MIMO system capacity with imperfect feedback channel

The capacity for multiple-input multiple-output (MIMO) with imperfect feedback channel is investigated. The expression of closed-loop MIMO capacity with imperfect feedback has been derived. A system capacity indicator, the feedback signal to noise ratio (SNR), that is used to measure the capacity gain of the closed-loop capacity over that of the open-loop capacity, has been proposed and investigated. Based on the derived closed form expression for the closed-loop MIMO capacity, the lower threshold of feedback SNR is derived and subsequently examined by numerical method. Numerical results show that the lower threshold of feedback SNR is increased with increasing antenna numbers and increasing MIMO system SNR.