CN104836759A - Robust underwater acoustic channel estimation method based on joint norm optimization - Google Patents

Abstract

The invention provides a robust underwater acoustic channel estimation method based on joint norm optimization. A detection signal is sampled to obtain a discrete time sequence; a cost function of underwater acoustic channel response estimation is established on the basis of the thought of joint norm optimization; a support domain of a channel function is defined by using a matched filtering method; and a channel estimation result is modified, and loop iteration is continued to obtain estimation of underwater acoustic channel pulse response. The cost function based on joint norm of a channel response function is constructed through the sparsity of an underwater acoustic channel, so that the requirement of an algorithm on the signal to noise ratio is lowered effectively. Meanwhile, the resolution capability of multipath time delay is enhanced; the problems of heavy computation, large storage amount and high time consumption in channel estimation are solved; and the 'false peak' effect occurring in channel estimation is reduced.

Description

Based on the sane underwater acoustic channel method of estimation of associating norm optimization

Technical field

The present invention relates to subsurface communication field, especially signal processing method.

Background technology

The signal sent when transmitting transducer via ocean transmission after, hydrophone Received signal strength x (t) can be modeled as the linear convolution of the former s of transmitting (t) and channel function h (t) and be superimposed with ambient sea noise $n\left(t\right):x\left(t\right)=s\left(t\right)\⊗h\left(t\right)+n\left(t\right)=\∫s(t-\mathrm{\τ})h\left(\mathrm{\τ}\right)\mathrm{d\τ}+n\left(t\right).$ Through the reflex in sea or seabed, the transmission path that different glancing angles is corresponding different.Therefore signal can arrive receiving terminal in the different time intervals, thus produces multipath effect.When data rate improves, intersymbol interval reduce, interval little to a certain extent time will there is intersymbol interference phenomenon.Under the marine environment of complexity, except multipath effect, underwater acoustic channel also has the feature of time variation and low signal-to-noise ratio, and these make channel estimating become particularly difficulty.Under the prerequisite of channel impulse response functions as prior information, primary signal can be recovered at receiving terminal by the method for deconvolution.But in practical communication environment, channel impulse response functions, by the impact of many factors, cannot set up accurate channel model.Therefore need first to adopt the method for some parameter Estimation to obtain channel transfer functions, and then equilibrium or compensation could be carried out to received signal.As can be seen here, one sane, efficiently underwater acoustic channel parameter estimation algorithm determine the overall performance of underwater communications system to a great extent.

The method that current underwater acoustic channel is estimated mainly is divided into two classes: blind Channel Estimation and the channel estimating based on pilot tone.Wherein blind Channel Estimation is not mainly when having pilot tone or training sequence, processes by means of only carrying out to received signal the process obtaining channel pulse function.This class methods amount of calculation is large, and computing time is long, therefore cannot the change of real-time tracking time-variant channel.Channel estimating based on pilot tone is then insert pilot signal in the data flow sent, and receiving terminal obtains the process of channel function by known pilot signal and channel estimation method computing.Under this kind of channel estimating ideological system, the typical algorithm of employing has least-squares algorithm, matched filtering method etc.Least-squares algorithm principle is simple, but relate to matrix inversion, thus least-squares algorithm is to signal to noise ratio sensitivity (T.G.Manickam and R.J.Vaccaro, " A non-iterative deconvolution method for estimating multipath channel responses; " in Proc.ICASSP, vol.1, pp.333-336, May 1993).The method of matched filtering or relevant copy is that receptions waveform is carried out relevant treatment with transmitting, and wherein the peak value of correlation output gives amplitude Estimation, and the time shaft that peak value is corresponding gives the time delay estimation of multipath.Delay resolution depends on the main lobe width of the auto-correlation function that transmits, and can be similar to by the inverse of signal bandwidth.The main feature of matched filtering method has very high tolerance to signal to noise ratio, is suitable for working in the environment of low signal-to-noise ratio.In underwater sound communication, available smaller bandwidth, therefore the temporal resolution of matched filtering is limited, that is cannot tell the adjacent many ways component being less than Rayleigh limit interval.In order to improve temporal resolution, first time delay estimation problem utilizes Fourier transform to be converted into Power estimation problem by a series of channel estimation methods, then the High Resolution Method of similar MUSIC is utilized to obtain estimation (the F. – X.Ge of delay parameter, D.Shen, Y.Peng, and V.Li, " Super-resolution time delay estimation in multipath environments; " IEEE Trans.Circuits Syst., pp.1977-1986, Sept.2007).But these class methods need the number in path, known many ways, and the estimated value of the fading channel factor cannot be provided simultaneously.

