EE620-homework_03

# EE620-homework_03 - accordingly What is the spectral...

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EE620: MIMO Wireless Communications Homework 3 (due on March 31, before the class) 1. (1 point) Determine the normalized coding gain of the following set of space-time signals: C 0 = 1 1 - 1 1 , C 1 = 1 - 1 1 1 , C 2 = - 1 - 1 1 - 1 , C 3 = - 1 1 - 1 - 1 . 2. (1 point) Determine the normalized coding gain of the following set of space-time signals: C 0 = r 2 3 j 1 - j - 1 - j - j , C 1 = r 2 3 - j - 1 - j 1 - j j , C 2 = r 2 3 - j 1 + j - 1 + j j , C 3 = r 2 3 j - 1 + j 1 + j - j . 3. Design cyclic space-time block codes for MIMO systems with two transmit antennas ( M t = 2) by exhaustive computer searching: C l = 2 ± e ju 1 θ l 0 0 e ju 2 θ l , where θ l = l L 2 π, l = 0 , 1 , ··· ,L - 1. (i) (2 points) When size L = 8, search optimal parameters u 1 ,u 2 ∈ { 0 , 1 , ··· ,L - 1 } such that the coding gain is maximized. Determine the normalized coding gain
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Unformatted text preview: accordingly. What is the spectral eﬃciency of this set ST signals? (ii) (2 points) Can we get larger coding gain if we allow non-integer parameters u 1 and u 2 ? To answer this question, please determine parameters u 1 and u 2 by exhaustive searching in the interval [0 , L-1] (you may use searching step 0 . 1 or smaller). What is the resulting normalized coding gain in this case? (iii) (4 points) Repeat questions (i) and (ii) for size L = 32. 1...
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