Outage Minimization for Intelligent Reflecting Surface Aided MISO Communication Systems via Stochastic Beamforming

Intelligent reflecting surface (IRS) has the potential to significantly enhance the network performance by reconfiguring the wireless propagation environments.
It is however difficult to obtain the accurate downlink channel state information (CSI) for efficient beamforming design in IRS-aided wireless networks.
In this article, we consider an IRS-aided downlink multiple-input single-output (MISO) network, where the base station (BS) is not required to know the underlying channel distribution.
We formulate an outage probability minimization problem by jointly optimizing the beamforming vector at the BS and the phase-shift matrix at the IRS, while taking into account the transmit power and unimodular constraints.
The formulated problem turns out to be a non-convex non-smooth stochastic optimization problem.
To this end, we employ the sigmoid function as the surrogate to tackle the non-smoothness of the objective function.
In addition, we propose a data-driven efficient alternating stochastic gradient descent (SGD) algorithm to solve the problem by utilizing the historical channel samples.
Simulation results demonstrate the performance gains of the proposed algorithm over the benchmark methods in terms of minimizing the outage probability.