WO2022184180A1 - 零吸引惩罚与吸引补偿组合的稀疏lms方法 - Google Patents
零吸引惩罚与吸引补偿组合的稀疏lms方法 Download PDFInfo
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- the invention belongs to the field of signal processing, and relates to a sparse LMS method combining zero attraction penalty and attraction compensation.
- l p -norm achieves better performance than l 0 -norm and l 1 -norm types of algorithms, but this method is difficult to implement in hardware due to its high complexity.
- l The typical algorithm in the 1 -norm type is Zero-attracting Least Mean Square (ZA-LMS), which gives the same zero-attraction penalty to all channel coefficients and does not distinguish between zero and non-zero channels coefficient, resulting in its mean square deviation (MSD) is not excellent.
- ZA-LMS Zero-attracting Least Mean Square
- Y.Chen also proposed a reweighted ZA-LMS (Reweight Zero-attracting Least Mean Square, RZA-LMS).
- Y.Gu proposes a l 0 -LMS method, which performs zero-attraction penalty only when the coefficients of the estimated filter are lower than a certain threshold, but this method has great limitations on the selection of optimal parameters and the accuracy of the estimated coefficients.
- Lei Luo proposed a l 0 -ILMS method with lower parameter constraints and lower MSD, which also did not deal with the larger coefficients of the estimated filter.
- the purpose of the present invention is to provide a sparse LMS method combining zero attraction penalty and attraction compensation.
- This method combines zero attraction penalty with attraction compensation, divides the coefficients of the estimated filter into close to zero coefficients, small coefficients and large coefficients, and then adopts different attraction methods for these three coefficients.
- each iterative update for the near-zero coefficients of the estimated filter, only the product term in the iterative update formula is used to calculate; for the large coefficients of the estimated filter, a slight attraction compensation is performed to speed up the estimated filtering
- the coefficient of the filter is used to approximate the convergence speed of the large coefficient of the channel; for the small coefficient of the estimated filter, if the coefficient approximates the zero coefficient value of the channel or the large coefficient value of the channel during the iteration process, then the estimation filter is approximated as described above. method with zero and large coefficients, otherwise, a simple zero-attraction penalty is applied to the coefficient.
- the present invention provides the following technical solutions:
- q(n) is the power of The covariance zero-mean white Gaussian noise of , its autocorrelation matrix I is the identity matrix; n(n) is the power of The zero-mean white Gaussian noise of ; assume that q(n), X(n) and n(n) are independent of each other;
- ⁇ is the strength of attraction
- ⁇ is the boundary parameter that distinguishes between near-zero coefficients and small coefficients
- ⁇ is the boundary parameter that distinguishes small coefficients from large coefficients, and effectively enlarges the small coefficient and reduces the large coefficient
- the function -W i (n) is substituted into (5) to cancel out Wi ( n) in each iterative update formula, so that the iterative update formula contains the product term ⁇ e(n)X(n) as the following Estimate the coefficients of the filter once to achieve a large zero-attraction penalty
- the function - ⁇ W i (n) amplifies the zero attraction penalty for small coefficients, called floating coefficients
- a new attraction method is adopted.
- an estimated filter W(n) is set, so that the estimated filter coefficients are iteratively updated by equation (7), and subtracted from the echo signal d(n) to obtain the final The error signal e(n) realizes echo cancellation.
- the main transmitting platform emits useful signals and transmits them to the same-frequency repeater station, and the same-frequency repeater station amplifies the useful signals through the power amplifier, and then transmits the useful signals to the receiving terminal;
- the input signal X(n) of the LMS is the signal transmitted by the transmitting platform, and H(n) represents the wireless sparse channel;
- the co-frequency repeater contains an estimation filter, and the co-frequency repeater will receive the transmitted
- the signal of the platform is generated by the estimation filter to generate the y(n) signal;
- the co-frequency repeater will receive the signal of the transmitting platform through the wireless sparse channel and the Gaussian white noise n(n) of the channel, and synthesize the d(n) signal ;
- carry out e(n) d(n)-y(n) calculation to cancel the echo signal.
