申論題

5. (Total=34%) The figure below depicts a scenario where two base stations transmit. simultaneously the same Quadrature Amplitude Modulation (QAM) signal to a car that is in the middle of two base stations and moves toward Base Station 2. The signal is expressed as
 
 in which f₀ is the carrier frequency, p(t) is a rectangular pulse with the width of T, and the amplitudes A_c and A_s can take on values from{±1, ±3}.

(e) (7%) Now consider the car's speed v and the Doppler effect (the carrier frequency is modified with, where c is the speed of light, and choosing the sign according to the moving direction). Derive the mathematical expression of the received signal.