Robust Linear Precoder Design for Multi-Cell Downlink Transmission

Abstract

Coordinated information processing by the base stations of multi-cell wireless networks enhances the overall quality of communication in the network. Such coordinations for optimizing any desired network-wide quality of service (QoS) necessitate the base stations to acquire and share some channel state information (CSI). With perfect knowledge of channel states, the base stations can adjust their transmissions for achieving a network-wise QoS optimality. In practice, however, the CSI can be obtained only imperfectly. As a result, due to the uncertainties involved, the network is not guaranteed to benefit from a globally optimal QoS. Nevertheless, if the channel estimation perturbations are confined within bounded regions, the QoS measure will also lie within a bounded region. Therefore, by exploiting the notion of robustness in the worstcase sense some worst-case QoS guarantees for the network can be asserted. We adopt a popular model for noisy channel estimates that assumes that estimation noise terms lie within known hyper-spheres. We aim to design linear transceivers that optimize a worst-case QoS measure in downlink transmissions. In particular, we focus on maximizing the worst-case weighted sum-rate of the network and the minimum worst-case rate of the network. For obtaining such transceiver designs, we offer several centralized (fully cooperative) and distributed (limited cooperation) algorithms which entail different levels of complexity and information exchange among the base stations.

Optimal Resource Allocation in Coordinated Multi-Cell Systems

“…The uncertainty originates from a variety of sources; for example, imperfect channel estimation, feedback quantization, inadequate channel reciprocity, and delays in CSI acquisition on fading channels. It is common to have an additive error model [9,17,26,50,239,241,242,257,286,289,328] with…”

“…The system cannot account for any error; the stochastic error vector˜ k could potentially cancel out the nominal vector as˜ k = − h k or be very large (the distribution is even unbounded for Rayleigh fading channels). This is often handled by only considering a subset of error vectors, the uncertainty set, that has high probability of containing the error [9,17,26,50,239,241,242,257,286,289,328]. If the design of these sets is explicitly included in the resource allocation (e.g., optimization with acceptable outage probabilities), it seems that conservative approximations 1 of each user's performance are required to achieve tractable problem formulations [50,241,289].…”

“…For analytic convenience and motivated by channel estimation [26,242,257], we consider (compact) ellipsoidal channel uncertainty sets. These sets can either be defined jointly for all base stations to a certain user, 2) or separately for the channel from each BS j to each user k ∈ C j , To elaborate the difference between (4.2) and (4.3), we consider the special case of…”

“…The distributed algorithm in [280] searches for beamforming vectors that satisfy the KKT conditions. A convex conservative approximation of the weighted sum information rate is obtained in [257], which enables distributed optimization of a lower bound on the system utility. The multi-cell resource allocation is decomposed into many single-cell problems in [291], thus enabling iterative use of algorithms developed for low-complexity single-cell sum information rate optimization.…”

“…There are many papers claiming that a large fraction of the optimal system utility can be achieved by suboptimal low-complexity optimization algorithms [18,257,291], but it is hard to verify for large and complicated multi-cell systems.…”