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Aiming to achieve the sum-rate capacity in multi-user multi-antenna systems where Nt antennas are implemented at the transmitter, opportunistic beamforming (OBF) generates Nt orthonormal beams and serves Nt 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 Nt 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 Nt and N, the sum-rate scales as N In (N/(N-Nt)) and it degrades monotonically with the number of beams N for fixed Nt. 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 Nt 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.