Concurrent and Distributed Projection through Local Interference for Wireless Sensor Networks Xabier Insausti 1 , Pedro M. Crespo 1 , Baltasar Beferull 2 , and Javier Del Ser 3 1 CEIT and TECNUN (University of Navarra). 20018 Donostia-San Sebasti´an, Spain {xinsausti,pcrespo}@ceit.es 2 University of Valencia. 46980, Paterna (Valencia), Spain baltasar.beferull@uv.es 3 TECNALIA Research and Innovation. 48170 Bilbao, Spain javier.delser@tecnalia.com Abstract. In this paper we use a gossip algorithm to obtain the pro- jection of the observed signal into a subspace of lower dimension. Gossip algorithms allow distributed, fast and efficient computations on a Wire- less Sensor Network and they can be properly modified to evaluate the sought projection. By combining computation coding with gossip algo- rithms we proposed a novel strategy that leads to important saving on convergence time as well as exponentially decreasing energy consump- tion, as the size of the network increases. Keywords: Wireless Sensor Networks, Computational Codes, Signal Subspace Projection, Neighborhood Gossip. 1 Introduction The fast spreading of wireless sensor networks has recently encouraged researchers to design and develop fast and efficient algorithms for such networks. The most common approach for computation and information exchange in wire- less sensor networks has been done by using a class of decentralized algorithms known as Randomized Gossip Algorithms [1]. Wireless sensor networks are char- acterized for having very particular properties, of which we can highlight the limited computation power and energy resources. Besides, such networks usually do not have a centralized entity that synchronizes communication and therefore the knowledge that nodes have about the topology of the entire network is very limited. In order to be more precise, consider a network composed of N sensors dis- tributed randomly (uniformly) within the unit area circle. Sensors are assigned a limited transmission power P T per source symbol. Therefore, they can com- municate reliably with a certain number of neighbors within their coverage area, which will be the set of sensors located to a distance less than d (that depends on P T ). Let N d (i) ⊂{1,...,N } denote the local neighborhood of node i, i.e., the set of nodes within distance d of node i. J. Del Ser et al. (Eds.): MOBILIGHT 2011, LNICST 81, pp. 109–119, 2012. c  Institute for Computer Sciences, Social Informatics and Telecommunications Engineering 2012