# A Framework for One-Bit and Constant-Envelope Precoding over Multiuser Massive MISO Channels

arXiv: https://arxiv.org/abs/1810.03159 · HTML: https://mlsanity.com/paper/1810.03159/

## Key facts

- Cited by 6 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 7 Oct 2018.

## Built on by (most cited first, 6 of 6)

- [Fast and Structured Block-Term Tensor Decomposition For Hyperspectral Unmixing](https://mlsanity.com/paper/2205.03798/) (2022)
- [Asymptotic SEP Analysis and Optimization of Linear-Quantized Precoding in Massive MIMO Systems](https://mlsanity.com/paper/2307.06714/) (2023)
- [Asymptotic Analysis of One-bit Quantized Box-Constrained Precoding in Large-Scale Multi-User Systems](https://mlsanity.com/paper/2502.02953/) (2025)
- [Rethinking Coupled Tensor Analysis for Hyperspectral Super-Resolution: Recoverable Modeling Under Endmember Variability](https://mlsanity.com/paper/2512.19489/) (2025)
- [Phase Shift Design in RIS Empowered Wireless Networks: From Optimization to AI-Based Methods](https://mlsanity.com/paper/2204.13372/) (2022)
- [Asymptotic Analysis of Nonlinear One-Bit Precoding in Massive MIMO Systems via Approximate Message Passing](https://mlsanity.com/paper/2509.13955/) (2025)

## Abstract (arXiv)

Consider the following problem: A multi-antenna base station (BS) sends multiple symbol streams to multiple single-antenna users via precoding. However, unlike conventional multiuser precoding, the transmitted signals are subjected to binary, unit-modulus, or even discrete unit-modulus constraints. Such constraints arise in the one-bit and constant-envelope (CE) massive MIMO scenarios, wherein high-resolution digital-to-analog converters (DACs) are replaced by one-bit DACs and phase shifters, respectively, for cutting down hardware cost and energy consumption. Multiuser precoding under one-bit and CE restrictions poses significant design difficulty. In this paper we establish a framework for designing multiuser precoding under the one-bit, continuous CE and discrete CE scenarios---all within one theme. We first formulate a precoding design that focuses on minimizations of symbol-error probabilities (SEPs), assuming quadrature amplitude modulation (QAM) constellations. We then devise an algorithm for our SEP-based design. The algorithm combines i) a novel penalty method for handling binary, unit-modulus and discrete unit-modulus constraints; and ii) a first-order non-convex optimization recipe custom-built for the design. Specifically, the latter is an inexact majorization-minimization method via accelerated projected gradient, which, as shown by simulations, runs very fast and can handle a large number of decision variables. Simulation results indicate that the proposed design offers significantly better bit-error rate performance than the existing designs.