This work studies the joint design of precoding and backhaul compression strategies for the downlink of cloud radio access networks. In these systems, a central encoder is connected to multiple multiantenna base stations (BSs) via finite-capacity backhaul links. At the central encoder, precoding is followed by compression in order to produce the rate-limited bit streams delivered to each BS over the corresponding backhaul link. In current state-of-the-art approaches, the signals intended for different BSs are compressed independently. In contrast, this work proposes to leverage joint compression, also referred to as multivariate compression, of the signals of different BSs in order to better control the effect of the additive quantization noises at the mobile stations (MSs). The problem of maximizing the weighted sumrate with respect to both the precoding matrix and the joint correlation matrix of the quantization noises is formulated subject to power and backhaul capacity constraints. An iterative algorithm is proposed that achieves a stationary point of the problem. Moreover, in order to enable the practical implementation of multivariate compression across BSs, a novel architecture is proposed based on successive steps of minimum mean-squared error (MMSE) estimation and per-BS compression. Robust design with respect to imperfect channel state information is also discussed. From numerical results, it is confirmed that the proposed joint precoding and compression strategy outperforms conventional approaches based on the separate design of precoding and compression or independent compression across the BSs.

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