阅读说明：本技术 基于信道稀疏度检测的正交多载波多普勒估计计算方法 (Orthogonal multi-carrier Doppler estimation calculation method based on channel sparsity detection ) 是由 王巍 钱斌 毕坤 于 2019-10-31 设计创作，主要内容包括：本发明提供了一种基于信道稀疏度检测的正交多载波多普勒估计计算方法包括以下步骤：S1,获取通过水声信道的OFDM信号；S2,对接收信号进行不同多普勒参数的重采样,获取多个多普勒搜索因子补偿后的解调导频向量样本；S3,对解调导频向量各个样本分别进行稀疏信道重建,计算各个样本匹配后的信道时域冲激响应；S4,选择稀疏度最大的样本信道对应的多普勒搜索因子作为最优压缩感知重采样因子,获取多普勒估计值。本发明采用算法的解调导频向量z<Sub>i,γ</Sub>是直接利用多普勒因子补偿后进行FFT产生的,不考虑插值影响,z<Sub>i,γ</Sub>不存在偏差；多普勒估计精度与多普勒搜索的步长与现有技术相比步长越小,本发明中多普勒估计的精度越高。(The invention provides an orthogonal multi-carrier Doppler estimation calculation method based on channel sparsity detection, which comprises the following steps of: s1, acquiring OFDM signals passing through an underwater acoustic channel; s2, resampling different Doppler parameters of the received signal, and obtaining a plurality of demodulation pilot frequency vector samples compensated by Doppler search factors; s3, performing sparse channel reconstruction on each sample of the demodulation pilot frequency vector, and calculating channel time domain impulse response after each sample is matched; and S4, selecting the Doppler search factor corresponding to the sample channel with the maximum sparsity as the optimal compressed sensing resampling factor, and obtaining the Doppler estimated value. Demodulation pilot vector z of the invention using an algorithm i,γ Is generated by FFT after directly utilizing Doppler factor compensation, and does not consider interpolation influence, z i,γ No deviation exists; the step length of Doppler estimation precision and Doppler search is smaller compared with the prior art, and more steps are required in the inventionThe higher the accuracy of the doppler estimation.)

1. A method for calculating orthogonal multi-carrier Doppler estimation based on channel sparsity detection is characterized by comprising the following steps:

s1, acquiring the OFDM signal passing through the underwater acoustic channel at the receiving end;

s2, at the receiving end, using Doppler factor lambda_iResampling the received signal to obtain I Doppler search factor compensated demodulation pilot frequency vectors, wherein I is the maximum Doppler search number;

s3, based on the matching pursuit algorithm of compressed sensing, carrying out sparse channel reconstruction on the I demodulation pilot frequency vectors subjected to parallel resampling, and calculating each matched channel time domain impulse response;

and S4, calculating the time domain impulse response sparsity of each channel, selecting the Doppler search factor corresponding to the channel with the largest sparsity as the optimal compressed sensing resampling factor, and obtaining the Doppler estimated value.

2. The doppler estimation calculation method according to claim 1, wherein in step S2, the doppler factor λ is applied at the receiving end_iResampling the received signal, FFT output of the mth subcarrier:

3. the doppler estimation calculation method according to claim 2, wherein in step S2, z is_i(m) is written under the OFDM signal model over the hydroacoustic channel:

z_i(m) writing the demodulated subcarrier vector z compensated for the ith Doppler search factor after parallel resampling_i＝[z_i(0),z_i(1),…,z_i(N-1)]^T(ii) a Using pilot position vector gamma and demodulation subcarrier vector z_iTo obtain a demodulation pilot vector z_i,γ＝[z_i(γ₁),z_i(γ₂),…,z_i(γ_k)]。

4. Doppler estimation according to claim 1The calculating method is characterized in that, in step S3, a channel sensing model is established in which inter-carrier interference is regarded as noise, and the positions of pilots in OFDM symbols are assumed as follows: gamma-gamma₁,γ₂,…,γ_k]Then, the demodulation pilot vector under the compensation of the ith doppler search factor can be written as:

z_i,γ＝H_i,γd_γ+η

wherein d is_γIs a pilot vector, H_i,γIs a channel;

definition of

5. The Doppler estimate calculation method according to claim 4, wherein in step S3, the pair of channels H_i,γThe reconstruction includes the following steps:

s31, constructing an overcomplete dictionary matrix psi with the size of kxL, wherein the overcomplete dictionary matrix psi is composed of atoms phi;

s32, order

s33, finding the atom with the largest inner product with the residual signal R in the overcomplete set psi, and calculating the weighting factor w_l：

