mohatta2015.pdf

PROBLEMS 147
the channel to minimum phase without changing the noise correlation properties
[Cla87, Abr98, Ger02b]. In [Bal97], to address stability concerns with the all-pass
filter, the channel is converted to maximum phase and the M-algorithm is used to
process the data backwards in time. Even without prefiltering, processing the data
in time reverse can be helpful [Mcg97].
For the purely MIMO scenario, an iterative clustering approach has been explored,
in which higher-order modulations are approximated with a few centroids
in the earliest iterations [Rup04, Jon05, Cui05, Agg07, Jia08].
There has also been work on assisted MLD (AMLD), in which simpler equalization
approaches are used to initially prune the search space [Fan04, Lov05, Nam09].
Many of these approaches are based on a form of Chase decoding [Cha72], in which
soft bit magnitudes are used to identify which bits need to be left undecided in the
pruning process. Multistage group detection forms of AMLD have been developed.
In serial forms, symbols are added to a single group one at a time, with pruning
after each addition [Kan04, Jia05]. In a parallel form, group detection is applied to
small groups, followed by pruning before combining small groups into larger groups
with additional pruning [BotlOb].
As for sub-block forms, sub-block DFE is described in [WÍ192]. Sub-block LE
can be found in [Bot08]. An approximate MLSD form uses MLSD per user with
coupling [MilOl].
PROBLEMS
The idea
6.1 Consider the Alice and Bob example. Suppose instead that n = — 1 and
r 2 = 4. Assume «o is unknown.
a) Form a table of metrics for all combinations of SQ, SI and «2-
b) Which metric is best? What is the detected sequence?
6.2 Consider the Alice and Bob example. Suppose instead that n = — 1 and
r-i = 4. Assume s () = +1.
a) Form a table of metrics for all combinations of s\ and β2·
b) Which metric is best? What is the detected sequence?
6.3 Consider the Alice and Bob example. Suppose instead that r\ is missing and
r 2 = 4.
a) Form a table of metrics for all combinations of si and si.
b) Which metric is best? What is the detected sequence?
More details
6.4 Consider the Alice and Bob example. Suppose instead that r\ = — 1 and
Γ2 = 4. Assume s» = +1. Consider the MLSD tree.
a) What are the two path metrics after processing ri?
b) What are the four path metrics after processing Γ2?
c) Which metric is best? What is the detected sequence?