Task-Oriented Precoding for Edge Inference over Large-Scale MIMO Systems

Future wireless networks are expected to support networked artificial intelligence (AI) services, where multiple devices transmit learned features to an edge server for distributed inference. This setting calls for task-oriented physical-layer optimization, where wireless transmission should preserve useful information for inference rather than only maximize the rate or reconstruct the transmitted signals. A key physical-layer control variable is the multiple-input multiple-output precoder, which determines how device features are shaped and combined over wireless channels. Existing task-oriented precoding methods typically adapt the precoder to instantaneous channel state information at the transmitter (CSIT). However, in multi-device MIMO systems, acquiring the aggregate channel, feeding back CSI or optimized precoders, and reoptimizing across coherence blocks introduce substantial overhead. This paper develops a random-matrix-theoretic framework based on statistical CSIT that designs a slow-timescale precoder from channel covariance statistics and training-set feature statistics, without requiring instantaneous CSIT. We adopt maximal coding rate reduction (MCR${^2}$) to measure the class separability of the received features, yielding a task-aware utility for MIMO precoder design. Since this utility still depends on random small-scale fading, we derive a deterministic approximation that converts it into a fixed-point objective depending only on long-term statistics and large-system dimension ratios via random matrix theory. A projected block-coordinate ascent and successive convex approximation algorithm is developed to optimize this deterministic objective under per-device power constraints. Experiments on ModelNet10 verify the approximation and show that the proposed statistical precoder improves task-aware mode allocation and inference performance over competitive benchmarks.