【信号处理】基于高阶统计量特征的通信系统中微弱信号检测附matlab代码

1 内容介绍

高阶统计量被广泛地应用在雷达、通信,生物医学、故障诊断中。传统的信号检测方法在低信噪比高动态下的检测性能很差。而双谱对高斯白噪声是不敏感的、高动态和低信噪比都是不敏感的。使用高阶统计量用于检测高动态和低信噪比的微弱信号,在此条件下高阶统计量方法得到了的优良性能。在不同的动态和信噪比条件下的实验结果都显示了优良性能。

2 仿真代码

function y_cum = cum2est (y, maxlag, nsamp, overlap, flag) %CUM2EST Covariance function. % Should be involed via "CUMEST" for proper parameter checks. % y_cum = cum2est (y, maxlag, samp_seg, overlap, flag)

% y: input data vector (column) % maxlag: maximum lag to be computed % samp_seg: samples per segment (<=0 means no segmentation) % overlap: percentage overlap of segments % flag: 'biased', biased estimates are computed % 'unbiased', unbiased estimates are computed. % y_cum: estimated covariance, % C2(m) -maxlag <= m <= maxlag % all parameters must be specified!

% RESTRICTED RIGHTS LEGEND % Use, duplication, or disclosure by the Government is subject to % restrictions as set forth in subparagraph (c) (1) (ii) of the % Rights in Technical Data and Computer Software clause of DFARS % 252.227-7013. % Manufacturer: United Signals & Systems, Inc., P.O. Box 2374, % Culver City, California 90231. % % This material may be reproduced by or for the U.S. Government pursuant % to the copyright license under the clause at DFARS 252.227-7013.

% C2(m) := E conj(x(n)) x(n+k)

% ---------- parameter checks are done by CUMEST ----------------

[n1,n2] = size(y); N = n1*n2;

overlap = fix(overlap/100 * nsamp); nrecord = fix( (N - overlap)/(nsamp - overlap) ); nadvance = nsamp - overlap;

y_cum = zeros(maxlag+1,1); ind = 1:nsamp;

for i=1:nrecord x = y(ind); x = x(:) - mean(x); % make sure we have a colvec for k = 0:maxlag y_cum(k+1) = y_cum(k+1) + x([1:nsamp-k])' * x([k+1:nsamp]); end ind = ind + nadvance; end if (flag(1:1) == 'b' | flag(1:1) == 'B') y_cum = y_cum / (nsamp*nrecord); else y_cum = y_cum ./ (nrecord * (nsamp-[0:maxlag]' )); end if maxlag > 0, y_cum = [conj(y_cum(maxlag+1:-1:2)); y_cum]; end

return

function y_cum = cum4est (y, maxlag, nsamp, overlap, flag, k1, k2)
%CUM4EST Fourth-order cumulants.
% Should be invoked via CUMEST for proper parameter checks
% y_cum = cum4est (y, maxlag, samp_seg, overlap, flag, k1, k2)

% Computes sample estimates of fourth-order cumulants
% via the overlapped segment method.
%
% y_cum = cum4est (y, maxlag, samp_seg, overlap, flag, k1, k2)
% y: input data vector (column)
% maxlag: maximum lag
% samp_seg: samples per segment
% overlap: percentage overlap of segments
% flag : 'biased', biased estimates are computed
% : 'unbiased', unbiased estimates are computed.
%   k1,k2 : the fixed lags in C3(m,k1) or C4(m,k1,k2); see below
%   y_cum : estimated fourth-order cumulant slice
%   C4(m,k1,k2) -maxlag <= m <= maxlag
%    Note: all parameters must be specified

% Copyright (c) 1991-2001 by United Signals & Systems, Inc.
% $Revision: 1.4 $
% A. Swami January 20, 1993

% Modified, Januar 20, 1994 to handle complex case properly:
% c4(t1,t2,t3) := cum( x^*(t), x(t+t1), x(t+t2), x^*(t+t3) )

% RESTRICTED RIGHTS LEGEND
% Use, duplication, or disclosure by the Government is subject to
% restrictions as set forth in subparagraph (c) (1) (ii) of the
% Rights in Technical Data and Computer Software clause of DFARS
% 252.227-7013.
% Manufacturer: United Signals & Systems, Inc., P.O. Box 2374,
% Culver City, California 90231.
%
% This material may be reproduced by or for the U.S. Government pursuant
% to the copyright license under the clause at DFARS 252.227-7013.

% c4(t1,t2,t3) := cum( x^*(t), x(t+t1), x(t+t2), x^*(t+t3) )
% cum(w,x,y,z) := E(wxyz) - E(wx)E(yz) - E(wy)E(xz) - E(wz)E(xy)
% and, w,x,y,z are assumed to be zero-mean.

% ---- Parameter checks are done in CUMEST ----------------------
[n1,n2] = size(y);
N = n1 * n2;
overlap0 = overlap;
overlap = fix(overlap/100 * nsamp);
nrecord = fix( (N - overlap)/(nsamp - overlap) );
nadvance = nsamp - overlap;

% ------ scale factors for unbiased estimates --------------------

nlags = 2 * maxlag + 1;
zlag = 1 + maxlag;
tmp = zeros(nlags,1);
if (flag(1:1) == 'b' || flag(1:1) == 'B')
scale = ones(nlags,1) / nsamp;
else
ind = [-maxlag:maxlag]';
kmin = min(0,min(k1,k2));
kmax = max(0,max(k1,k2));
scale = nsamp - max(ind,kmax) + min(ind,kmin);
scale = ones(nlags,1) ./ scale;
end
mlag = maxlag + max(abs([k1,k2]));
mlag = max( mlag, abs(k1-k2) );
mlag1 = mlag + 1;
nlag = maxlag;
m2k2 = zeros(2*maxlag+1,1);

if (any(any(imag(y) ~= 0))) complex_flag = 1;
else complex_flag = 0;
end

% ----------- estimate second- and fourth-order moments; combine ------

y_cum = zeros(2*maxlag+1,1);
R_yy = zeros(2*mlag+1,1);

ind = 1:nsamp;
for i=1:nrecord
tmp = y_cum * 0 ;
x = y(ind); x = x(:) - mean(x); z = x * 0; cx = conj(x);
% create the "IV" matrix: offset for second lag

if (k1 >= 0)
z(1:nsamp-k1) = x(1:nsamp-k1,:) .* cx(k1+1: nsamp,:);
else
z(-k1+1:nsamp) = x(-k1+1:nsamp) .* cx(1:nsamp+k1);
end

% create the "IV" matrix: offset for third lag

if (k2 >= 0)
z(1:nsamp-k2) = z(1:nsamp-k2) .* x(k2+1: nsamp);
z(nsamp-k2+1:nsamp) = zeros(k2,1);
else
z(-k2+1:nsamp) = z(-k2+1:nsamp) .* x(1:nsamp+k2);
z(1:-k2) = zeros(-k2,1);
end

tmp(zlag) = tmp(zlag) + z' * x;
for k = 1:maxlag
tmp(zlag-k) = tmp(zlag-k) + z([k+1:nsamp])' * x([1:nsamp-k]);
tmp(zlag+k) = tmp(zlag+k) + z([1:nsamp-k])' * x([k+1:nsamp]);
end

y_cum = y_cum + tmp .* scale ;

R_yy = cum2est(x,mlag,nsamp,overlap0,flag);
if (complex_flag) % We need E x(t)x(t+tau) stuff also:
M_yy = cum2x(conj(x),x,mlag,nsamp,overlap0,flag);
else
M_yy = R_yy;
end
y_cum = y_cum ...
- R_yy(mlag1+k1) * R_yy(mlag1-k2-nlag:mlag1-k2+nlag) ...
- R_yy(k1-k2+mlag1) * R_yy(mlag1-nlag:mlag1+nlag) ...
- M_yy(mlag1+k2)' * M_yy(mlag1-k1-nlag:mlag1-k1+nlag) ;

ind = ind + nadvance;
end

y_cum = y_cum / nrecord;
return

3 运行结果

4 参考文献

[1]翟逸群, 黄建国, 张群飞,等. 基于高阶统计量的高动态微弱信号检测[C]// 第七届全国信号和智能信息处理与应用学术会议会刊. 2013.

博主简介：擅长智能优化算法、神经网络预测、信号处理、元胞自动机、图像处理、路径规划、无人机等多种领域的Matlab仿真，相关matlab代码问题可私信交流。

部分理论引用网络文献，若有侵权联系博主删除。