Downlink Channel Matrix Estimation from PMI-Only Feedback in FDD Systems: Maximum Likelihood and Sharp Excess Risk Bound
This work addresses the challenging problem of channel estimation from highly quantized PMI feedback in 5G NR FDD systems, providing theoretical guarantees and practical improvements over baselines.
The paper proposes a maximum likelihood estimator for downlink channel estimation in FDD massive MIMO systems using only PMI feedback, achieving asymptotic optimality with a sharp excess risk bound of O(1/T) under identifiability conditions.
We study downlink channel estimation in a frequency-division duplex (FDD) massive MIMO system from PMI-only feedback under a 5G NR-type limited-feedback architecture. In this architecture, the user selects a preferred codeword from a shared codebook based on the reduced-dimensional channel and only reports its index (known as the precoding matrix indicator, PMI) back to the base station. Therefore, the channel must be estimated from these highly quantized, nonlinear PMI observations. Based on a probabilistic perturbation model, a constrained maximum likelihood estimator (MLE) is proposed for this estimation problem, whose objective can also be interpreted as a relaxation of the hard empirical decision error. The Cramér--Rao bound is derived for the complex-valued model, with the global phase ambiguity handled via gauge-fixing. For the real-valued setting, a global excess-risk bound of order $O(1/\sqrt{T})$ is established, which is then refined to a sharp local rate of order $O(1/T)$ under suitable identifiability conditions. Numerical results show that the MLE asymptotically attains the Cramér--Rao bound and outperforms several baseline methods on both synthetic data and realistic FDD channels.