Quasi-convex designs of max-min linear BC precoding with outage QoS constraints

We consider a broadcast channel (BC) in which the base station is equipped with multiple antennas and each user has a single antenna. We study the design of systems with linear precoders and probabilistically-constrained Quality of Service (QoS) requirements for each user, in scenarios with imperfect channel state information (CSI) at the transmitter. Each user's QoS is expressed as an upper bound on the outage probability of the received signal-to-interference-plus-noise ratio. Given a total power constraint on the transmitter, we consider the design of a linear precoder so as to maximize the minimum QoS requirement of all users. We propose stochastic models for the uncertainty in the CSI of each user that are suitable for uncertainties resulting from estimation errors, and those resulting from quantization errors in systems with quantized feedback of the CSI. We formulate the design problem as a chance constrained optimization problem, and we adopt a conservative approach that yields deterministic quasi-convex formulations that are efficiently-solvable. Our simulations indicate that the proposed methods can significantly increase the minimum QoS of all users when the QoS requirements are formulated as outage constraints.