CN111800362A - Improved ROMP underwater acoustic channel estimation algorithm - Google Patents

Abstract

The invention relates to an improved ROMP underwater acoustic channel estimation algorithm. The invention aims to reduce the iteration times and obtain a more accurate channel estimation result by selecting a proper regularization coefficient and changing the fixed step length of the original ROMP (regularized orthogonal matching pursuit) algorithm into three-section step length based on the improvement of an ROMP (regularized orthogonal matching pursuit) algorithm aiming at the pilot signal of a subcarrier in an MIMO-OFDM underwater acoustic communication system, wherein FIG. 1 in the attached drawing of the specification is a specific implementation flow chart of the invention.

Description

Improved ROMP underwater acoustic channel estimation algorithm

The technical field is as follows:

the invention belongs to the technical field of underwater acoustic communication, and particularly relates to an improved ROMP (regularized orthogonal matching pursuit) algorithm, which is characterized in that a more accurate channel estimation result is obtained by selecting a proper regularization coefficient and changing the fixed step length of the original ROMP algorithm into three-section step length.

Background art:

the acoustic channel is a complex and variable channel and has the characteristics of limited bandwidth, large multipath delay spread and the like. Low-rate communication systems have not been able to meet the demand for marine communication. The MIMO-OFDM communication system has the characteristic of stable high speed, has been emphasized by many scholars over the years, and is gradually a hot spot of research in the aspect of underwater acoustic communication. The MIMO technology can not only improve diversity gain through space-time coding, but also multiply increase channel capacity through spatial multiplexing, although the MIMO technology has the two advantages, the channel becomes more complex, and the multi-path interference and frequency selective fading problems of the underwater acoustic channel have a great influence on the MIMO communication system. The OFDM technology can effectively solve the problem, and selects a plurality of subcarriers in a limited bandwidth, so that a channel is also divided into a plurality of subchannels, the bandwidth of each subchannel is much smaller than the related bandwidth of the original channel, and the fading can be regarded as flat fading in the communication process, thereby eliminating intersymbol interference. MIMO-OFDM, while having some advantages, can effectively overcome some of the problems that arise in underwater acoustic communications. However, the MIMO channel it uses also mixes and amplifies some of the characteristics of the hydroacoustic channel, making the channel state more difficult to obtain. And the parameter information of the channel is needed to be known at the receiving end for processing the transmission signal and recovering the original signal. Therefore, it is an important ring in communications to be able to accurately and efficiently perform channel estimation.

The ROMP (regularization orthogonal matching pursuit) algorithm is a commonly used compressed sensing channel estimation algorithm in channel estimation, introduces a regularization process to further screen atoms, and has the characteristic of high stability, but the iteration step length is fixed, and the signal processing speed is slow.

According to the invention, energy is concentrated by changing the regularization coefficient, the accuracy is increased, the iteration times are reduced by setting three sections of step lengths, and the channel estimation can be carried out more accurately and effectively.

The invention content is as follows:

aiming at pilot signals of subcarriers in an MIMO-OFDM underwater acoustic communication system, the invention aims to reduce the iteration times and obtain a more accurate channel estimation result by selecting a proper regularization coefficient and changing the fixed step length of the original regularization orthogonal matching tracking algorithm into three-section step length based on the improvement of an ROMP (regularization orthogonal matching tracking) algorithm.

The technical scheme adopted by the invention is as follows:

the first step is as follows: according to the orthogonalization principle of the ROMP (regularized orthogonal matching pursuit) algorithm, a proper regularization coefficient r needs to be selected, according to the error rate performance, the proper regularization coefficient r is selected, the convergence of the algorithm is ensured, and the u inner product vector is expressed. J. the design is a square₀Representing the screening original subset, and the orthogonalization principle is represented as formula (1);

|u_i|≤r|u_j|，i,j∈J₀(1)

the second step is that: setting a receiving end signal of a pilot frequency as an observation vector y, a pilot frequency signal matrix as a measurement matrix X, sparsity as K, initialization iteration time t as 1, and residual error r₀＝y，

Λ_tSet of indices, X, representing t iterations_tRepresentation by index Λ_tA selected column set of the X matrix;

the third step: calculating the absolute value of the inner product of X and the residual vector by formula (2);

u＝abs[X^Tr_t-1](2)

the fourth step: if | | | Lambda | | non-woven phosphor is more than or equal to 0₀Selecting K/2 maximum values in u (i) if the K is less than or equal to 1/2K, and forming a set J by the sequence numbers J of the values corresponding to X; if 1/2K < | | | Λ₀Selecting K/4 maximum values in u (i) if | is less than or equal to 3/4K, and forming a set J by sequence numbers J of the values corresponding to X; if not, selecting 1 maximum value in u (i), and forming a set J by the sequence number J of X corresponding to the values;

the fifth step: performing one-step filtering operation on J according to the formula (1), and selecting J satisfying the following formula through the formula (3)₀；

And a sixth step: updating the index set by equation (4), where a_jThe jth column representing the matrix a;

Λ_t＝Λ_t-1∪J₀，X_t＝X_t-1∪{a_j}j∈J₀(4)

the seventh step: solving a least square solution through an equation (5);

eighth step: updating the residual error by equation (6);

the ninth step: let t be t +1 if t > K, or | | | Λ | | luminance₀Not less than K, or residual r_tIf 0, stop the operation and according to X_tAnd (5) obtaining a final result h, and if the final result h does not meet the condition, skipping to the third step to continue operation.

