# Determine the coherence bandwidth and the coherence time

Determine the coherence bandwidth and the coherence time

A multipath fading channel has a multipath spread of Tm = 1 s and a Doppler spread Bd = 0.01 Hz. The total channel bandwidth at band pass available for signal transmission is W = 5 Hz. To reduce the effects of inter symbol interference, the signal designer selects a pulse duration T = 10 s.

a. Determine the coherence bandwidth and the coherence time.

b. Is the channel frequency selective? Explain.

c. Is the channel fading slowly or rapidly? Explain.

d. Suppose that the channel is used to transmit binary data via (antipodal) coherently detected PSK in a frequency diversity mode. Explain how you would use the available channel bandwidth to obtain frequency diversity and determine how much diversity is available.

e. For the case in (d), what is the approximate SNR required per diversity to achieve an error probability of 10-6?

f. Suppose that a wideband signal is used for transmission and a RAKE-type receiver is used for demodulation. How many taps would you use in the RAKE receiver?

g. Explain whether or not the RAKE receiver can be implemented as a coherent receiver with maximal ratio combining.

h. If binary orthogonal signals are used for the wideband signal with square-law post detection combining in the RAKE receiver, what is the approximate SNR required to achieve an error probability of 10-6? (Assume that all taps have the same SNR.)