- the present invention proposes a new type of lc -LMS method, which combines zero attraction penalty and attraction compensation, and divides the coefficients of the estimated filter into coefficients close to zero, small coefficients and large coefficients , and then take different attraction methods for these three coefficients.
- each iterative update for the near-zero coefficients of the estimated filter, only the product term in the iterative update formula is used to calculate; for the large coefficients of the estimated filter, a slight attraction compensation is performed to speed up the estimated filtering
- the coefficient of the filter is used to approximate the convergence speed of the large coefficient of the channel; for the small coefficient of the estimated filter, if the coefficient approximates the zero coefficient value of the channel or the large coefficient value of the channel in the iterative process, then the estimation filter is approximated as described above. method with zero and large coefficients, otherwise, a simple zero-attraction penalty is applied to the coefficient.
- Figure 1 shows the sparse system identification model
- Fig. 2 is the structure diagram of lc -LMS method
- Figure 3 is the same frequency repeater
- Fig. 4 is the coefficient of the communication channel H
- Fig. 5 is the MSD simulation diagram of the theoretical MSD minimum value of ZA-LMS, RZA -LMS, l0 -LMS, l0 - ILMS , lc-LMS and lc-LMS at different attraction weights ⁇ ;
- Fig. 6 is the MSD simulation diagram of the theoretical MSD minimum value of l 0 -LMS, l 0 -ILMS, l c -LMS and l c -LMS at different ⁇ ;
- Fig. 7 is the MSD simulation diagram of the theoretical MSD minimum value of lc -LMS and lc -LMS at different ⁇ ;
- Figure 8 shows that the l c -LMS method achieves the same MSD value as l 0 -ILMS with lower complexity and faster convergence speed
- the main research of the present invention is based on the background of sparse system identification, and the sparse system identification model is given in FIG. 1 .
- n is the sequence number of the signal
- L is the filter length
- W(n) [w 0 w 1 ... w L-1 ]
- T is the coefficient of the estimation filter
- H(n) [h 0 h 1 . . . h L-1 ] are the coefficients of the sparse channel, most of which are equal to or close to zero in H(n).
- the vector H(n) is expressed as:
- q(n) is the power of The covariance zero-mean white Gaussian noise of , its autocorrelation matrix I is the identity matrix.
- n(n) is the power for zero mean Gaussian white noise.
- ⁇ is the step factor
- ⁇ ZA is the attraction weight
- ⁇ is a positive control parameter
- the l 0 -ILMS method Compared with the l 0 -LMS method, the l 0 -ILMS method only adds an additional term - ⁇ W i (n) to the zero attraction function, which makes the l 0 -ILMS method increase the accuracy of the estimated sparseness of the sparse system identification.
- ⁇ is the strength of attraction
- ⁇ is the boundary parameter that distinguishes the near-zero coefficient from the small coefficient
- ⁇ is the boundary parameter that distinguishes the small coefficient from the large coefficient, and effectively enlarges the small coefficient and reduces the large coefficient.
- the addition and multiplication operations of the l c -LMS method are 87.5% and 37.35% lower than that of the current best l 0 -ILMS method, respectively.
- the structure diagram of its l c -LMS method is shown in Figure 2.
- One practical application of the present invention is in repeaters for wireless communications.
- the main transmitting platform emits useful signals and transmits them to the co-frequency repeater, and the co-frequency repeater amplifies the useful signals through the power amplifier, and then transmits the useful signals to the receiving terminal.
- the co-frequency repeater transmits signals, a part of the signal is transmitted back to the receiving end of the co-frequency repeater through the wireless sparse channel, and this part of the signal will cause the co-frequency repeater to generate self-excitation.
