CN103684690A - Compressed sensing based channel shortening filter design method - Google Patents

Abstract

The invention discloses a channel shortening filter design method based on compressed sensing, which first divides the received signal received by the receiving end of the single-input single-output system into a plurality of modules; then chooses a module, calculates the selected module and The cross-correlation matrix of the module composed of all symbols corresponding to the transmitted signal, and calculate the autocorrelation matrix of the selected module; then according to the obtained cross-correlation matrix and autocorrelation matrix and the set maximum SNR loss, the selected The mean square error value-added upper bound of the module after the channel shortening filter; finally adopt the reconstruction method in the compressed sensing theory, and determine the channel shortening filter according to the mean square error value-added upper bound; the advantage is that the filter obtained by the method design of the present invention The calculation complexity is low, the calculation accuracy is high, and the calculation complexity of the application system can be reduced, and the degree of freedom of the application system can be increased.

Description

A Design Method of Channel Shortening Filter Based on Compressive Sensing

technical field

The invention relates to a channel shortening technology in a communication system, in particular to a design method of a channel shortening filter based on compressed sensing.

Background technique

With the rapid growth of communication services, people's requirements for communication quality and speed are also increasing. The impulse response of wideband communication channels is long, extending to tens of symbol periods, and causing severe intersymbol interference. In a single-input single-output system, in order to reduce intersymbol interference, a cyclic prefix needs to be added before each symbol, but the length of the cyclic prefix should not be less than the length of the impulse response of the broadband communication channel. However, a long cyclic prefix is required under broadband communication channels, which will seriously reduce the transmission rate of the single-input single-output system. Aiming at these problems, the channel shortening filter can be used to shorten the impulse response length of the broadband communication channel, so as to achieve the purpose of suppressing intersymbol interference and reducing the transmission rate loss caused by the cyclic prefix. However, the system complexity will increase proportionally with the increase in the number of non-zero taps in the channel shortening filter, which will lead to a very high system complexity using the traditional non-sparse filter, so the sparse filter is becoming more and more more people's attention.

A reasonable and effective sparse filter is an important guarantee for the superior performance of the communication system. In the existing sparse filter research, the computational complexity of the sparse filter design method has been unsatisfactory, such as the orthogonal matching pursuit method (OMP), Even if the desired design complexity is achieved, it is at the cost of sacrificing the accuracy of the sparse filter. For this reason, it is of practical significance to study a sparse filter with low design complexity under high precision.

Contents of the invention

The technical problem to be solved by the present invention is to provide a method for designing a channel shortening filter based on compressed sensing. The filter obtained by the design can not only increase the degree of freedom of a single-input single-output system, but also has low computational complexity and high computational accuracy. .

The technical scheme adopted by the present invention to solve the above-mentioned technical problems is: a kind of channel shortening filter design method based on compressed sensing, it is characterized in that comprising the following steps:

① At the sending end of the single-input single-output system, the sending end transmits the signal to the receiving end through a broadband communication channel;

个模块，其中，N表示接收信号中包含的符号的总个数，1≤N_f≤N并假定N_f能够被N整除；② At the receiving end of the single-input single-output system, starting from the first symbol, the received signal received by the receiving end is divided _into

modules, where N represents the total number of symbols contained in the received signal, 1≤N _f ≤N and it is assumed that N _f can be divisible by N;

Then a module is arbitrarily selected from all modules of the received signal, Nyquist sampling is performed on each symbol in the selected module, and the number of samples is l, and l sampling values of each symbol in the selected module are obtained, Record the k-th sampling value of the i-th symbol in the selected module as y _i,k , where, l∈[1,N _f ], 1≤i≤N _f , 1≤k≤l;

Then obtain the symbol corresponding to each symbol position in the selected module from the transmitted signal, and then calculate the cross-correlation matrix between the module formed by all the corresponding symbols obtained from the transmitted signal and the selected module, denoted as R _yx , and calculate the autocorrelation matrix of the selected module, denoted as R _yy ;

