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1 Purpose

The purpose of this assignment is to understand the Alamouti scheme and the dominant eigenmode transmission scheme, which are used to achieve diversity in MIMO systems when the channel is unknown and known to the transmitter (Lecture 7). The inflfluence of spatial correlation on diversity performance will also be studied.

1. Assume that BPSK is used as the modulation format, i.e., a sequence with {−1, +1} is to be transmitted. In a 2 × 2 MIMO channel, we use the fifirst 2 transmit and fifirst 2 receive elements from the MIMO measurement “LOS 8 8.mat”. Additive White Gaussian Noise (AWGN) is assumed at the receiver.

Simulate the bit error rate (BER) for difffferent SNRs (e.g., 0 – 12 dB), assuming that the channel is unknown at the transmitter but known at the receiver so that the Alamouti scheme is utilized. Compare the BER results to that of the SISO case which uses only the fifirst antenna pair.

1. Assume the channel is known at the transmitter so that the dominant eigenmode transmission scheme can be used. Simulate and compare its performance with the results from the 1st task. Comment on the diversity performance from the BER curve.
• Tips: Normalize the channel using the difffferent frequencies as difffferent channel realizations and the normalization method described in Project 1. Simulate a large number of transmitted symbols (e.g., at least 1000 or more) for each channel realization to get better statistics.
1. Study the inflfluence of spatial correlation on the diversity performance. Repeat the above simulation using only the Alamouti scheme, but with the Kronecker channel model instead of the measured channel, so that

H = R1/2RHwR1/2T,

in which Hw is the i.i.d. Rayleigh channel, and

RR = RT =  1r 1r  ,

are the receive and transmit correlation matrix respectively. Study the BER performance for difffferent correlation coeffiffifficient r, and r = [0.5, 0.6, 0.7, 0.8, 0.9, 1]. Compare the performance to the case of purely i.i.d. channel, i.e., H = Hw. Comment on the inflfluence of spatial correlation to the diversity performance. Is the array gain still available when the channel is correlated? If so, why? Give an intuitive explanation.

3 Report

Write a short report. In order to pass, you should (1) describe the methods you apply to solve the problem,(2) present the results, e.g., in readable fifigures, and (3) comment on the results (important!). Computer code can be included as an attachment.

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