position p of each vertice i is identified by the set of coordi nates p i x i y

Position p of each vertice i is identified by the set

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position p of each vertice i is identified by the set of coordi- nates p i = ( x i , y i and z i respective). An euclidean length d i,j between two vertices i, j V is refferred to as E . The network topology is then interpreted by a three/four row matrix, where the 2D/3D position of nodes are stored in individual columns, see Table I. Furthermore for a simplicity, only the 2D plane is considered for the simulation. TABLE I T OPOLOGY MATRIX I D 1 2 3 ... N X coor x 1 x 2 x 3 ... x N Y coor y 1 y 2 y 3 ... y N For the simulations, the networks are considered to be fully connected, meaning that all nodes are reachable due to the multihop communication. The connectivity depends on the radio range, thus the radio range of the nodes should be configured optimally. One can estimate the optimal radio range empirically or to use an Eq. 1 that estimates the minimum radio range ensuring the full connectivity. R = Θ r log N N (1) The Θ parameter stands for a 2D plane diameter directly proportional to the number of nodes N . Calculating the R for the 100 nodes randomly placed in the 2D plane with the 300m x 500m dimension, the minimal R should be 82 meters. According to the experiences with the Crossbow IRIS 2.4 GHz node [7], the radio range of 82 meters corresponds to the transmitting power of 3.2 dBm. Once the network matrix is created and radio range calcu- lated, the network topology can be printed. The layout of the network consists of the vertices and edges between vertices. The edge or link between two nodes can be printed only in case that the euclidean distance d i,j between two nodes i, j is smaller than R of the considered nodes. Since the wireless links are considered to be bidirectional and symmetric then d i,j = d j,i . A pseudocode of the layout printing is introduced in more details in the following section. In the real wireless network, a distance between two nodes can be derived from RSSI parameter (Receive Signal Strength Indication) or estimated by methods such as ToA (Time of Arrival) or AoA (Angle of Arrival) [11]. These techniques suffer from the certain distance estimation error and thus this error should be also implemented into the simulation model.
We consider that range-error of the distance measurement methods has a Gaussian distribution. The range error ε r is modeled by the Gaussian distribution with a mean μ = 0 and a standard deviation σ . In contrast to the many current researchers dealing with the range errors modeling, it is considered that σ is spread on the both sides from the μ value. Thus, the distance r i,j measured under the ε r can be calculated as shown in Eq. (2). The employed approach expresses situations where the measured signal strength is either strengthened by the interferences or suppressed by walls and obstacles. A decision about adding or subtracting the error portion to the distance should be made randomly.

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• Fall '18
• Mr. Bhullar
• Wireless sensor network

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