其中，

ε_x=E[x_k-Δ ²]，ε_x=E[x_k-Δ ²]中符号“||”为求模符号，E[x_k-Δ ²?]表示求x_k-Δ ²的统计平均值，x_k-Δ表示发送信号中与选取的模块中的第i个符号位置对应的符号，经l次奈奎斯特采样后得到的l个采样值中的第k个采样值x_k延时Δ后得到的信号值，Δ为整数且0≤Δ≤N_f，

为r_Δ的共轭转置，r_Δ=R_yxI_Δ，I_Δ表示(N_f+ν)×(N_f+ν)维的单位矩阵中的第Δ+1列，ν表示宽带通信信道的最大记忆长度，L^-1为L的逆矩阵，L^H为L的共轭转置，L是对R_yy进行Cholesky分解后得到的一个(l×N_f)×(l×N_f)维的下三角矩阵，R_yy=LL^H；③ Let ω represent the channel shortening filter, let γ _max represent the set maximum SNR loss, and then determine the upper bound of the mean square error increment of the selected module after passing ω according to γ _max , denoted as ε,

in,

ε _x =E[x _k-Δ ² ], the symbol "||" in ε _x =E[x _k-Δ ² ] is a modulo symbol, and E[x _k-Δ ² ?] means to calculate x _k-Δ ² The statistical average value of , x _k-Δ represents the symbol corresponding to the i-th symbol position in the selected module in the transmitted signal, and the k-th sample value among the l sample values obtained after l times of Nyquist sampling The signal value obtained after x _k delay Δ, Δ is an integer and 0≤Δ≤N _f ,

is the conjugate transpose of r _Δ , r _Δ =R _yx I _Δ , I _Δ represents the Δ+1th column in the (N _f +ν)×(N _f +ν)-dimensional identity matrix, and ν represents the broadband communication channel The maximum memory length of , L ^-1 is the inverse matrix of L, L ^H is the conjugate transpose of L, and L is a (l×N _f )×(l×N _f ) dimension obtained after Cholesky decomposition of R _yy The lower triangular matrix of , R _yy =LL ^H ;

令r₀表示初始的残差，r₀=L^-1r_Δ，令n表示迭代次数，n的初始值为1，其中，1≤K≤N_f+ν，n≤2K；④-2、在进行第n次迭代时，计算上一次迭代后的残差r_n-1与L中的每一列的相关系数，将上一次迭代后的残差r_n-1与L中的第j列的相关系数记为σ_j，其中，1≤j≤l×Nf，

表示r_n-1的共轭转置，L^H(j)表示L(j)的共轭转置，L(j)表示L中的第j列，在此符号“||”为求模符号；然后从所有相关系数中选出最大的K个相关系数，并将选出的K个相关系数的下标组成一个集合，记为c_n；④-3、令ω_s表示一个(N_f+ν)×1维的中间列向量，并令初始的ω_s的值为0；然后计算上一次迭代后的索引集合I_n-1与c_n的并集，记为b_n，b_n=I_n-1∪c_n；接着将初始的ω_s中下标属于b_n的所有元素按序组成初始的ω_s的子向量，记为ω_s(：,b_n)，并根据

得到ω_s(：,b_n)中的每个元素的值；最后根据ω_s(：,b_n)中的每个元素的值更新初始的ω_s中对应位置的元素的值，其中，符号“∪”为并集运算符号，L^H(：,b_n)表示L(：,b_n)的共轭转置，L(：,b_n)表示L中列序号属于b_n的所有列组成的L的子矩阵，

