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Understanding Radio Irregularities in MultihopWireless Networks with Log-normal Shadowing
Lixin Wang

To better understand connectivity of multihop wireless networks with the log-normal shadowing, we study the impact of radio irregularities on network connectivity under such a realistic shadowing model. Existing results indicate that connectivity increases when the radio propagation becomes more irregular. But all of these results were only based on simulation studies or the assumption that the important boundary effect is ignored to avoid the challenging technical analysis. Therefore, they can hardly be applied to any practical wireless networks. It is extremely challenging to take the complicated boundary effect into consideration under such a realistic model because the transmission area of each node is an irregular region other than a circular area. In this paper, we assume the wireless nodes are represented by a Poisson point process with density n over a unit-area disk. We investigate the impact of radio irregularity on network connectivity with different transmission power settings, taking the important boundary effect into consideration. When each node transmits at a fixed uniform power, we prove analytically that network connectivity increases as the radio propagation becomes more irregular under such a realistic shadowing model. When each node transmits at an adjustable power so that the average node degree of the network is kept constant, we prove analytically that the expected number of the isolated nodes in the network is also unchanged under such a realistic shadowing model. The results obtained in this paper are validated via numberical analysis. These results can be used as design guidelines for all practical multihop wireless networks in which both the shadowing and boundary effects must be taken into consideration.

Keywords: Connectivity, radio irregularity, random deployment, log-normal shadowing

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