Optimum Space-Time Block Code Design for MIMO Communications:
A Case for Linear MMSE Receivers

Kon Max Wong, PhD
McMaster University
Abstract
Multi-input multi-output (MIMO) wireless links are important recent developments in wireless
communication systems due to their enormous potential in meeting the demand of transmitting
signals at high rates under strict limitations of power and bandwidth in an environment rich of
scattering. Existing MIMO communications employ M transmitter antennas and N receiver antennas
and design space-time codes to enable the exploitation of both the high performance provided by
the space diversity and the high data rate afforded by the capacity available in the MIMO channels.
Recent research on space-time code design to exploit these factors has been mainly targeted for the
MIMO system equipped with a maximum likelihood(ML) receiver since an ML receiver is able to
achieve the full diversity gain provided by the multiple antenna system. However, ML receivers are
non-linear receivers well-known to have very high complexity often prohibiting practical
implementation. Thus, there is a need to study spacetime code designs for MIMO systems
employing linear receivers.

In this lecture, we examine the design of optimum space-time block codes (STBC) for MIMO
systems equipped with a linear MMSE receiver. From the analysis of the probability of detection
error of the system, we show the necessary and sufficient structures of a STBC for achieving
minimum bit-error rate (BER) from which the diversity gain of such a system is then derived.
Indeed, the diversity gain of such a system, even when employing optimum STBC, is shown to be
inferior to that of a MIMO system equipped with an ML detector. We then propose that the optimum
STBC design principle be extended to cover the transmission of multiple blocks of data.
Examination of the BER for the multi-block transmission system shows us that the extended
optimum STBC design has necessary and sufficient structures parallel to those of the optimum
single-block design. Analyses reveal that increasing the number of blocks covered by the optimum
code design increases the diversity gain, yet the order of the normalized detection complexity
remains virtually constant. Theoretical predictions confirmed by computer simulations showed that
the number of blocks covered by the optimum STBC design does not have to be very large for the
system performance to catch up with and surpass that for an ML receiver. Utilizing this optimum
code design extended to multi-block transmission, for applications permitting latency of signal
reception, the MIMO wireless system can be brought to practical implementation without losing any
of its advantages.