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Wireless sensor networks have attracted a lot of attention recently. In this paper, we develop a channel model based on the elliptical model for multipath components involving randomly placed scatterers in the scattering region with sensors deployed on a field. We verify that in a sensor network, the use of receive diversity techniques improves the performance of the system. Extensive performance analysis of the system is carried out for both single and multiple antennas with the applied receive diversity techniques. Performance analyses based on variations in receiver height, maximum multipath delay and transmit power have been performed considering different numbers of antenna elements present in the receiver array, Our results show that increasing the number of antenna elements for a wireless sensor network does indeed improve the BER rates that can be obtained.

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 [

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 [

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 [

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.

Wireless sensor networks have attracted a lot of attention recently. In [

A distributed algorithm capable of computing linear signal expansions for a sensor broadcast protocol is presented in [

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 [

In [

The system model used in this paper for a cluster based WSN architecture for _{r}

When the signal is transmitted, reflections from large objects, diffraction of the waves around objects, and signal scattering dominate the received signal resulting in the presence of multipath components, or multipath signals, at the receiver. _{l}_{l}_{l}_{d}^{th}

In the GBSBEM, scatterers are uniformly distributed within an ellipse, as shown in _{max}

Considering the distance between the sensor nodes and the receiver to be D, all the scatterers giving rise to single bounce components arriving between time _{m}_{m}_{max}_{max}_{max}

Let _{l}^{th}_{l}_{l}_{l}_{l}

To simplify the notation, it is convenient to introduce the normalized multipath delay,
_{l}_{m}

The idea is first to define an ellipse corresponding to the maximum multipath delay, _{m}_{m}_{l}_{l}_{l}_{l}

Thus, the multipath propagation distance, _{l}_{l}

The power of the direct path component (LOS) can be calculated as below:
_{ref}_{ref}_{ref}_{T}_{t}_{d}_{r}_{a}_{d}_{a}_{d}_{a}_{r}_{l}_{l}^{(Pl−P0)/20} ^{jγl}

It can be generally supposed that the signal transmitted by the cluster head travels through several resolvable discrete multipaths and arrives at the receiver arrays, each multipath having its own independent DOA, time delay, and amplitude. For example, the sensors are deployed in an open field where they collect data and send to the cluster head. The collected data is sampled and modulated using BPSK modulation and converted into a serial bit stream. This data bit stream needs to be transmitted to the sink to be analyzed.

Assuming that perfect channel state information (CSI) is available at the receiver, if at any time _{r}_{l}^{th}_{k}_{l}

For an N-element linear antenna array the channel impulse response of the ^{th}

Thus, the output received at the sink is given by _{l}_{i}_{l}_{l,i}) is defined as:
_{i}^{th}

The noise on each diversity branch is assumed to be uncorrelated. The collection of independently fading signal branches can be combined in a variety of ways to improve the received SNR. Since the chance of having two deep fades from two uncorrelated signals at any instant is rare, combining them can reduce the effect of the fades. Diversity is a powerful communication receiver technique that provides wireless link improvement at relatively low cost. It exploits the random nature of radio propagation by finding independent signal paths for communication. In virtually all applications, diversity decisions are made by the receiver, and are unknown to the transmitter. The diversity concept can be explained simply. If one radio path undergoes a deep fade, another independent path may have a strong signal. By having more than one path to select from, both the instantaneous and average SNRs at the receiver may be improved. There are a variety of ways in which the independently fading signal branches can be combined; hence, the three most prevalent space diversity-combining techniques used in this paper are the Maximal Ratio Combining (MRC) [

For example, the received signals are combined at the receiver using MRC to maximize the SNR and give the following expression:

In terms of the weight vector ^{H}

In the presence of channel _{j}_{j}, at ^{th}^{H}

The received symbols are then passed through a maximum-likelihood detector to produce the estimate of transmitted signal

In this section we present simulation results to evaluate the performance of our system. We discuss the reliability and robustness of a cluster based WSN system by using smart antennas at the receiver.

We used MATLAB to simulate the system. The proposed model has been simulated for a microcell environment. The focus of the model is to consider the scenario of local scattering giving rise to multipaths. These multipaths and the resulting fading are modeled as stochastic processes and channel characteristics like time-variation, amplitude, and angular spread are modeled using GBSBEM.

We consider a cluster-based model with N sensor nodes randomly scattered over a large area. These nodes collect a common message and transmit it towards the cluster head. The information received at the cluster head is filtered and modulated and transmitted to the receiving station. The cluster head is located within a range of 2 meters from this receiving station. In this case both the cluster head and the receiver are surrounded by scatterers and the receiving antenna array is not well above the surrounding objects. The model parameters were chosen to fit the scenario.

^{7}. The whole sequence is divided into frames of length 100 symbols and the total number of frames are 10^{5}. The channel considered here is a quasi-static channel;

We have carried out the simulations where we have different combining schemes at the receiver. We have compared the performance of these schemes with different number of antennas at the receiver. We further analyze the performance of the system by varying the system parameters like receiver height, maximum multipath delay, and transmit power and compare the performance with: (i) no diversity, and (ii) MRC at the receiver.

We present the performance analyses when we have multiple antennas at the receiver. We apply EGC, SC, and MRC at the receiver to exploit diversity.

