CN109088835A - Underwater sound time-varying channel estimation method based on time multiple management loading - Google Patents
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Abstract
The present invention relates to the underwater sound time-varying channel estimation methods based on time multiple management loading, comprising the following steps: step 1: input channel estimates parameter, comprising: receives symbolic vectorDictionary matrix Φp, maximum number of iterations rmax, terminate thresholding e, noise variance σ2；Step 2: initialization hyper parameter matrix Γ, iteration count r and correlation matrix B；Step 3: hyper parameter γ is solved using expectation-maximization algorithm；Step 4: correlation matrix B is updated；Step 5: stopping criterion for iteration judgement, if r < rmaxAndEnable r=r+1, return step three；If r < rmaxAndThen terminate iteration；If r >=rmax, then iteration is terminated；Step 6: output estimation parameter, including condition of sparse channel estimated matrix, hyper parameter estimate vector and the correlation matrix estimatedThe present invention takes full advantage of the correlation between underwater acoustic channel compared with SBL method in advance, improves the performance of channel estimation, reduces the bit error rate of system, in practical underwater sound ofdm communication system, has practical application value.
Description
Technical Field
The invention relates to an underwater sound sparse time-varying channel estimation method, in particular to an underwater sound sparse time-varying channel estimation method based on time multiple sparse Bayesian learning, and belongs to the field of underwater sound communication.
Background
Ocean observation and ocean resource development and utilization are one of the most concerned problems in many ocean countries, and the research agenda of the underwater acoustic communication technology as an important technical support for ocean development is proposed in recent years. Orthogonal Frequency Division Multiplexing (OFDM) technology has the characteristic of resisting frequency selective fading and high frequency band utilization rate, and is widely applied to underwater high-speed communication systems. The underwater acoustic channel is one of the most complex wireless channels, and causes interference such as multipath propagation, phase fluctuation and the like to an acoustic signal propagated therein, and meanwhile, the underwater acoustic channel is a time-varying and frequency-varying fading channel, and the complex and variable underwater acoustic channel causes distortion to a signal received by a receiving end. In order to demodulate a received signal accurately, the estimation of an underwater acoustic channel is indispensable, and accurate channel estimation is the key point of research on underwater acoustic communication.
The method provides a Time Multiple Sparse Bayesian Learning (TMSBL) underwater sound time-varying channel estimation method based on an underwater sound OFDM communication system, improves the accuracy of a channel estimation algorithm, and reduces the error rate of the system. The method firstly provides a joint channel model for multi-block joint processing, wherein the channel time delays of a plurality of continuous blocks are similar, the channel gains show time correlation, and the time correlation coefficient of the path gain is utilized to evaluate the correlation strength; next, a TMSBL based channel estimator is proposed, which jointly estimates the channel using the channel correlation between consecutive OFDM blocks. Through performance simulation and sea test data processing, the effectiveness of the method is verified under an underwater acoustic time-varying channel, and meanwhile, compared with an SBL method, the method provided by the invention realizes better channel estimation performance and lower bit error rate under a strong time-dependent channel and has better robustness under a weak time-dependent channel.
Disclosure of Invention
Aiming at the prior art, the invention aims to provide an underwater sound time-varying channel estimation method based on time multiple sparse Bayesian learning, which can improve the accuracy of an underwater sound OFDM system channel estimation algorithm.
In order to solve the technical problem, the invention discloses an underwater sound time-varying channel estimation method based on time multiple sparse Bayesian learning, which comprises the following steps of:
the method comprises the following steps: inputting channel estimation parameters, including: receiving a symbol vectorDictionary matrix phipMaximum number of iterations rmaxTermination 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 rmaxAnd isMaking r be r +1, and returning to the step three; if r < rmaxAnd isThe iteration is terminated; if r ≧ rmaxThen the iteration is terminated;
step six: outputting estimated parameters including sparse channel estimation matrix, hyperparametric estimated vector and estimated correlation matrix
The invention relates to an underwater sound time-varying channel estimation method based on time multiple sparse Bayesian learning, which further comprises the following steps:
1. in the second step, the initialized hyper-parameter matrix gamma meets the following conditions: gamma-shaped(0)＝ILThe initialization iteration count r satisfies: r is 0, the initialization correlation matrix B satisfies: b ═ IM(ii) a Wherein ILIs an L × L identity matrix, IMIs an M × M identity matrix.
