Compensation of Coarse Quantization Effects on Channel Estimation and BER in Massive MIMO

Low-resolution quantization is essential to reduce implementation cost and power consumption in massive multiple-input multiple-output (MIMO) systems for 5G and 6G. While most existing studies assume perfect channel state information (CSI), we model the impact of coarse quantization noise on both channel estimation and data transmission, yielding a more realistic assessment of system performance under imperfect CSI conditions in the uplink. We develop a tight approximation for the bit-error ratio (BER) of uncoded M-QAM with zero-forcing detection, based on the linear minimum mean-square error (LMMSE) channel estimate. These analytical results enable compensation strategies that jointly optimize quantization resolution, transmit power, and pilot length across different numbers of users and base station antennas. We further demonstrate the applicability of the proposed framework through several design scenarios that highlight its effectiveness in optimizing system parameters and improving energy efficiency under quantization constraints. For example, in a 16-QAM system, extending the pilot sequence by 2.5 times and lowering transmit power by 0.5 dB enables a 3-bit quantized system to match the BER of the full-resolution case. The proposed framework offers a fast and accurate alternative to Monte Carlo simulations, enabling practical system optimization under realistic quantization constraints.

💡 Research Summary

This paper addresses a critical gap in the analysis of massive multiple‑input multiple‑output (MIMO) systems that employ low‑resolution analog‑to‑digital converters (ADCs). While many prior works assume perfect channel state information (CSI) and focus on capacity metrics, the authors model the impact of coarse quantization noise on both the channel‑estimation phase and the data‑transmission phase, thereby providing a realistic assessment of system performance under imperfect CSI.

The system considered is an uplink single‑cell massive MIMO link with (K) single‑antenna users and a base station equipped with (N) antennas. Users transmit uncoded (M)-QAM symbols with equal average power (p_u). The received complex vector is first quantized by (b)-bit ADCs on each real and imaginary component. To keep the analysis tractable, the additive quantization noise model (AQNM) is adopted: the quantized signal is approximated as (y_q \approx \alpha y + n_q), where (\alpha) is a linear gain (tabulated for (b\le5) and approximated for larger (b)) and (n_q) is an independent Gaussian noise term whose covariance depends on (\alpha) and the signal power.

Channel Estimation under Quantization
During the pilot phase, orthogonal pilot sequences of length (\tau) are transmitted. The quantized pilot matrix is expressed as (Y_{pq}\approx \alpha\sqrt{p_u}HS_p + N_e), where (N_e) aggregates both thermal noise and quantization noise. By re‑solving the linear minimum‑mean‑square‑error (LMMSE) problem with this quantized observation, the authors derive a closed‑form estimator

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