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This paper focuses on downlink channel state information (CSI) acquisition. A frequency division duplex (FDD) of massive MIMO system is considered. In such systems, the base station (BS) obtains the downlink CSI from the mobile users' feedback. A key consideration is to reduce the feedback overhead while ensuring that the BS accurately recovers the downlink CSI. Existing approaches often resort to dictionary-based or tensor/matrix decomposition techniques, which either exhibit unsatisfactory accuracy or induce heavy computational load at the mobile end. To circumvent these challenges, this work formulates the limited channel feedback problem as a quantized and compressed matrix recovery problem. The formulation presents a computationally challenging maximum likelihood estimation (MLE) problem. An ADMM algorithm leveraging existing harmonic retrieval tools is proposed to effectively tackle the optimization problem. Simulations show that the proposed method attains promising channel estimation accuracy, using a much smaller amount of feedback bits relative to existing methods. 

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.