2. The expectation-maximization algorithm in the third step comprises a step E and a step M, wherein the step E satisfies the following conditions:
wherein the M step satisfies:
3. and step four, updating the correlation matrix B to satisfy the following conditions:
4. sparse channel estimation matrix in step sixThe hyper-parameter estimate vector is gamma.
5. Variance of noise σ2Satisfies the following conditions:
wherein,to receive null carriers.
The invention has the beneficial effects that: compared with the SBL method, the method of the invention fully utilizes the correlation between the underwater acoustic channels in advance, improves the performance of channel estimation, reduces the error rate of the system and has practical application value in the practical underwater acoustic OFDM communication system.
Drawings
FIG. 1 is a graph of SNR-MMSE performance comparison for strong time-dependent channels for the method of the present invention and the LS channel estimation method and the SBL channel estimation method;
FIG. 2 is a graph of the signal-to-noise ratio-error rate performance of the method of the present invention and LS channel estimation method and SBL channel estimation method under strong time correlation channel;
FIG. 3 is a comparison graph of SNR-MMSE performance of the method of the present invention and LS channel estimation method and SBL channel estimation method in weak time correlation channel;
FIG. 4 is a graph of the signal-to-noise ratio-error rate performance of the method of the present invention and the LS channel estimation method and the SBL channel estimation method under weak time correlation channels;
FIG. 5 shows the comparison of effective noise variance when the method of the present invention and the SBL channel estimation method process actual data;
FIG. 6 is a graph comparing error rate performance when the method of the present invention processes actual data with the SBL channel estimation method;
fig. 7 is a time-dependent coefficient calculated when processing actual data.
Detailed Description
The present invention will be described in further detail with reference to the accompanying drawings.
The invention provides a joint channel model for multi-block joint processing, in an underwater sound OFDM communication system, the channel time delays of a plurality of continuous OFDM blocks are similar, and the channel gain presents strong time correlation on the time scale smaller than the channel coherence time. Small delay variation caused by relative motion can be eliminated through Doppler compensation, so that a channel subjected to Doppler compensation can be modeled into a joint channel model, and the channel correlation is utilized to jointly estimate the channel.
Aiming at the characteristic that the underwater acoustic channel has time correlation, the method firstly establishes a joint channel model, and then adopts a TMSBL channel estimation method to jointly estimate the channel by utilizing the channel correlation between continuous OFDM blocks. Compared with a Sparse Bayesian Learning (SBL) channel estimation method, the method makes full use of the time correlation among channels and improves the accuracy of channel estimation.
The following is detailed according to four parts of a basic underwater acoustic OFDM communication system model, a joint channel model, an underwater acoustic sparse time-varying channel estimation method based on TMSBL and simulation performance analysis:
1. basic underwater sound OFDM communication system model
The invention considers a CP-OFDM system, assuming that an OFDM block has K subcarriers in common, wherein K is containeddIndividual data sub-carriers, KpA pilot subcarrier, KnThe null carriers, pilot subcarriers and null subcarriers are uniformly distributed. Then the symbol transmitted at the k-th subcarrier is Xk. Defining an OFDM block periodPeriod is T, cyclic prefix length is Tcp. Will f iscDefined as the center frequency, the k-th subcarrier frequency is
fk＝fc+k/T,k＝-K/2,…,K/2-1. (0.1)
The transmitted OFDM signal can be written as
Where q (t) is a 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 represented as
Wherein A isl，τlRespectively, the amplitude and the time delay of the ith path, and a represents the doppler factor of the path. Assuming that the path gain and doppler factor are constant within an OFDM block, block-to-block; the path delay remains stable over several consecutive OFDM blocks.
OFDM signals received via a channel can be written as
WhereinIs additive noise.
Representing the received signal after Doppler compensation and CP-OFDM demodulation as
Y＝XFh+W (0.6)
Wherein F is a K multiplied by L discrete Fourier transform matrix, X is a K multiplied by K diagonal matrix composed of K transmission symbols, W is additive Gaussian noise, and h is [ h ]1,h2,…,hL]TRepresenting the entire channel.
A system model considering only P pilot subcarriers can be written as
YP＝XPFPh+WP(0.7)
Wherein, YPIs receiving a pilot symbol, XPIs KpK consisting of one transmitted pilotp×KpOrder diagonal matrix, FPIs the matrix of rows in the F matrix where the corresponding pilots are located, WPIs gaussian noise at the pilot location.
