Adaptive Equalization for Wireless Channels - Adaptive Signal Processing in Wireless Communications - page 257

The algorithms compared in Figure 9.8 are the adaptive MMSE algorithm [10],
MERRY [50], and CNA [55, 56]. The optimal nonadaptive MMSE design with perfect
channel state information (CSI) is also shown. In principle, all of these could use either a
unit-norm or unit-tap constraint. Both are shown for the case of MERRY; however, since
there is no appreciable difference, only a single constraint is shown for the remainder.
Also, the blind algorithms can only update once per block (OFDM symbol), but the
MMSE design can update as often as once per sample. For a fair comparison, the MMSE
design was only updated once per block, so that the update complexity per symbol of the
various algorithms would be comparable.
Observe that the various algorithms considered all had comparable learning rates for
a given allowable complexity. However, the trained MMSE algorithm could in principle
update - times more often (with a corresponding increase in complexity).
To recap, trained and blind adaptive equalizers for multicarrier systems can be
designed using the same principles as more conventional communication systems.
Trained algorithms are generally based on an MMSE framework, and blind algorithms
are generally based on a property restoral framework. The unique aspects of adaptive
algorithms in multicarrier systems include the need for an adaptive target impulse
response for trained MMSE adaptation, the need for a constraint for most trained and
blind adaptive algorithms, and the trade-offs associated with operating at the block rate
versus the sample rate.

9.4 Ultrawideband Communication Systems

Like multicarrier systems, ultrawideband (UWB) systems have received much attention
in recent literature due to the fact that their modulation format is very distinct from sin-
gle-carrier amplitude modu lation formats, a lt hough it is not in as w idespread implemen-
tation as multicarrier modulation. This section reviews UWB modulation and discusses
the application of adaptive equalizer design principles to this modulation format.
A UWB system is often defined as one in which the bandwidth divided by the car-
rier frequency exceeds ¼. The idea is that a very large bandwidth is used, but the total
power is moderate—hence the power per Hertz is on the order of the noise floor. This
is akin to spread-spectrum modulation in its motivation, but the process of modulation
differs. Presently, there are two popular formats of UWB in the literature: pulse position
modulation (PPM) and a multiband format, much like OFDM. In this chapter, we focus
on PPM, due to its implications for adaptive equalizer design.
In the PPM version of UWB, information is transmitted by very short, infrequent
pulses. By transmitting an impulse-like pulse, the bandwidth is very large. In some
cases, the need for RF hardware can be avoided completely, since an impulsive transmis-
sion can spread the data up to very high frequencies without upconversion. Thus, PPM
UWB is sometimes called impulse radio.
Consider a PPM system that transmits one of M possible symbols each time slot. The
time slot is divided into K = M /2 chips. A symbol consists of transmitting a +1 in one
chip and zeros in the other K - 1 chips (so there are K of these to choose from), or