Non-Orthogonal Transmission in Multi-User Systems with Grassmannian Beamforming

Aiming to achieve the sum-rate capacity in multi user multi-input multi-output (MIMO) channels with N_t antennas implemented at the transmitter, opportunistic beamforming (OBF) generates N_t orthonormal beams and serves Nt users during each transmission, which results in high scheduling delay over the users, especially in densely populated wireless networks. Non-orthogonal OBF with more than N_t transmit beams can be exploited to serve more users simultaneously and further decreases scheduling delay. However, the inter-beam interference will inevitably deteriorate the sum-rate. Therefore, there is a tradeoff between the sum-rate and the increasing number of transmit beams. In this context, the sum-rate of non-orthogonal OBF with N >; N_t beams are studied, where the transmitter is based on the Grassmannian beamforming. Our results show that non-orthogonal OBF is an interference-limited system. Moreover, when the inter-beam interference reaches its minimum for fixed Nt and N, the sum-rate scales as N ln (N/N-N_t) and it decreases monotonically with N for fixed N_t. Numerical results corroborate the accuracy of our analyses.