Wherein phi is_jIs the j-th atom vector selected from the dictionary Ψ, w_lIs a weighting factor;

s34, updating the weight factor storage vector W ═ W W_l]And an atom

S35, updating residual error

S36, repeating the steps S33-S35 until

6. The Doppler estimate calculation method according to claim 5, wherein in step S3, the matched channel time domain impulse response is

7. The Doppler estimation calculation method according to claim 6, wherein in step S4, the channel with the largest sparsity is obtained by detecting a channel obtained by matching a channel time-domain impulse response

8. The doppler estimation calculation method according to claim 7, wherein in step S4, said optimal doppler resampling factor is represented as:

wherein, (.)^HRepresenting a conjugate transpose.

9. The Doppler estimation calculation method according to any one of claims 1 to 8, wherein the Doppler estimation calculation method is used for performing orthogonal multi-carrier Doppler estimation calculation in a complex multipath time-varying channel environment of an ice-water mixed water area.

Technical Field

The invention relates to the field of ultra-wideband orthogonal multi-carrier mobile communication, in particular to an orthogonal multi-carrier Doppler estimation calculation method based on channel sparsity detection.

Background

Orthogonal Frequency Division Multiplexing (OFDM) technology has the advantages of high data transmission rate and high spectrum utilization rate, and is receiving more and more attention in the field of underwater acoustic communication. However, OFDM underwater acoustic communication is sensitive to doppler effect, and doppler shift destroys orthogonality between subcarriers, causing interference between subcarriers, and seriously lowering communication performance of an OFDM system. The surface temperature of the ice-water mixing area in the medium and high latitude sea area is lower, and stable positive gradient sound velocity distribution is formed under the water surface, so that the sound waves frequently interact with the sea ice in the propagation process, and energy is continuously reflected, scattered and absorbed by the sea ice, so that the complexity of a multi-path structure is caused; furthermore, drifting of surface ice floes with sea winds or ocean currents causes the channel response to be randomly time-varying. Due to the complex time-varying characteristics of underwater acoustic channels in ice-water mixed areas at medium and high latitudes, the OFDM underwater acoustic communication which is sensitive to Doppler frequency shift is more difficult to apply under the conditions. Therefore, the rapid and accurate estimation and compensation of the Doppler frequency shift are the key for improving the communication performance of the OFDM system in the ice-water mixed area.

A great deal of research is carried out on doppler estimation and compensation by numerous scholars at home and abroad: the Doppler frequency offset estimation is carried out by measuring the time delay of the timing synchronization signal between adjacent frames, which is simple and easy to realize, but the algorithm is not suitable for a fast time-varying channel. Based on the resampling technology combined with the idle wave estimation Doppler algorithm, the Doppler estimation precision is improved, the Doppler difference of each multipath sound beam of a time domain variable sampling signal is adopted, the Doppler compensation under the condition of a sparse underwater sound channel is realized by using a matching method, and although the error rate of the system is reduced, the two methods have the problem of overlarge calculation cost and are not beneficial to real-time communication. The OFDM underwater acoustic mobile communication Doppler estimation method combining the frequency domain variable sampling technology with the channel sparsity detection realizes the Doppler tracking and compensation by utilizing the sparsity of an underwater acoustic channel, but the accuracy of the Doppler estimation is limited by the calculation resolution of a Fast Fourier Transform (FFT) algorithm, the application effect is poor in a complex channel environment of a medium and high latitude ice-water mixed area, and if the high-resolution FFT is adopted for Doppler estimation and compensation, a large amount of storage space is consumed and the calculation complexity is high.

Disclosure of Invention

The invention provides an orthogonal multi-carrier Doppler estimation method based on channel sparsity detection, which aims to solve the problems that underwater acoustic communication is sensitive to Doppler effect, interference between carriers is caused, and the communication performance of an OFDM system is seriously reduced in the prior art.

Specifically, the invention provides a method for calculating orthogonal multi-carrier Doppler estimation based on channel sparsity detection, which is characterized by comprising the following steps:

s1, acquiring the OFDM signal passing through the underwater acoustic channel at the receiving end;

s2, at the receiving end, using Doppler factor lambda_iResampling the received signal to obtain I Doppler search factor compensated demodulation pilot frequency vectors, wherein I is the maximum Doppler search number;

s3, based on the matching pursuit algorithm of compressed sensing, carrying out sparse channel reconstruction on the I demodulation pilot frequency vectors subjected to parallel resampling, and calculating each matched channel time domain impulse response;

and S4, calculating the time domain impulse response sparsity of each channel, selecting the Doppler search factor corresponding to the channel with the largest sparsity as the optimal compressed sensing resampling factor, and obtaining the Doppler estimated value.

