Digital Signal Processing Reference
In-Depth Information
The signal set is specified using equations (3.7) and (3.8) in
≤
E
N
∗
Mh
() max:
=
MP
s
,,
h
ρ
Pb
.
M
0
Note that
~
(
h
) is nondecreasing in
h
. Thus, the adaptive scheme can be specified by
the values
h
m
,
m
= 2, 4, 16, 64, where
h
m
is defined as the threshold such that for
h
≥
h
m
,
m
-QAM can be employed.
The discrete nature of the set of rates for any finite collection of signal sets hurts the
performance of the system; in particular, for all
h
such that
h
m
<
h
<
h
m
+1
, the estimate
is better than that required to use
m
-QAM but not good enough to use (
m
+ 1)-QAM.
Energy adaptation provides a means to solve this problem [31]. Rather than employing
the method of [31], an alternate method, which is analogous to truncated channel inver-
sion and the power pruning of [20], is described here. The advantage of this method is
that, with very little loss of optimality, it is easily extended to coded modulation struc-
tures, where the overall optimization problem of [31] is not easily framed when channel
prediction is not perfect [27]. Once a signal set has been chosen, the system is essentially
a fixed-rate system; thus, the goal changes from maximizing average rate to attempting
to allow communication at this fixed rate with the least amount of power. Thus, after the
signal set is chosen, equations (3.7) and (3.8) are used to decide the minimum energy
required to maintain
P
b
given the channel estimate
h
, and this energy is employed rather
than the average energy. Any excess energy is put into a “bank” on which successive
symbols can draw.
3.3.2.2 Numerical Results
As discussed in section 3.3.1, systems with a significant amount of decoding complexity
and allowable latency only have the potential for a small amount of improvement when
CSI is provided to the transmitter. As might be expected, uncoded systems, which have
the least decoder complexity and essentially no latency, benefit the most when transmitter
CSI is available. In particular, uncoded systems operating over frequency-non-selective
Rayleigh fading channels perform very poorly, because they do not achieve diversity.
Because of this, coherently decoded quadrature phase-shift keying (QPSK) with only
receiver CSI requires an SNR of 34 dB to achieve a bit error rate of 10
-4
on a frequency-
non-selective Rayleigh fading channel [53, p. 829], whereas the same technique requires
an SNR of less than 10 dB to achieve the same bit error rate on an AWGN channel. The
reason for this discrepancy is that the QPSK system operating over the Rayleigh fading
channel is extremely susceptible to deep signal fades. Although the occurrence of such is
relatively uncommon, the error rate during a bad fade can be orders of magnitude above
that occurring when the average received SNR is observed, and thus these bad fades
dominate the error rate.
In adaptive signaling, CSI is available at the transmitter. Arguably, the greatest utility of
such information is that signaling can be avoided when bad fades are present. In particular,
with perfect transmitter CSI [31], average rates in excess of 2 bits per symbol are possible
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