CN109088835A - Underwater sound time-varying channel estimation method based on time multiple management loading - Google Patents

Abstract

The present invention relates to an underwater acoustic time-varying channel estimation method based on time multiple sparse Bayesian learning, comprising the following steps: Step 1: Input channel estimation parameters, including: receiving symbol vectors The dictionary matrix Φ _p , the maximum number of iterations r _max , the termination threshold e, and the noise variance σ ² ; Step 2: Initialize the hyperparameter matrix Γ, the iteration count r and the correlation matrix B; Step 3: Use the expectation maximization algorithm to optimize the hyperparameter γ Solve; step 4: update the correlation matrix B; step 5: judge the iteration termination condition, if r<r _max and Set r=r+1, return to step 3; if r<r _max and Then terminate the iteration; if r≥r _max , then terminate the iteration; Step 6: Output estimated parameters, including sparse channel estimation matrix, hyperparameter estimation vector and estimated correlation matrix Compared with the SBL method, the present invention fully utilizes the correlation between underwater acoustic channels in advance, improves the performance of channel estimation, reduces the bit error rate of the system, and has practical application value in the actual underwater acoustic OFDM communication system.

Description

Time-varying Channel Estimation Method for Underwater Acoustics Based on Time Multiple Sparse Bayesian Learning

technical field

The invention relates to an underwater acoustic sparse time-varying channel estimation method, in particular to an underwater acoustic sparse time-varying channel estimation method based on time multiple sparse Bayesian learning, and the invention belongs to the field of underwater acoustic communication.

Background technique

Ocean observation and the development and utilization of marine resources are one of the most concerned issues of many oceanic countries. As an important technical support for ocean development, underwater acoustic communication technology has been put on the research agenda in recent years. Orthogonal Frequency Division Multiplexing (OFDM) technology has the characteristics of anti-frequency selective fading and high frequency band utilization, and is widely used in underwater high-speed communication systems. The underwater acoustic channel is one of the most complicated wireless channels, which will cause interference such as multipath propagation and phase fluctuations to the acoustic signals propagating in it. At the same time, the underwater acoustic channel is a time-varying and frequency-varying fading channel. The acoustic channel distorts the signal received at the receiver. In order to accurately demodulate the received signal, underwater acoustic channel estimation is essential, and accurate channel estimation is the focus of underwater acoustic communication research.

The method of the invention proposes a time-multiple sparse Bayesian learning (TMSBL) underwater acoustic time-varying channel estimation method based on the underwater acoustic OFDM communication system, which improves the accuracy of the channel estimation algorithm and reduces the bit error rate of the system. The method of the present invention first proposes a joint channel model for multi-block joint processing, wherein the channel delays of several consecutive blocks are similar and the channel gain shows time correlation, and the time correlation coefficient of the path gain is used to evaluate the correlation strength; then A channel estimator based on TMSBL is proposed, which uses the channel correlation between consecutive OFDM blocks to jointly estimate the channel. Through performance simulation and sea test data processing, the effectiveness of the method of the present invention in underwater acoustic time-varying channels is verified, and at the same time, it is verified that the method of the present invention achieves better channel estimation in strong time-correlated channels compared with the SBL method Performance and lower bit error rate, better robustness in weak time-correlated channels.

Contents of the invention

In view of the above prior art, the technical problem to be solved by the present invention is to provide an underwater acoustic time-varying channel estimation method based on time multiple sparse Bayesian learning that can improve the accuracy of the underwater acoustic OFDM system channel estimation algorithm.

In order to solve the above-mentioned technical problems, a kind of underwater acoustic time-varying channel estimation method based on time multiple sparse Bayesian learning of the present invention comprises the following steps:

Step 1: Input channel estimation parameters, including: receive symbol vector Dictionary matrix Φ _p , maximum number of iterations r _max , termination threshold e, noise variance σ ² ;

Step 2: Initialize hyperparameter matrix Γ, iteration count r and correlation matrix B;

Step 3: Use the expectation maximization algorithm to solve the hyperparameter γ;

Step 4: update the correlation matrix B;

