Problem with log_det in channel capacity maximization

(Guilherme Zilli) #1


I am trying to implement the antenna selection problema proposed in the following paper:
A. Dua, K. Medepalli e A. Paulraj, “Receive antenna selection in MIMO systems using convex optimization”, IEEE Transactions on Wireless Communications, vol. 5, n.o 9, pp. 2353-2357, 2006.

The problem consists of a channel maximization problem, described as follows:
variable x(Mr)
maximize( log_det( eye(Mr) + EbN0*diag(x)HfullHfull’ )/(log(2)) )
subject to
0 <= x <= 1;
trace(diag(x)) == L;

where Mr is the number of antennas in the full set, Hfull is the full channel matrix and L is the number of antennas to be selected.

The problem is that the CVX is returning ‘x’ with all elements equal to each other.
Does anyone know why this is happening and how I can solve it?

PS: This is a linear relaxation of the optimum problem, and I am supposed to get the L larger entries of ‘x’ as the selected antennas.

Thank you.