Performance-Energy Trade-offs in Finite-Dimensional Multi-Cell Massive MIMO Uplink Systems: A Benchmarking Study of Linear Detectors

Abstract This paper presents a finite-dimensional benchmarking framework for analyzing the spectral-efficiency (SE) and energy-efficiency (EE) performance of linear uplink detectors in multi-cell massive MIMO systems. Maximum-ratio combining (MRC), zero-forcing (ZF), and regularized zero-forcing (RZF) are investigated under both ideal channel state information (CSI) and MMSE-based imperfect CSI conditions. Closed-form Deterministic-equivalent signal-to-interference-plus-noise ratio (SINR) expressions are derived to characterize detector behavior under practical finite-dimensional operation. The analysis identifies several important operating characteristics. In particular, ZF and RZF begin to outperform MRC when the antenna-to-user ratio exceeds approximately M/K 2. 5 under symmetric fading conditions. The results further reveal load-dependent SE saturation due to persistent multi-cell interference, along with an interference-limited signal-to-noise ratio (SNR) region beyond approximately 8–10 dB, where additional transmit power yields only marginal throughput gains. A practical EE model incorporating amplifier efficiency and detector-processing overhead is further considered. Additional results examine the sensitivity of the detector crossover threshold under heterogeneous large-scale fading, the impact of pilot reuse on the SE–EE trade-off, and the influence of channel aging on detector performance. The results show that MRC is more robust under severe CSI degradation, whereas ZF achieves the highest EE under interference-limited conditions. RZF provides a balanced trade-off between interference suppression and robustness across different operating regimes. Monte Carlo simulations validate the analytical results and quantify the performance gap between ideal and imperfect CSI conditions. The proposed framework provides practical guidelines for detector selection, antenna dimensioning, user loading, pilot reuse configuration, and energy-efficient uplink operation in beyond-5G and emerging 6G wireless networks.