Step 5: Judgment of the iteration termination condition, if r<r _max and Set r=r+1, return to step 3; if r<r _max and Then terminate the iteration; if r≥r _max , then terminate the iteration;

Step 6: Output estimated parameters, including sparse channel estimation matrix, hyperparameter estimation vector and estimated correlation matrix

A kind of time-varying underwater acoustic channel estimation method based on multiple sparse Bayesian learning of the present invention also includes:

1. In step 2, the initialization hyperparameter matrix Γ satisfies: Γ ⁽⁰⁾ = I _L , the initialization iteration count r satisfies: r = 0, and the initialization correlation matrix B satisfies: B = I _M ; where _IL is the unit of L×L Matrix, I _M is the identity matrix of M×M.

2. The expectation maximization algorithm in step 3 includes E step and M step, where E step satisfies:

Among them, the M step satisfies:

3. Update the correlation matrix B in step 4 to satisfy:

4. Sparse channel estimation matrix in step 6 The vector of hyperparameter estimates is γ.

5. The noise variance σ ² satisfies:

in, To receive empty carrier.

Beneficial effects of the present invention: Compared with the SBL method, the present invention has the advantages of fully utilizing the correlation between underwater acoustic channels in advance, improving the performance of channel estimation, reducing the bit error rate of the system, and in actual underwater acoustic In OFDM communication system, it has practical application value.

Description of drawings

Fig. 1 is the signal-to-noise ratio-mean square error performance comparison chart of the method of the present invention and the LS channel estimation method and the SBL channel estimation method under the strongly time-correlated channel;

Fig. 2 is the signal-to-noise ratio-bit error rate performance comparison chart of the method of the present invention and the LS channel estimation method and the SBL channel estimation method under the strongly time-correlated channel;

Fig. 3 is the signal-to-noise ratio-mean square error performance comparison chart of the method of the present invention and the LS channel estimation method and the SBL channel estimation method under the weak time correlation channel;

Fig. 4 is the SNR-BER performance comparison chart of the method of the present invention and the LS channel estimation method and the SBL channel estimation method under the weak time correlation channel;

Fig. 5 is the comparison result of the effective noise variance when the method of the present invention and the SBL channel estimation method process actual data;

Fig. 6 is a comparison chart of bit error rate performance when the method of the present invention and the SBL channel estimation method process actual data;

Figure 7 shows the time correlation coefficients calculated when processing actual data.

Detailed ways

The present invention will be further described in detail below in conjunction with the accompanying drawings.

The present invention proposes a joint channel model for multi-block joint processing. In an underwater acoustic OFDM communication system, the channel delays of several consecutive OFDM blocks are similar, and the channel gain presents a strong time correlation on a time scale smaller than the channel coherence time . After Doppler compensation, small time delay changes caused by relative motion can be eliminated, so the Doppler compensated channel can be modeled as a joint channel model, and the channel correlation can be used to jointly estimate the channel.

The method of the invention aims at the characteristics of time correlation of the underwater acoustic channel, first establishes a joint channel model, and then adopts the TMSBL channel estimation method to jointly estimate the channel by using the channel correlation between continuous OFDM blocks. Compared with Sparse Bayesian Learning (SBL) channel estimation method, this method makes full use of the temporal correlation between channels and improves the accuracy of channel estimation.

The following is a detailed description of four parts: the basic underwater acoustic OFDM communication system model, the joint channel model, the TMSBL-based underwater acoustic sparse time-varying channel estimation method, and the simulation performance analysis:

1. Basic underwater acoustic OFDM communication system model

The invention considers a CP-OFDM system, assuming that an OFDM block has K subcarriers in total, including K _d data subcarriers, K _p pilot subcarriers, K _n empty carriers, and the pilot subcarriers and empty carriers are evenly distributed. Then the symbol transmitted on the kth subcarrier is X _k . Define an OFDM block period as T and cyclic prefix length as T _cp . Define f _c as the center frequency, then the frequency of the kth subcarrier is

f _k ＝f _c +k/T, k＝-K/2,...,K/2-1. (0.1)

The transmitted OFDM signal can be written as

where q(t) is the pulse shaping filter, written as

For the underwater acoustic sparse time-varying channel model, assuming there are L paths, the channel impulse response can be expressed as

Among them, A _l and τ _l represent the amplitude and time delay of the l-th path respectively, and a represents the Doppler factor of the path. It is assumed that the path gain and Doppler factor are constant within an OFDM block, and are different between blocks; the path delay remains stable within several consecutive OFDM blocks.