Subsurface communication experiment shows, the energy of underwater acoustic channel mainly concentrates in the time delay of way more than several, and the energy on the many ways of major part can be ignored.Show that discrete series h (n) of h (t) has openness feature thus.Consider the openness of underwater acoustic channel, some methods based on sparse solution are applied to underwater acoustic channel and estimate.(the W.Li andJ.C.Preisig such as W.Li, " Estimation of rapidly time-varying sparse channels; " IEEE J.Ocean.Eng.32, pp.927-939, Oct.2007) propose first order recursive Least squares matching track algorithm (LS-MP) based on matching pursuit algorithm (MP).The method utilizes least square solution to minimize the thought of residual error, selects main tap, and calculates main tap coefficient as being similar to underwater acoustic channel response function.LS-MP method computation complexity is low, is applicable to the estimation of time varying channel.But due to residual vector in MP algorithm to the atom selected (atom) the projection spatially of opening non-orthogonal projection, the method thus based on MP algorithm can only obtain suboptimal solution.For the defect of MP algorithm, researchers then propose orthogonal matching pursuit algorithm (OMP) to ensure the orthogonality projected.Based on OMP algorithm, (the S.H.Byun such as Byun, W.Seong, and S.M.Kim, " Sparse underwateracoustic channel parameter estimation using a wideband receiver array, " IEEE J.Ocean.Eng., 38, pp.718-729, Oct.2013) propose the method (SA-OMP) of orthogonal matching pursuit changed in space, further increase the resolution of OMP algorithm.No matter but MP algorithm or OMP algorithm all have employed the method for Local Search, therefore cannot ensure the global convergence of channel estimation method.Simultaneously under Low SNR, may there is " mismatch " phenomenon in the search of atom, thus the method is unsane in actual environment.

In sum, for above all kinds of algorithm application produced problem in the underwater acoustic channel of complexity is estimated, a kind of efficient channel estimation technique that steadily and surely can work under low signal-to-noise ratio, that have global convergence and high time delay resolution capability becomes research emphasis of the present invention.

Summary of the invention

In order to overcome the deficiencies in the prior art, solve existing underwater acoustic channel method of estimation precision under Low SNR not enough, multidiameter delay resolution capability is inadequate, and operand, the problem that memory space is large, the present invention utilizes reception data and the detectable signal of single hydrophone, channel function estimated value is obtained by carrying out associating norm optimization to channel function, then matched filtering is utilized to revise estimated result the insensitive characteristic of signal to noise ratio, and matrix operation is converted into the vector operation that can be realized by fast algorithm FFT/IFFT, thus realize the quick of channel under water, accurate estimation.

The technical solution adopted for the present invention to solve the technical problems comprises the following steps:

Step 1: any position in the seawater lays single transmitting transducer and single hydrophone respectively, when communication starts, transmitting transducer emission detection signal s ₀(t), 0 < t≤T ₀, wherein T ₀represent the time span of detectable signal, this signal arrives hydrophone via after the channel effect of ocean, in receiving course, voice signal is converted into voltage signal by hydrophone, blackout is occured to from hydrophone display, the Received signal strength of hydrophone recordings is x (t), 0 < t≤T, wherein T represents the time span of data record, and hydrophone Received signal strength x (t) obtains discrete-time series x (n) through data acquisition unit, n=0,1,, N-1, wherein NT _s=T, T _sfor signal sampling interval, T _s=1/f _s, f _sfor signal sampling frequency, with same f _ssample frequency to detectable signal s ₀(t), 0 < t≤T ₀sample, obtain discrete-time series s ₀(n), n=0,1 ..., N ₀-1, wherein N ₀t _s=T ₀;

Step 2: utilize discrete-time series x (n), n=0,1 ..., N-1 and s ₀(n), n=0,1 ..., N ₀-1 builds vector x and s respectively ₀: x=[x (0), x (1) ..., x (N-1)] ^t, s ₀=[s ₀(0), s ₀(1) ..., s ₀(N ₀-1)] ^t, because detectable signal signal length after the convolution effect of channel is elongated, then at signal vector s ₀add (N-N below _s) individual zero, obtain utilize s to build the circular matrix S of N × N dimension, wherein (i, j) individual element of matrix S is: S (i, j)=s ((i-j) modN), 1≤i, j≤N, in formula, mod represents and divides exactly remainder, utilize vector x and matrix S, linear convolution model about detectable signal and Received signal strength is rewritten as matrix form: x=Sh+n, wherein h=[h (0), h (1),, h (N-1)] ^t, n=[n (0), n (1) ..., n (N-1)] ^t, represent channel impulse response and discrete series corresponding to noise respectively;

