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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,

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