- most wireless communication channels are sparse, especially digital multimedia communication channels. Therefore, a low-complexity and high-performance lc -LMS method for sparse channel and echo cancellation is proposed to cancel the signal transmitted to the co-frequency repeater through the wireless sparse channel.
- the input signal X(n) of the LMS is the signal transmitted by the transmitting platform, and H(n) represents the wireless sparse channel.
- the co-frequency repeater contains an estimation filter, and the co-frequency repeater generates the y(n) signal by passing the received signal of the transmitting platform through the estimation filter; the co-frequency repeater passes the received signal of the transmitting platform through the wireless
- the sparse channel and the white Gaussian noise n(n) of the channel are synthesized to produce a d(n) signal.
- Equation (15) and Equation (16) are chosen to estimate the filter iteration update equation.
- H(n ) represents the unknown sparse channel
- W(n) represents the estimated filter coefficients.
- 1000 Monte Carlo iterations were used to obtain each point.
- the selected input signal power is 1 and the noise power is 10 -2 .
- channel coefficient The coefficient simulation of its channel is shown in Figure 4.
- Figure 5 Figure 5 and Figure 7 show the simulation diagrams of the three parameters.
- the l 0 -ILMS and l c -LMS methods are not sensitive to tuning parameters, and the ⁇ value when the MSD value of the ZA-LMS, RZA-LMS and l 0 -LMS methods reaches the minimum value is marked in the figure.
- the tuning parameter ⁇ when the tuning parameter ⁇ is larger, the MSD value of the l c -LMS method is better than that of the LMS and l 0 -ILMS methods, and the effective range of the tuning parameter ⁇ of the l c -LMS method is much larger than that of the l 0 - ILMS. But when ⁇ is small, the l c -LMS method is not stable.