The OFDM signal received through the channel can be written as

in is additive noise.

The received signal after Doppler compensation and CP-OFDM demodulation is expressed as

Y=XFh+W (0.6)

Where F is a K×L discrete Fourier transform matrix, X is a K×K diagonal matrix composed of K transmitted symbols, W is additive Gaussian noise, h=[h ₁ ,h ₂ ,…,h _L ] ^T stands for all channels.

The system model considering only P pilot subcarriers can be written as

Y _P ＝X _P F _P h+W _P (0.7)

Among them, Y _P is the receiving pilot symbol, X _P is the K _p × K _p order diagonal matrix composed of K _p sending pilots, F _P is the matrix of the row corresponding to the pilot in the F matrix, and W _P is the pilot Gaussian noise at position.

2. Joint channel model

Underwater acoustic channels are typical time-varying sparse channels with a small number of sparse non-zero paths with similar delays and gains that exhibit strong time correlation on time scales smaller than the channel coherence time. The time variation of path delay caused by Doppler frequency shift can be eliminated by Doppler compensation. The Doppler compensated channel can thus be modeled as a joint channel model of M consecutive OFDM blocks. which is

where h ^m (m∈[1,M]) represents the channel vector of the mth block. For each h ^m , the locations of the non-zero delays are similar and the corresponding gains are time-dependent.

To describe the correlation of the overall path gain, the temporal correlation coefficient is expressed as

The coefficient η(m,n) describes the temporal correlation strength between the path gains of the mth block and the nth block

3. Underwater acoustic sparse time-varying channel estimation method based on TMSBL

Write formula (0.7) as

Wherein Φ _P = X _P F _P is a known dictionary matrix, is the received signal of the mth block, and M depends on the coherence time of the channel.

Using the TMSBL algorithm to utilize the time correlation pair A joint estimate is performed, combining each The conditional probability density function of the prior parameters is written as

in for The i-th line of , γ _i is a non-negative hyperparameter, representing row sparsity. Let Γ be a diagonal matrix, and the elements on the diagonal are γ=[γ ₁ ,γ ₂ ,…,γ _L ] ^T , when γ _i →0, The elements in are zero. B _i is a positive definite matrix that describes Correlation structure (correlations between multiple blocks).

according to Can be The conditional probability density function of the prior parameters is written as

The posterior probability density for each column is

The covariance and mean are respectively

μ ^m and respectively estimated and Γ ^(r) represents the updated Γ matrix in the r-th iteration. Hyperparameters can be estimated using the Expectation-Maximization (EM) algorithm. The E step needs to calculate the posterior parameters according to formula (3.5) and formula (3.6), while the M step is represented by the update rule, namely

in represent The ith row of the matrix.

The B matrix describes the correlation structure of all paths and is calculated as

where η is a positive scalar, this form of regularization ensures that the estimated is positive definite, which can increase the robustness of the estimation algorithm.

Specific steps are as follows:

(1) Input: receive symbol vector Dictionary matrix Φ _p , maximum number of iterations r _max , termination threshold e, noise variance σ ² .

(2) Initialization: hyperparameter matrix Γ ⁽⁰⁾ = I _L , iteration count r = 0, B = I _M .

(3) Step E:

(4) Step M:

(5) Update the B matrix:

(6) Iteration termination judgment: if r<r _max , let r=r+1, return to step (3); or if then terminate the iteration.

(7) Output: estimated sparse channel vector The estimated hyperparameter vector γ, the estimated matrix.

The noise variance ^σ2 is found with the empty carrier:

in Indicates reception of empty carrier symbols. And n is set to 2 to ensure that matrix B is positive.

