MMSE Detection for 1-Bit Quantized Massive MIMO with Imperfect Channel Estimation

In this paper, we study the uplink achievable rate by a massive multiple-input multiple-output (MIMO) system in which the base station is equipped with a large number of 1-bit analog-to-digital converters (ADCs). We propose a linear minimum mean-squared error (MMSE)-based detector that accounts for the non-linearity effects of the 1-bit quantization as well as for channel estimation error. An analytical framework that derives the achievable rate of the MMSE-based detector in a massive MIMO configuration under the assumption of 1-bit quantized ADCs and channel estimation error is presented. We compare the achievable rates of a massive MIMO system using a 1-bit ADC and a linear detector against a conventional MIMO system with higher-order modulation and near maximum likelihood (ML) detection. We show that in the low signal-to-noise ratio (SNR) regime with channel estimation error, the quantized massive MIMO system can outperform the conventional large MIMO system; however for high SNR, the conventional MIMO system with a near ML detector can outperform the quantized massive MIMO system.