Consider a binary signaling with two possible complex baseband transmitted
symbols s_(0)(t) and s_(1)(t) which satisfy (i) int_(-infty )^(infty ) |s_(0)(t)|^(2)dt=int_(-infty )^(infty ) |s_(1)(t)|^(2)dt=E_(b), and (ii)
int_(-infty )^(infty ) s_(0)(t)s_(1)^(**)(t)dt=0. The signal or 1
2.
Consider a binary signaling with two possible complex baseband transmitted
symbols so(t) and s(t) which satisfy (i) (so(t)2 dt = (."|s(t)|2 dt = E,, and (ii)
. so (t)s (t)dt = 0 . The signal s; (i = 0 or 1) is transmitted over a Rayleigh fading
channel and the received signal r(t) is given by r(t) =aes(t)+n(t) where n(t) is complex white Gaussian noise with E[n(t)n*(v)]=No8(t-v), a is Rayleigh distributed with probability density function p(a)=aexp(-a2)u(a), with u(a) being the unit step function, and is a random variable uniformly distributed between (0,2Tt). (a) Draw the optimum non-coherent receiver for this signaling scheme. (5%) (b) Given that the probability of error for the optimum non-coherent detection 1 E. when a=1 is -exp , compute the average probability of error over the 2 2N.
fading channel. (10%)