Further, in step S2, the doppler factor λ is applied at the receiving end_iResampling the received signal, FFT output of the mth subcarrier:

further, in step S2, z is_i(m) is written under the OFDM signal model over the hydroacoustic channel:

z_i(m) writing the ith Doppler search after parallel resamplingDemodulation subcarrier vector z under Soxhlet factor compensation_i＝[z_i(0)，z_i(1)，…，z_i(N-1)]^T(ii) a Using pilot position vector gamma and demodulation subcarrier vector z_iTo obtain a demodulation pilot vector z_i，γ＝[z_i(γ₁)，z_i(γ₂)，…，z_i(γ_k)]。

Further, in step S3, a channel sensing model is established that considers the inter-carrier interference as noise, and the positions of the pilots in the OFDM symbols are assumed as follows: gamma-gamma₁，γ₂，…，γ_k]Then, the demodulation pilot vector under the compensation of the ith doppler search factor can be written as:

z_i，γ＝H_i，γd_γ+η

wherein d is_γIs a pilot vector, H_i，γIs a channel;

definition of

Compensating for the ith Doppler search factor, setting the pilot frequency position as the channel estimation value under the condition of gamma, and carrying out the matching tracking algorithm based on compressed sensing on the channel H_i，γAnd (6) carrying out reconstruction.

Further, in step S3, the pair of channels H_i，γThe reconstruction includes the following steps:

s31, constructing an overcomplete dictionary matrix psi with the size of kxL, wherein the overcomplete dictionary matrix psi is composed of atoms phi;

s32, order

Let W be an empty set and chi be an empty set; where R is the residual signal, W is the weight factor storage vector, and χ is the atom φ_χlA position vector in the overcomplete set;

s33, finding the atom with the largest inner product with the residual signal R in the overcomplete set psi, and calculating the weighting factor w_l：

Wherein phi is_jIs the j-th atom vector selected from the dictionary Ψ, w_lIs a weighting factor;

s34, updating the weight factor storage vector W ═ W W_l]And the atom phi_χlPosition vector χ ═ χ in overcomplete set_l]；

S35, updating residual error R ═ R-w_lφ_χl；

S36, repeating the steps S33-S35 until

Is sufficiently decomposed.

Further, in step S3, the matched channel time domain impulse response is

The above-mentioned

All weights comprising the overcomplete set Ψ, only the value on the position vector χ is the weighting factor vector W, and the remaining position values are 0.

Further, in step S4, the channel with the largest sparsity is obtained by detecting the channel obtained by the matched channel time domain impulse responseAnd (4) obtaining the sparsity.

Further, in step S4, the optimal doppler resampling factor is expressed as:

wherein, (.)^HRepresenting a conjugate transpose.

Furthermore, the Doppler estimation calculation method is used for performing orthogonal multi-carrier Doppler estimation calculation under the complex multi-path time-varying channel environment of the ice-water mixed water area.

The invention has the beneficial effects that:

under the condition of consistent time domain interpolation and frequency domain interpolation performance, the Doppler estimation precision in the prior art algorithm is limited by the pilot frequency position deviation delta_mThe main reason is that the demodulation subcarrier vector z of the prior art algorithm is obtained by using high-order FFT, and the frequency domain calculation resolution is fixed, resulting in taking out the demodulation pilot vector z after doppler distortion_i，γThe deviation always exists, so that the sparsity detection after channel reconstruction is influenced, the Doppler estimation precision is reduced, and the communication performance of the system is influenced. Demodulation pilot vector z of the invention using an algorithm_i，γIs generated by FFT after directly utilizing Doppler factor compensation, and z is generated without considering the influence of interpolation_i，γThere is no deviation. Compared with the prior art, the accuracy of the Doppler estimation algorithm and the Doppler search step length are equivalent in magnitude, and the smaller the Doppler search step length is, the higher the accuracy of the Doppler estimation algorithm is.

Compared with the prior art, the Doppler estimation algorithm has remarkable reduction in the calculated amount, and when the number of sample points is 2048 points, 4096 points and 8192 points respectively, the calculated amount L of the algorithm in the prior art is reduced_FAre respectively 1.1 × 10⁶、2.3×10⁶And 4.9X 10⁶(ii) a The calculation method L adopted by the invention_TAre respectively 8.1 × 10⁴、1.6×10⁵And 3.2X 10⁵. Compared with the algorithm in the prior art, the invention greatly reduces the calculation amount of resampling compensation of the signal by adopting sinc interpolation check.

