mohatta2015.pdf

146 MAXIMUM LIKELIHOOD SEQUENCE DETECTION
For CDMA, the challenges of using WMF are discussed in [Wei96]. MLSD at
chip level for MUD is discussed in [SimOl, Tan03].
The expectation-maximization (EM) algorithm [Dem77] has been used to develop
iterative approaches to MLSD that resemble PIC [Nel96, BorOO, RapOO].
Other iterative approaches are given in [Var90, Var91, Shi96]. Interior point methods
are explored in [TanOlb].
While the Viterbi algorithm was originally developed for decoding convolutional
codes [Vit67, Vit71], we focus on its use in equalization. A tutorial on the Viterbi
algorithm can be found in [For73]. Bellman's law of optimality can be found control
theory textbooks, such as [Bro82]. The practical issues of decision depth, metric
renormalization, and initialization are discussed in [For73]. As for criteria for traceback,
the best metric rule is shown superior in [Erf94].
The Viterbi algorithm can be modified to keep more than just the best path
[For73]. This has motivated the generalized Viterbi algorithm [Has87] and the list
Viterbi [Ses94a] A discussion of these approaches, along with extensions, can be
found in [NH95].
Use of the Viterbi algorithm for MLSD is considered in [Kob71, For72]. A WMF
front end is assumed. The Viterbi algorithm can be simplified when the channel is
sparse [Dah89, Ben96, Abr98, Mcg98].
In the purely MIMO case, the metrics can be computed efficiently using an
expanding tree algorithm, which is based on rewriting the metric as a sum of terms
in which earlier terms depend on fewer symbols [Cro92]. Triangularization can
also be used in conjunction with sphere decoding [Hoc03[. Sphere decoding can
be combined with the Viterbi algorithm [Vik06[. Sphere decoding has also been
studied for CDMA multiuser detection [Bru04].
The M-algorithm can be found in the decoding literature [And84]. The use of the
M-algorithm and variations for equalization can be found in [Cla87, Ses89], though
the discussion of [Ver74] in [Bel79] suggests such an approach. The steps of the
M algorithm given in this chapter are merged from the steps given in [And84] and
[Jun95a]. The T algorithm can be found in [Sim90]. More sophisticated breadthfirst
pruning approaches can be found in [Aul99, Aul03]. Adapting the number of
states with the time variation of the fading channel is considered in [Zam99, Zam02].
Use of sequential decoding algorithms [And84], such as the stack algorithm, for
equalization can be found in [For73, Xie90b, Xio90, Dai94].
Early work on prefiltering or channel shortening is summarized in [Eyu88] and
includes [Fal73]. A survey of blind channel shortening approaches can be found
in [Mar05]. Channel shortening for EDGE is described in [AriOOa, SchOl, Dha02,
Ger02a], including the use of all-pass channel shortening.
Reduced-state sequence estimation (RSSE) is developed in [Eyu88]. The special
case of decision feedback sequence estimation (DFSE) was independently developed
in [Due89], where it is referred to as delayed DFSE (DDFSE). When unwhitened
decision variables are used, there is a bias in the decisions made by the DFSE
which can be somewhat corrected using tentative future symbol decisions [Haf98].
Extensions of these ideas can be found in [Kam96, KimOOb].
Recall that DFE is sensitive as to whether the channel is minimum phase or
not. A similar sensitivity occurs with approximate MLSD forms, such as DFSE.
When the channel is nonminimum phase, all-pass filtering can be used to convert