CN109818888B - Group sparse underwater acoustic channel estimation method in pulse interference environment - Google Patents

Abstract

The invention provides a group sparse underwater acoustic channel estimation method in a pulse interference environment. (1) Defining a new cost function; (2) calculating prior error and gain; (3) updating estimator tap coefficients and regularization parameters representing sparsity; (4) and continuously iterating until the error converges. The invention has the advantages that: (1) the p-norm of the estimation error is used as a cost function, so that the influence of pulse interference is effectively inhibited, and the robustness is strong; (2) the mixed norm is used as sparse constraint, and the group sparse characteristic of the channel is fully utilized; (3) the regularization parameters are updated in a self-adaptive mode, the size of applied constraint is adjusted continuously according to the change of the sparsity degree of the underwater acoustic channel, and the estimation performance is better.

Description

Group sparse underwater acoustic channel estimation method in pulse interference environment

Technical Field

The invention relates to an underwater acoustic signal processing method, in particular to a group sparse underwater acoustic channel estimation method in a pulse interference environment based on an RLP algorithm.

Background

The underwater acoustic signals are severely damaged in the transmission process, and accurate estimation of the channel is necessary in order to accurately recover the transmitted signals at the receiving end. Many underwater acoustic channels exhibit significant group sparsity, which means that the channels are distributed in groups by a small number of non-zero elements in the time domain. In such channels, a channel estimation algorithm based on general sparsity does not have good estimation performance because the group sparsity characteristics are not fully utilized.

Noise generated by organisms, ice layer cracking and the like in an underwater acoustic channel has a lot of impulses in a time domain, a probability density function has a heavy tail characteristic and does not obey Gaussian distribution any more, and the noise is generally described by using a symmetrical stable alpha distribution (S alpha S) model. In gaussian noise, the performance is optimal by using the square of the channel estimation error as a cost function, but the performance is seriously reduced under an impulse interference environment. In order to obtain a more robust channel estimation method, the method under gaussian noise must be improved.

Disclosure of Invention

The invention aims to provide a group sparse underwater acoustic channel estimation method in a pulse interference environment, which has strong robustness and better estimation performance.

The purpose of the invention is realized as follows:

(1) defining a new cost function;

(2) calculating prior error and gain;

(3) updating estimator tap coefficients and regularization parameters representing sparsity;

(4) and continuously iterating until the error converges.

The present invention may further comprise:

1. the new cost function is defined by combining a mixed norm characterizing the sparse characteristics of the channel and an RLP algorithm resisting the influence of impulse interference.

2. The defining of the new cost function specifically includes:

the cost function is defined as:

wherein: n is the estimation time, lambda is the forgetting factor,

estimate error for time i, y_iFor the signal to be expected at time i,

for channel estimates at time n-1, superscript^HDenotes the Hermite transposition, u_iInput vector, γ, for time i_nFor the regularization parameter, f (e)_i) In order to be a function of the loss,

a convex function for representing the sparsity of the channel;

loss function f (e) of RLP algorithm_i) Is composed of

Wherein: upper label^*The expression is the conjugate of complex number, p is more than or equal to 1, xi and delta are threshold values, and the value is related to the signal-to-noise ratio;

for channels with group sparsity, choose/_1,0And l_2,0Mixed norm sparsity constraints, i.e.

Or

Wherein G is the number of groups, beta is a parameter characterizing the size and range of the sparse constraint,

to comprise

G th_iA vector of group taps.

The invention provides a group sparse underwater acoustic channel estimation method combining RLP and group sparse norm, aiming at the underwater acoustic channel estimation problem under the pulse interference environment. RLP defines different costs in different error ranges, so that the RLP has a good inhibiting effect on large errors generated by pulse interference and strong robustness; and mixed norm constraint is added, so that the invention can fully utilize the sparse natural characteristic of the underwater acoustic channel group to obtain lower steady-state estimation error.

The invention has the advantages that: (1) the p-norm of the estimation error is used as a cost function, so that the influence of pulse interference is effectively inhibited, and the robustness is strong; (2) the mixed norm is used as sparse constraint, and the group sparse characteristic of the channel is fully utilized; (3) the regularization parameters are updated in a self-adaptive mode, the size of applied constraint is adjusted continuously according to the change of the sparsity degree of the underwater acoustic channel, and the estimation performance is better.

