On the Asymptotic Analysis of Average Interference Power Generated by a Wireless Sensor Network

Massive deployments of wireless sensor networks (WSNs) are expected in near future. In one of the most likely scenarios, these WSNs would share a licensed frequency band with a primary user. So, it is essential to understand the behavior of the interference generated by a WSN towards the primary user. This paper provides an asymptotic analysis of the average interference power generated by a WSN. The analysis is extended to a special but important shape of a sensor field. This shape can be used to provide an upper bound of the average interference power generated by any sensor field with an arbitrary shape. The paper shows that the expansion of the sensor field does not necessarily cause an increase in the average interference power. For most practical values of path loss exponent, the average interference power asymptotically approaches constant levels with the increase in the field size provided that the minimum distance from the field to the primary user is fixed. The paper provides expressions for these constants. Moreover, results indicate that a key parameter in determining the average interference power is the ratio of the radial depth of the field to the minimum distance from the field to the primary user. Also, this paper illustrates how a WSN can be equivalently represented by a single virtual node producing the same level of average interference power.