Discrete-time representations - Signal Processing and Optimization for Transceiver Systems - page 161

4.11 Concluding remarks
In this chapter we developed discrete-time representations for digital communica-
tion channels. These representations allow us to analyze the system as if it is an
all-digital system. For example, the problem of designing an optimal transceiver,
that is, jointly designing the pre- and postfilters to minimize the mean square
error, can be viewed entirely in the discrete-time domain. We shall return to
such optimization problems in Chaps. 9-19, and treat systems with and with-
out zero forcing in great detail. In this chapter we also discussed oversampled
receivers and fractionally spaced equalizers. Fractionally spaced equalizers have
been studied extensively in the literature, and the reader wishing to pursue the
history should refer to Proakis [1995]. Very interesting discussions on the design
issues can be found in Triechler, Fijalkow, and Johnson [1996], and advanced
research material can be found in Tong, Xu, and Kailath [1994], Borah et al.
[2001], Vaidyanathan and Vrcelj [2001, 2002], Vrcelj and Vaidyanathan [2002,
2003], and references therein. The use of fractionally spaced equalizers in jointly
optimal transceivers for MIMO channels is described in Weng and Vaidyanathan
[2008]. Fractionally spaced equalization allows us to equalize an FIR channel
with FIR rather than IIR filters. Another way to achieve the same goal would
be to introduce redundancy at the transmitter, instead of oversampling at the
receiver. This idea will be introduced in Chap. 7.