Inference-Optimal ISAC via Task-Oriented Feature Transmission and Power Allocation

This work is concerned with the coordination gain in integrated sensing and communication (ISAC) systems under a compress-and-estimate (CE) framework, wherein inference performance is leveraged as the key metric. To enable tractable transceiver design and resource optimization, we characterize inference performance via an error probability bound as a monotonic function of the discriminant gain (DG). This raises the natural question of whether maximizing DG, rather than minimizing mean squared error (MSE), can yield better inference performance. Closed-form solutions for DG-optimal and MSE-optimal transceiver designs are derived, revealing water-filling-type structures and explicit sensing and communication (S\&C) tradeoff. Numerical experiments confirm that DG-optimal design achieves more power-efficient transmission, especially in the low signal-to-noise ratio (SNR) regime, by selectively allocating power to informative features and thus saving transmit power for sensing.