Expected Density of Progress for Wireless Ad Hoc Networks with Nakagami-m Fading

We study the expected density of progress for wireless ad hoc networks with Nakagami-m fading, where the expected density of progress is defined as the expectation of the product between the number of simultaneous successful transmission per unit area and the per hop distance towards the final destination. In a multihop transmission scenario, by considering three next hop relay receiver (RX) selection strategies, i.e., the nearest RX selection, the random RX selection and the furthest RX selection, we derive the closed-form expressions to the expected density of progress. Numerical results show that, when the terminal density is low, the expected density of progress with the nearest RX selection strategy is nearly the same as that with the furthest RX selection strategy, and the expected density of progress with random RX selection strategy is the lowest; when the terminal density is high, the nearest RX selection strategy has the largest expected density of progress, while the furthest RX selection strategy has the smallest.