1. Doppler shifts: Effect on Communication systems Kartik Natarajan

2. Doppler Overview/Review Apparent shifts in frequency of transmitted signal due to motion of transmitter/receiver or both. Shift depend on the relative velocity of the transmitter and receiver. Non-relativistic motionRelativistic motion : Cellular communication hampered by multipath fading effects and receiver movement (non- relativistic Doppler).

3. Small Scale Fading Rapid fluctuations in receiving conditions due to small movement of the receiver. Fading is caused by phase differences between waves reaching the receiver. Some causes: –Multipath Fading (Rayleigh and Rician) –Frequency shift due to movement – Doppler

4. Doppler Fading (1/3) For a vehicle moving in a straight line at constant velocity v, the Doppler frequency shift, fd is given by : Typical frequency range : –Most Cellular - 800 to 1500MHz –UHF – 300 to 3000MHz (used by TV, PCS etc.) Typical Doppler shifts : –5Hz to 300 Hz For example, at for a carrier frequency of 2GHz and a mobile speed of 68 mph, max fd = 200Hz

5. Doppler Fading (2/3) Doppler Spread (B D ) – The difference between the maximum and minimum values of fd. Coherence Time (T C ) – Statistical measure of the time duration over which the channel is invariant. –Defined as 1/ B D. Doppler spread and Coherence time characterizes fading speed and its frequency selectiveness.

6. Doppler Fading (3/3) Characterization of fading channels: –Fast fading T S > T C, and B S < B D Higher the fading speed, more the distortion –Slow fading T S > B D –Flat fading B S << B D –Non-Flat of Frequency selective fading B S >= B D

7. Received Power Spectrum with Doppler (1/3) Assumptions : –Isotropic antenna with unity gain and receiving average power p (without Doppler). –PDF of the direction of waves reaching the receiver is uniformly distributed between 0 and 2 . –Waves coming in from different directions add up to give a PSD S(f). Received signal frequency, f = f 0 + f d The PSD for signals in the range f to f+df corresponds to the waves coming in the direction given by +/- (  +d  ). =>S(f)df = 2* d  *(p/2  ) = d  *p/ 

8. Received Power Spectrum with Doppler (2/3) Also, df = -fm*sin  where fd = fm*cos  But sin  =sqrt(1 – cos^2(  )) =sqrt(fm^2 – (f- f 0 )^2)/ fm So, df = - sqrt(fm^2 – (f- f 0 )^2) Substituting back, we get |S(f)| = p/(  *sqrt(fm^2 – (f- f0)^2))

9. Received Power Spectrum with Doppler (3/3) Doppler Power Spectrum :