Blind and Semiblind Channel Estimation - Nonlinear Signal and Image Processing: Theory, Methods and Applications - page 264

8.3 Signal Properties Used in Blind Equalization

In this section we consider various signal properties exploited in blind channel
equalization and identification. Most properties are presented in the context
of single-user receiver for the sake of simplicity. The extensions to MIMO
systems are considered as well.
If no exact knowledge of the transmitted sequence is available, blind al-
gorithms rely on some statistical and structural properties of the transmitted
signal. Communication channels typically alter these properties and blind
receiver algorithms then try to recover or restore these properties. Temporal
signal properties are typically considered but if several receivers are available,
spatial dimension may also be exploited. Consequently, spatial or space-time
processing also may take place at the receiver.
The following signal properties are commonly used in blind channel esti-
mation:

•

Cyclostationarity

•

Higher-order statistics (HOS)

•

Bussgang statistics

•

Finite alphabet property

•

Constant modulus

•

Shaping statistics at the transmitter

•

Uncorrelatedness and independence

•

Special matrix structures following from the system model

Each of these properties is discussed in more detail in the following subsec-
tions. Typically, blind methods exploit one or a combination of these proper-
ties in estimating the channel or the equalizer. In a multiuser communications
context, the interference caused by other users is often highly structured. One
may dramatically improve the performance by taking into account this prop-
erty of interference, as in the multiuser detection introduced by Verdu. 27
There are quite a few underlying assumptions needed in deriving blind
receivers. The signals may be assumed to be either random or deterministic.
Random sequences are typically assumed to be white and wide-sense station-
ary (WSS) when sampled at symbol rate. For efficiently source-coded signals
where the redundancy is removed, this is a reasonable assumption. It also
holds for many widely used channel coding schemes. 28
In the case of deterministic data models, the sequences are typically re-
quired to have linear complexity and sufficient excitation to ensure the iden-
tifiability of the channel. In practice, it follows that the sample covariance
matrix of the sequence is not rank deficient. The pulse shape employed at the