- the theoretical minimum MSD value of the l c -LMS method is basically consistent with the simulated minimum MSD value.
- the l c -LMS method achieves the same MSD value as l 0 -ILMS with lower complexity and faster convergence speed.
- the l c -LMS method in various sparse channel simulations, compared with l 0 -ILMS, the l c -LMS method has faster convergence speed, lower complexity and wider application range of the tuning parameter ⁇ .
- the method can be applied in sparse system identification and echo cancellation applications.
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Abstract
本发明涉及一种零吸引惩罚与吸引补偿组合的稀疏LMS方法，属于信号处理领域。该方法将零吸引惩罚与吸引补偿相结合，对估计滤波器的系数分成近零系数、小系数与大系数，然后采取不同的吸引方法。在每一次迭代更新中，对于估计滤波器的近零系数，仅用迭代更新公式中的乘积项来计算；对于估计滤波器的大系数，对其进行一种微量的吸引补偿，以加快估计滤波器的系数去逼近信道的大系数的收敛速度；对于估计滤波器的小系数，如果迭代过程中该系数逼近了信道的零系数值或信道的大系数值，则分别按前述针对估计滤波器近零系数和大系数的方法进行处理，否则，对该系数采取一种简单的零吸引惩罚。该方法收敛速度快、复杂度低、调谐参数适用范围广。
Description
本发明属于信号处理领域，涉及零吸引惩罚与吸引补偿组合的稀疏LMS方法。
许多信道都具有稀疏性，而辨识这种稀疏信道，就需要特定的自适应滤波算法。目前针对于稀疏系统辨识的算法类型有l
0-norm、l
1-norm和l
p-norm，其中l
0-norm是对估计滤波器的系数在某一较小的阈值内才进行零吸引惩罚，l
1-norm是对估计滤波器所有的系数进行零吸引惩罚，l
p是对估计滤波器所有的系数进行含有除法和指数的零吸引惩罚。l
p-norm实现了比l
0-norm和l
1-norm类型的算法更为优秀的性能，不过由于高复杂度，该方法难以硬件实现。l
1-norm类型中典型的算法是零吸引LMS(Zero-attracting Least Mean Square,ZA-LMS)，该方法对有所的信道系数给予了同样的零吸引惩罚，并没有区分零和非零信道系数，导致其稳态均方差(Mean Square deviation,MSD)并不优秀。Y.Chen又提出一种重新加权的ZA-LMS(Reweight Zero-attracting Least Mean Square,RZA-LMS),该方法的零吸引函数巧妙的分别将大系数和小系数进行了缩小与放大处理，使得对信道估计的更为合理，但是该方法需要进行除法运算。Y.Gu提出一种l
0-LMS方法，将估计滤波器的系数低于某一阈值才进行零吸引惩罚，但是该方法对最优参数选择和估计系数的精度有较大限制。为了获取更低的均方稳态差和降低参数的限制，Lei Luo提出参数限制更低与MSD更低的l
0-ILMS方法，该方法也并未对估计滤波器较大系数进行处理。
发明内容
