Adaptive Coded Modulation for Transmission over Fading Channels - Adaptive Signal Processing in Wireless Communications - page 72

1- p

0 0

p

?

p

1 1

1- p

FIgure 3.2 The binary erasure channel [16, p. 188] to represent a discrete-valued fading chan-
nel with channel state information available at the receiver.

of such system power drops is relatively unlikely. This results in a significantly higher
required average received SNR for a given level of performance relative to systems oper-
ating over additive white Gaussian noise (AWGN) channels [53, p. 820]. However, unlike
the effects of path loss and shadowing, which vary slowly and thus limit the ability of the
system designer to average their effects over time, multipath fading varies relatively rap-
idly with time, position, and frequency. Thus, in many scenarios, well-designed systems
achieve diversity, allowing them to average effectively over the effects of the multipath
fading and thus significantly reduce its impact [53, p. 821]—even if there is no channel
knowledge at the transmitter. For many systems, such nonadaptive solutions come at the
cost of system latency or complexity, which motivates the consideration of transmission
schemes that employ measurements of the multipath fading values.
Since this chapter will largely focus on the design of techniques for adaptation based
on measurements of the multipath fading, it is important to understand the applicabil-
ity of such adaptation. Thus, the gains from having knowledge of the channel at the
transmitter will be a key topic discussed, and as motivated in the previous paragraph, it
is often a question of the system complexity and latency allowable. To make this more
concrete, consider the simple information theoretic example drawn from [16, p. 188],
which is shown in Figure 3.2. First, to see how this represents a fading channel, consider
a binary transmission system for which there are essentially no errors when the signal
is transmitted over an AWGN channel (i.e., no fading); a simple example is coherently
detected binary phase-shift keying (BPSK) with a relatively high SNR [53, p. 820]. Now
assume that a BPSK system is operating over a discrete-valued fading channel described
as follows. First, the state of the channel is independent for separate channel uses, which
implies that a deep interleaver [53, p. 467] is employed. For a given channel use:

1. With probability p , the transmitted signal is multiplied by zero (hence disappears).

2. With probability 1 - p , the transmitted signal is multiplied by α = 1/(1 - p ) (hence
amplified, which keeps the average received SNR identical to the AWGN case).

Assuming that channel state information (CSI), which throughout this paper will be
the value of the multiplicative factor (in this case 0 or α), is available at the receiver, this
yields the model shown in Figure 3.2. Consider signaling over the channel shown in