## 1 Introduction  
Advances in directional antennas provide potential benefits in solving various problems in wireless sensor networks (WSNs). A WSN is a network of wirelessly interconnected devices, called sensor nodes, which are able to ubiquitously collect/retrieve data to be sent to a far receiver. Hundreds of nodes are scattered randomly throughout over a wide area, which assemble together, establish a routing topology, and transmit data back to a common collection point [1]. The main features of such networks are high density of nodes, low-mobility, severe power constraints, and high correlation of data among the nodes and also that the nodes can act both as a sensor and as a router towards a centralized node through multi-hop technique. With the development of new wireless technologies and a growing demand for miniaturized, low-powered, low-cost yet simpler and reasonably efficient wireless communication devices, there has been a growing interest in WSNs for a wide variety of applications ranging from seismic studies and life sciences, security-sensitive applications, social, military, and environmental problems.  
Wireless communication involves entire environment related effects on the propagated signals between the transmitter and the receiver. Conventional communication systems suffer from multipath signals, Doppler spread and high propagation delays. Due to the irregular distribution of scatterers present in the environment, multipath signals arrive at the receiver from different directions at different times. All of these multipaths taken by the wireless signal possess different properties, and hence, each multipath signal has its own distinctive carrier phase shift, amplitude, angle of arrival, and time delay. A possible approach to address these issues is through the geometrical definition of the scattering region to calculate the above parameters. The geometry of the multipath propagation plays a vital role for communication systems to suppress multipath [2]. A GBSBEM for single bounce multipath components involving randomly placed scatterers is presented here.  
In this paper, we combine the Geometrically Based Single Bounce Elliptical Model (GBSBEM) with other aspects of fading channel and establish a vector channel model requirement for smart antennas employed at the receiver. Since we are using a cluster-based WSN deployment model, the sensor nodes do not face the reachback problem as they have to transmit the information over a shorter distance to the cluster head, hence they can be designed to work with comparatively lower power. There are benefits to incorporating receive diversity into wireless sensor networks [3]. In addition to correct reception of data at the receiver and hence performance improvement, exploiting diversity techniques at the receiver can help in saving energy substantially and lead to reduced battery consumption, consequently increasing network lifetime.  
The rest of the paper is organized as follows. In Section 2, we discuss some of the related work. Section 3 describes the system model and the GBSBE channel model for the proposed system. In Section 4, we discuss the receiver structure exploiting receive diversity followed by various diversity combining techniques at the receiver. In Section 5 we present the simulation results and analyze the performance based on different variables for different number of receive antenna elements. Finally we present our conclusions in Section 6.