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 ( ΣΔ) 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), zero-forcing (ZF) and LMMSE receivers and provide a lower bound for the achievable rate with the MRC receiver. Numerical results show superior channel estimation and sum spectral efficiency performance using the ΣΔ architecture compared to conventional 1- or 2-bit quantized massive MIMO systems.
Highlights
Massive multiple-input multiple-output (MIMO) systems provide high spatial resolution and throughput, but the cost and power consumption of the associated RF hardware, the analog-to-digital converters (ADCs) and digital-to-analog converters (DACs) can be prohibitive, especially at higher bandwidths and sampling rates
Channel estimation based on generalized approximate message passing [12], near maximum likelihood [4] and linear approaches [1] using one-bit ADCs, support vector machines [13], recursive least-squares using two-bit ADCs [14] and with dithered feedback signals [15] using 1-3 bit ADCs have been proposed
After performing the analysis for the one-bit case, we show how the analysis can be extended for a Σ∆ array implemented with two-bit quantization, and similar extensions are possible for higher resolution ADCs
Summary
Massive MIMO systems provide high spatial resolution and throughput, but the cost and power consumption of the associated RF hardware, the analog-to-digital converters (ADCs) and digital-to-analog converters (DACs) can be prohibitive, especially at higher bandwidths and sampling rates. We consider optimal linear minimum mean squared error (LMMSE) channel estimation for massive MIMO systems with first-order one-bit and two-bit spatial Σ∆ ADCs. Our initial results on this problem in [42] were derived based on a vector-wise Bussgang decomposition similar to what was used for standard one-bit quantization in [1]. For the case of MRC, the two-bit Σ∆ architecture provides 99% of the spectral efficiency of a system with infinite resolution ADCs. The results presented go beyond the preliminary work in [42], [49] by providing details of the derivations of the channel estimator and sum spectral efficiency expressions, incorporation of mutual coupling and correlated receiver noise in the channel model, and including analysis of the LMMSE receiver performance. X 0 cost−1 t dt and cosine and sine integral functions, respectively, where η is the Euler–Mascheroni constant
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