A spatio-temporal model for physical carrier sensing wireless ad-hoc networks

In this paper, we propose a simple analytic model for a physical carrier sensing wireless ad-hoc network. Attempted packet transmissions are modeled as a three dimensional Poisson point process in space and time. Each node measures the total interference power before an attempted transmission, and proceeds with the transmission only if the total interference power is below a threshold, called the idle threshold. A completed transmission is successfully received if the interference power at the intended destination is suitably low during the transmission. The total interference process is modeled as a shot noise that is a filtered in space and time, which accounts for an infinite number of concurrent transmissions on the infinite plane. We make a Gaussian approximation for the power of the interference process. A key mechanism for physical carrier sensing we take into account in our model is the inhibitory effect of nearby neighbors around an existing transmission. The inhibiting model is based on the threshold on the interference level rather than a geographically defined region. We model this effect using the conditional intensity of transmissions given an existing transmission, which can be solved using a system of two fixed point equations. We further approximate the conditional statistics of transmissions as Poisson to obtain a simpler model. We compare the predictions using the simpler model to Monte Carlo simulations results based on the model without the Poisson approximation, and we find a reasonably close match. Our results suggest the simpler model can be used as a guide to set the protocol parameters such as transmission attempts intensity, distance between the transmitter and its intended receiver, transmission power, packet duration, idle and packet detection threshold, in order to optimize network throughput