有鉴于此，本发明的目的在于提供一种零吸引惩罚与吸引补偿组合的稀疏LMS方法。该方法将零吸引惩罚与吸引补偿相结合，对估计滤波器的系数分成接近零的系数、小系数与大系数，然后对这三种系数采取不同的吸引方法。在每一次迭代更新中，对于估计滤波器的近零系数，仅用迭代更新公式中的乘积项来计算；对于估计滤波器的大系数，对其进行一种微量的吸引补偿，以加快估计滤波器的系数去逼近信道的大系数的收敛速度；对于估计滤波器的小系数，如果迭代过程中该系数逼近了信道的零系数值或信道的大系数值，则分别按前述针对估计滤波器近零系数和大系数的方法进行处理，否则，对该系数采取一种简单的零吸引惩罚。
为达到上述目的，本发明提供如下技术方案：
零吸引惩罚与吸引补偿组合的稀疏LMS方法，建立稀疏系统辨识模型：
如附图1中，输入信号X(n)＝[x(n) x(n-1)...x(n-L+1)]
T是功率为
的零均值高斯信号，n为信号的序列号，L是滤波器长度；W(n)＝[w
0 w
1...w
L-1]
T是估计滤波器的系数，H(n)＝[h
0 h
1...h
L-1]是稀疏信道的系数，H(n)中大部分系数等于零或接近。考虑时变性，则向量H(n)表现为：
H(n+1)＝H(n)+q(n) (1)
其中q(n)是功率为
的协方差零均值高斯白噪声，其自相关矩阵
I是单位矩阵；n(n)是功率为
的零均值高斯白噪声；假设q(n)、X(n)与n(n)都相互独立；
y(n)和d(n)分别为
y(n)＝W
T(n)X(n) (2)
d(n)＝H
T(n)X(n)+n(n) (3)
其误差输出信号为
l
c-LMS方法的迭代更新方程
W(n+1)＝W(n)+μe(n)X(n)+f
C1(W(n)) (5)
其中
根据等式(5)与(6)，其估计滤波器迭代方程改为
W(n+1)＝μe(n)X(n)+f
C2(W(n)) (7)
其中
其中，ρ为吸引的强度；β为区分接近零系数与小系数的分界参数；φ为区分小系数与大系数的分界参数，并有效的将小系数进行放大，大系数进行缩小；在
范围内，函数-W
i(n)代入(5)中将每一次的迭代更新公式中的W
i(n)抵消掉，从而迭代更新公式中含有乘积项μe(n)X(n)作为下一次的估计滤波器的系数，以实现较大的零吸引惩罚；在
范围内，函数-φW
i(n)针对小系数进行放大的零吸引惩罚，称为浮动系数；在
范围内，采用全新的吸引方式，在每一次迭代更新该类型的系数值时，增加微量的补偿，促使估计滤波器的系数更快的逼近信道的大系数值；
可选的，在所述方法中，设置一个估计滤波器W(n)，使得估计滤波器系数进行等式(7)的迭代更新，并与回波信号d(n)相减，得到最后的误差信号e(n)，实现回波抵消。
可选的，将所述方法应用于无线通信的直放站中，布置同频直放站，以扩大信号覆盖范围，采用自适应滤波算法解决回波导致直放站自激的问题；
主发射平台发射出有用信号，传输到同频直放站，同频直放站又经过功放进行放大有用信号，再将有用信号发射到接收终端；
l
c-LMS的输入信号X(n)就是发射平台所发射的信号，而H(n)代表无线稀疏信道；同频直放站内含有一个估计滤波器，同频直放站将接收到的发射平台的信号经过估计滤波器生成y(n)信号；同频直放站将接受到的发射平台的信号经过无线稀疏信道与信道的高斯白噪声n(n)，合成产生出d(n)信号；在同频直放站内部，进行e(n)＝d(n)-y(n)计算，抵消回波信号。
本发明的有益效果在于：本发明提出一种全新类型的l
c-LMS方法，该方法将零吸引惩罚与吸引补偿相结合，对估计滤波器的系数分成接近零的系数、小系数与大系数，然后对这三种系数采取不同的吸引方法。在每一次迭代更新中，对于估计滤波器的近零系数，仅用迭代更新公式中的乘积项来计算；对于估计滤波器的大系数，对其进行一种微量的吸引补偿，以加快估计滤波器的系数去逼近信道的大系数的收敛速度；对于估计滤波器的小系数，如果迭 代过程中该系数逼近了信道的零系数值或信道的大系数值，则分别按前述针对估计滤波器近零系数和大系数的方法进行处理，否则，对该系数采取一种简单的零吸引惩罚。
本发明的其他优点、目标和特征在某种程度上将在随后的说明书中进行阐述，并且在某种程度上，基于对下文的考察研究对本领域技术人员而言将是显而易见的，或者可以从本发明的实践中得到教导。本发明的目标和其他优点可以通过下面的说明书来实现和获得。
