Robust Analog Function Computation via Wireless Multiple-Access Channels

Abstract

Wireless sensor network applications often involve the computation of pre-defined functions of the measurements such as for example the arithmetic mean or maximum value. Standard approaches to this problem separate communication from computation: digitized sensor readings are transmitted interference-free to a fusion center that reconstructs each sensor reading and subsequently computes the sought function value. Such separation-based computation schemes are generally highly inefficient as a complete reconstruction of individual sensor readings at the fusion center is not necessary to compute a function of them. In particular, if the mathematical structure of the channel is suitably matched (in some sense) to the function of interest, then channel collisions induced by concurrent transmissions of different nodes can be beneficially exploited for computation purposes. This paper proposes an analog computation scheme that allows for an efficient estimate of linear and nonlinear functions over the wireless multiple-access channel. A match between the channel and the function being evaluated is thereby achieved via some pre-processing on the sensor readings and postprocessing on the superimposed signals observed by the fusion center. After analyzing the estimation error for two function examples, simulations are presented to show the potential for huge performance gains over time-and code-division multipleaccess based computation schemes.

Time-efficient cooperative spectrum sensing via analog computation over multiple-access channel

“…This paper computes the global statistic by following the routine of CoMAC. Although the CoMAC [28] was successfully applied to accelerate the converging speed of consensus algorithms in wireless sensor networks [32,33] , to the best of our knowledge, the conference version of this paper [1] is the first one that proposes to combine CoMAC with CSS schemes in CRNs to reduce the long delay in the reporting phase of CSS schemes. Despite few contributions in CoMAC itself, this paper explores the use of CoMAC in the field of CSS schemes, innovatively analyzes and optimizes the spectrum sensing performance of the proposed CSS scheme.…”

“…This paper combines the CoMAC method [28] with conventional CSS schemes to reduce the reporting delay in the reporting phase, which finally enhances the average throughput of the CRN.…”

“…. , M ) and T i (or w i μ i ) act as sensor i and its sensor reading x i in the CoMAC scheme [28] , respectively. In order to maintain the consistency with the formulation of the CoMAC method, we use x i to represent the local statistic of SU i .…”

“…Motivated by the recent robust analog function computation scheme-computation over multiple-access channel (CoMAC) [28] , this paper proposes a novel CoMAC-based CSS scheme, in which each SU first transmits a distinct complex-valued sequence at a transmit power depending on the SU reading and consequently the received energy at the fusion center equals the sum of all transmit energies corrupted by background Gaussian noise. The fusion center then takes advantage of the collected energy information to estimate the desired weighted arithmetic mean of the local statistics from SUs, based on which the spectrum availability is determined.…”

Energy-Efficiency Maximization for Cooperative Spectrum Sensing in Cognitive Sensor Networks

“…However, the drawback of CSS schemes is that both the energy consumption and the reporting time grow linearly with the number of cooperative SUs. Our recent work [18] proposed a time-efficient CSS scheme that takes advantage of the computation over multiple-access channel (CoMAC) method [19] to accelerate the CSS process via merging the reporting and the computation steps of CSS, which noticeably reduces the reporting delay in conventional CSS schemes. However, the issue of high energy consumption still exists due to the fact that each SU has to send a long sequence of encoded symbols to the fusion center during the CSS process.…”