
Fig. 3 shows the channel impulse response at 1500s in the observation history chart of fig. 2, and it can be seen that the channel multipath is dense, the multipath energy is strong, and the maximum multipath time delay reaches 250 ms.
Fig. 4 shows the results of relative motion velocity estimation by using sparsity detection method after compensation of different doppler compression factors in the two methods under the channel condition, wherein the higher-order FFT length of the comparison method is 65536. The relative motion speed of the signal receiving and transmitting end is-0.6 m/s in simulation, and the in-band signal-to-noise ratio is 0 dB. Under the simulation condition, the two methods can realize effective estimation of signal Doppler distortion, but the curve smoothness of the estimation of the channel sparsity by adopting the method is obviously superior to that of a comparison method.
Fig. 5 shows the simulation result of the two methods for the speed measurement error statistics of the signal transceiving end, under this simulation condition, both the two methods can achieve effective estimation of the relative motion speed of the signal transceiving end, and the estimation accuracy is improved along with the improvement of the signal-to-noise ratio. The average speed measurement error of the method is obviously lower than that of the comparison method under the condition of the same signal-to-noise ratio. When the signal-to-noise ratio is higher than 5dB, the average speed measurement error of the method is stabilized at 0.04m/s, and is improved by about 2.5 times compared with the speed measurement error of a comparison method.
5. Description of the sea test
In order to verify the reliability of the method in a complex multipath time-varying channel environment, sea trial verification is performed in 2018. During the test, the signal receiving ship is anchored at sea, and the receiving transducer is hung and placed 10 meters under water. The signal transmitting ship is positioned 1.5km north of the receiving ship, the ship body slowly drifts along with ocean current, and the transmitting transducer is hung 8 meters under water.
Communication system using etaTurboThe sub-carrier adopts QPSK mapping when the code rate is 1/2 Turbo coding, and the OFDM frequency band utilization rate eta is at the momentBEach frame of signal contains 4 OFDM symbols, and other communication system main parameters are as in table 1. According to table 1, the bandwidth B of the communication system can be calculated to be 4kHz, and the communication rate R of each frame of signal can be calculated according to equation (21)
Figure GDA0002896184860000101
FIG. 6 shows the estimation results of the comparison algorithm and the improved algorithm on the relative movement speed between two ships, and the two algorithms have a velocity measurement deviation of about 0.06m/s when measuring the relative movement speed between the two ships.
Fig. 7 and 8 show the constellation diagram obtained after doppler compensation and equalization of the 1 st frame received signal by using the comparison method and the method respectively, and the constellation diagram obtained by using the method has a convergence degree obviously superior to that of the comparison method.
During the test, 9 frames of signals are received in total, and each frame is obtained according to the table 12040bits of signal transmission and 18360bits of total transmission. Fig. 9 shows the error rate of demodulation after compensating for the doppler distortion of the signal by using the doppler results estimated by the two methods, both of which can estimate and compensate for the doppler distortion of the received signal. After the Doppler distortion of the signals is compensated by using the estimation result of the comparison method, the original bit error rate of the communication system is 8.6 percent; after the signal Doppler distortion is compensated by using the estimation result of the method, the original error rate is 4.9%, and the effect of the signal Doppler estimation on the signal compensation of the method is obviously better than that of the comparison method. After the data obtained by demodulation by the method is decoded by the Maximum A Posteriori (MAP) of Turbo coding, 9 frames of received signals have no error code, and the error rate is superior to 5.4 multiplied by 10-5(ii) a After the data obtained by demodulation by using the comparison method is subjected to Turbo coding MAP decoding, the data is influenced by the error code inheritance problem caused by higher original code-free rate of the 6 th frame receiving signal, and the average error probability reaches 3.9 percent.
Although embodiments of the present invention have been shown and described, it will be appreciated by those skilled in the art that changes, modifications, substitutions and alterations can be made in these embodiments without departing from the principles and spirit of the invention, the scope of which is defined in the appended claims and their equivalents.

Claims (1)

1. An improved orthogonal multi-carrier underwater acoustic mobile communication channel estimation and compensation method is characterized by comprising the following steps:
A. a receiving end receives a Doppler distortion signal;
B. calculating a frequency domain response of the received Doppler distortion signal;
C. doppler compression factor estimated through p-1 th OFDM symbol
Figure FDA0002896184850000011
Construction of a received Signal yp(n) matrix samples for doppler demodulation of pilot subcarriers,
the step C comprises the following steps:
C1. the matrix sample is gammaM×Ns＝[Λ-M Λ-M+1…Λm…ΛM-1 ΛM]Wherein Ns is the length of comb-shaped pilot vector s adopted by the signal sending end, and gammaM×NsElement in matrix ΛmExpressed in a Doppler compensation factor of
Figure FDA0002896184850000012
A pilot frequency subcarrier orthogonal demodulation matrix generated by a time receiving end, wherein delta lambda is a search wavelength, and m is the mth search sample in a Doppler search range matrix; definition of γ ═ γ0,γ1,…,γNs-1]For a set of sub-carriers at OFDM band positions carrying a comb pilot vector s, the matrix ΛmCan be expressed as:
Figure FDA0002896184850000013
wherein N ismTo make the Doppler compensation factor be lambdamThe continuous sampling point number of the time demodulation carrier, wherein beta is j2 pi delta fn;
D. matching the frequency domain response in the step B with the matrix sample in the step C to obtain a received signal yp(n) the data subcarrier demodulation matrix;
the step D comprises the following steps:
D1. using ΛmFor the p-th OFDM symbol ypDemodulation is performed to obtain a compression factor of lambda at the Doppler compensationmTime-pilot subcarrier frequency domain response vector
Figure FDA0002896184850000014
Wherein (·)HRepresents a conjugate transpose;
at this time, the channel impulse response estimation value
Figure FDA0002896184850000015
Can be calculated to obtain:
Figure FDA0002896184850000016
D2. constructing an overcomplete dictionary psi consisting of a plurality of atoms phi, and estimating a channel estimation result by using a matching pursuit sparse channel estimation technology
Figure FDA0002896184850000021
Carrying out matching estimation to obtain a weighted vector Wm,p；
Figure FDA0002896184850000022
To Wm,pAnd (3) carrying out normalization treatment:
Figure FDA0002896184850000023
D3. according to formula (5) searching
Figure FDA0002896184850000024
Corresponding when sparsity is maximum
Figure FDA0002896184850000025
Calculating Doppler compression factor
Figure FDA0002896184850000026
Figure FDA0002896184850000027
M is the matrix search range boundary,
Figure FDA0002896184850000028
for the best match within the search range, subscript p is for the p-th OFDM symbol;
using lambdapConstructing a data subcarrier demodulation matrix;
E. d, demodulating the received signal y according to the matched data subcarrier in the step Dp(n) performing DFT demodulation to obtain transmission data of the p-th OFDM symbol, and estimating the Doppler compression factor lambda of the p-th OFDM symbolpAnd C, returning to the step C to construct a matrix sample of the Doppler demodulation of the pilot subcarriers of the next sequence.
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