On the scalability and capacity of planar wireless networks with omnidirectional antennas

Onur Arpacioglu, Zygmunt J. Haas
2004 Wireless Communications and Mobile Computing  
We extend the previously well-known results on the capacity of wireless networks and present the implications of our results on network scalability. In particular, we find bounds on the maximum achievable per-node end-to-end throughput, ! e , and the maximum number of simultaneously successful wireless transmissions, N max t , under a more general network scenario than previously considered. Furthermore, in the derivation of our results, we make no restrictions on the mobility pattern of the
more » ... es or on the number simultaneous transmissions and/or receptions that nodes are capable of maintaining. In our derivation, we analyze the effect of parameters such as the area of the network domain, A, the path loss exponent, , the processing gain, G, and the SINR threshold, . Specifically, we prove the following results for a wireless network of N nodes that are equipped with omnidirectional antennas: (1) ! e is Â(1/N) under very general conditions. This result continues to hold even when the communication bandwidth is divided into sub-channels of smaller bandwidth. (2) N max t has an upper bound that does not depend on N, which is the simultaneous transmission capacity of the network domain, N Q t . For a circular network domain, N Q t is OðA minf=2;1g Þ if 6 ¼ 2 and OðA=logðAÞÞ if ¼ 2. In addition, N Q t is Oð 2 Þ and OðG=Þ. Moreover, lack of attenuation and lack of space are equivalent, where N Q t cannot exceed 1 þ G=. (3) As N ! 1 a desired per-node end-to-end throughput is not achievable, unless the average number of hops between a source and a destination does not grow indefinitely with N, A grows with N and N is OðA minf=2;1g Þ if 6 ¼ 2 and OðA=logðAÞÞ if ¼ 2.
doi:10.1002/wcm.216 fatcat:ugnyqmj23rfadcpwo7iszgdmmm