Drawings

Fig. 1 is a schematic diagram of a method for calculating an orthogonal multi-carrier doppler estimation based on channel sparsity detection according to the present invention;

FIG. 2 is a schematic diagram of the steps of a method for calculating an orthogonal multi-carrier Doppler estimation based on channel sparsity detection according to the present invention;

FIG. 3 is an observation process diagram of a channel in a medium-north pole and ice-water mixed sea area according to an embodiment of the present invention;

FIG. 4 is a diagram of the channel impulse response in the central arctic region according to an embodiment of the present invention;

FIG. 5 is a graph showing the relationship between channel sparsity and Doppler in a first embodiment of the present invention;

FIG. 6 is a comparison graph of Doppler estimation effect under different SNR conditions according to one embodiment of the present invention;

FIG. 7 is a chart of frame error rates under different SNR conditions according to an embodiment of the present invention;

FIG. 8 is a sound velocity profile of a second marine test area according to an embodiment of the present invention;

FIG. 9 is a channel observation history during a communication period according to a second embodiment of the present invention;

fig. 10 is a channel impulse response diagram of a first frame received signal according to a second embodiment of the present invention;

FIG. 11 is a graph of relative velocity between two vessels according to a second embodiment of the present invention;

FIG. 12 is a bit error rate comparison graph of a communication algorithm according to a second embodiment of the present invention;

fig. 13 is a constellation diagram obtained after demodulating the 1 st frame signal by using the prior art algorithm in the second embodiment of the present invention;

fig. 14 is a constellation diagram of the demodulated signal of the 1 st frame obtained by the algorithm of the present invention in the second embodiment of the present invention.

Detailed Description

The technical solution of the present invention is further described in detail by the following embodiments with reference to fig. 1 to 14.

As shown in fig. 1-2, a method for calculating an orthogonal multi-carrier doppler estimation based on channel sparsity detection includes the following steps:

s1, acquiring the OFDM signal passing through the underwater acoustic channel at the receiving end;

s2, at the receiving end, using Doppler factor lambda_iResampling the received signal to obtain I Doppler search factor compensated demodulation pilot frequency vectors, wherein I is the maximum Doppler search number;

s3, based on the matching pursuit algorithm of compressed sensing, carrying out sparse channel reconstruction on the I demodulation pilot frequency vectors subjected to parallel resampling, and calculating each matched channel time domain impulse response;

and S4, calculating the time domain impulse response sparsity of each channel, selecting the Doppler search factor corresponding to the channel with the largest sparsity as the optimal compressed sensing resampling factor, and obtaining the Doppler estimated value.

Specifically, the core idea of the orthogonal multi-carrier doppler estimation method based on channel sparsity detection is to perform doppler factor matching on pilot subcarriers in received signals after doppler distortion, estimate channel responses of the received signals under different doppler compensation conditions, select a doppler factor corresponding to a channel with the largest sparsity as doppler estimation by using the sparsity of an underwater acoustic channel, and then perform doppler compensation on the signals. The Doppler estimation of the current symbol is used as the initial Doppler of the next symbol, and the Doppler estimation is carried out symbol by symbol.

In step S1, considering that the remote communication is performed under the ice-water mixed shallow water sea area, the multipath incident angles are close, the floating ice drifts with the water flow, the multipath dopplers are approximately equal, and at this time, the underwater acoustic channel time domain impulse response may be represented as:

in which a and τ_pRespectively representing the Doppler factor and the time delay on the p-th path, A_pIs the amplitude of the p-th path, L is the longest multiple, and 6 is the impulse function.

Assume that the transmitted OFDM signal is:

where T represents the symbol duration of an OFDM symbol, g (T) 1, -T_cpT is greater than or equal to T and is a pulse forming signal, N is the number of subcarriers, d [ k ]]For the kth information data, e is a natural constant, and j is an imaginary number.

The transmitted OFDM signal passes through the underwater acoustic channel, and the received signal can be represented as:

where w (t) is white Gaussian noise.