为了使本发明的目的、技术方案和优点更加清楚，下面将结合附图对本发明作优选的详细描述，其中：
图1为稀疏系统辨识模型；
图2为l
c-LMS方法结构图；
图3为同频直放站；
图4为通信信道H的系数；
图5为ZA-LMS、RZA-LMS、l
0-LMS、l
0-ILMS、l
c-LMS和l
c-LMS的理论MSD最小值在不同的吸引权重ρ的MSD仿真图；
图6为l
0-LMS、l
0-ILMS、l
c-LMS和l
c-LMS的理论MSD最小值在不同的β的MSD仿真图；
图7为l
c-LMS和l
c-LMS的理论MSD最小值在不同的φ的MSD仿真图；
图8为l
c-LMS方法以更低的复杂度、更快的收敛速度达到了与l
0-ILMS同样的MSD值；
图9为描述了稀疏信道中的系数分别对应H
i(i＝1,2,3)的MSD曲线图。
以下通过特定的具体实例说明本发明的实施方式，本领域技术人员可由本说明书所揭露的内容轻易地了解本发明的其他优点与功效。本发明还可以通过另外不同的具体实施方式加以实施或应用，本说明书中的各项细节也可以基于不同观点与应用，在没有背离本发明的精神下进行各种修饰或改变。需要说明的是，以下实施例中所提供的图示仅以示意方式说明本发明的基本构想，在不冲突的情况下，以下实施例及实施例中的特征可以相互组合。
其中，附图仅用于示例性说明，表示的仅是示意图，而非实物图，不能理解为对本发明的限制；为了更好地说明本发明的实施例，附图某些部件会有省略、放大或缩小，并不代表实际产品的尺寸；对本领域技术人员来说，附图中某些公知结构及其说明可能省略是可以理 解的。
本发明实施例的附图中相同或相似的标号对应相同或相似的部件；在本发明的描述中，需要理解的是，若有术语“上”、“下”、“左”、“右”、“前”、“后”等指示的方位或位置关系为基于附图所示的方位或位置关系，仅是为了便于描述本发明和简化描述，而不是指示或暗示所指的装置或元件必须具有特定的方位、以特定的方位构造和操作，因此附图中描述位置关系的用语仅用于示例性说明，不能理解为对本发明的限制，对于本领域的普通技术人员而言，可以根据具体情况理解上述术语的具体含义。
本发明的主要研究基于稀疏系统辨识的背景，图1给出了的稀疏系统辨识模型。
在图1中，输入信号X(n)＝[x(n) x(n-1)...x(n-L+1)]
T是功率为
的零均值高斯信号,n为信号的序列号，L是滤波器长度。W(n)＝[w
0 w
1...w
L-1]
T是估计滤波器的系数。H(n)＝[h
0 h
1...h
L-1]是稀疏信道的系数，H(n)中大部分系数等于零或接近零。考虑时变性，则向量H(n)表现为：
H(n+1)＝H(n)+q(n) (1)
其中q(n)是功率为
的协方差零均值高斯白噪声，其自相关矩阵
I是单位矩阵。n(n)是功率为
的零均值高斯白噪声。假设q(n)、X(n)与n(n)都相互独立。
在图1中，y(n)和d(n)分别为
y(n)＝W
T(n)X(n) (2)
d(n)＝H
T(n)X(n)+n(n) (3)
其误差输出信号为
ZA-LMS方法的迭代更新公式
W(n+1)＝W(n)+μe(n)X(n)-ρ
ZA sgn[W(n)] (5)
其中μ为步长因子，ρ
ZA为吸引权重，
RZA-LMS方法的迭代更新方程为
其中ρ
RZA为吸引权重。
l
0-LMS方法的迭代更新方程为
W(n+1)＝W(n)+μe(n)X(n)+ρf
1(W(n)) (8)
其中ρ为吸引权重，
β是正控制参数。
l
0-ILMS方法的迭代更新方程为
W(n+1)＝W(n)+μe(n)X(n)+ρf
2(W(n)) (10)
其中
l
0-ILMS方法相较于l
0-LMS方法，只在零吸引函数多增加了一项-εW
i(n)，使得l
0-ILMS方法对稀疏系统识别的估计稀疏的精度有所增加。
以下是l
c-LMS方法的迭代更新方程
W(n+1)＝W(n)+μe(n)X(n)+f
C1(W(n)) (13)
其中
根据等式(13)与(14)，其估计滤波器迭代方程也可改为
W(n+1)＝μe(n)X(n)+f
C2(W(n)) (15)
其中
其中，ρ为吸引的强度；β为区分接近零系数与小系数的分界参数；φ为区分小系数与大系数的分界参数，并有效的将小系数进行放大，大系数进行缩小。