Step 3: based on the thought of associating norm optimization, sets up underwater acoustic channel response and estimates cost function: wherein λ represents L _1-the penalty factor of norm, || || ₂with || || ₁represent 2-norm and the 1-norm of vector respectively; Utilization obtains twice, front and back channel estimating to the method that cost function carries out second approximation quadratic approximation with iteration expression formula: ${\hat{h}}_{k+1}=T_{\mathrm{\&lambda;}/L}({\hat{h}}_k-L^{-1}{S}^T(S{\hat{h}}_k-x)),$ Wherein L value is matrix (S ^ts) eigenvalue of maximum, T _λ/Lrepresent threshold function table, utilize any vectorial z defined function T _λ/L(z): [T _λ/L(z)] _i=sgn (z _i) max{0, | z _i|-λ/L}, wherein $\mathrm{sgn}\left(z_i\right)=\left\{\begin{array}{c}1,z_i>0\\ 0,z_i\&le;0\end{array}\right.,$ Z _irepresent i-th component of z, be the requirement of the reduction operand that proposes in satisfied invention and required memory space, the present invention utilizes the character of real circular matrix to derive, and obtains the iteratively faster solution of cost function: in formula, " ~ " expression operates the DFT of vector, and " * " represents that conjugate operation accords with;

Step 4: for the phenomenon of channel estimating existence " pseudo-peak " that step 3 provides, adopt and weaken this effect to the insensitive matched filtering technique of signal to noise ratio, improve the precision of channel estimating further, utilizes the supporting domain C of the method definition channel function of matched filtering _sand revise with this result to channel estimating, wherein, matched filtering is equivalent to the cross-correlation of x and s, and the sequence of Output rusults to be length be 2N-1, gets the envelope of this sequence, and intercept N point sequence thereafter, subscript is followed successively by N:2N-1, is then normalized the energy about detectable signal, obtains new N point sequence and is designated as will the value that middle numerical value is less than 10% of its greatest measure is set to zero, and the set that the subscript that now non-zero position is corresponding is formed is denoted as support set E, utilizes support set E to define the supporting domain C of underwater acoustic channel response function _s: for ensureing the robustness of channel estimation methods, this supporting domain no longer changes in successive iterations, according to supporting domain, acts on follow-up channel estimation vector by the mode of projection ${\left[P_s{\hat{h}}_k\right]}_i=\left\{\begin{array}{c}{\hat{h}}_k\left(i\right),i\&Element;E\\ 0,i\&NotElement;E\end{array}\right.,$ Wherein P _srepresent that supporting domain restriction is in the projection operator of channel response vector; Repeat step 3 and step 4, until the estimated value of priority twice channel impulse response with meet one of following two conditions of convergence:

1. wherein δ needs according to precision the iteration convergence thresholding that provides, is generally less than 10 ^-6;

2. k >=K, the maximum cycle of wherein K representation program setting;

Amount of orientation at the end of the circulation of step 3 and step 4 for the Output rusults of channel impulse response, obtain the estimation of underwater acoustic channel impulse response.

The invention has the beneficial effects as follows owing to adopting owing to utilizing the openness of underwater acoustic channel, the cost function based on associating norm of structure channel response function significantly reduces the requirement of algorithm to signal to noise ratio, improves the resolution capability of multidiameter delay simultaneously.Utilize the character of circular matrix matrix operation to be converted into and by the vector operation of fast algorithm implementation, thus the problem that operand in channel estimating is large, memory space is large and elapsed time is long can be solved.By the supporting domain of the method definition channel function of matched filtering, and revised by the result of mode to channel estimating of projection, and then reduce " pseudo-peak " effect occurred in channel estimating.

Accompanying drawing explanation

Fig. 1 is that sound ray propagates schematic diagram under water.

Fig. 2 is sparse underwater acoustic channel impulse response.

Fig. 3 is detectable signal.

Fig. 4 is Received signal strength.

