Adaptive Coded Modulation for Transmission over Fading Channels - Adaptive Signal Processing in Wireless Communications - page 74

3.2 Adaptive System Model

3.2.1 Model for a Wireless Link

The transmitted signal in a wireless communications system is affected by three factors:
path loss, shadowing, and multipath fading. In complex baseband notation [53], the sig-
nal r ( t ) that is received when the signal s ( t ) is transmitted can be written as

() = () ()() + () ,

rt LtXtst nt (3.1)

where L ( t ) is a real-valued random process that represents the combined effect of the
path loss and shadowing, X ( t ) is a complex random process representing the effect of
the multipath fading, and n ( t ) is a stationary complex Gaussian random process with
(two-sided) power spectral density S N ( f ) = N 0 /2, representing additive noise. In equa-
tion (3.1), the fading has been assumed to be frequency-non-selective [53, p. 816]; this
is appropriate for a narrowband single-carrier system or a single subcarrier of a wide-
band orthogonal frequency division multiplexing (OFDM) system [6, 71]. Extensions of
the concepts presented in this chapter to frequency-selective channels are conceptually
straightforward, although such channels offer inherent natural diversity with little sys-
tem latency, and hence often reduce the gain available through adaptive signaling.
Understanding the characteristics of the processes L ( t ) and X ( t ) in equation (3.1) is
crucial in determining methods of adaptation based on such. The random process L ( t )
is caused by path loss, which is determined by the distance the receiver is from the trans-
mitter, and shadowing, which is determined by the existence of large objects between
the transmitter and receiver. For a stationary user, the path loss and shadowing are gen-
erally modeled as constant, despite the fact that it could be argued that the movement
of large objects can affect the shadowing. For a user in motion, the shadowing will be
the more variable of the two effects, and the distance over which it is highly correlated
can be roughly modeled as 100 m in a macrocellular suburban environment [35]. For a
user at walking speed (say, 2 m/s), this implies that the shadowing correlation time is on
the order of 50 s; for a user in a vehicle (say, 88 km/h), this implies that the shadowing
correlation time is on the order of 4 s. This suggests that it is quite plausible to make
estimates of the path loss and shadowing and to employ such in wireless communica-
tions systems. In fact, this is very often done in current and next-generation cellular
system implementations [48]. Also, since L ( t ) varies at a relatively long timescale, it will
be assumed throughout the remainder of this chapter that it is measured accurately and
known at the transmitter and receiver.
In contrast, consider the random process X ( t ), which represents the multipath fading.
In a wireless environment, the signal s ( t ) is reflected to the receiver from many objects.
Because the propagation distance is different for each of these reflections, the reflected
signals will arrive at slightly different times at the receiver. For a narrowband system,
which has a relatively long symbol interval, there will not be appreciable intersymbol
interference (ISI) [53, p. 817]. However, because of the large carrier frequencies typi-
cally employed in modern wireless communications systems, even a small difference in