On a Ratio of Functions of Exponential Random Variables and Some Applications

Consider independent and identically distributed exponential random variables (r.vs) 1, 2, . . . , and positive scalars 1, 2, . . . , . 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 =( =1 )2 / ( =1 ) . We show that the r.v appears in various communication systems such as ) maximal ratio combining of signals received over multiple channels with mismatched noise variances, ) -ary phase-shift keying with spatial diversity and imperfect channel estimation, and ) coded multi-carrier code-division multiple access reception affected by an unknown narrow-band interference, and the statistics of the r.v derived here enable us to carry out the performance analysis of such systems in closed-form.

• Type: Journal
• Year: 2010
• Where: TCOM
• Authors: Ramesh Annavajjala, Ananthanarayanan Chockalingam, Saif K. Mohammed
• Keywords: Cumulative Distribution Function, Exponential Random Variables, Probability Density Function, Software Engineering, TCOM 2010