Let the received signals after presteering delays be denoted by x′(t). As these are delayed versions of x(t), it follows that their lth components are related by

	(6.30)
This along with (1.9) imply that x′(t) are related to x(t) by
	(6.31)
where Φ0 is a diagonal matrix defined as
	(6.32)

Note that Φ0 satisfies the relation, (Φ0)H*S0 = 1, where 1 is a vector of ones.

Figure 10 : Generalized side-lobe canceler structure.

These signals are used to form the main beam as well as M – 1 interference beams. The main beam is formed using fixed weights on all channels. These weights are selected to be of equal to 1/L so that a unity response is maintained in the look direction. Let these be denoted by an L-dimensional vector V given by

(6.33)

The M – 1 interference beams are formed using a blocking matrix B. Let these be denoted by an M – 1 dimensional vector q(t), given

	(6.34)
where matrix B has rank M – 1 and satisfies
	(6.35)

Expressions for the main beam, interference beams, and GSC output are then, respectively, given by

	(6.33)
	(6.37)
and
	(6.38)

It can easily be verified that an expression for the mean output power of the GSC for a given w is given by

	(6.39)
Where
	(6.40)

is the array correlation matrix after steering delays.
Comparing (6.15) and (6.39), one notes that the expression for the mean output power of the GSC for a given w is analogous to that given by (6.15), with V and R, respectively, given by (6.33) and (6.40) and B satisfying (6.35). Thus, the expression for GSC optimal weights is analogous to (6.18), with R replaced by R, that is,

	(6.41)
The expression for the mean output noise power of the optimal GSC then becomes
	(6.42)
and the output SNR is given by (6.28). For more information about Generalized Side-Lobe Canceler you can click here. In the next page Postbeamformer Interference Canceler is discussed. Back To Contents .