Abstract:

Consider L independent and identically distributed exponential random variables (r.vs) X1,X2,...,XL, and positive scalars b1,b2,...,bL. In this letter, we present the probability density function (pdf), cumulative distribution function and the Laplace transform of the pdf of the composite r.v Z = (X1 + X2 + ... + XL)2 /(b1*X1 + b2*X2 + ... + bL*XL). We show that the r.v Z appears in various communication systems such as 1) maximal ratio combining of signals received over multiple channels with mismatched noise variances, 2) M-ary phase-shift keying with spatial diversity and imperfect channel estimation, and 3) coded multi-carrier code-division multiple access reception affected by an unknown narrow-band interference, and the statistics of the r.v Z derived here enable us to carry out the performance analysis of such systems in closed-form.