Doppler Spread and Coherence Time

Doppler spread and Coherence time Doppler spread (𝐵 𝐷 ) : The Doppler spread is the frequency shift in the received signal due to its mobility. The parameters decide Doppler spreads are velocity (v) of user, wavelength (λ) of signal and angle between base station and user (θ). It can be expressed as: 𝑓 𝑑 = 𝑣𝜆 𝑐𝑜𝑠θ Where θ is the angle between base station and user. If the mobile user moving towards base station 𝑓 𝑑 will be positive. It the user moves away, 𝑓 𝑑 will be negative. Jakes Doppler spectrum Jakes Doppler spectrum will be having a bandwidth (𝐵 𝐷 ), 𝑐𝑎𝑙𝑙𝑒𝑑 𝐷𝑜𝑝𝑝𝑙𝑒𝑟 𝑆𝑝𝑟𝑒𝑎𝑑 of 2𝑓 𝑑 . It ranges from 𝑓𝑐 − 𝑓𝑑 𝑡𝑜 𝑓𝑐 + 𝑓𝑑, where fc is the transmit signal frequency. Coherence Time (𝑻𝒄): 𝑇 𝐶 = 1 𝐵 𝐷

The inverse of Doppler spread is called Coherence time. It is the time over which the channel is time invariant. So as velocity of the user increases, the Doppler shift and Doppler spread increases, it will reduce the coherence time, i.e., channel will become more time variant. In wireless communication 5G system supports a velocity of 500km/h, in 4G it is 350km/h. So as the technology updates, need more accurate system which works in time variant channel. Let 𝑇𝑠 be the symbol duration, and 𝑇𝑐 be the coherence time, If 𝑇𝑠 < 𝑇𝑐 - called slow fading condition If 𝑇𝑠 > 𝑇𝑐 - called fast fading condition In slow fading system, symbol experience same channel condition throughout transmission. There are channels called doubly dispersive channel, which will be time varying and time dispersive. Following figure shows the overall relation. Fig Ref: Wireless Communications: Principles and Practice, T. S. Rappaport