Evolutionary AP Switch ON/OFF Techniques for Energy-efficient Cell-free Massive MIMO Networks

Technical Summary: Evolutionary AP Switch ON/OFF Techniques for Energy-efficient Cell-free Massive MIMO Networks

Problem Statement
Cell-free massive multiple-input multiple-output (CF-mMIMO) is a leading architecture for next-generation wireless systems, offering uniform service quality through coordinated distributed access points (APs). However, the dense deployment of APs and their fully cooperative nature result in significant energy consumption. While dynamically adapting the set of active APs to spatio-temporal traffic variations is a proven strategy for energy savings, existing solutions face critical limitations. Current AP ON/OFF mechanisms typically rely on worst-case dimensioning or greedy heuristics (e.g., goodness-of-fit metrics) that inadequately explore the combinatorial activation space. These methods often fail to find global optima, particularly under realistic, spatially inhomogeneous traffic loads where user distributions are irregular. Furthermore, the optimization problem is NP-hard; for a network with 100 APs, there are $2^{100}$ possible activation patterns, rendering exhaustive search infeasible. Additionally, balancing energy efficiency (EE) and spectral efficiency (SE) remains a challenge, as improving one often penalizes the other.

Methodology
The paper proposes two evolutionary optimization strategies tailored to the AP activation problem in large-scale CF-mMIMO networks under heterogeneous traffic conditions. The system model assumes a time-division duplexing (TDD) architecture with $L$ APs serving $K$ mobile stations (MSs), utilizing either Conjugate Beamforming (CB) or Minimum Mean Square Error (MMSE) processing.

1. Constrained Genetic Algorithm (CGA): This approach addresses the optimization of EE for a fixed number of active APs ($L_A$). The algorithm employs a genetic algorithm where the population is constrained such that every individual (solution) contains exactly $L_A$ active APs. An outer search loop iterates over different values of $L_A$ to identify the globally optimal operating point. The CGA uses elitist selection, crossover, and mutation to navigate the solution space, ensuring that the constraint on the number of active APs is maintained throughout the evolutionary process.
2. Pareto-driven Genetic Algorithm (PDGA): This is a multi-objective optimization technique designed to jointly optimize EE and SE. Instead of fixing the number of active APs, the PDGA evolves a population to construct a Pareto front representing the trade-off between the two metrics. The algorithm incorporates specific mechanisms to maintain diversity: it biases mutation toward deactivating APs (to find energy-efficient solutions) while explicitly retaining an "all-APs-ON" individual to preserve the high-SE region of the solution space. This allows network operators to select operating points based on specific QoS constraints (e.g., minimum required SE).

Both methods are compared against a benchmark greedy search strategy based on Goodness-of-Fit (GoF) tests, which aligns AP activation with MS distribution but lacks global coordination.

Key Contributions

• Evolutionary Framework: The development of a GA-based framework that effectively explores the global combinatorial space of AP ON/OFF patterns, overcoming the limitations of greedy heuristics in heterogeneous traffic scenarios.
• CGA Implementation: A constrained GA that identifies near-optimal AP subsets for fixed cardinalities, combined with an external search to determine the optimal number of active APs.
• PDGA Implementation: A multi-objective GA that explicitly characterizes the EE–SE trade-off via a Pareto front, enabling decision-oriented network configuration rather than seeking a single optimal point.
• Complexity Analysis: A detailed computational complexity analysis of both proposed algorithms, comparing their costs against the benchmark and analyzing the dominance of fitness evaluation costs versus algorithmic operations.
• Performance Evaluation: Extensive simulations under realistic spatially inhomogeneous traffic distributions (modeled using log-normal distributions) for both CB and MMSE processing schemes.

Results
Simulation results demonstrate that the proposed evolutionary strategies consistently outperform state-of-the-art greedy benchmarks:

• Energy Efficiency Gains: Under CB precoding, the CGA achieved a maximum EE of approximately $11.41 \times 10^5$ bit/Joule (with 24 active APs), representing a 6.50% improvement over the GoF benchmark. Under MMSE processing, the gain was 7.12% ($44.29 \times 10^5$ bit/Joule with 37 active APs).
• Trade-off Characterization: The PDGA successfully generated Pareto fronts that revealed large regions of dominated solutions found by random or greedy selection. It highlighted that MMSE processing allows for higher EE and SE simultaneously compared to CB due to effective interference suppression.
• Operational Flexibility: The framework allows operators to select operating points along the Pareto front that satisfy specific SE constraints while maximizing EE. For instance, relaxing SE constraints significantly reduces the number of required active APs and increases EE.
• Robustness: The methods proved robust across different spatial MS distributions (single hotspot, multiple hotspots, and uniform), adapting the active AP configuration to match the traffic density.
• Computational Feasibility: While GA-based methods require longer runtimes than the GoF benchmark (e.g., ~184 hours for CGA-MMSE on a single workstation vs. ~55 minutes for GoF), the analysis confirms feasibility for slow-timescale network planning (hourly or daily updates). The PDGA was found to be computationally more efficient than CGA, requiring fewer equivalent workstation nodes for the same update periods.

Significance and Claims
The paper claims that evolutionary optimization offers a powerful and reliable approach for energy-efficient CF-mMIMO deployments, particularly in scenarios with spatially heterogeneous traffic where greedy methods fail to find global optima. The authors emphasize that their work provides not only improved energy efficiency but also new insights into the interplay between AP activation, traffic heterogeneity, and processing schemes (CB vs. MMSE).

Crucially, the paper positions these methods as deployment-agnostic tools. Unlike reinforcement learning approaches that require extensive training on specific distributions and may struggle with generalization, the proposed evolutionary strategies generate configurations for specific, given spatial distributions without prior training. The solutions can be precomputed offline and implemented in real-time via lookup tables. The authors conclude that while the computational cost is higher than greedy heuristics, it is manageable for network planning scenarios where traffic patterns evolve over hours, making the framework suitable for practical, green network design.