Massive Mimo Channel Estimation with 1-Bit Spatial Sigma-delta ADCS

Abstract

We consider channel estimation for an uplink massive multiple input multiple output (MIMO) system where the base station (BS) uses an array with low-resolution (1-2 bit) analog-to-digital converters and a spatial Sigma-Delta (Σ∆) architecture to shape the quantization noise away from users in some angular sector. We develop a linear minimum mean squared error (LMMSE) channel estimator based on the Bussgang decomposition that reformulates the nonlinear quantizer model using an equivalent linear model plus quantization noise. We also analyze the uplink achievable rate with maximal ratio combining (MRC) and zero-forcing (ZF) receivers and provide a closed-form expression for the achievable rate with the MRC receiver. Numerical results show superior channel estimation and sum spectral efficiency performance using the Σ∆ architecture compared to conventional 1-or 2-bit quantized massive MIMO systems.

Divide and Conquer: One-bit MIMO-OFDM Detection by Inexact Expectation Maximization

“…gn,w(zn,w, qn,w), (11) where qn,w = {q R n,w , q I n,w }; q R n,w ∈ D Re(yn,w ) , q I n,w ∈ D Im(yn,w ) ; gn,w(zn,w, qn,w) := g(Re(zn,w), q R n,w ) + g(Im(zn,w), q I n,w ) with g given by (9). Problem (11) shows a structure suitable for the application of block coordinate descent (BCD), which we will explore in the subsequent subsections.…”

“…One-bit massive MIMO systems have spurred immense research interest in aspects such as asymptotic system performance analyses and efficient channel estimation/data detection. For instance, the performances of linear estimators and detectors have been studied in [2,6,7]; maximum-likelihood (ML) data detection has been considered in [3,9]; approximate message passing algorithms for data detection have been studied in [4,10]; the Σ∆ ADC architecture has been used in [11].…”

Channel Estimation Techniques for Millimeter-Wave Communication Systems: Achievements and Challenges

“…Some of these works include, [179] where a joint channel-and-data estimation algorithm for lowprecision ADCs system was proposed based on the optimal Bayes estimator, and [196] where the bilinear generalized approximate message passing (BiG-AMP) technique was employed. A recent paper [197] studied channel estimation for multi-user uplink massive MIMO systems with 1-bit spatial sigma-delta ADCs. The authors explain the benefits of using the sigma-delta ADCs in reducing the noise on the signal, where it was shown through simulation results that the sigmadelta modulation reduces the quantization error of the lowresolution ADCs.…”

Millimeter Wave MIMO Channel Estimation with 1-bit Spatial Sigma-Delta Analog-to-Digital Converters

“…Like the time domain, the shaping of the quantization noise to higher spatial frequencies is achieved via spatial oversampling and by integrating the quantization noise across the antennas [10,11]. MIMO transceiver architectures with low-resolution (including 1bit) spatial Σ∆ ADCs and DACs have been used for interference cancellation [12], precoding [13], and channel estimation [14].…”