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🔥 内容介绍
在当今的通信领域中，多用户多输入多输出（MU-MIMO）系统已经成为无线通信网络中的重要组成部分。MU-MIMO技术的出现，使得基站能够同时与多个用户进行通信，从而显著提高了系统的容量和性能。然而，MU-MIMO系统中的无穷大范数检测问题一直是一个具有挑战性的研究方向。
无穷大范数检测是指在MU-MIMO系统中，通过接收到的信号来估计发送信号的无穷大范数。由于MU-MIMO系统中存在多个用户和多个天线，无穷大范数检测问题变得非常复杂。为了解决这个问题，研究者们提出了许多不同的方法和算法。
其中一种被广泛应用的方法是基于交替方向乘子法（ADMM）的无穷大范数检测算法。ADMM是一种迭代算法，通过将原始问题分解为几个子问题来求解。在MU-MIMO系统中，ADMM算法可以将无穷大范数检测问题转化为一个带有约束的凸优化问题，然后通过迭代求解该问题来得到最优解。
ADMM算法的优势在于它具有较好的收敛性和适应性。它可以有效地解决MU-MIMO系统中的无穷大范数检测问题，并且在实际应用中具有较高的性能。此外，ADMM算法还可以与其他优化算法相结合，进一步提高检测性能。
然而，尽管ADMM算法在无穷大范数检测问题中具有很大的潜力，但仍然存在一些挑战和限制。其中一个挑战是算法的复杂性和计算开销。由于MU-MIMO系统中的天线和用户数量通常很大，ADMM算法需要处理大规模的优化问题，这将导致计算复杂度的增加。另外，ADMM算法的收敛速度也可能受到系统参数和信道条件的影响
📣 部分代码
disp('using default simulation settings and parameters...') % set default simulation parameters par.suffix = 'exp'; % simulation name suffix: 'exp' experimental par.runId = 0; % simulation ID (used to reproduce results) par.MR = 64; % receive antennas par.MT = 16; % user terminals (set not larger than MR!) par.mod = '64QAM'; % modulation type: 'BPSK','QPSK','16QAM','64QAM' par.simName = ['ERR_' num2str(par.MR) 'x' num2str(par.MT) '_' par.mod '_' par.suffix] ; % simulation name (used for saving results) par.trials = 100; % number of Monte-Carlo trials (transmissions) par.SNRdB_list = 10:2:20; % list of SNR [dB] values to be simulated par.detector = {'Conjugate-Gradient','Neumann','Gauss-Seidel','OCDBOX','ADMIN'}; % define detector(s) to be simulated % algorithm specific par.alg.maxiter = 3;else disp('use custom simulation settings and parameters...') par = varargin{1}; % only argument is par structure end% -- initialization% use runId random seed (enables reproducibility)% rng(par.runId);% set up Gray-mapped constellation alphabet (according to IEEE 802.11)switch (par.mod) case 'BPSK' par.symbols = [ -1 1 ]; case 'QPSK' par.symbols = [ -1-1i,-1+1i, ... +1-1i,+1+1i ]; case '16QAM' par.symbols = [ -3-3i,-3-1i,-3+3i,-3+1i, ... -1-3i,-1-1i,-1+3i,-1+1i, ... +3-3i,+3-1i,+3+3i,+3+1i, ... +1-3i,+1-1i,+1+3i,+1+1i ]; case '64QAM' par.symbols = [ -7-7i,-7-5i,-7-1i,-7-3i,-7+7i,-7+5i,-7+1i,-7+3i, ... -5-7i,-5-5i,-5-1i,-5-3i,-5+7i,-5+5i,-5+1i,-5+3i, ... -1-7i,-1-5i,-1-1i,-1-3i,-1+7i,-1+5i,-1+1i,-1+3i, ... -3-7i,-3-5i,-3-1i,-3-3i,-3+7i,-3+5i,-3+1i,-3+3i, ... +7-7i,+7-5i,+7-1i,+7-3i,+7+7i,+7+5i,+7+1i,+7+3i, ... +5-7i,+5-5i,+5-1i,+5-3i,+5+7i,+5+5i,+5+1i,+5+3i, ... +1-7i,+1-5i,+1-1i,+1-3i,+1+7i,+1+5i,+1+1i,+1+3i, ... +3-7i,+3-5i,+3-1i,+3-3i,+3+7i,+3+5i,+3+1i,+3+3i ]; end% extract average symbol energypar.Es = mean(abs(par.symbols).