EE620-homework_04

# EE620-homework_04 - CN(0 1 The additive noise at the...

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1 EE620: MIMO Wireless Communications Homework 4 (due on April 21, before the class) 1. A MIMO system with 4 t M = transmit antennas uses the following space-time code 1 2 3 * * 2 1 3 4 * * 3 1 2 * * 3 2 1 0 0 , 0 0 x x x x x x G x x x x x x - = - - - where 1 x , 2 x and 3 x can be chosen from arbitrary signal constellations. (a) Show that 2 2 2 4 4 1 2 3 4 (| | | | | | ) . H G G x x x I = + + (b) If 1 x , 2 x and 3 x are chosen independently from QPSK signals {1, -1, j, -j}, what is the spectral efficiency of the space-time code? (c) Prove that the space-time code can achieve the full diversity. (d) Determine the normalized coding gain for the space-time code when 1 x , 2 x and 3 x are chosen independently from QPSK signals {1, -1, j, -j}. (e) Prove that the space-time code has fast ML decoding at the receiver, i.e., 1 x , 2 x and 3 x can be decoded separately, not jointly. 2. Matlab simulations : Assume that channels are Rayleigh fading, which are modeled as independent complex Gaussian random variables with mean zero and variance one, i.e.,
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Unformatted text preview: CN(0, 1). The additive noise at the receiver side is also modeled as independent complex Gaussian random variables with mean zero and variance one. (a) Simulate a MIMO system with 2 t M = transmit antennas and one receive antenna by using the orthogonal space-time code 2 1 2 ( , ) G x x , i.e., the Alamouti scheme, in which 1 x and 2 x are chosen from QPSK signals {1, -1, j, -j}. (b) Simulate a conventional communication system with single transmit antenna and single receive antenna, also use QPSK signals. Plot simulation results in terms of bit-error-rate (BER) vs signal-to-noise ratio (SNR). Compare the results from (a) and (b), and explain your observations. (Note: Use ‘semilogy’ to plot the BER curves and convert the SNR in dB.)...
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## This note was uploaded on 02/24/2011 for the course EE 620 taught by Professor Dr.weifengsu during the Spring '11 term at SUNY Buffalo.

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