Response to the following problem:
The scattering function S(τ ; λ) for a fading multipath channel is nonzero for the range of values 0 ≤ τ ≤ 1 ms and -0.1 Hz ≤ λ ≤ 0.1 Hz. Assume that the scattering function is approximately uniform in the two variables.
a. Give numerical values for the following parameters:
(i) The multipath spread of the channel.
(ii) The Doppler spread of the channel.
(iii) The coherence time of the channel.
(iv) The coherence bandwidth of the channel.
(v) The spread factor of the channel.
b. Explain the meaning of the following, taking into consideration the answers given in (a):
(i) The channel is frequency-nonselective.
(ii) The channel is slowly fading.
(iii) The channel is frequency-selective.
c. Suppose that we have a frequency allocation (bandwidth) of 10 kHz and we wish to transmit at a rate of 100 bits over this channel. Design a binary communication system with frequency diversity. In particular, specify
(i) The type of modulation.
(ii) The number of subchannels.
(iii) The frequency separation between adjacent carriers.
(iv) The signaling interval used in your design. Justify your choice of parameters.