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Sum-rate optimal multi-antenna downlink beamforming strategy based on clique search Edit

  • T. Yoo and A. Goldsmith,“Sum-rate optimal multi-antenna downlink beamforming strategy based on clique search,” in Proc. IEEE GLOBECOM, Nov. 2005, pp. 1510–1514.

Theorem 1: Assume the i.i.d Rayleigh fading channel model of Section II. Assume that users have equal SNRs, i.e., \mathrm{SNR}_k \triangleq E[ || \mathbf{h}_k ||^2 ] = \mathrm{SNR},~ \forall k. Then the probability that the optimal ZFBF user set S_\mathrm{ZFBF} forms a clique approaches 1 as K \rightarrow 1. That is,

 \lim_{K \rightarrow \inf} P(S_\mathrm{ZFBF} \in C_{g(\epsilon))}) = 1, 
 ~~0 < \epsilon \leq \frac{1}{M}.

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