Deflection-optimal data forwarding over a Gaussian multiaccess channel

We look at the simple scenario where multiple sensors make conditionally independent observations of a binary source and process the measurement data using a function U(x) before forwarding them to a fusion center via a Gaussian multiaccess channel. Subject to a total power constraint, we obtain the optimal U(x) that maximizes the deflection; the latter can also be interpreted as the output signal-to-noise ratio for an equivalent binary detection problem. The shape of the optimal function only depends on the probability density function of the observation noise, which we assume symmetric around zero, while the height is scaled by the allowed transmission power. We emphasize that the optimal function herein is derived for an arbitrary distribution of the observation noise. It reduces to a tanh(middot) function when the observation noise is additive Gaussian, which has been studied in the literature.