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Suppression of Narrowband Interference in a Wideband Signal 601
detection, where the desired signal sequence {w(n)} is a spread-spectrum
signal, while the narrowband interference represents a signal from another
user of the frequency band or some intentional interference from a jammer
who is trying to disrupt the communication or detection system.
From a filtering point of view, our objective is to design a filter that
suppresses the narrowband interference. In effect, such a filter should place
a notch in the frequency band occupied by the interference. In practice,
however, the frequency band of the interference might be unknown. Moreover,
the frequency band of the interference may vary slowly in time.
The narrowband characteristics of the interference allow us to estimate
s(n) from past samples of the sequence x(n) =s(n)+w(n) and to
subtract the estimate from x(n). Since the bandwidth of {s(n)} is narrow
compared to the bandwidth of {w(n)}, the samples of {s(n)} are
highly correlated. On the other hand, the wideband sequence {w(n)} has
a relatively narrow correlation.
The general configuration of the interference suppression system is
shown in Figure 11.3. The signal x(n) isdelayedbyD samples, where
the delay D is chosen sufficiently large so that the wideband signal components
w(n) and w(n − D), which are contained in x(n) and x(n − D),
respectively, are uncorrelated. The output of the adaptive FIR filter is the
estimate
ŝ(n) =
N−1
∑
k=0
h(k)x(n − k − D) (11.13)
The error signal that is used in optimizing the FIR filter coefficients is
e(n) =x(n) − ŝ(n). The minimization of the sum of squared errors again
leads to a set of linear equations for determining the optimum coefficients.
Due to the delay D, the LMS algorithm for adjusting the coefficients
recursively becomes
h n (k) =h n−1 (k)+△e(n)x(n − k − D),
k =0, 1,...,N − 1
n =1, 2,...
(11.14)
Adaptive filter for estimating and suppressing a narrowband in-
FIGURE 11.3
terference
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