Distributionally Robust Relay Beamforming in Wireless Communications

We consider a wireless network with densely deployed user devices (e.g., a device-to-device or wireless sensor network) underlaying a cellular system, in which some user devices act as relays to facilitate data transmissions between a distant transceiver pair under imperfect channel information. Motivated by the observation that most of the channel distributions are unimodal, we formulate a novel distributionally robust beamforming problem, in which the random channel coefficient follows a class of unimodal distribution with known first- and second-order moments. Our design objective is to maximize the worst-case signal-to-noise ratio (SNR) at the dedicated user device while satisfying a probabilistic interference constraint at the cellular user equipment (CUE). Though such a unimodal distributionally robust (UDR) beamforming problem is non-convex, we show that an approximate solution can be computed efficiently using semidefinite programming. Our simulation results show that under mild conditions, the UDR model yields significant beamforming performance improvement over conventional robust models that merely rely on first- and second-order moments of the channel distribution.