Problems
MIMO transceivers
Adaptive Antenna Systems
Persefoni Kyritsi
November 18, 2010
Transmission techniques for MIMO

Spatial multiplexing

Eigenmode transmission
• ZF receiver
• BLAST receiver
Problem 0
From slide 6 (Slides_transceivers): ompute the
covariance matrix of:
H k xk  n ~ CN (0, Rk )
Problem 1
2 1
Pt  1,   1, H  
, BPSK

3 1
2



What is the matrix that a ZF, MMSE receiver would
use?
What is the post-processing SNR of both streams?
Assume you send
x1  1, x2  1
n1  0.5, n2  0.3
What are the detector decisions?
Problem 2
2 1 
Pt  1,   1, H  
, BPSK

3 1.2
2



What is the matrix that a ZF, MMSE receiver would
use?
What is the post-processing SNR of both streams
Assume you send
x1  1, x2  1
n1  0.5, n2  0.3
What are the detector decisions? Why?
Problem 3


Do Problem 2 assuming a V-BLAST receiver.
Comment on the results
Problem 4


Find the eigenvectors and the eigenchannels
of the channel transfer matrices in problem 1
and 2.
What is the difference?
Problem 5
MISO System. Consider a MISO channel with two transmit antennas. The channel
from the first transmit antenna to the receiver is h1 and the channel from the second
transmit antenna is h2. A signal s is to be transmitted. The average power available
to the transmitter is P, i.e., E{|s|2} = P. The noise power at the receiver is N0. Assume
for now that h1 = h2 = 1.
• If we transmit simultaneously from each transmit antenna what is the total
transmit power? What is the SNR at the receiver? What is the array gain? (How
does this compare to the SISO case where we transmit s from just one antenna
and 0 from the other?)
• Now if h1 and h2 = −1 and we were to transmit from each antenna, what is the
array gain?
• If h1 = 1 and h2 = −1 is transmit array gain possible? What does this imply about
the requirement of channel knowledge at the transmitter to exploit transmit array
gain?