Non-Orthogonal Opportunistic Beamforming: Performance Analysis and Implementation

Aiming to achieve the sum-rate capacity in multi-user multi-antenna systems where N_t antennas are implemented at the transmitter, opportunistic beamforming (OBF) generates N_t orthonormal beams and serves N_t users during each channel use, which results in high scheduling delay over the users, especially in densely populated networks. Non-orthogonal OBF with more than N_t transmit beams can be exploited to serve more users simultaneously and further decrease scheduling delay. However, the inter-beam interference will inevitably deteriorate the sum-rate. Therefore, there is a tradeoff between sum-rate and scheduling delay for non-orthogonal OBF. In this context, system performance and implementation of non-orthogonal OBF with N >; Nt beams are investigated in this paper. Specifically, it is analytically shown that non-orthogonal OBF is an interference-limited system as the number of users K → ∞. When the inter-beam interference reaches its minimum for fixed N_t and N, the sum-rate scales as N In (N/(N-N_t)) and it degrades monotonically with the number of beams N for fixed N_t. On the contrary, the average scheduling delay is shown to scale as ¹/_N K ln K channel uses and it improves monotonically with N. Furthermore, two practical non-orthogonal beamforming schemes are explicitly constructed and they are demonstrated to yield the minimum inter-beam interference for fixed N_t and N. This study reveals that, if user traffic is light and one user can be successfully served within a single transmission, non-orthogonal OBF can be applied to obtain lower worst-case delay among the users. On the other hand, if user traffic is heavy, non-orthogonal OBF is inferior to orthogonal OBF in terms of sum-rate and packet delay.