In step S2, the doppler factor λ is applied to the receiving end_iResampling the received signal, FFT output of the mth subcarrier:

by bringing formula (3) into formula (4), it is possible to obtain:

wherein:

H(k，m)＝Q″(m)G″(k，m) (6)

z_i(m) can be written as demodulated subcarrier vector z under compensation of ith Doppler search factor after parallel resampling_i＝[z_i(0)，z_i(1)，…，z_i(N-1)]^T. Using pilot position vector gamma and demodulation subcarrier vector z_iA demodulation pilot vector z can be obtained_i，γ＝[z_i(γ₁)，z_i(γ₂)，…，z_i(γ_k)]。

In step S3, the compressed sensing-based Matching Pursuit (MP) algorithm is particularly suitable for the estimation problem of the underwater acoustic sparse channel because it fully utilizes the sparse characteristic of the underwater acoustic channel. The invention adopts a matching tracking algorithm to reconstruct the channel.

With a channel sensing model that treats inter-carrier interference as noise, equation (5) can be rewritten as:

suppose the positions of the pilots in the OFDM symbol are: gamma-gamma₁，γ₂，…，γ_k]Writing equation (7) as a matrix:

z_i，γ＝H_i，γd_γ+η (8)

wherein z is_i，γFor the demodulation pilot vector under compensation of the ith Doppler search factor, d_γIs a pilot vector, H_i，γIs a channel.

Definition of

And compensating for the ith Doppler search factor, wherein the pilot frequency position is the channel estimation value under the condition of gamma.

For channel H by MP algorithm_i，γPerforming the reconstruction further comprises the steps of:

step S31, constructing an overcomplete dictionary matrix psi with the size of k multiplied by L, wherein the overcomplete dictionary matrix psi is composed of atoms phi;

step S32, initializing: let the residual signal

Let W be an empty set and chi be an empty set; w is the weight factor memory vector, and χ is the atom φ_χlA position vector in the overcomplete set;

step S33, searching the atom with the largest inner product with the residual signal R in the overcomplete set psi, and calculating the weighting factor w_l：

Wherein phi is_jIs the j-th atom vector selected from the dictionary Ψ, w_lIs a weighting factor;

in step S34, the weight-factor storage vector W is updated to [ W W ]_l]And the atom phi_χlPosition vector χ ═ χ in overcomplete set_l]。

Step S35, updating residual R ═ R-w_lφ_χl。

Step S36, repeating steps S33-S35 until

Is sufficiently decomposed, and the raw materials are fully decomposed,

is composed of

The channel time domain impulse response after being matched,

all weights, including the overcomplete set Ψ, are only in placeThe value on the position vector χ is the weighting factor vector W, and the remaining position values are 0.

In step S4, the channel sensing model of equation (7) is considered as well, and when the doppler search at the receiving end compensates for the factor λ_iWhen the number is equal to a, the number is,

assuming that the cyclic prefix is larger than the maximum multipath delay, equations (11) and (12) can be obtained from equation (6):

H(k，m)＝Q″(m)G″(k，m) (6)

at this time, channel estimation can be obtained from equations (11), (12) and (6):

from the expressions (11) to (13), it can be seen that the Doppler search factor λ is_iWhen a, the channel estimation is performed

Equal to the true frequency domain response of the channel H m]. The sparsity of the channel is the largest at this time according to the sparsity characteristics of the underwater acoustic channel. When lambda is_iNot equal to a, channel estimation at this time

The frequency domain response Q (m) and G (k, m) of the channel are multiplied, the time delay superposition equivalent to the time domain impulse response of the channel on the time domain is converted, and the sparsity of the channel is reduced.

Thus, the channel obtained by detecting the matched channel time domain impulse response

The doppler search factor corresponding to the channel with the maximum channel sparsity is selectedAnd obtaining the optimal Doppler resampling factor:

in the formula: (.)^HRepresenting a conjugate transpose.

Compared with the frequency domain algorithm adopted in the prior art, under the condition that the time domain interpolation and the frequency domain interpolation are consistent in performance, the Doppler estimation in the prior art is limited by the pilot frequency position deviation delta_m(ii) a The calculation method of the invention overcomes the influence of the position deviation of the algorithm in the prior art. The main reason is that the demodulation subcarrier vector z in the prior art is obtained by using high-order FFT, and the frequency domain calculation resolution is fixed, so that the demodulation pilot frequency vector z subjected to Doppler distortion is taken out_i，γThe deviation always exists, so that the sparsity detection after channel reconstruction is influenced, the Doppler estimation precision is reduced, and the communication performance of the system is influenced. Demodulation pilot frequency vector z of calculation method adopted by the invention_i，γIs generated by FFT after directly utilizing Doppler factor compensation, and z is generated without considering the influence of interpolation_i，γThere is no deviation. Therefore, the Doppler estimation precision is improved, and the method is more suitable for the complex multipath channel environment of the ice-water mixed water area.