2. Joint channel model
An underwater acoustic channel is a typical time-varying sparse channel with a few sparse non-zero paths whose delays are similar and whose gains exhibit strong time correlation on a time scale smaller than the coherence time of the channel. The time variation of the path delay due to the doppler 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. Namely, it is
Wherein h ism(m∈[1,M]) Representing the channel vector of the mth block. For each hmThe positions of the non-zero delays are similar and the corresponding gains have a time dependence.
To describe the correlation of the overall path gain, the time correlation coefficient is expressed as
the coefficient η (m, n) describes the strength of the time correlation between the mth block and the nth block path gain
3. Underwater sound sparse time-varying channel estimation method based on TMSBL
Writing formula (0.7) as
Wherein phiP＝XPFPIs a known dictionary matrix and is used for the purpose of, for the received signal of the mth block, M depends on the coherence time of the channel.
Exploiting time correlation pairs using TMSBL algorithmPerforming joint estimation to eachThe conditional probability density function of the prior parameter is written as
WhereinIs composed ofRow i of (2), γiIs a non-negative hyperparameter, representsLine sparsity. Let gamma be a diagonal matrix, and the element on the diagonal is gamma ═ gamma1,γ2,…,γL]TWhen is γiOn a time scale of → 0,the element in (1) is zero. B isiIs a positive definite matrix, describesCorrelation structure (correlation between multiple blocks).
According toCan be combined withThe conditional probability density function of the prior parameter is written as
The posterior probability density of each column is
Covariance and mean are respectively
μmAndare respectively estimatedAndΓ(r)representing the updated Γ matrix in the r-th iteration. The hyper-parameters may be estimated using an expectation-maximization (EM) algorithm. The E step requires calculation of a posteriori parameters according to equations (3.5) and (3.6), while the M step is represented by an update rule, i.e.
WhereinRepresentsRow i of the matrix.
B matrix describes the correlation structure of all paths, and the calculation method is
where η is a positive scalar quantity, this regularization form ensures the estimationIs positive, the robustness of the estimation algorithm can be increased.
The method comprises the following specific steps:
(1) inputting: receiving a symbol vectorDictionary matrix phipMaximum number of iterations rmaxTermination threshold e, noise variance σ2。
(2) Initialization: hyper-parametric matrix gamma(0)＝ILThe iteration count r is 0, B is IM。
(3) E, step E:
(4) and M:
(5) updating the B matrix:
(6) and (3) iteration termination judgment: if r < rmaxReturning to step (3) when r is r + 1; or ifThe iteration is terminated.
(7) And (3) outputting: estimated sparse channel vectorEstimated hyperparametric vector gamma, estimatedAnd (4) matrix.
Variance of noise σ2The following are determined by the idler:
whereinrepresenting a received null carrier symbol, and η 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, an underwater sound OFDM system is built, and the underwater sound OFDM system comprises 256 subcarriers, wherein the data subcarriers Kd200 pilot subcarriers Kp32, no carrier wave Kn24, bandwidth B1.5 kHz, center frequency fc2.25kHz, sample rate fs12kHz, signal length T171 ms, cyclic prefix TcpOne frame signal contains 4 OFDM blocks for 10 ms. The underwater sound sparse time-varying channel model adopts 10 randomly generated paths, the delay interval follows exponential distribution with the average value of 0.5ms, the Doppler factor of each OFDM block is assumed to be randomly changed, and the range is [ -v ]p/c,vp/c]Wherein the relative velocity vp1.5m/s and the speed of sound in water c 1500m/s, the path amplitude follows a rayleigh distribution with path delay. QPSK modulation is adopted, and 1/2 non-binary LDPC coding is adopted.
In the simulation, an LS channel estimation method, an SBL channel estimation method and the channel estimation method of the invention are compared.
Firstly, verifying the performance comparison of three channel estimation algorithms under a strong time correlation channel, and setting the time correlation coefficients of different blocks between 0.7 and 0.99.
FIG. 1 is a comparison graph of SNR-MMSE performance of the method of the present invention and LS channel estimation method and SBL channel estimation method under strong time correlation channel. From simulations, it can be seen that the Mean Square Error (MSE) performance of the TMSBL channel estimation method taking into account the time correlation is the best, 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 graph of SNR-BER performance of the method of the present invention, LS channel estimation method and SBL channel estimation method under strong time correlation 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 mode. This shows that under strong time correlation channel, the performance of TMSBL channel estimation algorithm is better than that of SBL algorithm, and the advantage of joint estimation is reflected.
