On the statistics of the Nakagami-m signal

This paper proposes a fading model that leads to a formal, but simple, method to obtain the exact formula of the Nakagami-m distribution for m=n/2, n a non-zero integer number. Based on such a model the joint distribution of the envelope and its time derivative is accomplished and exact formulas for the level crossing rate (closed-form formula) and for the average fade duration are derived. Simulation curves and exact formulas are checked against each other and a perfect agreement between them is attained. Although derived for discrete values of m (m being an integer multiple of ½) there are no mathematical constraints for these expressions to be used for any real value m⩾½