Efficiently and Globally Solving Joint Beamforming and Compression Problem in the Cooperative Cellular Network via Lagrangian Duality

TL;DR

This paper introduces an efficient, globally optimal algorithm for joint beamforming and compression in cooperative cellular networks, leveraging Lagrangian duality and semidefinite relaxation to minimize power while satisfying SINR and fronthaul constraints.

Contribution

It proves the absence of duality gap and develops a computationally efficient algorithm based on Lagrangian duality and fixed-point iterations for the joint beamforming and compression problem.

Findings

The algorithm guarantees finding the global optimal solution.

Simulation results confirm the algorithm's efficiency and correctness.

No duality gap exists for the formulated problem.

Abstract

Consider the joint beamforming and quantization problem in the cooperative cellular network, where multiple relay-like base stations (BSs) connected to the central processor (CP) via rate-limited fronthaul links cooperatively serve the users. This problem can be formulated as the minimization of the total transmit power, subject to all users' signal-to-interference-plus-noise-ratio (SINR) constraints and all relay-like BSs' fronthaul rate constraints. In this paper, we first show that there is no duality gap between the considered problem and its Lagrangian dual by showing the tightness of the semidefinite relaxation (SDR) of the considered problem. Then we propose an efficient algorithm based on Lagrangian duality for solving the considered problem. The proposed algorithm judiciously exploits the special structure of the Karush-Kuhn-Tucker (KKT) conditions of the considered problem and finds the solution that satisfies the KKT conditions via two fixed-point iterations. The proposed algorithm is highly efficient (as evaluating the functions in both fixed-point iterations are computationally cheap) and is guaranteed to find the global solution of the problem. Simulation results show the efficiency and the correctness of the proposed algorithm.