Robust Beamforming and Power Allocation for Coherent Cell-Free Massive MIMO with Residual Calibration Errors

This paper investigates robust downlink transmission to tolerate calibration aging in time-division duplex cell-free massive multiple-input multiple-output (CF-mMIMO) systems with residual calibration errors (RCEs). Unlike existing studies that typically treat RCEs as static impairments, we develop a time-evolving RCE model that characterizes the joint effects of residual phase mismatches, residual carrier frequency offsets, and oscillator phase noise. Based on this model, two practical processing architectures are considered: instantaneous calibrated-channel-based robust beamforming (BF) and statistical beamformed-channel-based robust power allocation (PA). For both architectures, tractable achievable rate lower bounds are derived, which explicitly reveal the impact of calibration aging on coherent combining, BF-gain uncertainty, and inter-user interference. Using these lower bounds as design metrics, we formulate an effective weighted sum-rate (EWSR) maximization problem over the data transmission interval, so that the resulting BF and PA designs can account for the temporal evolution of RCEs rather than a single calibrated instant. To efficiently solve the resulting problems, a Gauss--Legendre quadrature-based weighted minimum mean square error (WMMSE) optimization framework is developed, where both robust BF and PA are updated in an access point (AP)-block manner with closed-form solutions under per-AP power constraints. Simulation results demonstrate that: i) the proposed algorithms exhibit stable convergence; ii) the proposed robust BF and PA schemes achieve higher EWSR by explicitly accounting for calibration aging than their non-robust counterparts; and iii) robust BF achieves higher spectral efficiency (SE), whereas robust PA provides a more favorable tradeoff between SE and implementation cost in terms of computational complexity and fronthaul overhead.