hw7_2010 - EE 5505 Prof N Jindal Wireless Communication...

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Unformatted text preview: EE 5505 Prof. N. Jindal Wireless Communication April 1, 2010 Homework 7 Due: Thursday, April 8, 11:15 AM 1. In this problem we will compare the performance of using a bank of matched filter (MF, or MRC), zero forcing (ZF), and MMSE filters (without successive interference cancellation) for a n T = n R = N channel. (a) The general formula for the SINR after correlating with linear filter v i is: (SNR /N ) | v H i h i | 2 (SNR /N ) ∑ j ̸ = i | v H i h j | 2 + ∥ v i ∥ 2 If we define K i as the covariance matrix of the interference (from the perspective of the i-th stream): K i , I + SNR N ∑ j ̸ = i h j h H j (in this expression we have divided out a factor of N for convenience), show that the SINR can alternatively be written as: SNR N v H i ( h i h H i ) v i v H i K i v i . (b) The matched filter is in the direction of the channel, i.e., v i = h i / ∥ h i ∥ . Explain why the distribution of the SINR for this filter is the same as: (SNR /N ) χ 2 2 N (SNR /N ) χ 2 2( N − 1) + 1 . Based on this equation, argue that the SINR converges to N/ ( N − 1) as SNR → ∞ . (c) The MMSE filter (unnormalized) is given by: ( I + SNR N ∑ j ̸ = i h j h H j ) − 1 h i ....
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hw7_2010 - EE 5505 Prof N Jindal Wireless Communication...

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