mohatta2015.pdf

CHAPTER 6
MAXIMUM LIKELIHOOD SEQUENCE
DETECTION
So far, we have either subtracted ISI using past decisions or suppressed ISI using
copies of interfering symbols in other received values. Such approaches sacrifice
signal energy to reduce ISI. It would be nice not to lose signal energy in the equalization
process. This is possible by using an approach that accounts for ISI rather
than removing it. One such approach is maximum likelihood sequence detection
(MLSD), which involves determining the symbol sequence that best explains the
received signal. This approach is sometimes called maximum likelihood sequence
estimation (MLSE).
6.1 THE IDEA
We know that the symbol values can only be +1 or —1. Thus, there are a finite
number of possible symbol combinations. For each combination or hypothesis,
we can predict what the received samples should be (e.g., r\, ί^), at least in the
absence of noise. We can then compare them to the actual received values. When
we consider the correct combination, the difference between predicted and actual
received values should be small (just noise). Thus, we can form a metric that is
the sum of the squares of these differences and find the symbol combination that
minimizes this metric.
Channel Equalization for Wireless Communications: From Concepts to Detailed 115
Mathematics, First Edition. Gregory E. Bottomley.
© 2011 Institute of Electrical and Electronics Engineers, Inc. Published 2011 by John Wiley & Sons, Inc.