QoS-based Beamforming and Compression Design for Cooperative Cellular Networks via Lagrangian Duality

TL;DR

This paper develops an efficient, globally optimal algorithm for joint beamforming and compression in cooperative cellular networks, ensuring QoS and fronthaul constraints are met with proven duality and tight semidefinite relaxation.

Contribution

It introduces a novel duality-based algorithm that exploits problem structure to solve the joint optimization problem optimally and efficiently, with guaranteed feasibility detection.

Findings

The proposed algorithm achieves global optimality in beamforming and compression design.

It efficiently detects problem feasibility and computes solutions with linear convergence.

Numerical results confirm the algorithm's effectiveness and computational efficiency.

Abstract

This paper considers the quality-of-service (QoS)-based joint beamforming and compression design problem in the downlink cooperative cellular network, where multiple relay-like base stations (BSs), connected to the central processor via rate-limited fronthaul links, cooperatively transmit messages to the users. The problem of interest is formulated as the minimization of the total transmit power of the BSs, subject to all users' signal-to-interference-plus-noise ratio (SINR) constraints and all BSs' fronthaul rate constraints. In this paper, we first show that there is no duality gap between the considered joint optimization problem and its Lagrangian dual by showing the tightness of its semidefinite relaxation (SDR). Then, we propose an efficient algorithm based on the above duality result for solving the considered problem. The proposed algorithm judiciously exploits the special structure of an enhanced Karush-Kuhn-Tucker (KKT) conditions of the considered problem and finds the solution that satisfies the enhanced KKT conditions via two fixed point iterations. Two key features of the proposed algorithm are: (1) it is able to detect whether the considered problem is feasible or not and find its globally optimal solution when it is feasible; (2) it is highly efficient because both of the fixed point iterations in the proposed algorithm are linearly convergent and evaluating the functions in the fixed point iterations are computationally cheap. Numerical results show the global optimality and efficiency of the proposed algorithm.