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运用波束形成技术，利用麦克风阵列估计指定方向上的混有噪声和干扰的期望信号。这些麦克风阵元位于不同的空间位置，对声波进行空间采样，然后对采样信号进行处理以衰减干扰信号并提取期望信号。这样就得到一个特定的阵列空间响应，其主瓣指向期望信号而对干扰进行陷波。
自适应波束形成能够分离在相同载波频率上传输的用户信号，因此提供了在空分多址场景中支持多用户的实用手段。此外，为了进一步提高可实现的带宽效率，高吞吐量正交幅度调制QAM方案在许多无线网络标准中变得流行，特别是在最近的WiMax标准中。多天线辅助多用户系统的自适应波束形成辅助检测其采用高阶QAM信令。
传统上，最小均方误差（MMSE）自适应波束形成辅助接收机的设计被认为是最先进的。然而，最近工作[1]提出了一种新的波束形成辅助最小符号误码率（MSER）设计并且证明了这种MSER设计提供了显著的性能增强，在可实现的符号错误率方面超过标准MMSE设计。该MSER波束形成设计在此贡献中得到充分发展。特别是MSER的自适应实现详细研究了波束形成算法，即最小符号误码率算法。在仿真中评估了所提出的自适应MSER波束形成方案，并与自适应MMSE波束形成基准。
该算法的流程和理论公式如下：
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clc;clear;close all;warning off;SNR_set = [10:1:24];BER = 1;nRx = 4;nTx = 3;
frame_length = 1000;Bers = [];%论文table 2alpha = [0,-70,65,32];SIR = [0,0,0,0];
for SNR = SNR_set; N0 = 1/(10^(SNR/10)); delta2 = N0; error_count = 0;
bit_count = 0; index = 0; ERR_NUM = []; tmps = 0;
while error_count < 500000 index = index+1; for kk=1:nTx
bits(kk,:) = round(rand(1,frame_length)); symbols(kk,:) = qammod(bits(kk,:),16);
end %transmit signal s = symbols; u = reshape(s,nTx,nRx,length(s)/nRx);
%Channel h = 1/sqrt(2)*[randn(nRx,nTx,length(s)/nRx) + j*randn(nRx,nTx,length(s)/nRx)];
for ij = 1:nTx p(:,ij,:) = h(:,ij,:).*exp(j*alpha(ij)*pi/180); end
%mmse beamforming WK = []; WK2 = []; w = []; LMS = zeros(1,length(s)/nRx);
dt = []; for i=1:length(s)/nRx for ii = 1:length(SIR)
u2(:,ii) = u(:,ii,i)*10^(SIR(ii)/10); end XN(:,:,i)= awgn(u2,SNR,'measured');
%定义接收信号 w(:,:,i) = inv(p(:,:,i)*p(:,:,i)'+2*delta2^2*eye(nRx))*p(:,1,i);
Nsb = nRx; M = nRx; r =(2*sqrt(M)-2)/sqrt(M);
if i == 1 WK = w(:,:,i)'*p(:,:,i); dt = -0.0001*[ones(1,Nsb)]';
else bk = bits(1,nRx*(i-2)+1:nRx*(i-1)); bk = 2*bk-1;
x1_ = bk; p1 = p(:,1,i); yr = real(yhat(:,:,i-1));
cr = real(w(:,:,i)); for iii = 1:Nsb l = iii;
ul = 2*l-sqrt(M) - 1; Rt{iii} = exp(-(yr(iii) - cr(iii)*(ul-1))^2/(2*delta2^2))*
((yr(iii) - cr(iii)*(ul-1))*w(:,:,i) - x1_(iii) + (ul-1)*p1); end
PER= r/(2*Nsb*sqrt(2*pi)*delta2) * (Rt{1} + Rt{2} + Rt{3} + Rt{4}); yi
= imag(yhat(:,:,i-1)); ci = imag(w(:,:,i)); for iii = 1:Nsb
q = iii; uq = 2*q-sqrt(M) - 1;
It{iii} = exp(-(yi(iii) - ci(iii)*(uq-1))^2/(2*delta2^2))*((yi(iii) - ci(iii)*(uq-1))*w(:,:,i) +
sqrt(-1)*x1_(iii) + (uq-1)*p1); end PEI= r/(2*Nsb*sqrt(2*pi)*delta2) *
(It{1} + It{2} + It{3} + It{4}); PEB= PER + sqrt(-1)*PEI;
for is = 1:length(PEB) if isnan(abs(PEB(is))) == 1 PEB(is) = 1;
end end WWt(:,i-1) = PEB; if i>3
fai=max(min((abs(WWt(:,i-1)).^2)./(abs(WWt(:,i-2)).^2),1),0); else
fai=ones(nRx,1); end dt = fai.*dt - PEB; miu
= 5e-6; WK = WK + miu*[dt(1:nTx)]'; end
= WK/(max(abs(WK))); yhat(:,:,i) = WK*XN(:,:,i); R1 = real(yhat(:,:,i));
I1 = imag(yhat(:,:,i)); s_hat(:,:,i)= qamdemod(R1+sqrt(-1)*I1,16);
end s_hat1 = squeeze(s_hat); recovered_bits = reshape(s_hat1,1,length(s));
ERR_NUM = sum(recovered_bits ~= bits(1,:)); %异常错误不进行统计%
if index <= 200% tmps = tmps + ERR_NUM; % else%
if ERR_NUM/(tmps/200) < 20 SNR error_count
error_count = error_count + ERR_NUM; bit_count = bit_count + frame_length;
% end% end end %Calculate the BER BER = error_count/bit_count;
Bers = [Bers,BER];enderror_countbit_countfigure;semilogy(SNR_set,Bers,'b-o');axis([10,40,1.0001e-6,1]);
ylabel('BER');xlabel('SNR');grid on% save r2ber.mat SNR_set Bers 1.2.3.4.5.6.7.8.9.10.11.12.13.14.15.16.17.
18.19.20.21.22.23.24.25.26.27.28.29.30.31.32.33.34.35.36.37.38.39.40.41.42.43.44.45.46.47.48.49.50.51.52.53.
54.55.56.57.58.59.60.61.62.63.64.65.66.67.68.69.70.71.72.73.74.75.76.77.78.79.80.81.82.83.84.85.86.87.88.89.
90.91.92.93.94.95.96.97.98.99.100.101.102.103.104.105.106.107.108.109.110.111.112.113.114.115.116.117.118.119.
120.121.122.123.124.125.126.127.128.129.130.131.132.仿真结果如下：
提出了一种用于多天线辅助的自适应MSER波束形成技术采用高通量QAM信令的多用户通信系统。已经证明了MSER波束形成设计可以在可实现系统的SER方面提供比标准MMSE设计显著的性能增强。它已经还已经证明，MSER波束形成设计提供了更高的用户容量与传统的MMSE波束形成相比，在远近传感器中更为鲁棒设计已经使用称为LSER技术的随机梯度自适应算法实现了MSER波束形成解决方案的自适应实现。模拟研究结果清楚地表明，自适应LSER波束形成能够：在快速衰落条件下成功运行，其性能始终优于自适应LMS波束形成基准。
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