MIMO capacity with antenna selection and interference

System capacity is considered for a group of interfering users employing single user detection and antenna selection of multiple transmit and receive antennas for flat Rayleigh fading channels with independent fading coefficients for each path. The case considered is that where there is very limited channel state information (only the selected antennas) at the transmitter, but channel state information is assumed at the receiver. The focus is on extreme cases with very weak interference or very strong interference. It is shown that the optimum signaling covariance matrix is sometimes different from the standard scaled identity matrix. In fact this is true even for cases without interference if SNR is sufficiently weak. Further the scaled identity matrix is actually that covariance matrix that yields worst performance if the interference is sufficiently strong.