Wireless data sums transmitted via silence rather than signal energy
Occupancy-Domain Over-the-Air Computation
Information Theory
Summary
AirComp is a way to add up data sent across wireless networks directly in the air, but usual methods need detailed knowledge of the signal or are affected by signal fading. The authors propose a new method where data sums are represented by the amount of silence across shared wireless resources rather than the signal strength. This method uses probabilities of devices being silent to compute the sum, avoiding issues typical to other approaches. They also develop a balanced method to reduce randomness and improve accuracy, validating their ideas through simulations.
What this means in practice
- •For wireless network engineers: Implement data aggregation techniques that use silence-based encoding to reduce the need for channel information and improve reliability.
- •For sensor network designers: Design sensor data collection systems that aggregate data over shared wireless resources with reduced sensitivity to signal fading and power control complexity.
Authors
Seyed Mohammad Azimi-Abarghouyi
Abstract
Over-the-air computation (AirComp) aggregates distributed data through the wireless multiple-access channel, but coherent implementations require channel state information (CSI), phase alignment, and power control, whereas non-coherent energy methods remain affected by fading. Signal superposition at the receive antenna is linear but requires coherence, and energy superposition is linear only in expectation over fading. We introduce occupancy-domain computation (ODC), whose observable is neither a received amplitude nor an energy: the sum is carried by the silence of the shared resources. With exponential Bernoulli activation, the individual silence probabilities multiply, and the server recovers the sum from the idle fraction using binary activity decisions alone, so that once an activation is detected the amplitude that produced it does not enter the estimate. We characterize the maximum-likelihood estimator, optimal load, and a scale-integrated Fisher-information bound for non-adaptive operation over unknown dynamic ranges. We then introduce balanced occupancy computation (BOC), where each device forms a data-dependent quota of random burst placements. This removes the random placement-count fluctuation of Bernoulli activation; under ideal detection, the leading-order asymptotic root-mean-square error of BOC is no larger than that of Bernoulli ODC at any load and approaches $1/\sqrt{2M}$, where $M$ is the number of resource elements, as the number of devices becomes small relative to $M$. We further analyze unknown-scale operation, finite-frame deviations, and heterogeneous detection misses. Simulations validate the theory and compare ODC/BOC with affine non-coherent energy aggregation and REED.