Doppler shifts: Effect on Communication systems Kartik Natarajan

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).

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

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 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

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.

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

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/ 

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))

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