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

Abstract

In this paper, we focus on 1-bit precoding approaches for downlink massive multiple-input multiple-output (MIMO) systems, where we exploit the concept of constructive interference (CI). For both PSK and QAM signaling, we firstly formulate the optimization problem that maximizes the CI effect subject to the requirement of the 1-bit transmit signals. We then mathematically prove that, when employing the CI formulation and relaxing the 1-bit constraint, the majority of the transmit signals already satisfy the 1-bit formulation. Building upon this important observation, we propose a 1-bit precoding approach that further improves the performance of the conventional 1-bit CI precoding via a partial branch-and-bound (P-BB) process, where the BB procedure is performed only for the entries that do not comply with the 1-bit requirement. This operation allows a significant complexity reduction compared to the fully-BB (F-BB) process, and enables the BB framework to be applicable to the complex massive MIMO scenarios. We further develop an alternative 1-bit scheme through an 'Ordered Partial Sequential Update' (OPSU) process that allows an additional complexity reduction. Numerical results show that both proposed 1-bit precoding methods exhibit a significant signal-to-noise ratio (SNR) gain for the error rate performance, especially for higherorder modulations.Index Terms-Massive MIMO, 1-bit precoding, constructive interference, Lagrangian, branch-and-bound. I. INTRODUCTIONM ASSIVE multiple-input multiple-output (MIMO) has become a key enabling technology for the fifthgeneration (5G) and future wireless communication systems [1]-[6]. In the downlink transmission of a massive MIMO system, existing non-linear precoding methods such as Tomlinson-Harashima precoding (THP) [7] or vector perturbation (VP) precoding [8]-[11] are not preferred, due to their prohibitive computational complexity when the number of antennas is large. Instead, it has been shown in [12] that lowcomplexity linear precoding approaches such as zero-forcing (ZF) [13] and regularized ZF (RZF) [14] can achieve nearoptimal performance. Manuscript received XX; revised XX; A. Li, Y. Li and B. Vucetic are with the

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“…Therefore, the long-term problem is decomposed into sub-problems focusing on per-slot optimization. Since the sub-problem in each time slot is a nonlinear mixed-integer programming, which can be solved by branch and bound method [28].…”

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“…Next we describe a near-optimal 1-bit solution which leverages a partial branch-and-bound (P-BB) framework, applicable to both PSK and QAM modulations. This method is based on that most entries in the 1-bit transmit signal of the solution to the LP formulation discussed in Section III-A already satisfy the 1-bit requirement, and the quantization losses are due to the relatively small portion of entries that fail to obey the 1-bit constraint [11]. The approach in [11] leaves the entries already satisfying the constraint unchanged, and only applies the BB procedure to those for which the constraint is inactive.…”

“…This method is based on that most entries in the 1-bit transmit signal of the solution to the LP formulation discussed in Section III-A already satisfy the 1-bit requirement, and the quantization losses are due to the relatively small portion of entries that fail to obey the 1-bit constraint [11]. The approach in [11] leaves the entries already satisfying the constraint unchanged, and only applies the BB procedure to those for which the constraint is inactive. As a result, the complexity relative to previous BB approaches is significantly reduced, and meanwhile the error-rate performance has been improved over the '1-bit LP' method because the introduced P-BB framework returns a near-optimal solution.…”

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