假设信道中有P个非零系数(大系数值)，即f
C2(W
i(n))函数中有P个系数服从
假设M个服从
L-P-M服从
假设f
2(W
i(n))函数中有N个服从
L-P-N个服从
表1给出了针对各类算法的迭代更新方程的复杂度比较。
表1各类算法的复杂度比较
以
为例，l
c-LMS方法的加法运算和乘法运算分别比现性能最优的l
0-ILMS方法低了87.5％、37.35％。其l
c-LMS方法的结构图如图2。
如今，回波消除是自适应滤波的重要应用，同频直放站存在有耦合回波，麦克风与扬声器之间也存在有耦合回波。针对于这一回波问题，提出了复杂度更低、收敛速度更快、调谐参数适用范围更广的l
c-LMS方法。其在图1中，X(n)为有用信号，H(n)为无线通信系统中的回波路径的稀疏信道，d(n)为接收到的回波信号，该回波信号并不是需要的信号。回波抵消便是将这一回波信号抵消掉。即设置一个估计滤波器W(n)，使得估计滤波器系数进行等式(15)的迭代更新，并与回波信号d(n)相减，得到最后的误差信号e(n)，这一过程便是回波抵消。
本发明的一个实际应用是用于无线通信的直放站中。
在无线通信系统中，在距离主发射天线过远和楼房密度大的地方等，会存在弱信号或信号丢失。为了解决这种问题，需要布置同频直放站，以扩大信号覆盖范围，但存在有回波导致直放站自激的问题，为解决直放站存在的问题，就可以采用自适应滤波算法解决该问题。同频直放站如图3。
如图3，主发射平台发射出有用信号，传输到同频直放站，而同频直放站又经过功放进行放大有用信号，再将有用信号发射到接收终端。然而在同频直放站发射信号的时候，有一部分信号经过无线稀疏信道又传回了同频直放站的接收端，而这一部分信号会使得同频直放站产生自激。研究表明，大部分无线通信信道都具有稀疏性，尤其是数字多媒体通信信道。所以提出一种低复杂度和性能较为优秀的用于稀疏信道和回波抵消的l
c-LMS方法，以抵消掉经无线稀疏信道传输到同频直放站的信号。
l
c-LMS的输入信号X(n)就是发射平台所发射的信号，而H(n)代表无线稀疏信道。同频直放站内含有一个估计滤波器，同频直放站将接收到的发射平台的信号经过估计滤波器生成y(n)信号；同频直放站将接受到的发射平台的信号经过无线稀疏信道与信道的高斯白噪声n(n)，合成产生出d(n)信号。在同频直放站内部，就将进行e(n)＝d(n)-y(n)计算，抵消回波信号。
稀疏信道仿真实验
在仿真中，估计滤波器迭代更新方程选用等式(15)和等式(16)。MSD被用作信道估计的准则，它是MSD(n)＝Tr(E{(W(n)-H(n))(W(n)-H(n))
T})，其中H(n)表示未知的稀疏信道，W(n)表示估计的滤波器系数。以下的所有试验，都采用了1000次蒙特卡洛来获取每一个点。选用输入信号功率为1，噪声功率为10
-2。信道系数
其信道的系数仿真如图4。
为了验证本发明算法的有效性，以上述的系统环境仿真出上述所有的算法的参数选择。表2设置了三种参数的示例。
表2参数变化设置
由图5、图6和图7给出了三种参数的变化仿真图。
图5中，l
0-ILMS和l
c-LMS方法对调谐参数都不敏感，并在图中标注了ZA-LMS、RZA-LMS和l
0-LMS方法的MSD值达到最小时的ρ值。图6中，当调谐参数β较大时，l
c-LMS方法的MSD值比LMS与l
0-ILMS方法更为优秀，l
c-LMS方法的调谐参数β的有效范围远远大于l
0-ILMS。但是β较小时，l
c-LMS方法并不稳定。图5、图6、图7中，l
c-LMS方法的理论的最小MSD值与仿真的最小MSD值基本吻合。
由此，设置仿真参数β＝100，ZA-LMS、RZA-LMS、l
0-LMS、l
0-ILMS和l
c-LMS的ρ分别为7×10
-5、1.9×10
-4、3×10
-5、2×10
-4和2×10
-4。图8、图9每一个数据点都是经过了1000次蒙特卡洛仿真得出。
图8，l
c-LMS方法以更低的复杂度、更快的收敛速度达到了与l
0-ILMS同样的MSD值。
现为了测试算法的稳定性，将上述所有算法在各种稀疏信道进行仿真。将稀疏信道的非零系数分别设置为P＝8、16、32，其信道的系数分别为H
