Consider a multipath fading channel with three rays; a direct ray with power P0, a Rayleigh…

Consider a multipath fading channel with three rays; a
direct ray with power P0, a Rayleigh distributed ray with average power P1 =
2_1 2 , arriving to the receiver with same delay _0 as the direct
ray, and a delayed Rayleigh distributed ray of average power P2 = 2_2 2 .
The average delay _m, relative to that of the direct ray, and the delay
spread __ are given by

a. Assuming that the delay of the direct wave is equal to
zero and the delay difference between the direct wave and the delayed wave is
denoted by __, show that

Consider a multipath fading channel with three rays; a
direct ray with power P0, a Rayleigh distributed ray with average power P1 =
2_1 2 , arriving to the receiver with same delay _0 as the direct
ray, and a delayed Rayleigh distributed ray of average power P2 = 2_2 2 .
The average delay _m, relative to that of the direct ray, and the delay
spread __ are given by

a. Assuming that the delay of the direct wave is equal to
zero and the delay difference between the direct wave and the delayed wave is
denoted by __, show that

c. Show that the pdfs of the amplitudes of the direct rays
and the delayed ray can be written as

where I0(x) denotes the modified Bessel function of the
first kind and order zero.

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