Blind and Semiblind Channel Estimation - Nonlinear Signal and Image Processing: Theory, Methods and Applications - page 271

w 1

h 11
h 1j

y 1

s 1

w j

h ij

y j

s i

w n

h mj
h mn

y n

s m

FIGURE 8.2
FIR-MIMO model.

of n received signals, and k is the time index. If the elements of matrix H are
complex scalars, we have an instantaneous MIMO (I-MIMO) model, which
is typical in systems with frequency-flat fading. The channel may, however,
be time varying.
If the elements of the channel matrix H are FIR filters, the n -dimensional vec-
tor of received signals y k is assumed to be produced from the m -dimensional
vector of transmitted signals using the following z -domain representation:

y ( z ) = H ( z ) s ( z ). (8.15)

Assuming that the channels from transmitter i to receiver j have equal order
L (Figure 8.2), we have

L

H l s k − l + y k = w k . (8.16)

l = 0

This model, shown in Figure 8.2, may be called the finite impulse response
multiple-input multiple-output (FIR-MIMO) model. Finally, if the channel
matrix is allowed to be time varying, we will use the notation H l H l k . The

channel matrix is typically assumed to have a full column rank. For individ-
ual transmit vector component sequences, similar assumptions as in the SISO
case earlier in this chapter are usually employed. Depending on the transmis-
sion and channel coding scheme employed, assumptions on dependencies or
independence among the transmitted signal component may be employed
in deriving the receiver algorithms. Obviously, space-time coding introduces
redundancy, whereas in spatial multiplexing schemes the signal components
are assumed to be independent.
Many of the blind methods derived for SISO and SIMO models have been
extended to MIMO models. For example, there are blind subspace methods,
prediction error filtering methods, as well as CMA-related methods for MIMO
systems; see References 1 and 2 for more detail.

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