Digital Signal Processing Reference
In-Depth Information
present in more detail two well-established second-order methods:
subspace decomposition
and
linear prediction
.
•
In
Section 5.4
, we change the main focus from equalization itself to
the problem of
multiuser processing
, which is closely related to MIMO
configurations. The problem consists in recovering a given transmit-
ted signal that is subject to the channel impairments and also to the
effect of interfering signals arriving at the same receiver. We present
two types of methods: the first one involves the equalization crite-
rion together with an auxiliary term that penalizes the correlation
between the received signals; the other methodology relies on the
use of an orthogonalization approach based on the Gram-Schmidt
procedure.
Historical Notes
The evolution of the blind equalization algorithms from SISO to SIMO sys-
tems can be traced back to the work from Tong et al. in 1991 [287]. In
this work, they proposed a method for blind equalization and identifica-
tion of SIMO channels using only the second-order statistics of the involved
signals. After the so-called TXK algorithm, a number of algorithms and
methods using second-order statistics were proposed in the 1990s, making
use of prediction error structures, subspace methods, and fractionally spaced
equalizers. Among which we can mention the references in [207,211,229,289].
Moreover, it is important to mention the works of Gardner [116, 117], also
in the 1990s, which exploit second-order statistics, but in the context of the
cyclic spectrum of cyclostationary signals.
The methods based on higher-order statistics for SIMO systems have
been concentrated on the generalization of the SISO algorithms. The con-
sideration of FS equalizers led to the proposal of the fractionally-spaced
constant modulus algorithm (FS-CMA) by Li and Ding [184], as one of the
most known algorithms on such class. A variant of the super-exponential
algorithm for multichannel are also reported in [129].
As far as MIMO channels are concerned, results are also reported by the
literature since the early 1990s, with methods based on both second-order
and higher-order statistics. Among important contributions to the theme, we
can we can point out the works by Hua and Tugnait [146, 296], and other
techniques that consider subspace methods, matrix pencil decomposition,
channel decorrelation, etc. [15,130,193,207,309].
The problem of multiuser processing in a MIMO environment is in fact
closely related to those of source separation and independent component
analysis, to be considered in the next chapter, although these topics and
their corresponding scientific communities made their own independent
