Computation over fading multiple-access channels based on free deconvolution

Wireless sensor networks (WSNs) enable the collection of physical measurements over a large geographic area. It is often the case that the authors are interested in computing and tracking the spatial-average of a function of the sensor measurements over a region covered by the WSN. Unfortunately, conventional methods need a large number of channel uses for collecting sensor data in the case of a large amount of sensors. They propose a novel computation scheme over fading multiple-access channels based on the asymptotic free behaviour of random matrices and the property of limit spectrum distribution of random matrices. The proposed scheme can greatly reduce the channel uses and does not need channel estimation. Moreover, the performance evaluations over multiple-input-multiple-output (MIMO) and MIMO-orthogonal frequency division multiplexing system demonstrate that the proposed method offers reliable mean computation of common functions of sensor data even for the case of small sample sizes.