Joint Channel Estimation and Robust Beamforming Design for AF Relaying Using IMM Kalman Filters

Abstract

This paper addresses the joint problem of recursive channel estimation and robust beamformer design in peer-to-peer communication through a network of relays over time-varying radio channels. Using observed signal samples at the relay and receiver nodes, the Channel State Information (CSI) is estimated centrally by taking advantage of a Markov model for the transmitter-relay and relay-receiver channels, and employing either the Extended Kalman Filter (EKF) or the Cubature Kalman Filter (CKF). Based on the estimated CSI, two robust approaches are conceived for designing the relay beamforming where the aim is to minimize the total transmission power of the relays subject to Signal-to-Interference plus Noise Ratio (SINR) constraints at each of the receiver nodes. Furthermore, the Interacting Multiple Model (IMM) approach for mixing non-stationary and stationary Markov models is employed to extend the time-varying robust beamforming design to non-stationary environments. Through numerical simulations, the recursive CSI estimation methods are shown to be efficient, i.e., unbiased and converging to the Cramer-Rao Lower Bound (CRLB). Furthermore, the results confirm the better performance of the proposed robust relay beamforming design algorithms compared to existing methods in terms of relevant transmission metrics, including relay power consumption and spectral efficiency.