History and outline - Signal Processing and Optimization for Transceiver Systems - page 318

q ( n )

s ( n )

s ( n ) M P J

M

F ( z ) H ( z ) G ( z )

transmitter channel receiver

Figure 9.1 . The general form of a transceiver sytem with channel H ( z ) , precoder
F ( z ) , and equalizer G ( z ) .

ceivers. Such special cases are useful to convert scalar channels into MIMO
channels without interblock interference; examples include OFDM and DMT
transceivers (Sec. 7.3). This will be elaborated further in Chaps. 17 and 18.
For the most part we will assume that the signal s ( n ) and noise q ( n ) are zero
mean, uncorrelated WSS processes, with covariances σ s I and σ q I .Th e s
nearly no loss of generality in this, as explained in Chap. 12. In Chap. 14,
which considers bit allocation as in DMT systems, the users s k ( n ) are allowed
to have different powers, so the covariance of s ( n ) is allowed to be a diagonal
matrix which may not be identity.

9.2 A brief history of transceiver optimization

Transceiver optimization has had a long history starting from the late 1950s. In
the context of digital communications, research in this area has been especially
intense starting from the 1990s, thanks to the technological breakthroughs that
led to DSL, MIMO, and wireless communication systems. However, since much
of the recent work has its roots in the rich history of transceivers, it is important
to appreciate the historical perspective. With this in mind we now give a brief
overview of the excellent body of research in this field. Many good papers had
to be omitted in the interest of brevity. The discussion of the papers mentioned
will only be brief. However, the essence of many of these papers will be covered
in detail in later chapters, as outlined later in Sec. 9.3.

9.2.1 General remarks on early work on equalization

Work on the optimization of equalizers in digital communications started in
the early 1960s. Tufts considered the problem with and without zero-forcing
constraints [Tufts, 1960, 1965]. The joint optimization of the transmitter and
receiver was considered by Smith [1965]. Besides zero-forcing, the case of par-
tial zero forcing (duobinary) was also considered. Lucky [1965] showed how an
FIR equalizer can actually be designed in practice by taking into account the
knowledge of the channel impulse response. The maximum possible intersym-
bol interference at the receiver was shown to be proportional to the 1

norm