%% This program evaluates the minimum mean-squared error (MMSE) of the symbol-spaced % and half symbol-spaced equalizers. The equivalent baseband channel cBB(t)% is obtained according to (3.54). The MMSE values are then calculated, following % the formulations in Section 11.3.1. %% The variance of data symbols s[n], sigmas2, is set equal to one.% The noise variance sigmanuc2 is also set equal to one.  %clear allTb=0.0001; L=100; Ts=Tb/L; fs=1/Ts; fc=100000; alpha=0.5; sigmas=1; sigmanuc=0.01; c=[1 zeros(1,91) 0.4];c=[0.5 zeros(1,60) 1 zeros(1,123) 0.25]; c=[1 zeros(1,67) 0.75 zeros(1,145) 0.4]; c=[1 zeros(1,75) 0.6 zeros(1,103) 0.2]; c=c/sqrt(c*c');pT=sr_cos_p(16*L,L,alpha)'; pR=pT; %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%  Construction of the equivalent baseband channel    %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%p=conv(pT,pR);c=c.*exp(-j*2*pi*[0:length(c)-1]*Ts*fc);cBB=conv(c,p);pR=sqrt(L/2)*pR(1:L/2:end);N=31;           % Equalizer orderN1=N+1;          % Equalizer length%%%%%%%%%%%%%%%%%%%%%%%%%%%  Tb spaced equalizer   %%%%%%%%%%%%%%%%%%%%%%%%%%%for k=1:L    cBB0=cBB(k:L:end);    Delta=round((length(cBB(1:L:end))+N1)/2);    C=toeplitz([cBB0 zeros(1,N)],[cBB0(1) zeros(1,N)]);    P0=toeplitz([pR(1:2:end) zeros(1,N)],[pR(1) zeros(1,N)]);    P1=toeplitz([pR(2:2:end) zeros(1,N)],[pR(2) zeros(1,N)]);    Q=[C; (sigmanuc/sigmas)*P0; (sigmanuc/sigmas)*P1];    d=[zeros(Delta,1); 1;zeros(length(Q(:,1))-(Delta+1),1)];    Ryy=(Q'*Q+1e-12*eye(N1));    pyd=(Q'*d);    w=Ryy\pyd;    mmse0(k)=sigmas^2*real(1-w'*pyd);    spower(k)=sum(abs(cBB0).^2);    D(k)=Delta;end%%%%%%%%%%%%%%%%%%%%%%%%%%%%  Tb/2 spaced equalizer  %%%%%%%%%%%%%%%%%%%%%%%%%%%%cBBf=cBB(1:L/2:end);Delta=round((length(cBBf)+N1)/4); for k=1:L    cBBf=cBB(k:L/2:end);    C=toeplitz([cBBf zeros(1,N)],[cBBf(1) zeros(1,N)]); C=C(1:2:end,:);    P=toeplitz([pR zeros(1,N)],[pR(1) zeros(1,N)]);    Q=[C; (sigmanuc/sigmas)*P];    d=[zeros(Delta,1); 1;zeros(length(Q(:,1))-(Delta+1),1)];    Ryy=(Q'*Q+1e-6*eye(N1));    pyd=(Q'*d);    w=Ryy\pyd;    mmsef1(k)=sigmas^2*real(1-w'*pyd);endN=61;N1=N+1;cBBf=cBB(1:L/2:end);Delta=round((length(cBBf)+N1)/4);for k=1:L    cBBf=cBB(k:L/2:end);    C=toeplitz([cBBf zeros(1,N)],[cBBf(1) zeros(1,N)]); C=C(1:2:end,:);    P=toeplitz([pR zeros(1,N)],[pR(1) zeros(1,N)]);    Q=[C; (sigmanuc/sigmas)*P];    d=[zeros(Delta,1); 1;zeros(length(Q(:,1))-(Delta+1),1)];    Ryy=(Q'*Q+1e-6*eye(N1));    pyd=(Q'*d);    w=Ryy\pyd;    mmsef2(k)=sigmas^2*real(1-w'*pyd);endfiguresubplot(2,1,1),plot([0:L-1]/L,spower); ylabel('Signal Power')subplot(2,1,2),semilogy([0:L-1]/L,mmse0,'-',[0:L-1]/L,mmsef1,'--',[0:L-1]/L,mmsef2,'-.')xlabel('Timing Phase'),ylabel('MMSE'),legend('T_b spaced equalizer (N=31)','T_b/2 spaced equalizer (N=31)','T_b/2 spaced equalizer (N=61)')