Assignment #4
1. It can be shown that if the learning gain
μ
is such that 0
< μ <
1
λ
max
+
α
where
λ
max
is
the maximum eigenvalue of the input autocorrelation matrix and
α
is the normsquare
weight, LeakyLMS converges in the mean.
(a) Assume that this condition is indeed satisFed and the LeakyLMS converges in the
mean. ±ind lim
n
→∞
E
{
b
w
n
}
.
(b) Based on your Fnding in Part (a), modify the input of the regular
μ
gain LMS to
achieve the same e²ect.
2. Develop a recursive procedure analogous to the signerror LMS to adapt a complex beam
former
w
(
t
) with complex input
r
(
t
) and complex desired signal
d
(
t
) and error
e
(
t
).
3. Consider again the antennaarray and signal model of Problem 3 of Assignment #3.
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 Spring '12
 d.ramalingam
 Signal Processing, input autocorrelation matrix, regular µgain LMS, bn ATb wH, complex desired signal

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