HW4 - Assignment #4 1 1. It can be shown that if the...

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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 norm-square weight, Leaky-LMS converges in the mean. (a) Assume that this condition is indeed satisFed and the Leaky-LMS 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 sign-error 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 antenna-array and signal model of Problem 3 of Assignment #3.
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