This paper studies the optimization of transmit beamforming and backhaul compression strategies for the uplink of cloud radio access networks (C-RAN), in which multi-antenna user terminals communicate with a cloud-computing based central processor (CP) through multi-antenna base-stations (BSs) serving as relay nodes. The BSs perform compress-and-forward strategy to quantize the received signals and send the quantization bits to the CP via capacity-limited backhaul links for decoding. In contrast to the previous works on the uplink C-RAN, which mostly focus on the backhaul compression strategies only, this paper proposes the joint optimization of the transmit beamformers and the quantization noise covariance matrices at the BSs for maximizing the benefit brought by the C-RAN architecture. A weighted sum-rate maximization problem is formulated under the user power and backhaul capacity constraints. A novel weighted minimum-mean-square-error successive convex approximation (WMMSE-SCA) algorithm is developed for finding a local optimum solution to the problem. This paper further proposes a low-complexity approximation scheme consisting of beamformers matching to the strongest channel vectors at the user side along with per-antenna scalar quantizers with uniform quantization noise levels across the antennas at each BS. This simple separate design strategy is derived by exploring the structure of the optimal solution to the sum-rate maximization problem under successive interference cancellation (SIC) while assuming high signal-to-quantization-noise ratio (SQNR). Simulation results show that with optimized beamforming and backhaul compression, C-RAN can significantly improve the overall performance of wireless cellular networks. With SIC, the proposed separate design performs very close to the optimized joint design in the SQNR regime of practical interest.
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