表示(L^H(：,b_n))的伪逆；④-4、从更新后的ω_s中选出绝对值最大的K个元素，并将选出的K个元素的下标组成第n次迭代的索引集合，记为I_n，然后计算第n次迭代的残差，记为r_n，r_n=L^-1r_Δ-L^H(：,I_n)ω_s(：,I_n)，其中，L^H(：,I_n)表示L(：,I_n)的共轭转置，L(：,I_n)表示L中列序号属于I_n的所有列组成的L的子矩阵，ω_s(：,I_n)表示更新后的ω_s中下标属于I_n的所有元素按序组成的更新后的ω_s的子向量；④-5、保留更新后的ω_s中与ω_s(：,I_n)中的每个元素对应的元素的值，而将更新后的ω_s中其余元素的值置0，并重新记为ω_s'；④-6、判断n≤2K是否成立，如果n≤2K成立，则比较r_n的模的平方值与ε的大小，如果r_n的模的平方值大于ε，则令n=n+1，然后返回步骤④-2继续执行，进行下一次迭代，如果r_n的模的平方值小于或等于ε，则结束迭代过程，并令ω=ω_s'；如果n≤2K不成立，则结束迭代过程，并令ω=ω_s'；其中，n=n+1和ω=ω_s'中的“=”为赋值符号。④Adopt the reconstruction method in compressed sensing theory, and determine ω according to ε. The specific process is: ④-1. Assume that the number of non-zero tap coefficients in the final determined ω is K, and let I ₀ represent the initial index set ,

Let r ₀ represent the initial residual, r ₀ =L ^-1 r _Δ , let n represent the number of iterations, and the initial value of n is 1, where 1≤K≤N _f +ν, n≤2K; ④-2, When performing the nth iteration, calculate the correlation coefficient between the residual r _n-1 after the last iteration and each column in L, and compare the residual r _n-1 after the last iteration with the jth column in L The correlation coefficient is denoted as σ _j , Among them, 1≤j≤l×Nf,

Represents the conjugate transpose of r _n-1 , L ^H (j) represents the conjugate transpose of L(j), L(j) represents the jth column in L, where the symbol "||" is the modulo symbol ; Then select the largest K correlation coefficients from all correlation coefficients, and form a set of subscripts of the selected K correlation coefficients, which is denoted as c _n ; ④-3. Let ω _s represent a (N _f + ν)×1-dimensional intermediate column vector, and let the initial value of ω _s be 0; then calculate the union of the index set I _n-1 and c _n after the last iteration, denoted as b _n , b _n =I _n-1 ∪c _n ; then all the elements in the initial ω _s whose subscripts belong to b _n form the subvectors of the initial ω _s in sequence, denoted as ω _s (:, b _n ), and according to

Get the value of each element in ω _s (:, b _n ); finally update the value of the element at the corresponding position in the initial ω _s according to the value of each element in ω _s (:, b _n ), where the symbol "∪" is the union operation symbol, L ^H (:, b _n ) means the conjugate transpose of L (:, b _n ), L (:, b _n ) means that the column number in L belongs to all the columns of b _n The submatrix of L,

Represents the pseudo-inverse of (L ^H (:, b _n )); ④-4. Select K elements with the largest absolute value from the updated ω _s , and form the subscripts of the selected K elements into the nth The index set of the iteration, denoted as I _n , and then calculate the residual of the nth iteration, denoted as r _n , r _n =L ^-1 r _Δ -L ^H (:,I _n )ω _s (:,I _n ), where L ^H (:, _In ) represents the conjugate transpose of L (:, In ₎ , and L (:, _In ) represents the submatrix of L composed of all columns whose column number belongs to In _{in L} , ω _s (:, I _n ) represents the sub-vector of the updated ω _s composed of all elements whose subscripts belong to I _n in the updated ω _s in order; ④-5. Keep the updated ω _s and ω _s (:,I _n ) corresponds to the value of each element in the element, and the value of the remaining elements in the updated ω _s is set to 0, and re-recorded as ω _s '; ④-6. Determine whether n≤2K It is established, if n≤2K is established, then compare the square value of the modulus of r _n with the size of ε, if the square value of the modulus of r _n is greater than ε, set n=n+1, and then return to step ④-2 to continue execution, For the next iteration, if the square value of the modulus of r _n is less than or equal to ε, then end the iterative process and set ω=ω _s '; if n≤2K is not established, then end the iterative process and set ω=ω _s '; Among them, "=" in n=n+1 and ω=ω _s ' is an assignment symbol.

The sending signal in step ① is a baseband complex signal, and the broadband communication channel is a discrete time-invariant noisy channel.

Compared with the prior art, the present invention has the advantages of:

1) The channel shortening filter designed by the method of the present invention is a sparse filter, which has fewer non-zero tap coefficients compared with the traditional non-sparse filter, thereby effectively reducing the number of sparse filters designed by the method of the present invention. The computational complexity of the system of the converter is increased, and the degree of freedom of the single-input and single-output system is increased.

