On the Capacity of Wireless Sensor Networks with Omnidirectional Antennas

O. Arpacioglu, Z.J. Haas
2004 Journal of Communication and Information Systems  
We establish some new results on the capacity of wireless sensor networks that employ single-user detection, and we present the implications of our results on the scalability of such networks. In particular, we find bounds on the maximum achievable per-sensor end-to-end throughput, 4" and the maximum number of simultaneously successful wireless transmissions, N,max, under a more general network scenario than previously considered. Furthermore, in the derivation of our results, we make no
more » ... tions on the mobility pattern of the sensor and the destination nodes or on the number simultaneous transmissions and/or receptions that the nodes are capable of maintaining. In our derivation, we also analyze the effect of parameters such as the area of the network domain, A, the path loss exponent, y, the processing gain, G, and the SINR threshold, /3. Specifically, we prove the following results for a wireless sensor network of N sensor nodes and M destination nodes that are equipped with omnidirectional antennas: (1) 4" is 8(1/N) under very general conditions that we identify in this paper. (2) N,max has an upper bound that does not depend on N, which is the simultaneous transmission capacity of the network domain, NP. For a circular network domain, NP is O(A min (yI2. 1I ) if r"t. 2 and O(A/log(A» if r = 2. In addition, NP is O( r 2 ) and O(GI/3). Moreover, lack of attenuation and lack of space are equivalent, where NP cannot exceed 1+GI/3 . (3) As NO 00 a desired per-sensor end-to-end throughput is not achievable, unless the average number of hops between a sensor-destination node pair does not grow indefinitely with N, both M and A grow with N such that M is Q(N), and Nis O(A min \y/2.1 1 ) if r "t. 2 and O(A/log(A» if r =2. On capacity of wireless sensor networks with omnidirecitional antennas a uniform distribution of node locations, a random traffic pattern, and a common transmission power that decreases with N, while ensuring the connectivity of the network as N tends to infinity. From a sensor network perspective, the arbitrary and the random network models correspond to sensor networks for which each node has the ability to be a sensor node and a destination node. Additionally, in [1], two models for successful reception are proposed. The first reception model is the protocol model, which considers a transmission unsuccessful if the receiver is within the interfering range of an unintended transmitter. The second model is the physical model, which better represents realistic reception in practical wireless networks. In the physical model, for a transmission to be successful, the Signal-to-Interference-and-Noise Ratio, SINR, at the receiver of the transmission has to be above some threshold value. It is assumed that the antennas are omnidirectional and that PixY is the power received at a distance x from a given transmitter, where P is the transmitted power and the path loss exponent r is assumed to be larger than 2. [I] concluded that, with the protocol model, 4( is 2 0(11 $) for arbitrary networks, whereas 4( is o (11 .JN log( N») for random networks. With the physical model, they concluded that 4( is 0 (I I @) and 12 (I I $) for arbitrary networks, whereas, 4( is 0(11 $) and 12(11 .JNlog(N») forrandom networks.
doi:10.14209/jcis.2004.14 fatcat:pzgadvlwafc2vdqdiojx7xcdny