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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. 

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. 

Coarsely quantized MIMO signalling methods have gained popularity in the recent developments of massive MIMO as they open up opportunities for massive MIMO implementation using cheap and power-efficient radio-frequency front-ends. This paper presents a new one-bit MIMO precoding approach using spatial Sigma-Delta (∑Δ) modulation. In previous one-bit MIMO precoding research, one mainly focuses on using optimization to tackle the difficult binary signal optimization problem that arise from the precoding design. Our approach attempts a different route. Assuming angular MIMO channels, we apply ∑Δ modulation—a classical concept in analog-to-digital conversion of temporal signals—in space. The resulting ∑Δ precoding approach has two main advantages: First, we no longer need to deal with binary optimization in ∑Δ precoding design. Particularly, the binary signal restriction is replaced by convex signal amplitude constraints. Second, the impact of the quantization error can be well controlled via modulator design and under appropriate operating conditions. Through symbol error probability analysis, we reveal that the very large number of antennas in massive MIMO provides favorable operating conditions for ∑Δ precoding. In addition, we develop a new ∑Δ modulation architecture that is capable of adapting the channel to achieve nearly zero quantization error for a targeted user. Furthermore, we consider multi-user ∑Δ precoding using the zero-forcing and symbol-level precoding schemes. These two ∑Δ precoding schemes perform considerably better than their direct one-bit quantized counterparts, as simulation results show. 

Hyperspectral super-resolution refers to the task of fusing a hyperspectral image (HSI) and a multispectral image (MSI) in order to produce a super-resolution image (SRI) that has high spatial and spectral resolution. Popular methods leverage matrix factorization that models each spectral pixel as a convex combination of spectral signatures belonging to a few endmembers. These methods are considered state-of-the-art, but several challenges remain. First, multiband images are naturally three dimensional (3-d) signals, while matrix methods usually ignore the 3-d structure, which is prone to information losses. Second, these methods do not provide identifiability guarantees under which the reconstruction task is feasible. Third, a tacit assumption is that the degradation operators from SRI to MSI and HSI are known - which is hardly the case in practice. Recently [1], [2] proposed a coupled tensor factorization approach to handle these issues. In this work we propose a hybrid model that combines the benefits of tensor and matrix factorization approaches. We also develop a new algorithm that is mathematically simple, enjoys identifiability under relaxed conditions and is completely agnostic of the spatial degradation operator. Experimental results with real hyperspectral data showcase the effectiveness of the proposed approach. 

This work focuses on the problem of fusing a hyperspectral image (HSI) and a multispectral image (MSI) to produce a super-resolution image that admits high spatial and spectral resolutions. Existing algorithms are mostly based on joint low-rank factorization of the ma-tricized HSI and MSI. This framework is effective to some extent, but several challenges remain. First, it is unclear whether or not the super-resolution image is identifiable in theory under this framework, while identifiability usually plays an essential role in such estimation problems. Second, most algorithms assume that the degradation operators from the super-resolution image to the HSI and MSI are known or can be easily estimated - which is hardly true in practice. In this work, we propose a novel coupled tensor decomposition method that can effectively circumvent these issues. The proposed approach guarantees the identifiability of the super-resolution image under realistic conditions. The method can work even without knowing the spatial degradation operator, which could be hard to accurately estimate in practice. Simulations using AVIRIS Cuprite data are employed to demonstrate the effectiveness of the proposed approach.