And then verifying the performance comparison of the three channel estimation algorithms under the weak time correlation channel, and setting the time correlation coefficient between 0.1 and 0.3.
Fig. 3 and 4 are a signal-to-noise ratio-mean-square error performance comparison graph and a signal-to-noise ratio-bit error rate performance comparison graph of the method, the LS channel estimation method and the SBL channel estimation method under a weak time correlation channel. From the simulation, it can be seen that under the weak time correlation 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 weak time correlation channels, the advantages of the TMSBL algorithm cannot be exploited but still better robustness is maintained.
(2) Processing sea test data:
the algorithm was further verified using experimental data obtained 2014 in south China sea. The transmitting transducers were spaced about 5km apart, with a transmitting transducer depth of 27m and a receiving transducer depth of 30 m.
One OFDM symbol contains K681 subcarriers, where the data subcarrier Kd571 pilot subcarriers Kp86, no carrier wave Kn24, bandwidth B4 kHz, center frequency fc8kHz, sample rate fs48kHz, signal length T170 ms, cyclic prefix TcpOne frame signal contains 8 OFDM blocks for 20 ms. QPSK modulation and convolutional code coding are adopted. 12 frames of OFDM symbols are transmitted consecutively with a time interval of 2s between each frame. The LFM signal is set before each frame of signal for synchronization.
The performance of the channel estimation is evaluated by introducing the effective noise variance, which is defined as follows
Wherein,is obtained by fourier transformation of the estimated sparse channel. This value includes the error of the channel estimate, the ambient noise and the residual doppler shift.
FIG. 5 shows the comparison of the effective noise variance between the method of the present invention and the SBL channel estimation method. As can be seen, the effective noise variance of the TMSBL channel estimation method is lower than that of the SBL algorithm when processing real data.
Fig. 6 is a graph comparing BER performance of the method of the present invention and SBL channel estimation method. It can be seen that the error rate of the TMSBL algorithm is still lower than that of the SBL algorithm when processing actual data, and especially in the signals of frames 2, 11 and 12, the advantages of the TMSBL channel estimation algorithm are more obvious, and in the signals of frames 6 and 9, the performance of the TMSBL algorithm is similar to that of the SBL algorithm.
fig. 7 is a diagram of calculated time correlation coefficients, which are calculated for 8 blocks in a frame signal, and calculated for η (1, m), m ∈ 1,4 and η (5, n), n ∈ 5,8, it can be seen that in the 2 nd, 11 th and 12 th frame signals, the time correlation coefficients are mostly greater than 0.5, so that they can be considered as strong time correlation channels, and the time correlation of the channels can be fully utilized, while the time correlation coefficients of the 6 th and 9 th frame signals fall rapidly between the blocks, and are considered as weak time correlation channels, which is also consistent with the result of fig. 6, verifies the advantages of the TMSBL algorithm under the strong time correlation channels, and has better robustness under the weak time correlation channels.
The specific implementation mode of the invention also comprises the following steps:
(1) inputting channel estimation parameters, including: receiving a symbol vector, a dictionary matrix, a maximum iteration number, a termination threshold and a noise variance.
(2) Initializing, including: initializing a hyper-parameter matrix, initializing iteration count and initializing a correlation matrix.
(3) And solving the hyper-parameters by adopting an EM algorithm.
(4) The correlation matrix is updated.
(5) Judging iteration termination conditions, and if the conditions are met, terminating the iteration; and if not, returning to the step (3).
(6) And outputting estimation parameters comprising a sparse channel vector estimation set, a hyperparameter estimation set and an estimated correlation matrix.
The method utilizes the time correlation of the underwater acoustic channel to model the channel into a combined channel model, adopts a channel estimator based on TMSBL to carry out multi-block combined processing on the signal, adopts an Expectation Maximization (EM) algorithm to solve the hyperparameter, realizes the estimation of the underwater acoustic time-varying sparse channel, improves the accuracy of channel estimation and reduces the 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 phipMaximum number of iterations rmaxTermination 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 rmaxAnd isMaking r be r +1, and returning to the step three; if r < rmaxAnd isThe iteration is terminated; if r ≧ rmaxThen 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)＝ILThe initialization iteration count r satisfies: r is 0, the initialization correlation matrix B satisfies: b ═ IM(ii) a Wherein ILIs an L × L identity matrix, IMIs 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.
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