1＝[0
16×1；0.2；0.5；-0.3；0.5；0
56×1；0.5；-0.3；0.6；-0.4；0
48×1]，H
2＝[0
24×1；0.6；-0.5；0.2；-0.3；0.8；-0.4；0.9；-0.4；0
56×1；0.2；-0.2；0.8；0.4；-0.4；-0.8；0.3；-0.2；0
32×1]，
仿真参数β＝100，μ＝0.005，ZA-LMS、RZA-LMS、l
0-LMS、l
0-ILMS和l
c-LMS的ρ分别为7×10
-5、1.9×10
-4、3×10
-5、2×10
-4和2×10
-4。上述算法的仿真如图9所示。
图9中，在多种稀疏信道仿真中，l
c-LMS方法与l
0-ILMS相比，收敛速度更快、复杂度 更低和调谐参数β的适用范围更广。该方法可应用在稀疏系统辨识和回波抵消应用中。
最后说明的是，以上实施例仅用以说明本发明的技术方案而非限制，尽管参照较佳实施例对本发明进行了详细说明，本领域的普通技术人员应当理解，可以对本发明的技术方案进行修改或者等同替换，而不脱离本技术方案的宗旨和范围，其均应涵盖在本发明的权利要求范围当中。
Claims (3)
- 零吸引惩罚与吸引补偿组合的稀疏LMS方法，其特征在于：建立稀疏系统辨识模型，输入信号X(n)＝[x(n) x(n-1)...x(n-L+1)] T是功率为的零均值高斯信号，n为信号的序列号，L是滤波器长度；W(n)＝[w 0 w 1...w L-1] T是估计滤波器的系数，H(n)＝[h 0 h 1...h L-1]是稀疏信道的系数，H(n)中大部分系数等于零或接近；考虑时变性，则向量H(n)表现为：
H(n+1)＝H(n)+q(n) (1)其中q(n)是功率为的协方差零均值高斯白噪声，其自相关矩阵
I是单位矩阵；n(n)是功率为
的零均值高斯白噪声；假设q(n)、X(n)与n(n)都相互独立；
y(n)和d(n)分别为y(n)＝W T(n)X(n) (2)d(n)＝H T(n)X(n)+n(n) (3)其误差输出信号为
l c-LMS方法的迭代更新方程W(n+1)＝W(n)+μe(n)X(n)+f C1(W(n)) (5)其中
根据等式(5)与(6)，其估计滤波器迭代方程改为W(n+1)＝μe(n)X(n)+f C2(W(n)) (7)其中
其中，ρ为吸引的强度；β为区分接近零系数与小系数的分界参数；φ为区分小系数与大系数的分界参数，并有效的将小系数进行放大，大系数进行缩小；在范围内，函数-W i(n)代入(5)中将每一次的迭代更新公式中的W i(n)抵消掉，从而迭代更新公式中含有乘积项μe(n)X(n)作为下一次的估计滤波器的系数，以实现较大的零吸引惩罚；在
范围内，函数-φW i(n)针对小系数进行放大的零吸引惩罚，称为浮动系数；在
范围内，采用全新的吸引方式，在每一次迭代更新该类型的系数值时，增加微量的补偿，促使估计滤波器的系数更快的逼近信道的大系数值。
- 根据权利要求1所述的零吸引惩罚与吸引补偿组合的稀疏LMS方法，其特征在于：在所述方法中，设置一个估计滤波器W(n)，使得估计滤波器系数进行等式(7)的迭代更新，并与回波信号d(n)相减，得到最后的误差信号e(n)，实现回波抵消。
- 根据权利要求1所述的零吸引惩罚与吸引补偿组合的稀疏LMS方法，其特征在于：将所述方法应用于同频直放站中存在的回波自激问题、麦克风中的声回波现象和降噪耳机；在无线通信的直放站中，布置同频直放站，以扩大信号覆盖范围，采用自适应滤波算法解决回波导致直放站自激的问题；主发射平台发射出有用信号，传输到同频直放站，同频直放站又经过功放进行放大有用信号，再将有用信号发射到接收终端；l c-LMS的输入信号X(n)就是发射平台所发射的信号，而H(n)代表无线稀疏信道；同频直放站内含有一个估计滤波器，同频直放站将接收到的发射平台的信号经过估计滤波器生成y(n)信号；同频直放站将接受到的发射平台的信号经过无线稀疏信道与信道的高斯白噪声n(n)，合成产生出d(n)信号；在同频直放站内部，进行e(n)＝d(n)-y(n)计算，抵消回波信号。
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