A multipath fading channel has multipath delay spread sigmat

A multipath fading channel has multipath delay spread sigma_tau = 250 n sec and Doppler spread B_D = 5 kHz. The total channel bandwidth at bandpass available for signal transmission is W = 12 MHz. To reduce the effects of intersymbol interference (ISI), the signal designer selects a pulse duration T_s = 1 psec. Determine the coherence bandwidth B_c and the coherence time t_c. Is the channel frequency selective? Why? Is the channel fading slowly or rapidly? Why?

Solution

(a) Coherence bandwidth = 1/multipath delay = 4MHz and coehrent time = 9/(2*pi*16*doppler spread) = 17.9 microsec

(b) as the Signal bandwidth(Bs) is 1MHz given 1/1microsec and Tc =17.9 microsec and Bc = 1/Tc = 55.85KHz

Bs >>>Bc and Tc <<<< multipath delay spread(250 nsec) Therefore it is a frequency selective fading

(c) as Ts<<<Tc and Bs >>> BD (BD is doppler spread = 5KHz).Therefore it is a slow fading