Performance of Conjugate and Zero-Forcing Beamforming in Large-Scale Antenna Systems

Large-Scale Antenna Systems (LSAS) is a form of multi-user MIMO technology in which unprecedented numbers of antennas serve a significantly smaller number of autonomous terminals. We compare the two most prominent linear pre-coders, conjugate beamforming and zero-forcing, with respect to net spectral-efficiency and radiated energy-efficiency in a simplified single-cell scenario where propagation is governed by independent Rayleigh fading, and where channel-state information (CSI) acquisition and data transmission are both performed during a short coherence interval. An effective-noise analysis of the pre-coded forward channel yields explicit lower bounds on net capacity which account for CSI acquisition overhead and errors as well as the sub-optimality of the pre-coders. In turn the bounds generate trade-off curves between radiated energy-efficiency and net spectral-efficiency. For high spectral-efficiency and low energy-efficiency zero-forcing outperforms conjugate beamforming, while at low spectral-efficiency and high energy-efficiency the opposite holds. Surprisingly, in an optimized system, the total LSAS-critical computational burden of conjugate beamforming may be greater than that of zero-forcing. Conjugate beamforming may still be preferable to zero-forcing because of its greater robustness, and because conjugate beamforming lends itself to a de-centralized architecture and de-centralized signal processing.