4. Simulation performance analysis

(1) MATLAB simulation:

In order to verify the performance of the channel estimation method of the present invention, an underwater acoustic OFDM system is built, including K=256 subcarriers, wherein data subcarriers K _d =200, pilot subcarriers K _p =32, and empty carriers K _n =24 , bandwidth B=1.5kHz, center frequency _fc =2.25kHz, sampling rate _fs =12kHz, signal length T=171ms, cyclic prefix _Tcp =10ms, one frame signal contains 4 OFDM blocks. The underwater acoustic sparse time-varying channel model uses 10 randomly generated paths, and the delay interval obeys an exponential distribution with a mean value of 0.5ms. It is assumed that the Doppler factor of each OFDM block changes randomly, and the range is [-v _p /c,v _p /c], where the relative velocity v _p =1.5m/s and the speed of sound in water c=1500m/s, the path amplitude follows the Rayleigh distribution with the path delay. Using QPSK modulation, 1/2 non-binary LDPC encoding.

In the simulation, the LS channel estimation method, the SBL channel estimation method and the channel estimation method of the present invention are compared.

First, verify the performance comparison of the three channel estimation algorithms under the strong time correlation channel, and set the time correlation coefficients of different blocks between 0.7 and 0.99.

FIG. 1 is a comparison chart of SNR-mean square error performance between the method of the present invention and the LS channel estimation method and the SBL channel estimation method under a strongly time-correlated channel. It can be seen from the simulation that the mean square error (MSE) performance of the TMSBL channel estimation method considering the time correlation is the best, which is about 2dB better than that of the SBL channel estimation method, while the MSE performance of the LS channel estimation method is the worst.

Fig. 2 is a comparison chart of SNR-BER performance between the method of the present invention and the LS channel estimation method and the SBL channel estimation method under a strongly time-correlated channel. It can be seen that the bit error rate (BER) performance of the LS channel estimation method is the worst, the BER performance of the SBL channel estimation method is worse than that of the TMSBL channel estimation method, and the performance of the TMSBL channel estimation algorithm is closer to the CSI method. This shows that under strong time-correlated channels, the performance of TMSBL channel estimation algorithm is better than that of SBL algorithm, and the advantages of joint estimation are reflected.

Then verify the performance comparison of the three channel estimation algorithms under the weak time correlation channel, and set the time correlation coefficient between 0.1 and 0.3.

Fig. 3 and Fig. 4 are SNR-mean square error performance comparison diagrams and SNR-BER performance comparison diagrams of the method of the present invention, the LS channel estimation method and the SBL channel estimation method under a weakly time-correlated channel. It can be seen from the simulation that under the weak time-correlated channel, the estimation performance of the LS channel estimation method is still the worst, and the performance of the TMSBL channel estimation algorithm is very close to that of the SBL algorithm. This shows that in the weak time-correlated channel, the advantages of TMSBL algorithm can not be reflected, but still maintain good robustness.

(2) Processing sea trial data:

The algorithm is further verified by using the experimental data obtained in the South China Sea in 2014. The sending and receiving transducers are about 5km apart, the depth of the transmitting transducer is 27m, and the depth of the receiving transducer is 30m.

One OFDM symbol contains K=681 subcarriers, wherein data subcarriers K _d =571, pilot subcarriers K _p =86, empty carriers K _n =24, bandwidth B=4kHz, center frequency _fc =8kHz, Sampling rate f _s =48kHz, signal length T=170ms, cyclic prefix _Tcp =20ms, one frame signal contains 8 OFDM blocks. It adopts QPSK modulation and convolution code encoding. Continuously send 12 frames of OFDM symbols, and the time interval between each frame is 2s. Set the LFM signal before each frame signal for synchronization.

The effective noise variance is introduced to evaluate the performance of channel estimation, which is defined as follows

in, is obtained by the Fourier transform of the estimated sparse channel. This value includes channel estimation error, ambient noise and residual Doppler shift.

Fig. 5 is a comparison result of effective noise variance between the method of the present invention and the SBL channel estimation method. It can be seen from the figure that when dealing with actual data, the effective noise variance of the TMSBL channel estimation method is lower than that of the SBL algorithm.

