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 may offer larger channel capacity in the multiple-input multiple-output（MIMO） communication systems. In this letter, a simple proof is presented for the fact that the channel capacity increases with an increase in the number of receiving antennas. The proof is based on the famous capacity formula of Foschini and Gans with matrix theory.