The invention has the advantages that:

1. the characteristic of high stability of the original ROMP (regularized orthogonal matching pursuit algorithm) is reserved;

2. a proper regularization coefficient can be selected to improve the accuracy;

3. the iteration times are reduced by setting three sections of step lengths, and the processing speed is improved.

Drawings

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

The specific implementation mode is as follows:

the present invention will be described in detail with reference to specific examples.

The first step is as follows: assuming that the water depth is 100m in the experimental condition, the depths of the transmitting transducers are 20m and 30m respectively, the receiving end transducers are 40m and 50m below the sea level, the horizontal distance between the transmitting transducers and the receiving transducers is 1km, the sound velocity is 1500m/s, and the maximum delay of the channel is 40 ms. According to the channel condition, the selection parameters of the OFDM are as follows, the length of the cyclic prefix is 60ms, the number of subcarriers is 512, the subcarrier interval is 2.5Hz, the carrier frequency is 20480Hz, a proper regularization coefficient r needs to be selected according to the orthogonalization principle of the ROMP (regularized orthogonal matching pursuit) algorithm, r is selected to be 1.5 according to the error rate performance diagram, and at the moment, the orthogonalization principle is expressed as an expression (1);

|u_i|≤1.5|u_j|，i,j∈J₀(1)

the second step is that: setting a receiving end signal of a pilot frequency as an observation vector y, a pilot frequency signal matrix as a measurement matrix X, sparsity as K, initialization iteration time t as 1, and residual error r₀＝y，

Λ_tSet of indices, X, representing t iterations_tRepresentation by index Λ_tA selected column set of the X matrix;

the third step: calculating the absolute value of the inner product of X and the residual vector by formula (2);

u＝abs[X^Tr_t-1](2)

the fourth step: if | | | Lambda | | non-woven phosphor is more than or equal to 0₀Selecting K/2 maximum values in u (i) if the K is less than or equal to 1/2K, and forming a set J by the sequence numbers J of the values corresponding to X; if 1/2K < | | Λ | | pre-ventilation₀Selecting K/4 maximum values in u (i) if the K is less than or equal to 3/4K, and forming a set J by the sequence numbers J of the values corresponding to X; if not, selecting 1 maximum value in u (i), and forming a set J by the sequence number J of X corresponding to the values;

the fifth step: performing one-step filtering operation on J according to the formula (1), and selecting J satisfying the following formula through the formula (3)₀；

And a sixth step: updating the index set by equation (4), where a_jThe jth column representing the matrix a;

Λ_t＝Λ_t-1∪J₀，X_t＝X_t-1∪{a_j}j∈J₀(4)

the seventh step: solving a least square solution through an equation (5);

eighth step: updating the residual error by equation (6);

the ninth step: let t be t +1 if t > K, or | | | Λ | | luminance₀Not less than K, or residual r_tIf 0, stop the operation and according to X_tAnd (5) obtaining a final result h, and if the final result h does not meet the condition, skipping to the third step to continue operation.

Claims (1)

1. An improved ROMP underwater acoustic channel estimation algorithm is characterized by comprising the following steps:

the first step is as follows: according to the orthogonalization principle of the ROMP (regularized orthogonal matching pursuit) algorithm, a proper regularization coefficient r needs to be selected, according to the error rate performance, the proper regularization coefficient r is selected, the convergence of the algorithm is ensured, and the u inner product vector is expressed. J. the design is a square₀Representing the screening original subset, and the orthogonalization principle is represented as formula (1);

|u_i|≤r|u_j|，i,j∈J₀(1)

the second step is that: setting a receiving end signal of a pilot frequency as an observation vector y, a pilot frequency signal matrix as a measurement matrix X, sparsity as K, initialization iteration time t as 1, and residual error r₀＝y，

Λ_tSet of indices, X, representing t iterations_tRepresentation by index Λ_tA selected column set of the X matrix;

the third step: calculating the absolute value of the inner product of X and the residual vector by formula (2);

u＝abs[X^Tr_t-1](2)

the fourth step: if | | | Lambda | | non-woven phosphor is more than or equal to 0₀Selecting K/2 maximum values in u (i) if the K is less than or equal to 1/2K, and forming a set J by the sequence numbers J of the values corresponding to X; if 1/2K < | | Λ | | pre-ventilation₀Selecting K/4 maximum values in u (i) if the K is less than or equal to 3/4K, and forming a set J by the sequence numbers J of the values corresponding to X; if not, selecting 1 maximum value in u (i), and forming a set J by the sequence number J of X corresponding to the values;

the fifth step: performing one-step filtering operation on J according to the formula (1), and selecting J satisfying the following formula through the formula (3)₀；

And a sixth step: updating the index set by equation (4), where a_jJ-th of the representation matrix AColumns;

Λ_t＝Λ_t-1∪J₀，X_t＝X_t-1∪{a_j} j∈J₀(4)

the seventh step: solving a least square solution through an equation (5);

eighth step: updating the residual error by equation (6);

the ninth step: let t be t +1 if t > K, or | | | Λ | | luminance₀Not less than K, or residual r_tIf 0, stop the operation and according to X_tAnd (5) obtaining a final result h, and if the final result h does not meet the condition, skipping to the third step to continue operation.

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