## 2 Related Work  
Wireless sensor networks have attracted a lot of attention recently. In [4], the average bit-error rate performance of wireless sensor networks based on the generalized approach to signal processing in the presence of noise under the use of multiple antennas at the sensor sink is investigated as a function of the transmit antenna update rate at the sensor nodes when using binary phase-shift keying signals in flat Rayleigh fading channels. In [3], the benefits of incorporating receive diversity into wireless sensor network (WSN) applications that require high data fidelity and resolution upon event triggering is demonstrated. In [5], a cooperative diversity scheme that increases the network lifetime and the communication reliability has been proposed where the identical sensors are randomly scattered over a wide area. These nodes collect a common message and transmit it towards a fusion centre placed in an unarmed air vehicle (UAV). Practically these scenarios face the reachback problem where the nodes are designed with low power transmitters and are often not capable enough to directly transmit data to the far receiver [6].  
A distributed algorithm capable of computing linear signal expansions for a sensor broadcast protocol is presented in [7], where each sensor collects the correlated samples, broadcasts a rate-constrained encoding of its samples to every other sensor and forms an estimate of the entire field. To decorrelate, the sensors only need access to samples from a few nearby sensors. Typical applications include collection of data from a remote area. A distributed diversity approach capable of exploiting spatial distribution of sensor nodes has been proposed and analyzed in [8]. However, idealistic assumptions like synchronization and cooperation are introduced to ensure improvement in the network performance.  
Other than correct reception of data at the far end receiver and hence performance improvement, exploiting diversity techniques at the receiver can help in saving the energy substantially and leading to reduced battery consumption and subsequently increasing network lifetime. New relaying strategies based on Luby Transform Codes were presented in [9] by exploiting diversity in WSNs. It is understood that the diversity was applied at the transmitter side involving decoding complexity, though light-weight complexity, at the receiver. While the model proposed in [9] required some extra power for performing the encoding and decoding tasks, a cluster based cooperative scheme for multihop WSN was presented in [10] that could minimize the energy consumption of the sensor nodes.  
In [11], energy efficiency of a cooperative multiple input single output (MISO) system using two different cluster based models was investigated for a multi-hop WSN. Space-Time Block Coding (STBC) has been used to encode the data, which means more power requirement by the cooperative nodes for the encoding task. The performance of cluster based WSN over GBSBE model has been presented in [12], based on the transmitting power and the varying number of receive antennas. In this paper, we extend the performance based on other quantities like the maximum multipath delay and the receiver height. We have tried to keep the complexity low at the sensor nodes to minimize the amount of power consumed by these nodes. Also, while on one hand we have tried to keep track of the channel properties by using GBSBE Model, on the other hand we have been successful in minimizing the effect of multipaths and fading by exploiting diversity at the receiver.