^2);% precompute bit labelspar.Q = log2(length(par.symbols)); % number of bits per symbolpar.bits = de2bi(0:length(par.symbols)-1,par.Q,'left-msb');% track simulation timetime_elapsed = 0;% -- start simulation% initialize result arrays (detector x SNR)res.VER = zeros(length(par.detector),length(par.SNRdB_list)); % vector error rateres.SER = zeros(length(par.detector),length(par.SNRdB_list)); % symbol error rateres.BER = zeros(length(par.detector),length(par.SNRdB_list)); % bit error rate% generate random bit stream (antenna x bit x trial)bits = randi([0 1],par.MT,par.Q,par.trials);% trials loopticfor t=1:par.trials % generate transmit symbol idx = bi2de(bits(:,:,t),'left-msb')+1; s = par.symbols(idx).'; % generate iid Gaussian channel matrix & noise vector n = sqrt(0.5)*(randn(par.MR,1)+1i*randn(par.MR,1)); H = sqrt(0.5)*(randn(par.MR,par.MT)+1i*randn(par.MR,par.MT)); % transmit over noiseless channel (will be used later) x = H*s; % SNR loop for k=1:length(par.SNRdB_list) % Current SNR point in dBs SNR_dB = par.SNRdB_list(k); % Linear SNR SNR_lin = 10.^(SNR_dB./10); % Variance of complex noise per receive antenna N0 = par.Es*par.MT/SNR_lin; % transmit data over noisy channel y = x+sqrt(N0)*n; % algorithm loop for d=1:length(par.detector) switch (par.detector{d}) % select algorithms case 'MF' % Matched Filter [idxhat,bithat] = MF(par,H,y,N0); case 'MMSE' % MMSE detector [idxhat,bithat] = MMSE(par,H,y,N0); case 'SIMO' % SIMO lower bound [idxhat,bithat] = SIMO(par,H,y,N0,s); case 'ADMIN' % ADMM-based Infinity Norm detector [idxhat,bithat] = ADMIN(par,H,y,N0); case 'OCDBOX' % co-ordinate descent (optimized) detector [idxhat,bithat] = OCDBOX(par,H,y); case 'Neumann' % coordinate descent [idxhat,bithat] = Neumann(par,H,y,N0); case 'Gauss-Seidel' % Gauss-Seidel detector [idxhat,bithat] = Gauss_Seidel(par,H,y,N0); case 'Conjugate-Gradient' % conjugate gradient detector [idxhat,bithat] = CG(par,H,y,N0); otherwise error('par.detector type not defined.') end % -- compute error metrics err = (idx~=idxhat); res.VER(d,k) = res.VER(d,k) + any(err); res.SER(d,k) = res.SER(d,k) + sum(err)/par.MT; res.BER(d,k) = res.BER(d,k) + sum(sum(bits(:,:,t)~=bithat))/(par.MT*par.Q); end % algorithm loop end % SNR loop % keep track of simulation time if toc>10 time=toc; time_elapsed = time_elapsed + time; fprintf('estimated remaining simulation time: %3.0f min.\n',time_elapsed*(par.trials/t-1)/60); tic end end % trials loop
⛳️ 运行结果
🔗 参考文献
S. Shahabddin, M. Juntti and C. Studer, "ADMM-based infinity-norm detector for large-scale MIMO", IEEE International symposium of circuits and systems, Maryland, USA, May 2017.
