Approximation to independent lognormal sum with α–μ distribution and the application

• We adopt the α–μ distribution to approximate the probability density function of the sum of independent and possibly non-identically distributed lognormal variables.
• We investigate two typical parameter estimation methods, i.e., the moment-based method and the non-linear least square based method.
• For maximal-ratio combining receiver, we derive an analytical expression of the average bit error probability of the M-ary noncoherent frequency-shift keying modulation resorting to the new α–μ approximation.

This paper considers the statistical distribution of the sum of independent and possibly non-identically distributed lognormal random variables (RVs). The α–μ distribution is employed to approximate the probability of density function (PDF) of the lognormal sum. Two approaches, e.g., the moment-based and non-linear least square based (LS-based) methods, are used to obtain the parameters of α–μ distribution. Accounting for maximal-ratio combining (MRC) receiver, an analytical expression of the average bit error probability (ABEP) of the M-ary noncoherent frequency-shift keying (M-NFSK) modulation is derived. Finally, the performances of the α–μ approximation and the ABEP are evaluated via numerical experiments.