## On Multi hop Distances in Wireless Sensor Networks with Random Node Locations

**Abstract****:**

Location and inter sensor distance estimations are important functions for the operation of wireless sensor networks, especially when protocols can benefit from the distance information prior to network deployment. The maximum multi hop distance that can be covered in a given number of hops in a sensor network is one such parameter related with coverage area, delay, and minimal multi hop transmission energy consumption estimations. In randomly deployed sensor networks, inter sensor distances are random variables. Hence, their evaluations require probabilistic methods, and distance models should involve investigation of distance distribution functions. Hence we propose a greedy method of distance maximization and evaluate the distribution of the obtained multi hop distance through analytical approximations and multi hop distance with random node locations. Our method is based on restricting the propagation direction outward from the propagation source in each hop and greedily searching the furthest neighbor each time.

**Existing System:**

Exists a trade-off between reaching more nodes in a single hop by using more power and reaching fewer nodes in a single hop by using less power but requiring multiple hops for reaching all the nodes in the multicast group parent nodes.

**Proposed System:**

We Proposed multi hop distance is limited; however, there are several studies that focus on estimation of single-hop or multi hop distances. Methods in and estimate the distances to designated anchor nodes using optimization algorithms. There are also analytical methods that address the probabilistic evaluation of the Euclidean distances such as that given in and. In, the probability distribution of the single-hop distance between two randomly chosen neighbors is investigated. In, the distribution of the remaining distance in multi hop greedy forwarding to a destination node is derived. Furthermore, in, the distribution of Euclidean distances

To nth neighbor in a Poisson point process is analyzed.

Considering all nodes in the previous hops and recursively reaches the source node of the multi hop propagation, which becomes intractable even for small instances. Hence, we propose a greedy method of maximization of the Euclidean multi hop distance. By selecting locally maximally distant nodes, the multi hop propagation intends to reach further distances to the source node. After selecting an initial propagation direction, the following iterative definition is provided for our greedy distance maximization scheme. It should be noted that our method does not locate the node with maximum distance to the source node for a given number of hops, yet it maximizes the Euclidean distance toward a chosen initial direction greedily. For the definition of this distance,

Modules:

**1. Multi hop Tree Network Module**

**We make the following assumptions in our model:**

1) Nodes are stationary in the WANET.

2) Each node in the WANET uses Omni-directional antennas.

3) Each node knows the distance between itself and its neighboring nodes using distance estimation

The nodes between two randomly located sensors are analytically computed via iteration based on expressions for connectivity in one or two hops. In, the distribution of hop distance and its expected value are analyzed with simulations. It is shown that beam forming antennas significantly reduce the hop distance compared to Omni-directional antennas for medium and large networks with random node locations.

**2. Random Node Location Module:**

The random node locations. Our method is based on restricting the propagation direction outward from the propagation source in each hop and greedily searching the furthest neighbor each time for each topology, a single sample multi hop path is selected for each hop distance n. Second, we place the source node at randomly selected locations and vary the node density. Similarly, we form 2,000 independent topologies for each node density value the effect is a decrease in the expected multi hop Euclidean distance of a randomly chosen n-hop path. In the simulations, it is observed that the reduction in the multi hop Euclidean distance is largely caused by the decrease in the distance taken in the final hop under the edge effects.

**3. Greedy Maximization of Multi hops Distance Module:**

Distance estimation the results demonstrate that for a smaller node density, the edge effect is less pronounced. This is an expected result since the edge effect reduces the final hop distance of a multi hop path, which has a stronger limitation on higher densities with larger single-hop spans. As the node density gets smaller, the node with the maximum distance in the final hop is located closer to the most recently selected node and its location is limited less frequently by the topology border. The diminishing character in the average percent error values is caused by the decrease in the ratio between the amounts of distance in the final hop to the multi hop path distance as the hop distance increases.

**4. Energy Efficiency Euclidean distance **

The unit disk model defines the communication range as the minimum radius of a circular reception area within which all transmissions are successfully received if no interference or packet collisions exist. In the event that the wireless medium is subject to the effects of fading, the reception power at receiver nodes is affected by the distance to the transmitter and decays exponentially with distance. Furthermore, with the presence of Gaussian noise, the received power becomes a random variable. This makes the reception of a packet a probabilistic event dependent on the distance to the transmitter node, the statistical characteristics of the channel noise, transmission power, and the threshold of reception power.

**System Specifications:**

**Hardware Requirements:**

- System : Pentium IV 2.4 GHz.
- Hard Disk : 40 GB.
- Floppy Drive : 1.44 Mb.
- Monitor : 15 VGA Colour.
- Mouse : Logitech.
- Ram : 512 Mb.

**Software Requirements:-**

Language: Java, J2ME

OS: Windows XP

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