Single-input single-output transceiver optimization - Signal Processing and Optimization for Transceiver Systems - page 367

The transmitting elements transmit orthogonal waveforms u k ( t ). At the receiver,
thesignalfromeachofthe N antenna elements is processed through a bank of
M matched filters, each filter matched to one of the waveforms u k ( t ) . In this
way, MN independent signals can be generated at the receiver. If the M trans-
mitting antennas and the N receiving antennas are spaced appropriately, then
these MN signals can be used to define a virtual array with MN elements. This
increases the number of degrees of freedom available at the receiver for beam-
forming. For example if we have ten transmitting and ten receiving antennas,
the number of degrees of freedom can be as large as 100, even though there are
only 20 physical antenna elements. The advantages and compromises involved
in the design of MIMO radars are discussed extensively in the references cited
above.
An important problem in the field of MIMO radars is the design of the
waveforms u k ( t ). When the target has range spread (i.e., an impulse response
h ( t ) that is not a delta function), then the design of the waveforms should be
such that the signal-to-noise ratios at the outputs of the MN matched filters
are maximized. A challenging problem in such waveform optimization is to take
into account the signal-dependent clutter components which are, unfortunately,
always present in the received signal.
10.7 Concluding remarks
In this chapter we considered single-input single-output channels. Expressions
for the optimal prefilter and postfilter were derived for various different choices
of criteria. These results, which involve ideal unrealizable filters, are important
from a theoretical point of view. In practice SISO channels are often equalized
indirectly by first introducing a redundancy at the transmitter such as zero
padding or cyclic prefixing (Chap. 7). Such redundancy converts the channel
into a memoryless MIMO system, which is easier to equalize using practically
realizable means such as matrix multiplications and so forth.