Hi,
I am trying to use CVX to implementing the antenna selection problem 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:
cvx_begin
variable x(Mr)
maximize( log_det( eye(Mr) + EbN0*diag(x)*Hfull*Hfull' )/(log(2)) )
subject to
0
Your relaxation looks like a conventional MIMO capacity maximization problem. The output of the problem should depend a lot on what value of Hfull that you are using. Have you tried different values of Hfull?
There is generally no guarantee that diag(x) will have only L dominating values in the optimal solution.
Hi Emil,
I figured out how to solve it, though I can`t explain why it happens.
I used the alternative form to express the capacity.
Considering that Hfull is an Mr x Mt matrix, I used instead:
C(x) = log_det( eye(Mt) + EbN0*Hfull'*diag(x)*Hfull )/(log(2))
I believe that is some sort of numerical bug from CVX.
Thanks a lot, though.
Dear
I think the results you got are somehow reasonable under the problem formulation you provide.
Assume at the current moment that we relax the constraint 0
Dear Mohannad Al-Ali,
I think the "x" would depend on the choice of Hfull. As I am generating a random Hfull, I was expecting "x" with different entries.
In fact, I found out that using the equivalent form of the capacity, that is:
C(x) = log_det( eye(Mt) + EbN0*Hfull'*diag(x)*Hfull )/(log(2))
(instead of C(x) = log_det( eye(Mr) + EbN0*diag(x)*Hfull*Hfull' )/(log(2)) ),
the optmization problem can be properly solved.
For this reason, I believe that it may be caused by some numerical problem from cvx toll.
Using this equivalent form, the solution I found pretty much matches the optimal solution all the time. Also, I am comparing with the methods porposed in the following paper:
Gorokhov, A. (2002). Antenna selection algorithms for mea transmission systems, (2), 2857–2860.
Gharavi-Alkhansari, M., & Gershman, A. B. (2004). Fast Antenna Subset Selection in MIMO Systems. IEEE Transactions on Signal Processing, 52(2), 339–347. https://doi.org/10.1109/TSP.2003.821099
Thanks for helping though.
Thanks. you are right that "x" should depend on the realization of Hfull at the receiver side ...
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