Design and Analysis of a Multiple and Wide Nulling Collaborative Beamforming Scheme in the Domain of 3-Dimensional Wireless Sensor Networks

Abstract

Null steering is essential in collaborative beamforming (CB) in wireless sensor networks (WSNs) to ensure minimal radiation power and interference in the direction of unintended receivers. Current research in null steering in CB in WSNs is mainly from the perspective of planar arrangements of sensor nodes and sink(s). Furthermore, there is no research dedicated to the formation of multiple wide nulls during CB in 3-dimension WSNs. Wide nulls are ideal in scenarios featuring mobile unintended sink(s). A new multiple and wide null steering scheme applicable to CB in WSNs is presented in this work (from the perspective of a 3-dimensional random arrangement of static sensor nodes). It is assumed that desired nulling directions are implicitly known at a CB cluster head. A particle swarm optimization (PSO) algorithm variant is applied in concurrent node transmit amplitude and phase perturbation with an aim of achieving beam steering alongside multiple and wide null steering. The performance of the proposed null steering scheme is validated against a basic null steering approach (with reference to current literature). Furthermore, a comparative null depth, width, and nulling accuracy analysis are done upon varying the count of collaborating nodes and the collaborating cluster radius. An increase in the number of collaborating nodes is found to increase nulling depth at an exponentially decaying rate. An increase in the collaborating nodes’ cluster radius yields a reduction in null width. The contributions of this work to the existing literature are as follows: (i) the design and investigation of a null steering scheme from the perspective of a 3-dimension random arrangement of sensor nodes; (ii) the design of a concurrent beam steering and multiple wide null steering scheme on the basis of concurrent node transmit amplitude and phase perturbation whilst ensuring null depth uniformity; (iii) a statistical analysis of the impact of a count of collaborating nodes and collaborating cluster radius on nulling performance; (iv) investigation of capacity improvement at unintended receivers upon null steering.