Adaptive Coded Modulation for Transmission over Fading Channels - Adaptive Signal Processing in Wireless Communications - page 73

Figure 3.2 with and without channel state information at the transmitter. With CSI at
the transmitter, transmission is halted when α = 0 and a single bit is transmitted when-
ever α = 1/(1 - p ). Thus, with a very simple receiver identical to that for the BPSK system
operating over the AWGN channel, the system reliably transmits 1 - p information bits
per channel use. Next, consider the case where there does not exist channel state infor-
mation at the transmitter. Using information theoretic results [16, p. 188], the capacity
of the channel without transmitter CSI is still 1 - p information bits per channel use, but
now it requires very long code words and the typical sequence decoding employed for
the achievability statement of Shannon's capacity [59]. This simple example captures the
key idea to adaptive signaling in response to the multipath fading in many cases—it will
often not make sense from a Shannon capacity, but it can greatly simplify system design
in practical systems [30].
Thus, adaptation in response to transmitter knowledge of the multipath fading has
the promise of greatly simplifying the system design or, for a fixed system complexity,
has the promise of greatly improving system performance (such as average data rate)
[31, 32]. However, it is the very property that makes adaptation fruitful that also com-
plicates its implementation; in particular, adaptation can be exploited because of the
time-varying nature of user needs, path loss, shadowing, and multipath fading. But
this time-varying nature makes that adaptation difficult; in particular, although changes
in user needs and path loss generally happen over a long enough timescale that they can
be reliably estimated, the time-varying nature of the shadowing [66] and the multipath
fading [24, 27] make channel measurements outdated by the time they are ready to be
used. In other words, the channel has changed since the measurements were performed,
and thus the utility of such measurements in representing the current state of the chan-
nel can be questioned. This will be particularly exacerbated, of course, in systems that
seek to adapt to the multipath fading [48].
The consideration of the design of signaling schemes that employ inherently outdated
or noisy measurements is best done by carefully considering the channel characteristics
conditioned on the measurements available. Naturally, if the support of the probability
density function of the conditional channel given the measurements is very narrow,
indicating that the system is fairly certain of the channel value, one can design coded
modulation structures and rules for adapting those structures based on the assumption
that the channel is fully known [31, 32] and suffer only mild degradations. However,
such schemes can be very sensitive, even if the probability density function only shows a
little spread around the estimated value [24, 27]. In such cases, not only must the rules of
adaptation consider such spread, but the spread often will affect the types of coding and
modulation structures that are effective, as demonstrated in section 3.3.3.
This chapter is organized as follows. In section 3.2, the system model that will be
used throughout this work is presented. Section 3.3 provides a detailed derivation of the
key issues in adaptive signaling using the simplest case of a system where there is only
a single antenna employed at each the transmitter and receiver. Section 3.4 discusses
recent extensions of these results to systems with multiple antennas at the transmitter
and receiver, and section 3.5 presents conclusions and avenues for future work in the
field.