mohatta2015.pdf

AN EXAMPLE 93
between z and s. This is in contrast to MMSE LE, which minimizes the expected
value of the sum of the squares.
Another interpretation is that (4.133) is the unconstrained ML estimate of s.
This means that if we ignore the constraint that the elements of s can only take
on certain values (the signal alphabet), then ML detection leads to a Euclidean
distance metric, which is minimized with the least-squares solution.
For MMSE equalization, we don't have any requirements on the number of rows
of H. The decision variable vector is given by
z = H H (HH H +C„)- 1 r. (4.135)
With sub-block equalization, the sub-block often corresponds to a set of symbol
periods and the received samples processed correspond to a window of samples. In
this case, it is common to either 1) only keep the detected values for a subset of
the symbols in the sub-block (the middle ones), or 2) model symbols at the edge of
the sub-block as colored noise.
4.4.8 Group linear equalization
As in Chapter 2, we can consider a group of symbols as one supersymbol. With
group linear equalization, we will use MLD to sort out symbols within a group and
linear equalization to suppress symbols outside the group. For TDM, a group can
be G consecutive symbols. For example, the first two symbols can form the first
group or supersymbol, the next two symbols can form the second group, and so on.
It is also possible to use overlapping groups and only keep results for the middle
symbols. For CDM and OFDM, it is natural to group symbols in parallel together
(G = K in this case). As MLD performs better than LE, it is best to group symbols
together that strongly interfere with one another.
With group detection, an ML formulation makes more sense. The impairment
covariance matrix consists of noise and interference terms, where the interference
terms contain contributions from the symbols outside the group. There is a weight
vector per symbol within the group, giving rise to G decision variables. These
variables are used together to jointly detect the members of the group using, for
example, (2.101).
4.5 AN EXAMPLE
Here we consider the High Speed Downlink Packet Access (HSDPA) system, an
evolution of the WCDMA 3G system [Dah98]. A similar system is (HDR) [BenOO],
an evolution of IS-95 (US CDMA) now referred to as 1X-EVDO (the IX refers to
the bandwidth being the same as IS-95). On the downlink of both these systems,
CDM is used to achieve high data rates. In a dispersive channel, orthogonality is
lost between spreading codes, making ISI a problem.
MMSE or ML linear equalization can be used to obtain reasonable receiver performance.
To reduce complexity without significant change in performance, code
averaging can be used. Code-averaged transversal linear equalizers for CDM systems
have been developed at the chip-level [Gha98, JarOl, Fra02, Kra02] and despread
level [Gha98, BotOO, TanOO, Fra02, Mud04].