1 Purpose

The purpose of this assignment is to investigate the impact of LOS component and spatial correlation on MIMO performance. The Ricean channel model and Kronecker channel model will be used.

2 Channel Normalization

1 Since channel capacity depends on the receive signal-to-noise ratio (SNR), it is important to properly normalize the measured channel matrices for correct interpretation of the results. For channel matrices

H(n), 1 n N, where N stands for the number of channel realizations, normalized MIMO channel matrices can be computed as

H(n)norm= H(n) ” NM 1TMRNnX=1||H(n) ||2F# 1/2,

where ||·||F is the Frobenius norm, MT and MR denotes the number of transmitting and receiving antennas,respectively. Note that,

• By setting N = 1, the difffferences in power levels among a number of channel matrices are removed through the normalization of each matrix independently.
• Using N > 1, the relative power levels among the N difffferent channel realizations are preserved.

• Consider the Ricean MIMO channel described in lecture with MT = MR = 2. The channel H may be expressed as (assuming no spatial fading correlation)

H = r 1 + KK H + r 1 + 1 K Hw,

where K is the Ricean K-factor of the channel.

The condition number η of a channel is often viewed as a measure of the quality of the multiplexing gain offffered by a channel. η is defifined as

η =λmax/λmin,

where λmax and λmin are the maximum and minimum eigenvalues of HHH, respectively. While η = 1 is highly desirable and implies an orthogonal channel, a higher η corresponds to decreased reliability in separating the multiplexed symbol streams.

1. Justify the above statement on the condition number η, explain why an orthogonal channel results η = 1 and why this is desired for high multiplexing gain.
1. For the following two channels, plot the average condition number (averaging eigenvalues over a number of realizations of Hw) as a function of increasing K from 0 to 20 dB,

H1 =  1 1

1 1  , H2 =  1 1

1 1  .

1. Do you observe any difffferences between these two channels? What is the reason behind that?Based on these observations, comment on the statement “Ricean fading signifificantly impacts the multiplexing gain of a MIMO channel”.
• Use the Kronecker model ((4.38), pp. 77 of textbook) and with SNR of 20 dB, plot 10% outage capacity (assuming no channel knowledge at transmitter) as a function of r = [0, 0.1, 0.2, . . . , 1] for correlation matrices of

RR = RT = [1 r r2

r 1r

r2r 1 ] .

Comment on the inflfluence of spatial correlation on MIMO performance.

4 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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