A rigorous proof of MIMO channel capacity’s increase with antenna number

It is well known that adding more antennas at the transmitter or at the receiver offers larger channel capacity in the multiple-input multiple-output communication systems. In this paper, a rigorous proof is presented for the fact that the channel capacity increases with an increase in the number of receive antennas and the number of transmit antennas. The proof is based on the famous capacity formula of Foschini and Gans and matrix theory.