mohatta2015.pdf

PROBLEMS 95
Another aspect of cochannel interference is its cyclostationarity. We saw cyclostationarity
in the formation of the data covariance matrix, which depends on the
path delays of the interfering symbols. Cyclostationarity of cochannel interference
is addressed in [Ree90, Pet91, Gar93]. Suppression of narrowband interference in a
wideband system is discussed in [Mil88, Gel98].
In CDMA systems, early work focused on multiuser detection in the MIMO/cochannel
scenario. The ZF solution for the synchronous CDMA case (referred to as
the decorrelating receiver) is proposed in [Sch79] and developed in [Lup89]. The
MMSE solution can be found in [Mad94].
For the dispersive/asynchronous case, early work focused on the CDMA uplink
(different channel per user/code). Work on ZF LE is found for the asynchronous
case in [Lup90] and for the dispersive case in [Zvo96a, Zvo96b]. The MMSE solution
can be found in [Xie90a]. When the spreading codes of other users are unknown,
code averaging can be applied [Won98, Won99]. Sub-block linear equalization using
a sliding window is described in [Wij92, Rup94, Wij96, Jun97]. Block linear
equalization is examined in [Kle96]. Linear multiuser detection in rapidly varying
channels is addressed in [Say98]. Linear equalization with continuous-time signals
is considered for CDMA in [Mon94, Yoo96].
Later, the dispersive case was considered for the CDMA downlink (same channel
per user/code). Early work in [Bot93] uses a maximum-SINR approach to
despread-level transversal linear equalization to determine the weight solution. ZF
and MMSE block equalization at the chip level are considered in [Kle97]. In remaining
work, transversal equalization is considered at the chip level [Gha98, JarOl,
Fra02, Kra02] and despread level [Gha98, BotOO, TanOO, Fra02, Mud04]. The chip
level solution is formulated in terms of MMSE estimation of the transmitted composite
chip values (summed over all users). The despread level solution is formulated
in terms of ML [BotOO] or MMSE [Gha98, TanOO, Fra02, Mud04] estimation of the
symbol. In [JarOl], ML block equalization is also considered.
Some form of code averaging is considered in all downlink work cited as a way to
simplify receiver design. With code averaging, expressions for the weights involve
infinite sums, which have a closed form expression for certain chip pulse shapes
[Jat04]. Equivalence of MMSE and ML solutions is shown in [Had04].
Group linear equalization has been studied primarily for CDMA systems. In
[Sch96], ZF LE is used to suppress interference from symbols outside the group.
Code averaging can be used in designing the LE in the MIMO/cochannel [Gra03,
Mai05] and dispersive/asynchronous scenarios [BotlOa].
PROBLEMS
The idea
4.1 Consider the Alice and Bob example. Suppose instead that n = — 1 and
r 2 = 4.
a) What is the value of zi and s