Abstract
We examine the uplink spectral efficiency of a massive MIMO base station employing a one-bit Sigma-Delta sampling scheme implemented in the spatial rather than the temporal domain. Using spatial rather than temporal oversampling, and feedback of the quantization error between adjacent antennas, the method shapes the spatial spectrum of the quantization noise away from an angular sector where the signals of interest are assumed to lie. It is shown that, while a direct Bussgang analysis of the Sigma-Delta approach is not suitable, an alternative equivalent linear model can be formulated to facilitate an analysis of the system performance. The theoretical properties of the spatial quantization noise power spectrum are derived for the Sigma-Delta array, as well as an expression for the spectral efficiency of maximum ratio combining (MRC). Simulations verify the theoretical results and illustrate the significant performance gains offered by the Sigma-Delta approach for both MRC and zero-forcing receivers.
Highlights
To reduce complexity and energy consumption in large-scale MIMO systems, researchers and system designers have recently considered implementations with low-resolution analogto-digital and digital-to-analog converters (ADCs, DACs)
We see that the quantization noise power for the Σ∆ array is substantially lower over the angles where the users are present, while the effect is the opposite for standard one-bit quantization – the quantization noise is higher for angles where the amplitude of the received signals is larger
We studied the performance of massive MIMO systems employing spatial one-bit Σ∆ quantization
Summary
To reduce complexity and energy consumption in large-scale MIMO systems, researchers and system designers have recently considered implementations with low-resolution analogto-digital and digital-to-analog converters (ADCs, DACs). Delta (Σ∆) approach, which quantizes the difference (∆) between the signal and its previously quantized value, and integrates (Σ) the resulting output [28]–[30] This has the effect of shaping the quantization noise to higher frequencies, while the signal occupies the low end of the spectrum due to the oversampling. The results of the analysis indicate the significant gain of the Σ∆ approach compared with standard one-bit quantization for users that lie in the angular sector where the shaped quantization error spectrum is low. For MRC, the one-bit Σ∆ array performs essentially the same for such users as a BS with infinite resolution ADCs. The angular sectorization of users in the spatial domain is not necessarily a drawback in cellular implementations, where cells are typically split into 120◦ regions using different arrays on the BS tower.
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