From f5c9f10e0d7834a1c27a064583aa9766652171fd Mon Sep 17 00:00:00 2001 From: Josh Gao Date: Mon, 5 Feb 2024 16:47:55 +0800 Subject: [PATCH] update MVDR simulation --- source/_posts/2024-02-01-algo-MVDR.md | 176 ++++++++++++++- ...02-01-algo-MVDR-010-IdealCaponSpectrum.svg | 135 +++++++----- ...-01-algo-MVDR-020-IdealCaponResolution.svg | 201 ++++++++++++++++++ 3 files changed, 448 insertions(+), 64 deletions(-) create mode 100644 source/images/post/2024-02-01-algo-MVDR/2024-02-01-algo-MVDR-020-IdealCaponResolution.svg diff --git a/source/_posts/2024-02-01-algo-MVDR.md b/source/_posts/2024-02-01-algo-MVDR.md index 6c3a944..3b3c273 100644 --- a/source/_posts/2024-02-01-algo-MVDR.md +++ b/source/_posts/2024-02-01-algo-MVDR.md @@ -82,13 +82,25 @@ $$\begin{equation} # MVDR 算法仿真 -## 理想空域谱 +  使用 ULA（Uniform Linear Array，均匀线阵）对 MVDR 算法进行仿真，阵元间距为半波长。 -![理想 Capon 谱](../images/post/2024-02-01-algo-MVDR/2024-02-01-algo-MVDR-010-IdealCaponSpectrum.svg){width=800px} +## 理想情况 + +  在理想情况下，各阵元的位置与预期一致，各阵元的复加权器是没有误差的，目标信号来向与期望方向一致，且信号和干扰加噪声可以分离。 + +### 空域谱 + +  Capon 空域谱表示 MVDR 复加权在整个空域范围内的响应。假设 1 个信号和 6 个干扰同时入射，信噪比 $\mathrm{SNR}=30\mathrm{dB}$，干噪比 $\mathrm{INR} = 70\mathrm{dB}$，信号和干扰来向在 $[0^\circ,180^\circ]$ 内服从均匀分布，使用 1000 个快拍进行仿真。 + +  得到的空域谱如[图 1](#fig.1)，其中期望来向用红色点划线表示，干扰来向用绿色点划线表示。仿真同时还计算了输出 SINR，用于衡量残余干扰的大小。 + + + +![图 1 理想 Capon 谱](../images/post/2024-02-01-algo-MVDR/2024-02-01-algo-MVDR-010-IdealCaponSpectrum.svg){width=700px} {% note primary MATLAB Code %} -``` matlab mvdr_idea.m +``` matlab mvdr_spec.m %% High-Resolution Frequency-Wavenumber Spectrum Analysis % J. Capon, “High-Resolution Frequency-Wavenumber Spectrum Analysis,” _Proceedings % of the IEEE_, vol. 57, no. 8, pp. 1408–1418, Aug. 1969, doi: + +![图 2 Capon 分辨率](../images/post/2024-02-01-algo-MVDR/2024-02-01-algo-MVDR-020-IdealCaponResolution.svg){width=700px} + +{% note primary MATLAB Code %} + +``` matlab mvdr_resolution.m +%% High-Resolution Frequency-Wavenumber Spectrum Analysis +% J. Capon, “High-Resolution Frequency-Wavenumber Spectrum Analysis,” _Proceedings +% of the IEEE_, vol. 57, no. 8, pp. 1408–1418, Aug. 1969, doi: . +% +% H. L. Van Trees, _Optimum Array Processing: Part IV of Detection, Estimation, +% and Modulation Theory_. New York, NY: Wiley, 2002. + +clear +close all + +rng(253) + +%% Scan Configuration +elemNumArr = [4,8,12,16]; +intAngArr = 0.1:0.1:50; + +sinrOut = zeros(length(elemNumArr),length(intAngArr)); + +for elemNumIdx = 1:length(elemNumArr) +for intAngIdx = 1:length(intAngArr) + +%% Array Parameters + +% elements in array +elemNum = elemNumArr(elemNumIdx); + +% spacing wrt wavelength +elemSpac = 0.5; + +% element locations +elemLoc = 0:elemSpac:(elemNum-1)*elemSpac; + +% Signal Parameters + +% signal number +sigNum = 2; + +% direction of arrival +desAng = 90; +sigAng = [desAng,desAng+intAngArr(intAngIdx)]; + +% signal to noise ratio +snr = [0,70]; + +% sample number +sampleNum = 1024; + +%% Impinging Waves/Signal + +% wave generation, here are some sets of