Fig. 5 is the channel estimating that matched filtering technique provides.

Fig. 6 is the channel estimating that the present invention provides.

Embodiment

Below in conjunction with drawings and Examples, the present invention is further described.

In communication start time, transmitting transducer emission detection signal s ₀(t).This detectable signal arrives hydrophone via after the effects such as ocean medium, sea, seabed, and is x (t) by hydrophone recordings.X (t), through data acquisition unit sampling, obtains discrete form x (n) of Received signal strength.With same sample frequency discretization detectable signal s ₀t () obtains sequence s ₀(n).Signal transacting end utilizes the inventive method processing signals x (n) and s ₀n (), obtains the estimation of underwater acoustic channel unit impulse response.

Figure 1 shows that transmitting transducer and the single hydrophone layout schematic diagram in ocean in underwater sound communication system.

The concrete implementing procedure of the present invention is as follows:

Input: transmitting transducer transmits s ₀(t), 0 < t≤T ₀, Received signal strength x (t) of hydrophone, 0 < t≤T.

Export: the estimated value of channel response

Step 1: any position in the seawater lays single transmitting transducer and single hydrophone respectively, when communication starts, transmitting transducer emission detection signal s ₀(t), 0 < t≤T ₀, wherein T ₀represent the time span of detectable signal, this signal arrives hydrophone via after the channel effect of ocean, in receiving course, voice signal is converted into voltage signal by hydrophone, blackout is occured to from hydrophone display, the Received signal strength of hydrophone recordings is x (t), 0 < t≤T, wherein T represents the time span of data record, and hydrophone Received signal strength x (t) obtains discrete-time series x (n) through data acquisition unit, n=0,1,, N-1, wherein NT _s=T, T _sfor signal sampling interval, T _s=1/f _s, f _sfor signal sampling frequency, with same f _ssample frequency to detectable signal s ₀(t), 0 < t≤T ₀sample, obtain discrete-time series s ₀(n), n=0,1 ..., N ₀-1, wherein N ₀t _s=T ₀;

Step 2: utilize discrete-time series x (n), n=0,1 ..., N-1 and s ₀(n), n=0,1 ..., N ₀-1 builds vector x and s respectively ₀: x=[x (0), x (1) ..., x (N-1)] ^t, s ₀=[s ₀(0), s ₀(1) ..., s ₀(N ₀-1)] ^t, because detectable signal signal length after the convolution effect of channel is elongated, then at signal vector s ₀add (N-N below _s) individual zero, obtain utilize s to build the circular matrix S of N × N dimension, wherein (i, j) individual element of matrix S is: S (i, j)=s ((i-j) modN), 1≤i, j≤N, in formula, mod represents and divides exactly remainder, utilize vector x and matrix S, linear convolution model about detectable signal and Received signal strength is rewritten as matrix form: x=Sh+n, wherein h=[h (0), h (1),, h (N-1)] ^t, n=[n (0), n (1) ..., n (N-1)] ^t, represent channel impulse response and discrete series corresponding to noise respectively;

Step 3 and step 4 is utilized to perform iteration below:

Initialization: k=1; Setting program maximum iteration time K and iteration convergence thresholding δ.

Judge item: if k < is K, then order performs step 3 and step 4; Otherwise exit circulation.

Step 3: based on the thought of associating norm optimization, sets up underwater acoustic channel response and estimates cost function: wherein λ represents L _1-the penalty factor of norm, || || ₂with || || ₁represent 2-norm and the 1-norm of vector respectively; Utilization obtains twice, front and back channel estimating to the method that cost function carries out second approximation quadratic approximation with iteration expression formula: ${\hat{h}}_{k+1}=T_{\mathrm{\&lambda;}/L}({\hat{h}}_k-L^{-1}{S}^T(S{\hat{h}}_k-x)),$ Wherein L value is matrix (S ^ts) eigenvalue of maximum, T _λ/Lrepresent threshold function table, utilize any vectorial z defined function T _λ/L(z): [T _λ/L(z)] _i=sgn (z _i) max{0, | z _i|-λ/L}, wherein $\mathrm{sgn}\left(z_i\right)=\left\{\begin{array}{c}1,z_i>0\\ 0,z_i\&le;0\end{array}\right.,$ Z _irepresent i-th component of z, be the requirement of the reduction operand that proposes in satisfied invention and required memory space, the present invention utilizes the character of real circular matrix to derive, and obtains the iteratively faster solution of cost function: in formula, " ~ " expression operates the DFT of vector, and " * " represents that conjugate operation accords with;

Step 4: for the phenomenon of channel estimating existence " pseudo-peak " that step 3 provides, adopt and weaken this effect to the insensitive matched filtering technique of signal to noise ratio, improve the precision of channel estimating further, utilizes the supporting domain C of the method definition channel function of matched filtering _sand revise with this result to channel estimating, wherein, matched filtering is equivalent to the cross-correlation of x and s, and the sequence of Output rusults to be length be 2N-1, gets the envelope of this sequence, and intercept N point sequence thereafter, subscript is followed successively by N:2N-1, is then normalized the energy about detectable signal, obtains new N point sequence and is designated as will the value that middle numerical value is less than 10% of its greatest measure is set to zero, and the set that the subscript that now non-zero position is corresponding is formed is denoted as support set E, utilizes support set E to define the supporting domain C of underwater acoustic channel response function _s: $C_s=\{h:h\left(i\right)=0,i\&NotElement;E,i=\mathrm{0,1},\&CenterDot;\&CenterDot;\&CenterDot;,N-1\},$ For ensureing the robustness of channel estimation methods, this supporting domain no longer changes in successive iterations, according to supporting domain, acts on follow-up channel estimation vector by the mode of projection ${\left[P_s{\hat{h}}_k\right]}_i=\left\{\begin{array}{c}{\hat{h}}_k\left(i\right),i\&Element;E\\ 0,i\&NotElement;E\end{array}\right.,$ Wherein P _srepresent that supporting domain restriction is in the projection operator of channel response vector; Repeat step 3 and step 4, until the estimated value of priority twice channel impulse response with meet one of following two conditions of convergence:

1. wherein δ needs according to precision the iteration convergence thresholding that provides, is generally less than 10 ^-6;

2. k >=K, the maximum cycle of wherein K representation program setting;

Amount of orientation at the end of the circulation of step 3 and step 4 for the Output rusults of channel impulse response, obtain the estimation of underwater acoustic channel impulse response.

The projection operator P utilizing step 4 to define _s, improve the precision of channel estimating:

${\hat{h}}_k\&LeftArrow;P_s{\hat{h}}_k$

If then upgrade iterations: k=k+1 also returns judgement item; Otherwise exit circulation.

At the end of circulation, the estimated value of delivery channel response by the estimated value of the channel response that time iteration of kth in step 4 obtains as the final estimation of underwater acoustic channel response and export final estimation

As shown in Figure 2, be underwater acoustic channel impulse response in given marine environment; This channel response comprises five multipath components, and the negative amplitude attenuation in figure represents that Received signal strength experienced by the phasing back of 180 degree.The CW pulse signal that transmitting transducer length launch time is 0.1s, frequency is 1000Hz, as shown in Figure 3, received after the channel effect of ocean by single hydrophone, wherein sample frequency is 8kHz.Receive waveform as shown in Figure 4, now corresponding receiving terminal Whole frequency band signal to noise ratio is 3dB.In order to realize the low complexity under Low SNR, sane underwater acoustic channel is estimated, first utilizes the method for matched filtering to obtain channel estimation value, and using the contrast of its result as the inventive method.The underwater acoustic channel unit impulse response that matched filtering technique exports is estimated as shown in Figure 5.Comparison diagram 2 is visible with Fig. 5: matched filtering technique cannot tell the multipath component under this marine environment, and Output rusults can not reflect the phase information of multipath.And the underwater acoustic channel method of estimation based on associating norm optimization adopting the present invention to propose, then can obtain underwater acoustic channel unit impulse response comparatively accurately, as shown in Figure 6, λ=10.In order to ensure the reliability of experimental result, in this example, two kinds of methods all have employed the method for Monte Carlo, and wherein Monte Carlo number of times is 100 times.

