Comparison of two analog feedback schemes for transmit side MIMO channel estimation

System performance can be quite improved by timely full channel state information at the transmitter (CSIT), especially for multidimensional channels as MIMO. For obtaining full CSIT, it is necessary to feed back the transmit channel knowledge from the receiver to the transmitter. There are two schemes to feed back the transmit channel knowledge: One is that channel estimation is done at the receiver with feeding back the channel estimate result subsequently; the other is that the received training signals are fed back to the transmitter with channel estimation subsequently. In this paper, we assume that the channel is quasi-static Rayleigh-fading, the channel knowledge is fed back from the receiver to the transmitter in a time-discrete uncoded linear analog way without any quantization on the information, and the least-square estimator is used. We give explicit expressions of estimate error of two feedback schemes. The two schemes are compared with respect to mean-square error. It comes out that the channel-estimate-based feedback scheme is less imperfect than the received-signal-based feedback scheme with respect to mean-square error. Nevertheless, the difference is trivial at high SNR.