B. P. Lathi, Zhi Ding - Modern Digital and Analog Communication Systems-Oxford University Press (2009)

12.12 MATLAB Exercises 719
After a matched filter has been applied at the receiver (root-raised cosine), the QAM signal will
be sampled, equalized, and decoded. The subroutine program 1 inear _ eq . m designs a T-spaced finite
length MMSE equalizer oforder M = 8 as described in Sec. 12.3 [Eq. (12.43b )] . The equalizer is designed
by applying the first 200 QAM symbols as training data. The equalizer filters the matched filter output
before making a 16-QAM decision according to the decision region of Fig. 10.24b in Chapter 10.
% MATLAB PROGRAM <linear_eq .m>
% This is the receiver part of the QAM equalization example
%
Ntrain=200;
% Number of training symbols for Equalization
Neq=8;
% Order of linear equalizer (=length-1)
u = O;
% equali zation delay u must be <= Neq
SERneq= [] ;
SEReq= [];
for i=l:13,
Eb2N (i)=i*2-l;
Eb2N_num=l0 A (Eb2N(i) /10) ;
Var_n=Es/ (2*Eb2N_num) ;
signois=sqrt (Var_n/ 2) ;
zl=out_mf +signois*noisesamp ;
%(Eb/N in dB)
% Eb/N in numeral
%1/SNR is the noise variance
% standard deviation
% Add noise
Z=toeplitz (zl (Neq+l:Ntrain) ,zl (Neq+l :-1:1) ) ; % signal matrx for
% computing R
dvec= [ s_data (Neq+l-u : Ntrain-u)]; % build training data vector
f=pinv(Z'*Z)*Z' *dvec ;
% equalizer tap vector
dsig=filter (f,l,z l) ;
% apply FIR equalizer
% Decision based on the Re / Im parts of the samples
deq=sign (real (dsig (l:L) ) ) +sign (real (dsig (l:L) )-2)+...
sign ( real (dsig (l:L) )+2)+...
j*( sign ( imag (dsig (l:L) ) ) +sign(imag (dsig (l:L) )-2)+...
sign ( imag (dsig (l:L) ) +2 ) );
% Now compare against the original data to compute SER
% (1) for the case wi thout equalizer
dneq=sign (real (zl (l:L) ))+ sign (real (zl (l:L) )-2)+...
sign (real (zl(l:L) )+2)+...
j*(sign (imag (dsig (l: L) ) ) +sign (imag (zl (l:L) )-2)+...
sign ( imag (zl(l :L) )+2) );
SERneq= [ SERneq; sum (abs ( s_data-=dneq) )/(L )];
% (2) for the case with equalizer
SEReq= [SEReq; sum ( s_data-=deq) /L] ;
end
Once the linear equalization results are available, the main program Ex12_1 . m calls another
subroutine program, plotQAM_resul ts . m, to provide illustrative figures. In Fig. 12.21, the noisefree
eye diagram of the in-phase component at the output of the receiver matched filter before sampling
shows a strong ISI effect. The QAM signal eye is closed and, without equalization, a simple QAM
decision leads to very high probabilities of symbol error (also known as symbol error rate).
% MATLAB PROGRAM <plotQAM_results .m>
% Thi s program plots symbol error rate comparison before and after
% equalization
%
%
figure (2)
constellation points
eye-diagrams before equalization