[Paper Review] Distributed Power Control In Downlink Cellular Massive Mimo Systems

Trinh Van Chien, Emil Björnson+2 more|arXiv (Cornell University)|Feb 20, 2018

Advanced MIMO Systems Optimization16 references4 citations

TL;DR

This paper proposes a distributed power control algorithm for downlink Massive MIMO systems using dual decomposition to minimize total transmit power while satisfying user quality-of-service (QoS) constraints. Although the method converges to the global optimum with few iterations and ensures theoretical convergence, it does not significantly reduce backhaul signaling compared to centralized approaches due to the channel hardening property, making centralized implementation preferable in Massive MIMO for signaling and complexity reasons.

ABSTRACT

This paper compares centralized and distributed methods to solve the power minimization problem with quality-of-service (QoS) constraints in the downlink (DL) of multi-cell Massive multiple-input multiple-output (MIMO) systems. In particular, we study the computational complexity, number of parameters that need to be exchanged between base stations (BSs), and the convergence of iterative implementations. Although a distributed implementation based on dual decomposition (which only requires statistical channel knowledge at each BS) typically converges to the global optimum after a few iterations, many parameters need to be exchanged to reach convergence.

Motivation & Objective

• To evaluate whether distributed power control can achieve the same optimal solution as centralized methods in multi-cell Massive MIMO systems.
• To identify the minimal set of parameters that must be exchanged between base stations (BSs) for distributed implementation.
• To assess the trade-offs in computational complexity, convergence speed, and backhaul signaling between centralized and distributed approaches.
• To determine whether distributed methods offer practical advantages in Massive MIMO, where channel statistics dominate over instantaneous CSI.

Proposed method

• The paper formulates a total transmit power minimization problem with QoS constraints in a multi-cell Massive MIMO downlink system using TDD and pilot-based channel estimation.
• It applies dual decomposition to decompose the centralized problem into $L$ subproblems, one per base station, enabling distributed optimization.
• Each base station solves a second-order cone (SOC) program using local knowledge and Lagrange multipliers $\lambda_{l,k}^i$ representing inter-cell interference constraints.
• The algorithm iteratively updates the Lagrange multipliers using a subgradient method, with information exchange limited to interference-strength parameters $\theta_{l,k}^i$ and $\tilde{\theta}_{l,k}^i$.
• The method assumes only large-scale fading coefficients are exchanged, leveraging the channel hardening property to reduce signaling overhead.
• Convergence is theoretically guaranteed and evaluated via Monte Carlo simulations under various user and cell configurations.

Experimental results

Research questions

• RQ1 Can a distributed implementation based on dual decomposition achieve the global optimum solution of the centralized power minimization problem in Massive MIMO?
• RQ2 What is the minimal set of parameters that must be exchanged between base stations to enable distributed optimization while maintaining optimality?
• RQ3 How does the number of iterations and convergence behavior of the distributed algorithm depend on network size and user distribution?
• RQ4 Does the distributed approach significantly reduce backhaul signaling and computational complexity compared to centralized implementation in Massive MIMO systems?
• RQ5 Under what conditions is centralized implementation preferable to distributed implementation in terms of signaling and complexity?

Key findings

• The distributed dual decomposition algorithm converges to the global optimum after only a few iterations in most user location realizations, with theoretical convergence guarantees.
• The number of iterations increases with the number of users, as shown in Fig. 3, where $K=10$ requires more iterations than $K=1$ to reach 95% of the optimal solution.
• The actual user QoS at 95% of the global optimum is well-satisfied for most users, though some experience higher-than-required rates, indicating robustness to suboptimal convergence.
• Despite distributed design, the total number of exchanged parameters is not substantially reduced compared to centralized implementation due to the low-dimensional channel representation in Massive MIMO.
• The backhaul signaling cost is dominated by large-scale fading coefficients, not small-scale fading, making distributed implementation less advantageous in terms of signaling overhead.
• For power minimization problems involving only large-scale fading, centralized implementation is preferable due to lower complexity and signaling, especially in dense networks.