Drawings

FIG. 1 is a flow chart of the present invention;

FIG. 2 is a graph comparing the RLP algorithm with the recursive least squares algorithm (RLS);

FIG. 3 is a graph of RLP mean square error under different sparsity constraints;

fig. 4 is a table showing the updating process of the tap coefficient at each iteration of the present invention.

Detailed Description

The invention mainly comprises the following steps with reference to fig. 1:

(1) defining a system cost function by combining the channel sparse characteristic and the influence of pulse interference;

(2) calculating prior error and gain;

(3) updating estimator tap coefficients and regularization parameters representing sparsity;

(4) and continuously iterating until the error converges.

The group sparse channel estimation method in the present invention is described in detail below by way of example.

1、l_1,0-RLP、l_2,0Implementation of RLP

In order to overcome the influence of impulse interference and utilize the sparse characteristic of the channel, a cost function is defined as follows:

wherein n is the estimation time, lambda is the forgetting factor,

estimate error for time i, y_iFor the signal to be expected at time i,

for channel estimates at time n-1, superscript^HDenotes the Hermite transposition, u_iInput vector, γ, for time i_nFor the regularization parameter, f (e)_i) In order to be a function of the loss,

is a convex function characterizing the sparsity of the channel.

For the RLP algorithm, its penalty function f (e)_i) Is composed of

Wherein, the upper label^*The expression is the conjugate of complex number, p is more than or equal to 1, xi and delta are threshold values, and the value is related to the signal-to-noise ratio.

The RLP cost is different in different ranges, and large errors caused by impulse interference can be effectively resisted. For channels with group sparsity, choose/_1,0And l_2,0Mixed norm sparsity constraints, i.e.

Or

Wherein G is the number of groups, beta is a parameter characterizing the size and range of the sparse constraint,

to comprise

G th_iA vector of group taps.

Fig. 4 is a table showing the updating process of the tap coefficient at each iteration of the present invention.

2. Simulation research:

simulation conditions are as follows: the underwater sound sparse channel has the channel length of 64, the number of non-zero groups is 2, and each group comprises 4 taps. The non-zero positions are randomly distributed, and the sum of the squares of the amplitudes is 1. Adding impulse interference complying with the S alpha S distribution, wherein alpha is 1.6, and gamma is 0.07. The signal-to-noise ratio is 10 dB. The mean square error between the estimated value and the true value is used as a measure.

FIG. 2 is a graph showing the comparison of the RLP algorithm and the RLS in the steady-state error under the impulse interference environment. It can be seen that the traditional RLS algorithm cannot suppress the influence of pulse interference, and the steady-state error curve is not converged; the RLP algorithm in the invention can effectively inhibit the influence of impulse interference.

FIG. 3 shows the formula I_1,0-RLP、l_2,0Steady state error comparison of RLP with other sparse constraint algorithms. It can be seen that, compared to other algorithms, l in the present invention_1,0-RLP、l_2,0The RLP algorithm obtains lower steady-state error by fully utilizing the group sparsity of the channel, thereby proving the effectiveness of the invention.

Claims (1)

1. A group sparse underwater acoustic channel estimation method under a pulse interference environment is characterized by comprising the following steps: in order to obtain a more stable channel estimation method under the environment of pulse interference generated by the cracking of organisms and ice layers, the method under Gaussian noise is improved, and the method comprises the following steps:

(1) defining a new cost function; the method specifically comprises the following steps:

the cost function is defined as:

wherein: n is the estimation time, lambda is the forgetting factor,

estimate error for time i, y_iFor the signal to be expected at time i,

for channel estimates at time n-1, superscript^HDenotes the Hermite transposition, u_iInput vector, γ, for time i_nFor the regularization parameter, f (e)_i) In order to be a function of the loss,

convex function for characterizing channel sparsity, wherein loss function f (e) of RLP algorithm_i) Comprises the following steps:

wherein: upper label^*The expression is the conjugate of complex number, p is more than or equal to 1, xi and delta are threshold values, and the value is related to the signal-to-noise ratio;

for channels with group sparsity, choose/_1,0And l_2,0Mixed norm sparsity constraints, i.e.

Or

Wherein G is the number of groups, beta is a parameter characterizing the size and range of the sparse constraint,

to comprise

G th_iA vector of group taps;

(2) calculating a priori error

Gain of

(3) Updating estimator tap coefficients

And regularization parameters characterizing sparsity

M_n＝λ^-1(M_n-1-K_nu^H _nM_n-1)；

(4) And continuously iterating until the error converges.

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