Weighted sum rate maximization for cognitive MISO broadcast channel: Large system analysis

This paper considers the ergodic weighted sum rate (WSR) maximization problem for an underlay cognitive radio MISO broadcast channel, where a secondary network, consisting of a base-station with M transmit antennas and K single-antenna secondary users (SUs), is allowed to share the same spectrum with a primary user (PU), under an average transmit sum power (ATTP) constraint Pav and an average interference power (AIP) constraint on the PU. We show that the ATTP constraint is always active, and as Pav → ∞, the ergodic WSR approaches infinity similar to the conventional non-CR network case. A low-complexity suboptimal beamforming scheme (called partially-projected regularized zero-forcing beamforming `PP-RZFBF') with a closed-form beamformer is proposed. Due to the non-convexity of PP-RZFBF scheme, a large system analysis is conducted in the limit as M and K approach infinity with a fixed finite ratio r = K/M. We derive deterministic limiting approximations for the PP-RZFBF problem which enables us to determine asymptotically optimal beamformers for PP-RZFBF. Numerical simulations illustrate that the asymptotically optimal beamformers turn out to be quite effective even for small M, K.