Single-User Beamforming in Large-Scale MISO Systems with Per-Antenna   Constant-Envelope Constraints: The Doughnut Channel
  Large antenna arrays at the base station (BS) has recently been shown to achieve remarkable intra-cell interference suppression at low complexity. However, building large arrays in practice, would require the use of power-efficient RF amplifiers, which generally have poor linearity characteristics and hence would require the use of input signals with a very small peak-to-average power ratio (PAPR). In this paper, we consider the single-user Multiple-Input Single-Output (MISO) downlink channel for the case where the BS antennas are constrained to transmit signals having constant envelope (CE). We show that, with per-antenna CE transmission the effective channel seen by the receiver is a SISO AWGN channel with its input constrained to lie in a doughnut-shaped region. For single-path direct-line-of-sight (DLOS) and general i.i.d. fading channels, analysis of the effective doughnut channel shows that under a per-antenna CE input constraint, i) compared to an average-only total transmit power constrained MISO channel, the extra total transmit power required to achieve a desired information rate is small and bounded, ii) with N base station antennas an O(N) array power gain is achievable, and iii) for a desired information rate, using power-efficient amplifiers with CE inputs would require significantly less total transmit power when compared to using highly linear (power-inefficient) amplifiers with high PAPR inputs. 
Saif Khan Mohammed and Erik G. Larsson
cs.IT math.IT