This preview shows pages 1–2. Sign up to view the full content.
This preview has intentionally blurred sections. Sign up to view the full version.
View Full Document
Unformatted text preview: ECE 562 Fall 2010 Noncoherent Communication Rayleigh Random Variable. If Y = Y I + jY Q is distributed as CN (0 , 2 2 ), then we showed in class that Z =  Y  has a Rayleigh pdf, p Z ( z ) = z 2 exp z 2 2 2 11 { z } Furthermore = Y = tan 1 ( Y Q /Y I ) is uniformly distributed on [0 , 2 ], and Z and are independent. Also, X = Z 2 =  Y  2 is exponential p X ( x ) = 1 2 2 exp h x 2 2 i 11 { x } Ricean Random Variables. If Y CN ( e j , 2 2 ), then Z =  Y  has a Ricean pdf that does not depend on , but only on and 2 . p Z ( z ) = z 2 exp z 2 + 2 2 2 I z 2 11 { z } where I ( x ) = 1 2 Z 2 e x cos d is the zerothorder modified Bessel function of the first kind. Note that I ( x ) 0 for all x , I (0) = 1 and I ( x ) as x . In this case, = Y = tan 1 ( Y Q /Y I ) is not uniformly distributed on [0 , 2 ], and Z and are not independent, except when = 0. Channel with Phase Uncertainty. The received signal for one symbol period for communication on an ideal AWGN channel is given by:...
View Full
Document
 Fall '09

Click to edit the document details