Collaborative uplink transmit beamforming with robustness against channel estimation errors

We consider the uplink of collaborative wireless communication systems, where multiple relay terminals decode the signal of a nearby user and forward it to a distant single-antenna base station. We present a collaborative uplink transmit beamforming strategy that can be employed at the relay terminals to provide robustness against uncertainties in the channel state information. The proposed beamforming scheme is obtained using the available knowledge about the second-order statistics of the channel and the possibly erroneous channel state information. The beamforming weight vector is derived by minimizing the total transmitted power subject to a constraint that preserves the received signal at the base station for all the channel realizations within a prescribed uncertainty set. We present two beamforming algorithms based on different mathematical descriptions of the uncertainty set. Both algorithms can be applied to fine-of-sight (LOS) propagation and fiat-fading channels. In the first algorithm, the robust beamforming vector is computed at the base station using the uplink data and fed back to the cooperating relay terminals. This centralized processing scheme allows any additional convex constraint to be easily incorporated into the beamforming strategy. In the second algorithm, the beamforming vector of each terminal is locally computed using the available knowledge about the terminal's channel and a single parameter (Lagrange multiplier) that is broadcast from the base station to all the cooperating terminals. Simulation results are presented, showing the superior performance of our proposed algorithms compared with classical transmit beamforming techniques in both LOS propagation and fiat-fading channels. Index Terms--Array signal processing, convex optimization, cooperative systems, distributed beamforming.