2) Since the method of the present invention uses the maximum SNR loss as a constraint to design the channel shortening filter, the user can set different maximum SNR loss values according to different actual situations, so that the calculation can be simply realized The compromise between complexity and calculation accuracy, that is, if the user does not require high accuracy, the maximum signal-to-noise ratio loss can be appropriately increased to reduce the accuracy requirement, but at the same time the calculation complexity will also be reduced, that is, the calculation speed will be accelerated; if If the user has high requirements for accuracy, the maximum signal-to-noise ratio loss can be appropriately reduced, and the accuracy can be improved by increasing the computational complexity.

3) The method of the present invention uses the reconstruction method in compressive sensing theory when designing the sparse filter. It can detect and correct the index set of the sparse filter generated after the last iteration, thereby improving the calculation accuracy. At the same time, due to the inherent advantages of the reconstruction method, the number of iterations of the method of the present invention is also reduced compared with the existing orthogonal matching pursuit method Many, thereby reducing the computational complexity.

4) Under the same constraints (the same number of tap coefficients), the channel shortening filter designed by the method of the present invention has lower computational complexity and higher computational precision than the sparse filter designed by the prior art.

Description of drawings

Fig. 1 is the application block diagram of the inventive method;

Fig. 2 a is the overall realization block diagram of the method of the present invention;

FIG. 2b is a block diagram of a specific flow chart of determining the channel shortening filter by using the reconstruction method in the compressed sensing theory in FIG. 2a and determining the upper bound of the mean square error increment of the selected module after passing through the channel shortening filter;

Fig. 3 is a schematic diagram of the comparison of the simulation time of the channel shortening filter designed by using the method of the present invention and the channel shortening filter designed by using the existing orthogonal matching pursuit method (OMP) under different cyclic prefix lengths;

Fig. 4 is a schematic diagram showing the comparison of the residuals of the channel shortening filter designed by using the method of the present invention and the channel shortening filter designed by using the existing orthogonal matching pursuit method (OMP) under different cyclic prefix lengths.

Detailed ways

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

A kind of channel shortening filter design method based on compressed sensing proposed by the present invention, its overall realization block diagram is as shown in Figure 2a, and it comprises the following steps:

① At the sending end of the single-input single-output system, the sending end transmits the signal to the receiving end through a broadband communication channel. Here, in the specific implementation process, baseband complex signals may be used for sending signals, and discrete time-invariant noisy channels may be used for broadband communication channels.

② At the receiving end of the single-input single-output system, starting from the first symbol, the received signal received by the receiving end is divided _into modules, where N represents the total number of symbols contained in the received signal, that is, the total number of symbols contained in the transmitted signal, 1≤N _f ≤N and it is assumed that N _f can be divisible by N.

Then a module is arbitrarily selected from all modules of the received signal, Nyquist sampling is performed on each symbol in the selected module, and the number of samples is l, and l sampling values of each symbol in the selected module are obtained, The k-th sampling value of the i-th symbol in the selected module is recorded as y _i,k , where l∈[1,N _f ], 1≤i≤N _f , 1≤k≤l.

Then obtain the symbol corresponding to each symbol position in the selected module from the transmitted signal, and then calculate the cross-correlation matrix between the module formed by all the corresponding symbols obtained from the transmitted signal and the selected module, denoted as R _yx , and calculate the autocorrelation matrix of the selected module, denoted as R _yy .

