Omnidirectional Precoding for 3D Massive MIMO with Uniform Planar Arrays

In this paper, we investigate the omnidirectional precoding for three dimensional (3D) massive multi-input multi-output (MIMO) with uniform planar arrays (UPAs). The omnidirectional precoder is designed for public information transmission, where the channel state information (CSI) is usually not available at the base station (BS) and we would like to guarantee a performance to all users regardless of their angular positions. Thus, the first design objective of the precoding matrices is to satisfy the omnidirectional property, which means that the received mean power is constant at any angle. To ensure the power efficiency of each antenna, the per-antenna constant power constraint is also used in the design. Furthermore, the vectorized precoding matrices need to be mutually orthogonal to guarantee the spectral efficiency. The first two constraints can be satisfied by two dimensional Welti codes or two dimensional Golay arrays, whereas the third constraint is not necessarily satisfied by them. Furthermore, the methods to construct the Welti codes and Golay arrays are only given for certain array sizes. In this paper, we propose a novel and simple array design to construct the precoding matrices that satisfy the three properties. Based on the proposed array design, the design of the precoding matrices reduces to the design of a pair of complementary vectors having special structure, and the design of two sets of complementary orthonormal vectors with their aperiodic cross-correlation being zero. Finally, several examples of the omnidirectional precoding matrices for UPA generated by the proposed method are provided to verify the analytic results.