Adaptive Coded Modulation for Transmission over Fading Channels - Adaptive Signal Processing in Wireless Communications - page 77

6

5

4

3

2

1

Xmitter/rcvr knowledge
Rcvr knowledge only

0

0 2 4 6 8 10 12 14 16 18 20

SNR (E s /N 0 )

FIgure 3.3 The Shannon capacity of an independent and identically distributed Rayleigh fad-
ing channel, assuming (1) perfect CSI available only at the receiver, and (2) perfect CSI available
at both the transmitter and receiver [28]. Note that the gain in Shannon capacity resulting from
having perfect CSI available only at the transmitter is only slight, as discussed in section 3.3.1.

such a channel without CSI at the transmitter is shown as the lower curve in Figure 3.3,
where the SNR on the horizontal axis is the average received SNR (i.e., the SNR after the
path loss and lognormal shadowing are considered). The only requirement for the highly
efficient operation of such a system is the knowledge of this average received SNR at the
transmitter so that the rate of the transmitter can be set appropriately, and this can be
obtained by feedback of the path loss and shadowing. We emphasize that approaching
the curves in Figure 3.3 still requires high decoding complexity and significant latency,
which motivate whether adaptation with the additional knowledge of the values of the
multipath fading can improve on the performance in Figure 3.3 in terms of performance
versus system complexity.

3.2.3 Analytic Model for Fine-Scale Adaptation
The main portion of this chapter will be dedicated to the design and analysis of adap-
tive systems that use explicit measurements of the multipath fading to perform system
adaptation. This is a topic that was considered in the 1970s [11, 37, 38] and then became
popular again in the early 1990s [e.g., 1, 6, 14, 29, 30, 65].
A block diagram of the typically employed system is shown in Figure 3.4 . Given the
model shown in Figure 3.4 and channel model given in section 3.2.1, the key to design-
ing adaptive signaling systems is considering signaling for the conditional channel for
the symbol of interest (call it s k ) given the outdated measurement ˆ = ( ˆ ( t - τ 1 ), ˆ ( t - τ 2 ),
…, ˆ ( t - τ N )) T . It will be assumed that a measurement ˆ ( t - τ i ) is equal to the true value
X ( t - τ i ) plus additive Gaussian noise of variance