Generalized Zero-Forcing Techniques for the MIMO-GBC under per-antenna power constraints

We consider the MIMO broadcast channel (MIMO-BC) where an array equipped with M antennas transmits distinct information to K users, each equipped with N antennas. Because of the high complexity of the capacity-achieving dirty paper coding (DPC) technique, we focus on simpler linear beamforming techniques. In contrast to the typical sum-power constraint (SPC), we consider a per-antenna power constraint (PAPC) motivated by array architectures where antennas are powered by separate amplifiers and are either co-located or spatially separated. We first consider the N=1 case with zero-forcing (ZF) beamforming under a PAPC. We then generalize this technique to the N>1 case using a multiuser eigenmode transmission (MET) technique based on ZF. MET addresses the shortcomings of previous ZF-based beamformers by transmitting to each user on one or more eigenmodes chosen using a greedy algorithm.Maximizing the weighted rate sum for MET (and ZF) under PAPC is a constrained convex optimization problem that can be solved using interior point methods. We show that ZF techniques under PAPC achieve optimal capacity scaling with respect to M and N as the number of users K increases asymptotically, and using numerical simulations, we show that they achieve a significant fraction of the DPC capacity for a large range of finite K.