基于优化理论的MIMO收发器设计

liuwei_0613

Multiple-input multiple-output (MIMO) channels provide an abstract
and unified representation of different physical communication systems,
ranging from multi-antenna wireless channels to wireless digital subscriber
line systems. They have the key property that several data
streams can be simultaneously established.
In general, the design of communication systems for MIMO channels
is quite involved (if one can assume the use of sufficiently long and
good codes, then the problem formulation simplifies drastically). The
first difficulty lies on how to measure the global performance of such
systems given the tradeoff on the performance among the different data
streams. Once the problem formulation is defined, the resulting mathematical
problem is typically too complicated to be optimally solved
as it is a matrix-valued nonconvex optimization problem. This design
problem has been studied for the past three decades (the first papers
dating back to the 1970s) motivated initially by cable systems and
more recently by wireless multi-antenna systems. The approach was to
choose a specific global measure of performance and then to design the
system accordingly, either optimally or suboptimally, depending on the
difficulty of the problem.
This text presents an up-to-date unified mathematical framework
for the design of point-to-point MIMO transceivers with channel state
information at both sides of the link according to an arbitrary cost function
as a measure of the system performance. In addition, the framework
embraces the design of systems with given individual performance
on the data streams.
Majorization theory is the underlying mathematical theory on which
the framework hinges. It allows the transformation of the originally
complicated matrix-valued nonconvex problem into a simple scalar
problem. In particular, the additive majorization relation plays a key
role in the design of linear MIMO transceivers (i.e., a linear precoder
at the transmitter and a linear equalizer at the receiver), whereas the
multiplicative majorization relation is the basis for nonlinear decisionfeedback
MIMO transceivers (i.e., a linear precoder at the transmitter
and a decision-feedback equalizer at the receiver).