mohatta2015.pdf

FADING CHANNELS 191
where JA = A 2 /Nothe
SER is
For the M-QAM symbol formed from two iV-ASK symbols,
P. = 1 - (1 - PA) 2 , (A.7)
where JA is 0.5£ 8 /ΛΓ () .
Another useful calibration approach is to examine bit error rate (BER).. For
QPSK, the probability of a bit error is [Pro89]
P b = 0.5 erfc (y£*/M)),
(A.8)
where Et, is the energy per bit (E b = E s /2 for QPSK). For 16-QAM, there are two
"strong" bits (most significant bits or MSBs) and two "weak" bits (least significant
bits or LSBs). The two strong bits have lower error probabilities than the two weak
bits. Using standard, fixed detection thresholds for symbol detection (as opposed
to thresholds that depend on SNR [Sim05], the probabilities of bit error are given
by |Cho02]
P M
erfc
2Eb
5JVn
+ erfc
18^6
5 N n
(A.9)
rb,LSB
2 erfc
P b = (l/2)(P b¡MSB + P b¡LSB ).
2E b \ ( nSEb] l ßÖE b
5ÎVÔ +erfC VT^; " erfC [Ηπ
(A.10)
(A.ll)
It is important to run the simulation long enough so that accurate performance
results are obtained. For example, in measuring SER (or BER), a commonly used
rule of thumb is to ensure there are 100 error events. So, to measure SER in the
region of 10% SER, one would need to simulate 1000 symbols. Often a fixed number
of symbols are simulated, and it is understood that the results at high SNR (lower
SER values) are less accurate.
A.l
FADING CHANNELS
The wireless channel experiences multipath propagation, with the signal being scattered
and reflected by various objects. When the path delays are approximately the
same (relative to a symbol or chip period), the paths add constructively sometimes,
destructively other times, giving rise to signal fading. With enough paths, the fading
channel coefficient can be modeled as a zero-mean, complex Gaussian random
variable. Sometimes there is a line-of-sight (LOS) much stronger path, giving rise
to fading with a Rice distribution.
The fading response changes as the transmitter, scatterers, and/or receiver move.
Assuming scatterers form a ring around the receiver, we end up with a certain
autocorrelation function and spectrum known as the Jakes' spectrum. When a
system employs short, widely separated transmission bursts, we can approximate
the time-varying channel with a block fading channel, in which the fading channel
coefficient is constant during a burst and independent from burst to burst.
The results in this book were generated using a block, Raleigh fading channel
model. The simulation software generates a transmitted signal, fading realization,