其中，

εx₌E[|x_k-Δ|²]，ε_x=E[|x_k-Δ|²]中符号“||”为求模符号，E[|x_k-Δ|²]?表示求x_k-Δ ²的统计平均值，x_k-Δ表示发送信号中与选取的模块中的第i个符号位置对应的符号，经l次奈奎斯特采样后得到的l个采样值中的第k个采样值x_k延时Δ后得到的信号值，Δ为整数且0≤Δ≤N_f，

为r_Δ的共轭转置，r_Δ=R_yxI_Δ，I_Δ表示(N_f+ν)×(N_f+ν)维的单位矩阵中的第Δ+1列，ν表示宽带通信信道的最大记忆长度，L^-1为L的逆矩阵，L^H为L的共轭转置，L是对R_yy进行Cholesky分解后得到的一个(l×N_f)×(l×N_f)维的下三角矩阵，R_yy=LL^H。③ Let ω represent the channel shortening filter, let γ _max represent the set maximum SNR loss, and then determine the upper bound of the mean square error increment of the selected module after passing ω according to γ _max , denoted as ε,

in,

εx ₌ E[|x _k-Δ | ² ], the symbol "||" in ε _x =E[|x _k-Δ | ² ] is a modulo symbol, and E[|x _k-Δ | ² ]? The statistical average value of x _k-Δ ² , x _k-Δ represents the symbol corresponding to the i-th symbol position in the selected module in the transmitted signal, among the l sampling values obtained after l times of Nyquist sampling The signal value obtained after the kth sampling value x _k delay Δ, Δ is an integer and 0≤Δ≤N _f ,

is the conjugate transpose of r _Δ , r _Δ =R _yx I _Δ , I _Δ represents the Δ+1th column in the (N _f +ν)×(N _f +ν)-dimensional identity matrix, and ν represents the broadband communication channel The maximum memory length of , L ^-1 is the inverse matrix of L, L ^H is the conjugate transpose of L, and L is a (l×N _f )×(l×N _f ) dimension obtained after Cholesky decomposition of R _yy The lower triangular matrix of R _yy =LL ^H .

Here, the specific value of γ _max is determined by the user based on comprehensive calculation complexity and calculation accuracy.

令r₀表示初始的残差，r₀=L^-1r_Δ，令n表示迭代次数，n的初始值为1，其中，1≤K≤N_f+ν，n≤2K；④-2、在进行第n次迭代时，计算上一次迭代后的残差r_n-1与L中的每一列的相关系数，将上一次迭代后的残差r_n-1与L中的第j列的相关系数记为σ_j，

其中，1≤j≤l×Nf_，

表示r_n-1的共轭转置，L^H(j)表示L(j)的共轭转置，L(j)表示L中的第j列，在此符号“||”为求模符号；然后从所有相关系数中选出最大的K个相关系数，并将选出的K个相关系数的下标组成一个集合，记为c_n；④-3、令ω_s表示一个(N_f+ν)×1维的中间列向量，并令初始的ω_s的值为0；然后计算上一次迭代后的索引集合I_n-1与c_n的并集，记为b_n，b_n=I_n-1∪c_n；接着将初始的ω_s中下标（在此下标是指元素在初始的ω_s中的位置，例如初始的ω_s中的第1个元素的下标为1）属于b_n的所有元素按序组成初始的ω_s的子向量，记为ω_s(：,b_n)，并根据

得到ω_s(：,b_n)中的每个元素的值；最后根据ω_s(：,b_n)中的每个元素的值更新初始的ω_s中对应位置的元素的值，其中，符号“∪”为并集运算符号，L^H(：,b_n)表示L(：,b_n)的共轭转置，L(：,b_n)表示L中列序号属于b_n的所有列组成的L的子矩阵，

表示(L^H(：,b_n))的伪逆；④-4、从更新后的ω_s中选出绝对值最大的K个元素，并将选出的K个元素的下标组成第n次迭代的索引集合，记为I_n，例如，当K=3时，如果更新后的ω_s中最大的三个元素分别为第1个、第3个和第6个元素，则更新后的ω_s中最大的三个元素的下标组成的索引集合为｛136｝；然后计算第n次迭代的残差，记为r_n，r_n=L^-1r_Δ-L^H(：,I_n)ω_s(：,I_n)，其中，L^H(：,I_n)表示L(：,I_n)的共轭转置，L(：,I_n)表示L中列序号属于I_n的所有列组成的L的子矩阵，ω_s(：,I_n)表示更新后的ω_s中下标属于I_n的所有元素按序组成的更新后的ω_s的子向量；④-5、保留更新后的ω_s中与ω_s(：,I_n)中的每个元素对应的元素的值，而将更新后的ω_s中其余元素的值置0，并重新记为ω_s'；④-6、判断n≤2K是否成立，如果n≤2K成立，则比较rn的模的平方值与ε的大小，如果r_n的模的平方值大于ε，则令n=n+1，然后返回步骤④-2继续执行，进行下一次迭代，如果rn的模的平方值小于或等于ε，则结束迭代过程，并令ω=ω_s'；如果n≤2K不成立，则结束迭代过程，并令ω=ω_s'；其中，n=n+1和ω=ω_s'中的“=”为赋值符号。④Adopt the reconstruction method in compressed sensing theory, and determine ω according to ε, as shown in Figure 2b, the specific process is: ④-1. Assume that the number of non-zero tap coefficients in the final determined ω is K, let I ₀ represents the initial index set,