FIG. 6 is a comparison chart of BER performance between the method of the present invention and the SBL channel estimation method. It can be seen that the bit error rate of the TMSBL algorithm is still lower than that of the SBL algorithm when processing actual data, especially in the 2nd, 11th, and 12th frame signals, the advantages of the TMSBL channel estimation algorithm are more obvious, while in the 6th and 9th frame signals In the frame signal, the performance of the TMSBL algorithm is similar to that of the SBL algorithm.

Figure 7 shows the calculated time correlation coefficients, respectively calculate 8 blocks in a frame signal, calculate η(1,m), m∈[1,4] and η(5,n), n∈[5,8 ], it can be seen that in the 2nd, 11th, and 12th frame signals, the time correlation coefficients are greater than 0.5 most of the time, so they can be considered as strong time-correlated channels, and the time correlation of the channel can be fully utilized; while the 6th frame, The time correlation coefficient of the 9th frame signal drops rapidly between blocks, which is considered as a weakly time-correlated channel. This is also consistent with the results in Figure 6, which verifies the advantages of the TMSBL algorithm in strong time-correlated channels, and has better robustness in weak time-correlated channels.

The specific embodiment of the present invention also includes the following steps:

(1) Input channel estimation parameters, including: received symbol vector, dictionary matrix, maximum number of iterations, termination threshold, and noise variance.

(2) Initialization, including: hyperparameter matrix initialization, iteration count initialization, correlation matrix initialization.

(3) Use EM algorithm to solve hyperparameters.

(4) Update the correlation matrix.

(5) Judgment of the iteration termination condition, if the condition is met, the iteration is terminated; if not, return to step (3).

(6) Output estimated parameters, including sparse channel vector estimation set, hyperparameter estimation set and estimated correlation matrix.

The present invention uses the time correlation of the underwater acoustic channel to model the channel as a joint channel model, uses a channel estimator based on TMSBL to perform multi-block joint processing on the signal, and uses the expectation maximization (EM) algorithm to solve the hyperparameters, realizing The estimation of underwater acoustic time-varying sparse channel improves the accuracy of channel estimation and reduces the bit error rate of the system.

Claims (6)

1. An underwater sound time-varying channel estimation method based on time multiple sparse Bayesian learning is characterized by comprising the following steps:

the method comprises the following steps: inputting channel estimation parameters, including: receiving a symbol vectorDictionary matrix phi_pMaximum number of iterations r_maxTermination threshold e, noise variance σ²；

Step two: initializing a hyper-parameter matrix gamma, an iteration count r and a correlation matrix B;

step three: solving the hyperparameter gamma by adopting an expectation maximization algorithm;

step four: updating a correlation matrix B;

step five: judging iteration termination condition, if r is less than r_maxAnd isMaking r be r +1, and returning to the step three; if r < r_maxAnd isThe iteration is terminated; if r ≧ r_maxThen the iteration is terminated;

step six: outputting estimated parameters including sparse channel estimation matrix, hyperparametric estimated vector and estimated correlation matrix

2. The underwater acoustic time-varying channel estimation method based on time-multiplexed sparse Bayesian learning as recited in claim 1, wherein: in the second step, the initialized hyper-parameter matrix gamma meets the following conditions: gamma-shaped⁽⁰⁾＝I_LThe initialization iteration count r satisfies: r is 0, the initialization correlation matrix B satisfies: b ═ I_M(ii) a Wherein I_LIs an L × L identity matrix, I_MIs an M × M identity matrix.

3. The underwater acoustic time-varying channel estimation method based on time-multiplexed sparse Bayesian learning as recited in claim 1, wherein: the expectation-maximization algorithm in step three comprises a step E and a step M,

wherein the step E satisfies:

wherein the M step satisfies:

4. the underwater acoustic time-varying channel estimation method based on time-multiplexed sparse Bayesian learning as recited in claim 1, wherein: in step four, the updated correlation matrix B satisfies:

5. the underwater acoustic time-varying channel estimation method based on time-multiplexed sparse Bayesian learning as recited in claim 1, wherein: the sparse channel estimation matrix in the sixth stepThe hyper-parameter estimate vector is gamma.

6. The underwater acoustic time-varying channel estimation method based on time-multiplexed sparse Bayesian learning as recited in claim 1, wherein: the noise variance σ²Satisfies the following conditions:

wherein,to receive null carriers.