Closed-form Distribution and Analysis of a Combined Nakagami-lognormal Shadowing and Unshadowing Fading Channel

The realistic wireless channels face combined (time shared) Nakagami-lognormal shadowing and unshadowing fading because of time varying nature of radio channel and mobile user. These channels can be modeled as time-shared sum of multipath-shadowing and unshadowing Rician distributions. These fading create severe problems in long distance wireless systems where multipath fading is superim-posed on shadowing fading (called multipath-shadowing fading). The multipath effect can be modeled using Rayleigh, Rician, Nakagami-m or Weibull distribution and shadowing effect is modeled using lognormal distribution. In this paper, authors present a new closed-form probability distribution function of a Nakagami-lognormal fading channel. Using this result, the closed-form expression of combined Nakagami-lognormal shadowing and unshadowing fading is presented. The obtained closed-form result facilitates to derive the important performance metrics of a communication system such as amount of fading, outage probability, and average channel capacity in closed-form expressions.