Let r ₀ represent the initial residual, r ₀ =L ^-1 r _Δ , let n represent the number of iterations, and the initial value of n is 1, where 1≤K≤N _f +ν, n≤2K; ④-2, When performing the nth iteration, calculate the correlation coefficient between the residual r _n-1 after the last iteration and each column in L, and compare the residual r _n-1 after the last iteration with the jth column in L The correlation coefficient is denoted as σ _j ,

Among them, 1≤j≤l×Nf _,

Represents the conjugate transpose of r _n-1 , L ^H (j) represents the conjugate transpose of L(j), L(j) represents the jth column in L, where the symbol "||" is the modulo symbol ; Then select the largest K correlation coefficients from all correlation coefficients, and form a set of subscripts of the selected K correlation coefficients, which is denoted as c _n ; ④-3. Let ω _s represent a (N _f + ν)×1-dimensional intermediate column vector, and let the initial value of ω _s be 0; then calculate the union of the index set I _n-1 and c _n after the last iteration, denoted as b _n , b _n =I _n-1 ∪c _n ; then subscript the initial ω _s (the subscript refers to the position of the element in the initial ω _s , for example, the subscript of the first element in the initial ω _s is 1) All the elements belonging to b _n form the sub-vectors of the initial ω _s in sequence, denoted as ω _s (:, b _n ), and according to

Get the value of each element in ω _s (:, b _n ); finally update the value of the element at the corresponding position in the initial ω _s according to the value of each element in ω _s (:, b _n ), where the symbol "∪" is the union operation symbol, L ^H (:, b _n ) means the conjugate transpose of L (:, b _n ), L (:, b _n ) means that the column number in L belongs to all the columns of b _n The submatrix of L,

Represents the pseudo-inverse of (L ^H (:, b _n )); ④-4. Select K elements with the largest absolute value from the updated ω _s , and form the subscripts of the selected K elements into the nth The index set of iteration times, denoted as I _n , for example, when K=3, if the three largest elements in the updated ω _s are the first, third and sixth elements respectively, then the updated The index set composed of the subscripts of the largest three elements in ω _s is {136}; then calculate the residual of the nth iteration, denoted as r _n , r _n =L ^-1 r _Δ -L ^H (:,I _n )ω _s (:,I _n ), where, L ^H (:,I _n ) means the conjugate transpose of L(:,I _n ), and L(:,I _n ) means that the column number in L belongs to I _n The sub-matrix of L composed of all the columns of , ω _s (:, I _n ) represents the sub-vector of the updated ω _s composed of all elements whose subscripts belong to I _n in the updated ω _s in order; ④-5, Retain the value of the element corresponding to each element in ω _s (:,I _n ) in the updated ω _s , and set the value of the rest of the elements in the updated ω _s to 0, and re-record it as ω _s '; ④-6. Determine whether n≤2K is true. If n≤2K is true, compare the square value of the modulus of rn with the size of ε. If the square value of the modulus of r _n is greater than ε, set n=n+1, and then Return to step ④-2 and continue to execute for the next iteration. If the square value of the modulus of rn is less than or equal to ε, then end the iterative process, and set ω=ω _s '; if n≤2K is not established, end the iterative process, and Let ω=ω _s '; where, "=" in n=n+1 and ω=ω _s 'is an assignment symbol.

FIG. 1 shows a schematic diagram of a channel shortening filter designed by applying the method of the present invention.

