Wireless Linear Computation Broadcast

2026-08-06

AI Summary

This work addresses the problem of efficiently computing a common linear function of a dataset across multiple users in a Gaussian MIMO broadcast channel, where each user possesses noisy and heterogeneous side information. To tackle this challenge, the paper proposes a Wireless Linear Computation Broadcast (WLCBC) framework that jointly optimizes the linear precoder at the transmitter and the decoders at the receivers under known channel state information and transmit power constraints, aiming to minimize the weighted sum mean-square error (WSMSE). The study extends linear computation broadcast to wireless MIMO settings with noisy side information for the first time, devising an alternately optimizing algorithm with guaranteed monotonic convergence and deriving a semi-closed-form solution for the precoder. Numerical simulations demonstrate that the proposed method significantly outperforms existing baselines, achieving lower computation error, enhanced robustness, and reliable convergence.

Abstract

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.

Problem

• Wireless Linear Computation Broadcast
• Gaussian MIMO Broadcast Channel
• Noisy Side Information
• Linear Function Computation
• Transmit Power Constraint

Innovation

• Wireless Linear Computation Broadcast
• MIMO Broadcast Channel
• Weighted Sum-MSE Minimization
• Alternating Optimization
• LMMSE Estimation