Problem-1. Multipah channel models
A transmitter transmits a signal s(t) with carrier frequency fc. The signal reaches the receiving antennas through three paths. The path gains are a1, a2, and a3. The path delays are t1, t2, and t3. The Doppler shifts at the carrier frequency are f1, f2, and f3. What is the received signal? What is the transfer function characterizing the channel between the receiving and transmitting antenna?
Problem -2. Channel Parameters
Carrier frequency is 1 GHz. Moving speed is 2 m/sec. In the following, what are the reasonable numbers in indoors for the following parameters
a.) coherent bandwidth:
b.) coherent time:
c.) delay spread:
d.) Doppler spread:
Choose (just pick one value for each parameter) your answers from the following values:
1.) 1 sec; 2.) 0.1 sec; 3.) 0.01 sec; 4.) 1 msec; 5.) 0.1 msec; 6.) 0.01 msec; 7.) 1 sec; 8.) 0.1 sec; 9.) 0.01 sec; 10.) 1 nsec; 11.) 1 GHz; 12.) 0.1 GHz; 13.) 0.01 GHz; 14.) 1 MHz; 15.) 0.1 MHz; 16.) 0.01 MHz; 17.) 1 KHz; 18.) 0.1 KHz; 19.) 0.01 KHz; 20.) 1 Hz;
Problem 3. System Design
The delay spread in a given environment TD is 5 micro seconds.
The maximum Doppler spread FD is 200Hz.
We would like to design a digital communication system in this environment such that
1. Distortion per data symbol is negligible
2. The time variation during a symbol period is negligible
What is the appropriate range of the symbol duration in this communication system?