The performance of EGC is only marginally inferior to MRC. The implementation complexity for EGC is significantly less than the MRC because of the requirement of correct weighing factors. Hence, the basic idea of diversity reception is that, if two or more independent samples of a signal are taken, then these samples will fade in an uncorrelated manner. This means that the probability of all the samples being simultaneously below a given level is much less than the probability of any individual sample being below that level. Thus, a signal composed of a suitable combination of various samples will have much less severe fading properties than any individual sample alone.

In this section we analyze the performance when there is a single antenna in the receive array. The simulations were carried with different varying parameters. First, we perform the simulations based on varying receiver height. If the receiver height is low, there is a possibility that it may suffer from deep fades due to dense environment surrounding the receiver hence degrading the performance of the system. On the other hand, if the receiver is mounted on a higher ground, it will be less susceptible to fading and hence will collect the signal more efficiently.

_{max}, therefore, as we change τ_{max}, the geometry of the ellipse also changes. The results show that as τ_{max} is decreased, the system gives better performance. It can be explained in terms of the geometry of the ellipse. As τ_{max} increases, a_{m}and b_{m} also increases, thus making the ellipse larger, and vice-versa. Larger ellipse means increase in the propagation delays, hence poorer performance. Smaller ellipse means lesser propagation delays, hence better performance.

In this section, we repeat the simulations for different H_{R} and τ_{max} when we have multiple antennas at the receiver. As seen from the table, MRC gives the best performance, thus, for our further simulations we have focused on the system model with MRC at the receiver only and the implementation of EGC and SC is straight forward. _{max} and proves that BER improves with smaller τ_{max}. The simulations have been performed with number of receive antennas up to four but it is not limited and can be extended for higher numbers of receive antennas.

The BER values for multiple receive antennas at different receiver height with different maximum multipath delay have been summarized in

We analyze the problem from the overall performance of the system. The model presented in this paper has been developed for a microcell environment which has a quasi-static channel. A cluster based WSN architecture has been assumed at the transmission side. The cluster head is assumed to be surrounded by local scatterers giving rise to multipath and fading. At the receiver, receiving arrays are used to collect all the multipath components of the signal effectively. The advantage of using smart antennas in a cluster based WSN model has been demonstrated where performance improvements can be realized in terms of received SNR. The numerical simulations based on the variations in receiver height reveal that the performance of the system increases if the receiver height is increased above ground level. Also the numerical simulations based on maximum multipath delay shows that the semi-major and semi-minor axis of the ellipse changes with variations in the maximum multipath delay, hence affecting the performance of the overall system. The performance of the system is also improved as the transmission power increases. Since the cluster head is located very near to the sensor nodes, the sensor nodes do not require high transmission powers so they do not face the reachback problem. The paper justifies the use of receive diversity at the receiver for reliable communication between the cluster head and the receiving arrays and proves that MRC provides the best performance when applying receive diversity. We also quantify the fact that with the increase in the number of antenna elements, we are able to increase the reliability and robustness of the system. The number of antenna elements has been kept low while solving our problem. However, they can be extended to higher number of receive antennas for a large receiving array.

We are grateful to ARC Research Network on Intelligent Sensors, Sensor Networks and Information Processing (ISSNIP) for providing financial support.

High-Level System Model.

Geometry of the GBSBEM.

_{R}_{max}_{T}

_{R}_{R} = 1,2,3, and 4. _{max}_{R}

Parametric Values for the System Model.

No of frames | 100,000 |

Frame Length | 100 |

Path Loss (Lr) | 6 dB |

Path loss exponent (n) | 3 |

Number of multipaths (L) | 5 |

Carrier frequency (fc) | 900 MHz |

Distance between cluster head and receiver (D) | 1,000 m |

BER at various SNR for different number of receive antennas

2 | 1 |
0.0018 |
0.0014 |
0.0016 |

3 | 1.0e–003 * |
1.0e–003 * | ||

4 | 1.0e–003 * |
1.0e–003 * |
1.0e–003 * |

BER at various SNR with different number of receive antennas.

_{r} |
_{T} |
_{R} |
||||
---|---|---|---|---|---|---|

2 | 10 | 8 | 2 | 0.000834 | 0.000218 | 2.07e–05 |

5 | 0.000702 | 0.000143 | 9.7e–06 | |||

10 | 0.000607 | 0.000103 | 6.3e–06 | |||

10 | 5 | 10 | 0.000570 | 9.27e–05 | 4.8e–06 | |

8 | 0.000599 | 0.000103 | 7.6e–06 | |||

12 | 0.000603 | 0.000104 | 7.7e–06 | |||

3 | 10 | 8 | 2 | 0.000409 | 6.97e–05 | 2.2e–06 |

5 | 0.000295 | 3.93e–05 | 6e–07 | |||

10 | 0.000233 | 2.39e–05 | 4e–07 | |||

10 | 5 | 10 | 0.000204 | 1.88e–05 | 2e–07 | |

8 | 0.000238 | 0.000024 | 3e–07 | |||

12 | 0.000249 | 2.43e–05 | 4e–07 | |||

4 | 10 | 8 | 2 | 0.000212 | 2.42e–05 | 7e–07 |

5 | 0.000144 | 9.7e–06 | 1e–07 | |||

10 | 0.000102 | 5.4e–06 | 1e–08 | |||

10 | 5 | 10 | 8.95e–05 | 4.7e–06 | 1e–07 | |

8 | 0.000108 | 5.4e–06 | 3e–07 | |||

12 | 0.000115 | 6.8e–06 | 4e–07 |