A universal interpretation of receive diversity gain in MIMO systems over flat channels

We present universal bit-error rate (BER) performance ordering for different receive antenna sizes in Multiple-Input Multiple-Output (MIMO) wireless systems with linear equalizations, which hold for all SNR. We show that when the number of transmit antennas is fixed, BER of each symbol degrades with a decrease in the number of receive antennas even if the received SNR is kept constant. This is due to the convexity property of the BER functions. Then for any i.i.d. channels, we show that the BER averaged over random channels also degrades with a decrease in the number of receive antennas. These highlight the advantage and the limit of MIMO with linear equalizations.