Massive MIMO 1-Bit DAC Transmission: A Low-Complexity Symbol Scaling Approach

Abstract

We study multi-user massive multiple-input singleoutput (MISO) systems and focus on downlink transmission, where the base station (BS) employs a large antenna array with low-cost 1-bit digital-to-analog converters (DACs). The direct combination of existing beamforming schemes with 1-bit DACs is shown to lead to an error floor at medium-to-high SNR regime, due to the coarse quantization of the DACs with limited precision. In this paper, based on the constructive interference we consider both a quantized linear beamforming scheme where we analytically obtain the optimal beamforming matrix, and a non-linear mapping scheme where we directly design the transmit signal vector. Due to the 1-bit quantization, the formulated optimization for the non-linear mapping scheme is shown to be non-convex. To solve this problem, the non-convex constraints of the 1-bit DACs are firstly relaxed, followed by an element-wise normalization to satisfy the 1-bit DAC transmission. We further propose a lowcomplexity symbol scaling scheme that consists of three stages, in which the quantized transmit signal on each antenna element is selected sequentially. Numerical results show that the proposed symbol scaling scheme achieves a comparable performance to the optimization-based non-linear mapping approach, while its corresponding complexity is negligible compared to that of the non-linear scheme.

Interference Exploitation 1-Bit Massive MIMO Precoding: A Partial Branch-and-Bound Solution With Near-Optimal Performance

“…to denote a unit-norm constellation point, where we have further decomposed the constellation point into OF = s A k and OG = s B k that are parallel to the two detection boundaries of s k . The detailed expressions for s A k and s B k can be found in the appendix of [39] for a general M-PSK modulation, and Fig. 2: An illustrative example of CI condition for PSK are omitted here for brevity.…”

“…This observation has already been exploited in [10] and [42]- [45] by constructive interference (CI) precoding to achieve an improved BER performance in a traditional small-scale MIMO system. Following this concept, [38] and [39] have extended the idea of interference exploitation to 1-bit precoding designs, and the resulting BER performance is shown to be promising. Moreover, while not explicitly shown, [40] also adopts the formulation of CIbased 1-bit precoding, where a branch-and-bound (BB)-based algorithm that obtains the optimal solution is presented.…”

“…For clarity, we summarize the main contributions of this paper below: 1) For both PSK and QAM signaling, by constructing the Lagrangian function of the relaxed optimization problem and formulating the corresponding Karush-Kuhn-Tucker (KKT) conditions, we mathematically prove by contradiction that the majority of the output signals obtained from solving the relaxed problem already satisfy the 1bit constraint, and only a small portion of the entries need to be further quantized to obtain a feasible 1-bit solution, where the quantization losses are incurred. 2) Building on this important and interesting observation, we propose a 1-bit precoding algorithm through a P-BB process to further improve the performance of the conventional CI-based 1-bit precoding method in [39], where the BB process is only performed for part of the output signals that do not comply with the 1-bit requirement, and we adopt the adaptive subdivision rule to guarantee a faster convergence rate. For PSK signaling, we use the 'max-min' criterion to design the P-BB algorithm, while the MSE criterion and the alternating optimization framework are employed when QAM signaling is considered at the BS.…”

Near-Optimal Interference Exploitation 1-Bit Massive MIMO Precoding Via Partial Branch-and-Bound

“…1. We refer the interested readers to Section IV of [26] for the expression of s A k and s B k when a generic M-PSK modulation is employed, which are omitted here for brevity. We further denote the received signal excluding noise for user k by OB, which is similarly decomposed into…”

“…This observation has been exploited in [23] and the references therein by symbol-level CI precoding to achieve an improved error rate performance in traditional multi-user MIMO scenarios. Inspired by this concept, [24]- [26] extended the idea of CI to 1-bit precoding designs, and the resulting performance is shown to be promising. Moreover, while not explicitly shown, [27] also adopts the formulation of CI-based 1-bit precoding, where a branchand-bound (BB) based 1-bit precoding algorithm that returns the optimal solution is presented.…”