1 Purpose

The purpose of this assignment is to investigate the capacity for difffferent MIMO confifigurations. Both ergodic and outage capacities, and the difffference between the two, will be studied.

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.

• Using the measured MIMO channel, “LOS 8 8.mat”, calculate the ergodic capacity for MT = MR =M = [1, 2, 4, 8] MIMO systems of difffferent SNRs. Calculate for both cases when channel knowledge is known and unknown to transmitter. Verify that, when the channel is known to the transmitter, the ergodic capacity is always higher than when it is unknown. Is this true at higher SNR? Comment on the capacity gap between channel known and unknown to the transmitter with increasing M and SNR.
• Plot the ergodic capacities without channel knowledge at transmitter, for the i.i.d. channel Hw of SNR ranging from 0 to 25 dB for the following antenna confifigurations:

(a) MT = MR = 1; (SISO)

(b) MT = 2;MR = 1; (MISO)

(c) MT = 1;MR = 2; (SIMO)

(d) MT = MR = 2; (MIMO)

(e) MT = MR = 4; (MIMO)

1. Comment with specifific reasoning on the relative values of the capacities. How does the MIMO system achieve a linear increase in capacity with the number of antennas M comparing to SISO system? Do you observe higher capacity in SIMO system than in SISO system? Why or why not?