无线线性计算广播
Wireless Linear Computation Broadcast
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中文总结 AI 辅助
本文针对带噪声边信息的高斯MIMO广播信道，提出无线线性计算广播框架，将收发机设计建模为加权均方误差和最小化问题，通过交替优化算法实现收敛，性能优于现有基线。
中文摘要 AI 辅助
线性计算广播（LCBC）问题包含K个用户（接收器）和一个发射机。用户希望计算公共数据集的各种（向量）线性函数，且预先拥有对应其他各类线性计算的异构边信息。广播发射机已知该数据集以及所有期望函数和边信息函数，目标是尽可能高效地满足所有需求。现有研究已探讨了理想（无噪）广播信道（BC）上零差错有限域计算的LCBC信息论容量。本文针对高斯MIMO BC，在发射功率约束和任意天线配置下，提出了无线LCBC（WLCBC）框架，该框架考虑了接收器侧的噪声边信息。在WLCBC场景中，高斯源经过线性预编码后进行广播；每个用户请求源的一个线性函数，并通过将其信道观测值与噪声边信息进行线性组合来形成估计。假设存在完美信道状态信息，我们将集中式联合线性收发机设计建模为加权均方误差和（sum-MSE）最小化问题，并提出一种高效的交替优化算法。对于固定预编码器，最优解码器为线性最小均方误差（LMMSE）估计器；对于固定解码器，预编码器更新可简化为凸二次约束二次规划，其解为以单个对偶变量为参数的半闭式解。所得算法保证目标函数单调递减，且加权均方误差和（WSMSE）序列收敛。仿真结果表明，与现有工作得到的自然基线相比，该算法具有显著的鲁棒性增益。
英文摘要
A linear computation broadcast (LCBC) problem comprises $K$ users (receivers) and a transmitter. The users wish to compute various (vector) linear functions of a common dataset, and possess in advance heterogeneous side information corresponding to various other linear computations. The goal for the broadcast transmitter, who knows the dataset and all desired and side-information functions, is to satisfy all demands as efficiently as possible. Prior work has explored the information-theoretic capacity of LCBC for zero-error finite-field computation over an ideal (noiseless) broadcast channel (BC). This paper develops a wireless LCBC (WLCBC) framework for the Gaussian MIMO BC with noisy receiver-side information under a transmit power constraint and arbitrary antenna configurations. In the WLCBC setting, a Gaussian source is linearly precoded for broadcast; each user requests a linear function of the source and forms an estimate by linearly combining its channel observation with its noisy side information. Assuming perfect channel state information, we cast the centralized joint linear transceiver design as a weighted sum-MSE minimization problem and propose an efficient alternating optimization algorithm. For a fixed precoder, the optimal decoders are the linear minimum mean-square error (LMMSE) estimators. For fixed decoders, the precoder update reduces to a convex quadratically constrained quadratic program which leads to a semi-closed-form solution parameterized by a single dual variable. The resulting algorithm guarantees a monotonic decrease in the objective and convergence of the weighted sum-MSE (WSMSE) objective sequence. Simulations demonstrate pronounced robustness gains over natural baselines obtained from prior works.
