mohatta2015.pdf

APPENDIX A
SIMULATION NOTES
Performance evaluation and comparison are often obtained through Monte Carlo
simulation. The purpose of this appendix is to briefly share information that the
author has found useful on writing computer simulation programs. Most of the
information is probably available in the literature, though the author has not attempted
to track down the appropriate references.
In simulating the transmitter, it is useful to develop a Gray-coded QAM modulator
that can handle QPSK, 16-QAM, 64-QAM, etc. M-QAM can be obtained by
forming \/M-ASK symbols on the I and Q branches. Thus, we focus on TV-ASK
(TV = \/M). Let the "modulation" bits in a symbol be denoted mi, m 2 , etc., where
mi is the "weakest" bit (highest error rate in AWGN). There are K = log(TV)
bits. Using symbol values ±1, ±3, etc., symbol values can be generating in an
order-recursive way as
ΪΊ = mi (A.l)
T k = 2 fc - 1 m fc + m fc T fc _i, k = 2,...,K, (A.2)
where τη& take on values ±1 and Ta is the ASK symbol. In forming a QAM symbol,
the power needs to be normalized to 1/2 by multiplying by l/v2P, where P is the
average power in Τχ· It is straightforward to show that P = (1/3)(TV 2 — 1) for
TV-ASK.
At the receiver, a similar order-recursive demodulation can be performed. If z
is the ASK decision variable, normalized to the form z = s + re, where s is ±1, ±3,
Channel Equalization for Wireless Communications: From Concepts to Detailed 189
Mathematics, First Edition. Gregory E. Bottomley.
© 2011 Institute of Electrical and Electronics Engineers, Inc. Published 2011 by John Wiley & Sons, Inc.