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

10.12 MATLAB Exercises 599
Figure 1 0.49
Symbol error
probability of
16-QAM using
root-raised
cosine pulse in
comparison with
the analytical
result.
10 ° ---....-----.------.-----,,.......------------
10-1
-- Analytical
--+- Root-raised cosine
rn-4
10-s ,__ __ ...._ __ _,_ __ ___._ __ __, ___ .,__ __ _._ __ --'-_..____,
2 4 6 8 12 14 16 18
axis ( 'square ' )
xlabel ('Real part of matched filter output samples ')
ylabel ('Imaginary part of matched filter output samples ')
Because the signal uses 16-QAM constellations, instead of measuring the BER, we will measure
the symbol error rate (SER) at the receiver. Figure 10.49 illustrates that the measured SER matches the
analytical result from Sec. 10.6 very closely.
The success of the optimum QAM receiver can also be shown by observing the real part
and the imaginary part of the samples taken at the matched filter output. By using a dot to
represent each measured sample, we create what is known as a "scatter plot?' which clearly
demonstrates the reliability of the decision that follows. If the dots in the scatter plot are closely
clustered around the original constellation point, then the decision is mostly likely going to
be reliable. Conversely, large number of decision errors can occur. Figure 10.50 illustrates
the scatter plot from the measurement taken at the receiver when E b /N = 18 dB. The close
clustering of the measured sample points is a strong indication that the resulting SER will be
very low.
COMPUTER EXERCISE l 0.4: NONCOHERENT FSK DETECTION
To test the results of a noncoherent binary FSK receiver, we provide MATLAB program Exl0_4 .m,
which assumes the orthogonality of the two frequencies used in FSK. As expected, the measured BER
results in Figure 10.51 matches the analytical BER results very well.
% MATLAB PROGRAM <Exl0 4.m>
% This program provides simulation for noncoherent detection of
% orthogonal signaling including BFSK . Noncoherent MFSK detection
% only needs to compare the magnitude of each frequency bin .
L=l00000;
%Number of data symbols in the simulation