On the Double Doppler Effect Generated by Scatterer Motion

Abstract

In a time-varying transmission channel, the received signals are subject to frequency shifts due to the Dopplereffect. The Doppler frequency is dependent on the carrier frequency and channel variation rate. In a fixed wirelesschannel, the channel variations are caused by scatterer motion. In this paper, we investigate analytically the Dopplereffects generated by scatterer motion under different scatterer velocity distributions using the ring-of-scatterers geometricmodel. The proposed model considers Doppler frequency components caused by scatterer mobility to both received andreflected signals at each scatterer, and therefore is called the double Doppler model. The analytical curves are comparedand statistically tested with several measurement results published in the literature. At low scatterer speeds, e.g., generatedby moving foliage, the exponential velocity distribution is an appropriate model to describe the time-varying nature ofthe fixed wireless channels. The curve fitting results also show that our analytical model better approaches the empiricalcurves than the single Doppler model does. However, further investigation is still needed to find a suitable scatterer velocitydistribution that closely describes the double Doppler effect in fast-variation fixed wireless channels, e.g., caused by passingvehicles.