A New Statistical Model of the Complex Nakagami-m Fading Gain

The Nakagami-m distribution approximates a Rician distribution for the fading parameter m in the range 1 <; m <; ∞, and approximates a Hoyt or Nakagami-q distribution for m in the range 1/2 ≤ m <; 1, while it becomes a Rayleigh distribution for m=1. A uniformly distributed phase for all m ≥ 1/2 does not satisfy all these requirements. By using the distributions of the real and imaginary parts of complex fading gains having Rician and Hoyt distributed envelopes, we propose in this paper a new statistical model of the complex Nakagam-m fading gain for which the envelope has a Nakagami-m distribution and the phase has a nonuniform distribution. Numerical results show that, for a signal having a Nakagami-m distributed fading envelope, the proposed model closely approximates the distributions of the real and imaginary parts of signals with Rician and Hoyt fading envelopes for 1 <; m <; ∞ and 1/2 ≤ m <; 1, respectively, as well as the distributions of the corresponding phases.