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

TL;DR

This work addresses coarse quantization in uplink massive MIMO with imperfect CSI by deriving a closed-form LMMSE channel estimator under the Additive Quantization Noise Model, a SIQNR framework, and a tight BER approximation for uncoded M-QAM with zero-forcing detection. It introduces a joint optimization approach that tunes ADC resolution, pilot length, and transmit power, including an exact relation to match full-precision performance. The analytical results are validated against Monte Carlo simulations and demonstrated through practical design scenarios, showing how quantization-related losses can be mitigated to achieve energy-efficient, high-user-density massive MIMO systems. Overall, the framework provides fast, accurate performance prediction and design guidance for deployments with low-resolution ADCs in 5G/6G contexts.

Abstract

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.

Figures (9)

• Figure 1: An uplink quantized massive MIMO system with $K$ single-antenna users and one BS having $N$ antennas.
• Figure 2: Channel estimation error variance $\sigma_{eq}^2$ versus (a) $p_u$ given $\tau=\tau_q=K$, and (b) $\tau_q$ given $K=20$ and $b=3$
• Figure 3: BER of uplink massive MIMO with $N\!=\!256$, $K\!=\!20$, 16-QAM, $b$-bit ADCs, imperfect CSI: (a) $\tau\!=\!K$, (b) $\tau\!=\!2K$.
• Figure 4: BER of uplink massive MIMO with $\tau\!=\!K\!=\!20$, $b$-bit ADCs, and imperfect CSI for (a) 64-QAM, (b) 256-QAM.
• Figure 5: (a) Required $\tau_q$ and $E_b/N_0$ values to achieve a BER of $10^{-3}$ using (\ref{['eq:tau_q_p_uq']}) for $b$-bit ADCs, $N\!=\!256$, $K\!=\!20$, 16-QAM. (b) BER variation with $\tau_q$ and $E_b/N_0$ for the same system.

Theorems & Definitions (2)

• Lemma 1
• Lemma 2