In massive MIMO, replacing high-resolution ADCs/DACs with low-resolution ones has been deemed as a potential way to significantly reduce the power consumption and hardware costs of massive MIMO implementations. In this context, the challenge lies in how the quantization error effect can be suppressed under low-resolution ADCs/DACs. In this paper we study a spatial sigma-delta (ΣΔ) modulation approach for massive MIMO downlink precoding under one-bit DACs. ΣΔ modulation is a classical signal processing concept for coarse analog-to-digital/digital-to-analog conversion of temporal signals. Fundamentally its idea is to shape the quantization error as high-frequency noise and to avoid using the high-frequency region by oversampling. Assuming a uniform linear array at the base station (BS), we show how ΣΔ modulation can be adapted to the space, or MIMO, case. Essentially, by relating frequency in the temporal case and angle in the spatial case, we develop a spatial ΣΔ modulation solution. By considering sectored array operations we study how the quantization error effect can be reduced, and the effective SNR improved, for zero-forcing (ZF) precoding. Our simulation results show that ZF precoding under spatial ΣΔ modulation performs much better than ZF precoding under direct quantization.
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Multiuser Massive Mimo Downlink Precoding Using Second-Order Spatial Sigma-Delta Modulation
Massive MIMO using low-resolution digital-to-analog converters (DACs) at the base station (BS) is an attractive downlink approach for reducing hardware overhead and for reducing power consumption, but managing the large quantization noise effect is a challenge. Spatial Sigma-Delta modulation is a recently emerged technique for tackling the aforementioned effect. Assuming a uniform linear array at the BS, it works by shaping the quantization noise as high spatial-frequency, or angle, noise. By restricting the user-serving region to be within a smaller angular region, the quantization noise incurred by the users can be effectively reduced. We previously showed that, under the one-bit DAC case, the quantization noise can be satisfactorily contained using a simple first-order Sigma-Delta modulation scheme. In this work we study the potential of spatial Sigma-Delta modulation in the two-bit DAC case and under second-order
modulation. Our empirical results indicate that second-order spatial Sigma-Delta modulation provides better quantization noise suppression.
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- Award ID(s):
- 1824565
- NSF-PAR ID:
- 10188430
- Date Published:
- Journal Name:
- International Conference on Acoustics, Speech and Signal Processing
- Page Range / eLocation ID:
- 8966 to 8970
- Format(s):
- Medium: X
- Sponsoring Org:
- National Science Foundation
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Abstract We propose the use of low bit-depth Sigma-Delta and distributed noise-shaping methods for quantizing the random Fourier features (RFFs) associated with shift-invariant kernels. We prove that our quantized RFFs—even in the case of $1$-bit quantization—allow a high-accuracy approximation of the underlying kernels, and the approximation error decays at least polynomially fast as the dimension of the RFFs increases. We also show that the quantized RFFs can be further compressed, yielding an excellent trade-off between memory use and accuracy. Namely, the approximation error now decays exponentially as a function of the bits used. The quantization algorithms we propose are intended for digitizing RFFs without explicit knowledge of the application for which they will be used. Nevertheless, as we empirically show by testing the performance of our methods on several machine learning tasks, our method compares favourably with other state-of-the-art quantization methods.
- Free Publicly Accessible Full Text
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Accepted Manuscript1.0
- Conference Paper:
- https://doi.org/10.1109/ICASSP40776.2020.9053267
