Example: Using the Semianalytic Technique :: Performance Evaluation (Communications Toolbox)

Communications Toolbox

Example: Using the Semianalytic Technique

The example below illustrates the procedure described above, using 16-QAM modulation. It also compares the error rates obtained from the semianalytic technique with the theoretical error rates obtained from published formulas and computed using the berawgn function. The resulting plot shows that the error rates obtained using the two methods are nearly identical. The discrepancies between the theoretical and computed error rates are largely due to the phase offset in this example's channel model.

% Step 1. Generate message signal of length >= M^L.
M = 16; % Alphabet size of modulation
L = 1; % Length of impulse response of channel
msg = [0:M-1 0]; % M-ary message sequence of length > M^L

% Step 2. Modulate the message signal using baseband modulation.
modsig = qammod(msg,M); % Use 16-QAM.
Nsamp = 16;
modsig = rectpulse(modsig,Nsamp); % Use rectangular pulse shaping.

% Step 3. Apply a transmit filter.
txsig = modsig; % No filter in this example

% Step 4. Run txsig through a noiseless channel.
rxsig = txsig*exp(j*pi/180); % Static phase offset of 1 degree
% Step 5. Use the semianalytic function.
% Specify the receive filter as a pair of input arguments.
% In this case, num and den describe an ideal integrator.
num = ones(Nsamp,1)/Nsamp;
den = 1;
EbNo = [0:20]; % Range of Eb/No values under study
ber = semianalytic(txsig,rxsig,'qam',M,Nsamp,num,den,EbNo);

% For comparison, calculate theoretical BER.
bertheory = berawgn(EbNo,'qam',M);

% Plot computed BER and theoretical BER.
figure; semilogy(EbNo,ber,'k*');
hold on; semilogy(EbNo,bertheory,'ro');
title('Semianalytic BER Compared with Theoretical BER');
legend('Semianalytic BER with Phase Offset',...
   'Theoretical BER Without Phase Offset','Location','SouthWest');
hold off;

The example creates a figure like the one below.

Procedure for the Semianalytic Technique

Theoretical Performance Results