The feasibility and effectiveness of the method of the present invention are further illustrated below through computer simulation.

The simulation environment is the carrier service area (CSA, carrier service Area) loop 7 of ADSL8 standards. The allowed maximum signal-to-noise ratio loss γ _max is set to 1dB, and the length of IFFT (inverse Fourier transform) is 1024. The length of the cyclic prefix is from 50 to 120. In order to ensure the accuracy of the results, the average value is obtained after 1000 simulations.

Fig. 3 has provided the channel shortening filter that utilizes the method of the present invention to design and obtain and utilizes the channel shortening filter that utilizes existing orthogonal matching pursuit method (OMP) to design and obtain the comparison of simulation time under different cyclic prefix lengths, Fig. 4 shows The channel shortening filter designed by using the method of the present invention is compared with the channel shortening filter designed by using the existing orthogonal matching pursuit method (OMP) under different cyclic prefix lengths, as shown in Fig. 3 and Fig. 4 Invention-16 and Invention-24 correspond to channel shortening filters whose number K of non-zero tap coefficients designed by the method of the present invention is 16 and 24, and OMP-16 and OMP-24 correspond to existing orthogonal matching The tracking method (OMP) designs channel shortening filters with the number K of non-zero tap coefficients being 16 and 24. It can be seen from Fig. 3 that when the length of the cyclic prefix CP is constant, under the same number of non-zero tap coefficients, the channel shortening filter designed by the method of the present invention is better than the existing orthogonal matching pursuit method ( OMP) designed channel shortening filter operation time is reduced by nearly half. It can be seen from Figure 4 that under the same length of CP, the residual error of the channel shortening filter designed by the method of the present invention is smaller than that of the channel shortening filter designed by the existing orthogonal matching pursuit method (OMP) , which shows that the channel shortening filter designed by the method of the present invention has better performance, and the single-input single-output system using this channel shortening filter can estimate the transmitted signal more accurately. To sum up, no matter in terms of time complexity or system accuracy, the comprehensive performance of the channel shortening filter designed by the method of the present invention has been well improved.

Claims (2)

1. A channel shortening filter design method based on compressed sensing is characterized by comprising the following steps:

firstly, at a sending end of a single-input single-output system, the sending end transmits and sends signals to a receiving end through a broadband communication channel;

② at the receiving end of the single input single output system, starting from the 1 st symbol, with continuous N_fDividing the received signal received by the receiving end into one period of symbols

A module, wherein N represents the total number of symbols contained in the received signal, and 1 is less than or equal to N_fN and assuming N_fCan be divided exactly by N;

then, one module is randomly selected from all modules for receiving signals, Nyquist sampling is carried out on each symbol in the selected module, the sampling frequency is l, l sampling values of each symbol in the selected module are obtained, and the kth sampling value of the ith symbol in the selected module is recorded as y_i,kWherein l is ∈ [1, N ∈ ]_f]，1≤i≤Nf_，1≤k≤l；

Then obtaining the symbol corresponding to each symbol position in the selected module from the sending signal, and then calculating the cross-correlation matrix between the module formed by all the corresponding symbols obtained from the sending signal and the selected module, and recording the cross-correlation matrix as R_yxAnd calculating the autocorrelation matrix of the selected module, denoted as R_yy；

Let omega denote channel shortening filter, let gamma_maxIndicating a set maximum signal-to-noise ratio loss, then according to gamma_maxDetermining the upper bound of mean square error increment of the selected module after omega, marking as epsilon,

wherein,

ε_x=E[x_k-Δ²]，ε_x=E[x_k-Δ²]the middle symbol, "| |" is a modulo symbol, E [ x_k-Δ²]Expression to x_k-Δ²Statistical average of (a), x_k-ΔRepresenting a symbol corresponding to the ith symbol position in the selected module in the transmitted signal, and obtaining a kth sampling value x in l sampling values after l Nyquist sampling_kA signal value obtained after delaying delta, wherein delta is an integer and is more than or equal to 0 and less than or equal to N_f，

