On the throughput of opportunistic beamforming with imperfect CSI

The throughput of a multiple-antenna broadcast channel highly depends on the channel state information (CSI) at the transmitter side. However, due to the time variant nature of wireless channels, having perfect knowledge of the under- lying links appears to be a questionable assumption, especially when the number of users and/or antennas increases. Although it can become computationally prohibitive in practice, theoretically any point on the capacity region of a Gaussian broadcast channel is achievable using dirty paper coding (DPC) if full CSI is available. The aforementioned drawbacks of DPC have motivated the development of simpler transmission strategies that re- quire little CSI and yet can deliver a large portion of the capacity. One such scheme is opportunistic beam-forming that is shown to be able to achieve the same throughput scaling as that of DPC for the regime of large number of users. In this paper we investigate the performance of opportunistic beamforming when the perfect channel state information is not available; i.e., the channel estimation is erroneous. We will show that in order to maximize the throughput (sum rate capacity), the transmitter needs to back off the rate than what is suggested by the estimated channel state. We obtain the optimal back off and show that by using this modified opportunistic scheme, the same multiuser gain can be achieved

ON THE THROUGHPUT OF OPPORTUNISTIC BEAMFORMING WITH IMPERFECT CSI

The throughput of a multiple-antenna broadcast channel highly depends on the channel state information (CSI) at the transmitter side. Due to the time variant nature of wireless channels, having perfect knowledge of the underlying links appears to be a questionable assumption, especially when the number of users and/or antennas increases. For a broadcast channel with M transmit antennas and n users, each provided with one receive antenna, it is shown that opportunistic beamforming can achieve the same scaling as that of dirty paper coding for large n. Although the dirty paper coding scheme needs perfect CSI from all users, opportunistic beamforming needs very little feedback. In this paper we investigate the performance of opportunistic beamforming when the CSI is not perfect; i.e., the channel estimation is erroneous. We will show that in order to maximize the throughput, the transmitter needs to back off the rate than what is suggested by the estimated channel coefficient. We obtain the optimal back off and show that with this modified opportunistic scheme, the same multiuser gain will be achievable; in other words, the throughput scales like M log log n even with imperfect limited CSI. Index Terms — Broadcast channel, MIMO systems, channel state information(CSI), estimation error, multiuser diversity