On Favorable Propagation in Massive MIMO Systems and Different Antenna Configurations

Asymptotic orthogonality of channel vectors, also called favorable propagation (FP), plays a key role in massive multiple-input multiple-output (MIMO) systems, allowing linear processing to achieve optimality and maximize the information rate. Much research on the FP condition emerges under different assumptions, most of which has been proved to satisfy the FP condition for some massive MIMO implementations. A generic channel model without mutual coupling is proposed to study more general implementations than previously investigated. Two theorems establish: 1) conditions on the steering matrix alone that are sufficient to guarantee the FP condition holds and 2) that a simple condition on the steering matrix alone is sufficient to guarantee FP for all practical massive MIMO implementations. Then the uniform linear array, uniform planar array (UPA), and uniform circular array (UCA) antenna configurations are studied. Theoretical analyses indicate how close and how fast the inner product of different steering vectors converges to zero for a finite number of base station (BS) antennas, and prove that the FP condition is satisfied for the antenna configuration considered for an unlimited number of BS antennas only if the antenna spacing is not proportional to the reciprocal of the number of antennas. The analysis shows that the UCA has the shortest distance from the FP condition among the three antenna structures, while the UPA is especially suitable for massive MIMO systems for 5G owing to its good FP performance and compact physical size. Simulation results validate the theory.