Doppler shifts: Effect on Communication systems

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 motion Relativistic 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 - 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

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

Doppler Fading (3/3) Characterization of fading channels: Fast fading TS > TC, and BS < BD Higher the fading speed, more the distortion Slow fading TS << TC, and BS >> BD Flat fading BS << BD Non-Flat of Frequency selective fading BS >= BD

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 = f0 + fd 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- f0)^2)/ fm So, df = - sqrt(fm^2 – (f- f0)^2) Substituting back, we get |S(f)| = p/(*sqrt(fm^2 – (f- f0)^2))

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