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The opportunistic beamforming in the downlink of multiple-input single-output(MISO) systems forms $N$ transmit beams, usually, no more than the number oftransmit antennas $N_t$. However, the degrees of freedom in this downlink is aslarge as $N_t^2$. That is, at most $N_t^2$ rather than only $N_t$ users can besimultaneously transmitted and thus the scheduling latency can be significantlyreduced. In this paper, we focus on the opportunistic beamforming schemes with$N_t<N\le N_t^2$ transmit beams in the downlink of MISO systems over Rayleighfading channels. We first show how to design the beamforming matrices withmaximum number of transmit beams as well as least correlation between any pairof them as possible, through Fourier, Grassmannian, and mutually unbiased bases(MUB) based constructions in practice. Then, we analyze their system throughputby exploiting the asymptotic theory of extreme order statistics. Finally, oursimulation results show the Grassmannian-based beamforming achieves the maximumthroughput in all cases with $N_t=2$, 3, 4. However, if we want to exploitoverall $N_t^2$ degrees of freedom, we shall resort to the Fourier andMUB-based constructions in the cases with $N_t=3$, 4, respectively.

How to Fully Exploit the Degrees of Freedom in the Downlink of MISO Systems With Opportunistic Beamforming