Feedback requirements in MIMO broadcast channels: An asymptotic analysis

In this paper, we consider a downlink communication system in which a base station (BS) equipped with M antennas and power constraint P communicates with N users each equipped with K receive antennas. It is assumed that the receivers have perfect channel state information (CSI), while the BS only knows the partial CSI, provided by the receivers via feedback. We study the minimum amount of feedback required at the BS, to achieve the maximum sum-rate capacity in the asymptotic case of N rarr infin, considering various signal to noise ratio (SNR) regimes. The amount of feedback is defined as the total average number of binits sent to the BS from the users. It is shown in the paper that i) In the low and fixed SNR regimes, it is not possible to achieve the maximum sum-rate with finite amount of feedback. Moreover, in order to get arbitrarily close to the sum-rate capacity in the fixed SNR regime, the amount of feedback must grow logarithmically with the sum-rate capacity. It is also established that random beam-forming scheme, proposed in, is feedback optimal in these regimes. ii) In the high SNR regime, the minimum required amount of feedback to achieve the sum-rate capacity depends on the number of receive antennas; in the case of K < M and large enough SNR, the minimum amount of feedback grows linearly with the sum-rate capacity and in the case of K ges M, it grows at most logarithmically with the sum-rate capacity. Furthermore, the amount of feedback does not need to grow with SNR in the case of K ges M.