Claims (1)

1., based on a sane underwater acoustic channel method of estimation for associating norm optimization, it is characterized in that comprising the steps:

Step 1: any position in the seawater lays single transmitting transducer and single hydrophone respectively, when communication starts, transmitting transducer emission detection signal s ₀(t), 0 < t≤T ₀, wherein T ₀represent the time span of detectable signal, this signal arrives hydrophone via after the channel effect of ocean, in receiving course, voice signal is converted into voltage signal by hydrophone, blackout is occured to from hydrophone display, the Received signal strength of hydrophone recordings is x (t), 0 < t≤T, wherein T represents the time span of data record, and hydrophone Received signal strength x (t) obtains discrete-time series x (n) through data acquisition unit, n=0,1,, N-1, wherein NT _s=T, T _sfor signal sampling interval, T _s=1/f _s, f _sfor signal sampling frequency, with same f _ssample frequency to detectable signal s ₀(t), 0 < t≤T ₀sample, obtain discrete-time series s ₀(n), n=0,1 ..., N ₀-1, wherein N ₀t _s=T ₀;

Step 2: utilize discrete-time series x (n), n=0,1 ..., N-1 and s ₀(n), n=0,1 ..., N ₀-1 builds vector x and s respectively ₀: x=[x (0), x (1) ..., x (N-1)] ^t, s ₀=[s ₀(0), s ₀(1) ..., s ₀(N ₀-1)] ^t, because detectable signal signal length after the convolution effect of channel is elongated, then at signal vector s ₀add (N-N below _s) individual zero, obtain utilize s to build the circular matrix S of N × N dimension, wherein (i, j) individual element of matrix S is: S (i, j)=s ((i-j) modN), 1≤i, j≤N, in formula, mod represents and divides exactly remainder, utilize vector x and matrix S, linear convolution model about detectable signal and Received signal strength is rewritten as matrix form: x=Sh+n, wherein h=[h (0), h (1),, h (N-1)] ^t, n=[n (0), n (1) ..., n (N-1)] ^t, represent channel impulse response and discrete series corresponding to noise respectively;

Step 3: based on the thought of associating norm optimization, sets up underwater acoustic channel response and estimates cost function: wherein λ represents L ₁the penalty factor of-norm, || || ₂with || || ₁represent 2-norm and the 1-norm of vector respectively; Utilization obtains twice, front and back channel estimating to the method that cost function carries out second approximation quadratic approximation with iteration expression formula: wherein L value is matrix (S ^ts) eigenvalue of maximum, T _λ/Lrepresent threshold function table, utilize any vectorial z defined function T _λ/L(z): [T _λ/L(z)] _i=sgn (z _i) max{0, | z _i|-λ/L}, wherein $\mathrm{sgn}\left(z_i\right)=\left\{\begin{array}{cc}1,& z_i>0\\ 0,& z_i\&le;0\end{array}\right.,$ Z _irepresent i-th component of z, be the requirement of the reduction operand that proposes in satisfied invention and required memory space, the present invention utilizes the character of real circular matrix to derive, and obtains the iteratively faster solution of cost function: in formula, " ~ " expression operates the DFT of vector, and " * " represents that conjugate operation accords with;

Step 4: for the phenomenon of channel estimating existence " pseudo-peak " that step 3 provides, adopt and weaken this effect to the insensitive matched filtering technique of signal to noise ratio, improve the precision of channel estimating further, utilizes the supporting domain C of the method definition channel function of matched filtering _sand revise with this result to channel estimating, wherein, matched filtering is equivalent to the cross-correlation of x and s, and the sequence of Output rusults to be length be 2N-1, gets the envelope of this sequence, and intercept N point sequence thereafter, subscript is followed successively by N:2N-1, is then normalized the energy about detectable signal, obtains new N point sequence and is designated as will the value that middle numerical value is less than 10% of its greatest measure is set to zero, and the set that the subscript that now non-zero position is corresponding is formed is denoted as support set E, utilizes support set E to define the supporting domain C of underwater acoustic channel response function _s: for ensureing the robustness of channel estimation methods, this supporting domain no longer changes in successive iterations, according to supporting domain, acts on follow-up channel estimation vector by the mode of projection ${\left[P_s{\hat{h}}_k\right]}_i=\left\{\begin{array}{c}{\hat{h}}_k\left(i\right),i\&Element;E\\ 0,i\&NotElement;E\end{array}\right.,$ Wherein P _srepresent that supporting domain restriction is in the projection operator of channel response vector; Repeat step 3 and step 4, until the estimated value of priority twice channel impulse response with meet one of following two conditions of convergence:

1. wherein δ needs according to precision the iteration convergence thresholding that provides, is generally less than 10 ^-6;

2. k >=K, the maximum cycle of wherein K representation program setting;

Amount of orientation at the end of the circulation of step 3 and step 4 for the Output rusults of channel impulse response, obtain the estimation of underwater acoustic channel impulse response.