Is r_ΔConjugate transpose of (r)_Δ=R_yxI_Δ，I_ΔRepresents (N)_f+ν)×(N_fColumn Δ +1 in the unitary matrix of dimension + v), v representing the maximum memory length of the wideband communication channel, L^-1Is the inverse matrix of L, L^HIs a conjugate transpose of L, L being to R_yyOne obtained after Cholesky decomposition (l.times.N)_f)×(l×N_f) Lower triangular matrix of dimensions, R_yy=LL^H；

Fourthly, determining omega according to epsilon by adopting a reconstruction method in a compressed sensing theory, wherein the concrete process is as follows: fourthly-1, assuming that the number of the finally determined nonzero tap coefficients in the omega is K, and making I₀The initial set of indices is represented as,let r be₀Denotes the initial residual error, r₀=L^-1r_ΔLet N denote the number of iterations, the initial value of N is 1, where K is greater than or equal to 1 and less than or equal to N_fV, n is less than or equal to 2K; fourthly-2, calculating the residual error r after the last iteration when the nth iteration is carried out_n-1The residual error r after the last iteration is related to the correlation coefficient of each column in L_n-1The correlation coefficient with the j-th column in L is denoted as σ_j，

Wherein j is more than or equal to 1 and less than or equal to lxN_f，

Is represented by r_n-1By conjugate transposition of L^H(j) Denotes the conjugate transpose of L (j), L (j) denotes the jth column in L, where the symbol "|" is a modulo symbol; then, the largest K correlation coefficients are selected from all the correlation coefficients, and the subscripts of the selected K correlation coefficients form a set, which is marked as c_n(ii) a Fourthly-3, order omega_sRepresents one (N)_fA + v) x 1-dimensional intermediate column vector, and let the initial ω be_sIs 0; then calculating the index set I after the last iteration_n-1And c_nUnion ofIs denoted by b_n，b_n=I_n-1∪c_n(ii) a Then the initial ω_sThe middle subscript belongs to b_nAll elements of (a) constitute the initial ω in sequence_sThe subvector of (2), denoted as ω_s(：,b_n) According toTo obtain omega_s(：,b_n) A value of each element in (a); finally according to omega_s(：,b_n) Updates the initial ω by the value of each element in (1)_sWhere the symbol "U" is a union operation symbol, L^H(：,b_n) Represents L (: b is b_n) Conjugate transpose of, L (: b is b_n) Indicates that the column number in L belongs to b_nAll of the columns of (a) make up a sub-matrix of L,is represented by (L)^H(：,b_n) A pseudo-inverse of); 4, from the updated omega_sSelecting K elements with the maximum absolute value, and forming the subscripts of the selected K elements into an index set of the nth iteration, which is marked as I_nThen the residual error of the nth iteration is calculated and recorded as r_n，r_n=L^-1r_Δ-L^H(：,I_n)ω_s(：,I_n) Wherein L is^H(：,I_n) Represents L (: i, I_n) Conjugate transpose of, L (: i, I_n) Indicates that the column number in L belongs to I_nAll columns of (a) constitute a sub-matrix of L, ω_s(：,I_n) Represents updated ω_sThe middle subscript being of formula I_nAll elements of (a) in sequence constitute an updated ω_sThe subvectors of (1); fourthly-5, reserving updated omega_sMiddle and omega_s(：,I_n) And the value of the element corresponding to each element in (b), and ω to be updated_sThe values of the other elements are set to 0 and are recorded again as omega_s'; fourthly-6, judging whether n is less than or equal to 2K, if n is less than or equal to 2K, comparing r_nIf r is the magnitude of the square of the modulus of (2) and ∈_nOf the dieIf the square value is larger than epsilon, let n = n +1, then return to the step (r-2) to continue execution, carry out the next iteration, if r is larger than epsilon_nIs less than or equal to epsilon, the iterative process is ended and let ω = ω_s'; if n ≦ 2K does not hold, the iterative process ends and let ω = ω_s'; wherein n = n +1 and ω = ω_s"=" in' is an assigned symbol.

2. The method as claimed in claim 1, wherein the transmission signal in step (i) is a baseband complex signal, and the wideband communication channel is a discrete time invariant noisy channel.

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