uncorrelated white noise +txWave = randn(sigNum,sampleNum); + +% transmit power control based on given snr +if length(snr) == 1 + txWave = db2mag(snr)*txWave; +elseif length(snr) >= sigNum + if length(snr) > sigNum + disp('WARN: Extra SNRs are ignored.') + end + for i = 1:sigNum + txWave(i,:) = db2mag(snr(i))*txWave(i,:); + end +elseif length(snr) < sigNum + disp('WARN: The last SNR is used for the rest of the signals.') + for i = 1:sigNum + if i <= length(snr) + txWave(i,:) = db2mag(snr(i))*txWave(i,:); + else + txWave(i,:) = db2mag(snr(end))*txWave(i,:); + end + end +end + +%% Array Manifold Matrix +if length(sigAng) > sigNum + disp('WARN: Extra angles are ignored.') +elseif length(sigAng) < sigNum + disp('ERROR: Angle number is less than signal number.') + return +end + +arrayMF = exp(-1i*pi*elemLoc'*cos(sigAng(1:sigNum)/180*pi)); + +% signal & interference manifold vector +sigMF = arrayMF(:,1); +intMF = arrayMF(:,2:end); + +% impinging signal & interference +rxSig = sigMF*txWave(1,:); +rxIpn = intMF*txWave(2:end,:) + randn(elemNum,sampleNum); + +%% AWGN Channel & Received Wave +rxWave = rxSig + randn(elemNum,sampleNum); + +%% Array Processing + +% interference-plus-noise covariance matrix +ipnCovar = rxIpn*rxIpn'; + +% MVDR weight vector +weight = ipnCovar\sigMF/(sigMF'*(ipnCovar\sigMF)); +% = inv(ipnCovar)*sigMF/(sigMF'*inv(ipnCovar)*sigMF); + +% nomarlized output SINR +sinrIdeal = snr(1)+pow2db(elemNum); +sinrOut(elemNumIdx,intAngIdx) = pow2db(var(weight'*rxSig)/ ... + var(weight'*rxIpn)) - sinrIdeal; + +end + +plot(intAngArr,smoothdata(sinrOut(elemNumIdx,:)),DisplayName=['$N=', ... + num2str(elemNumArr(elemNumIdx)),'$']) +hold on + +end + +%% figures +plot([min(intAngArr),max(intAngArr)],[-3,-3],HandleVisibility="off") +hold off + +title('MVDR Output SINR v.s. Angular Difference') +xlabel('Angular Difference between Desigred and Interference Signal (°)') +ylabel('Normalized Output SINR (dB)') +ylim([-5 max(smoothdata(sinrOut,2),[],'all')+1]) + +legend(Interpreter="latex",Location="southeast"); + +grid on +``` + +{% endnote %} + +### 理想误码率 + +## 失配情况 + +### 分辨率 + +### 误码率 # Reference diff --git a/source/images/post/2024-02-01-algo-MVDR/2024-02-01-algo-MVDR-010-IdealCaponSpectrum.svg b/source/images/post/2024-02-01-algo-MVDR/2024-02-01-algo-MVDR-010-IdealCaponSpectrum.svg index a6dca1b..cde137b 100644 --- a/source/images/post/2024-02-01-algo-MVDR/2024-02-01-algo-MVDR-010-IdealCaponSpectrum.svg +++ b/source/images/post/2024-02-01-algo-MVDR/2024-02-01-algo-MVDR-010-IdealCaponSpectrum.svg @@ -23,8 +23,8 @@ />-60-50-40-30-20-100Ideal Capon SpectrumCapon SpecDesiredInterference diff --git a/source/images/post/2024-02-01-algo-MVDR/2024-02-01-algo-MVDR-020-IdealCaponResolution.svg b/source/images/post/2024-02-01-algo-MVDR/2024-02-01-algo-MVDR-020-IdealCaponResolution.svg new file mode 100644 index 0000000..02de764 --- /dev/null +++ b/source/images/post/2024-02-01-algo-MVDR/2024-02-01-algo-MVDR-020-IdealCaponResolution.svg @@ -0,0 +1,201 @@ + + +