【阵列信号处理】空间匹配滤波器、锥形/非锥形最佳波束成形器、样本矩阵反演（SMI）研究（Matlab代码实现）

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📋📋📋本文目录如下：🎁🎁🎁

目录

💥1 概述

📚2 运行结果

🎉3 参考文献

🌈4 Matlab代码实现

💥1 概述

空间匹配滤波器（Spatial Matched Filter）是一种用于信号处理的滤波器。它的原理是通过将输入信号与预先存储的参考信号进行相关运算，从而增强目标信号并抑制噪声。空间匹配滤波器在雷达、声纳等领域广泛应用，用于目标检测、目标跟踪等任务。

锥形最佳波束成形器（Conical Beamformer）是一种用于信号处理的波束成形器。它通过调整传感器阵列中各个传感器的权重，使得阵列对特定方向的信号响应最大化，从而实现对目标信号的增强。锥形最佳波束成形器在无线通信、声纳等领域常用于信号接收和目标定位。

非锥形最佳波束成形器（Non-Conical Beamformer）是一种波束成形器的变种。与锥形最佳波束成形器不同的是，非锥形最佳波束成形器可以实现对多个目标信号的增强，而不仅仅是单个方向的信号。非锥形最佳波束成形器在多目标检测和定位等任务中具有重要应用。

样本矩阵反演（Sample Matrix Inversion）是一种用于信号处理的方法。它通过对接收到的信号进行采样和矩阵运算，估计信号源的位置和强度。样本矩阵反演在无线通信、雷达等领域常用于信号定位和信号源分离。

以上这些方法在阵列信号处理中都有广泛的研究和应用，它们可以提高信号的质量和可靠性，从而提升系统性能。

📚2 运行结果

部分代码：

% We illustrate the use of tapers with the spatial matched filter for the extraction
% of a radar signal in the presence of a jamming interference source using a ULA with M = 20
% elements with $\lambda/2$ spacing. The desired radar signal is known as a target and is
% present for only one sample in time. Here the target signal is at time sample (range gate)
% n = 100 and is at $\phi_s = 0^{\circ}$ with an array SNR of 20 dB. The jammer transmits a
% high-power, uncorrelated waveform (white noise). The angle of the jammer is $\phi_i = 20^{\circ}$
% and its strength is 40 dB. The additive, sensor thermal noise has unit power (0 dB).
%
% Copyright 2016 - 2026, Ilias S. Konsoulas.

%% Workspace Initialization.
clc; clear; close all;

%% Signal Definitions.
M = 20; % Number of Array Elements.
N = 200; % Number of Signal Samples.
n = 1:N; % Sample Index Vector.
lambda = 1; % Incoming Signal Wavelength in (m).
d = lambda/2; % Interelement Distance in (m).
SNR = 20; % target volatege signal array SNR in dBs.
INR = 40; % interference array SNR in dBs.
phi_s = 0; % target azimuth angle in degrees.
phi_i = 20; % interference azimuth angle in degrees.

u_s = (d/lambda)*sin(phi_s*pi/180); % Target Normalized Spatial Frequency.
u_si = (d/lambda)*sin(phi_i*pi/180); % Jammer Normalized Spatial Frequency.

s = zeros(M,N);
s(:,100) = 10^(SNR/20)*exp(-1i*2*pi*u_s*(0:M-1).')/sqrt(M);

% Uncorrelated unit power thermal noise samples drawn from a complex Gaussian distribution
w = (randn(M,N)+1i*randn(M,N))/sqrt(2);

% The interference (jammer) vector is generated by:
% v_i = exp(-1i*pi*[0:M-1]'*sin(phi_i*pi/180))/sqrt(M); mentioned in the book is wrong.
v_i = exp(-1i*2*pi*u_si*(0:M-1).')/sqrt(M);
i_x = 10^(INR/20)*v_i*(randn(1,N)+1i*randn(1,N))/sqrt(2);

%The three signals are added to produce the overall array signal
x = s + i_x + w;

% Two beamformers (steered to phi = 0.) are applied to the resulting array returns: a spatial matched
% filter and a tapered beamformer with a -50-dB sidelobe level. The resulting beamformer output
% signals are shown in Figure 11.15. The spatial matched filter is unable to reduce the jammer
% sufficiently to observe the target signal at n = 100. However, the tapered beamformer is able
% to attenuate the jammer signal below the thermal noise level and the target is easily extracted.
% The target signal is approximately 18.5 dB with the -1.5 dB loss due to the tapering loss in (11.2.24).

%% Spatial Matched Filter or Steering Vector Beamformer.
c_mf = exp(-1i*2*pi*u_s*(0:M-1).')/sqrt(M);

% Spatial Dolph-Chebychev Window of length M = 20 with -50 dB sidelobe attenuation:
w = chebwin(M,50);

% Compute the Combined Taper by taking the Hadamard product:
c_mft = c_mf.*w;

% Normalize the combined taper vector: