In this paper, we address robust design of symbol-level precoding (SLP) for the downlink of multiuser multiple-input single-output wireless channels, when imperfect channel state information (CSI) is available at the transmitter. In particular, we consider a well known model for the CSI imperfection, namely, stochastic Gaussian-distributed uncertainty. Our design objective is to minimize the total (per-symbol) transmission power subject to constructive interference (CI) constraints as well as the users’ quality-of-service requirements in terms of signal-to-interference-plus-noise ratio. Assuming stochastic channel uncertainties, we first define probabilistic CI constraints in order to achieve robustness to statistically known CSI errors. Since these probabilistic constraints are difficult to handle, we resort to their convex approximations in the form of tractable (deterministic) robust constraints. Three convex approximations are obtained based on different conservatism levels, among which one is introduced as a benchmark for comparison. We show that each of our proposed approximations is tighter than the other under specific robustness settings, while both of them always outperform the benchmark. Using the proposed CI constraints, we formulate the robust SLP optimization problem as a second-order cone program. Extensive simulation results are provided to validate our analytic discussions and to make comparisons with conventional block-level robust precoding schemes. We show that the robust design of symbol-level precoder leads to an improved performance in terms of energy efficiency at the cost of increasing the computational complexity by an order of the number of users in the large system limit, compared to its non-robust counterpart.

中文翻译：

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具有不完善信道知识的鲁棒 SINR 约束符号级多用户预编码

在本文中，我们针对多用户多输入单输出无线信道下行链路的符号级预编码 (SLP) 进行稳健设计，当发射机的信道状态信息 (CSI) 可用时。特别是，我们考虑了一个众所周知的 CSI 缺陷模型，即随机高斯分布不确定性。我们的设计目标是最大限度地减少受建设性干扰 (CI) 约束以及用户在信号干扰加噪声比方面的服务质量要求的总（每个符号）传输功率。假设随机信道不确定性，我们首先定义概率 CI 约束，以实现对统计上已知的 CSI 错误的鲁棒性。由于这些概率约束难以处理，我们以易处理的（确定性的）鲁棒约束的形式求助于它们的凸近似。根据不同的保守程度得到三种凸近似，引入其中一种作为比较基准。我们表明，在特定的鲁棒性设置下，我们提出的每个近似值都比另一个更严格，而它们总是优于基准。使用建议的 CI 约束，我们将稳健的 SLP 优化问题公式化为二阶锥程序。提供了广泛的模拟结果以验证我们的分析讨论并与传统的块级鲁棒预编码方案进行比较。