The Doppler Spread of a Channel

Question:  The Doppler spread of a channel is  𝐵 𝐷   = 80 Hz, if we need independent samples, what is the time  separation needed for the samples in the received signal?     Answer:   The coherence time of the channel         𝑇𝑐  ≈ 1 𝐵 𝐷 = 1 80         𝑇𝑐  =  12.5 ms    (refer mobile wireless communication notes-5 for theory)  the samples spaced 12.5 ms apart are uncorrelated,    So the uncorrelated samples will be independent of each other.    Question:  A user moving with velocity 60 miles per hour, the frequency of transmission is 1850MHz. What is the Doppler shift, Doppler spread and coherence time?  𝜃 = 90 0 .    Answer  The Doppler frequency shift can be found by using the equation:  𝑓 𝑑 =   𝑣𝜆 𝑐𝑜𝑠𝜃   𝑐𝑜𝑠𝜃 = 1 𝑠𝑖𝑛𝑐𝑒 𝜃 = 90 0     𝑣 =  60 𝑚𝑖𝑙𝑒𝑠 𝑝𝑒𝑟 ℎ𝑜𝑢𝑟 = 26.822 𝑚𝑒𝑡𝑒𝑟 𝑝𝑒𝑟 𝑠𝑒𝑐𝑜𝑛𝑑   (divide the speed value by 2.237)   𝜆 = 𝑙𝑖𝑔ℎ𝑡 𝑣𝑒𝑙𝑜𝑐𝑖𝑡𝑦 𝑓 𝑐 =   3 × 10 8 1850MHz =    0.1622 𝑚       𝑓 𝑑 =   𝑣𝜆 =   26.822  0.1622      𝑓 𝑑 = 165.47 Hz    So the Doppler shift is 165.47Hz   Doppler spread   𝐵 𝐷 = 2 × 𝑓 𝑑 = 330𝐻𝑧.   coherence  time          𝑇𝑐  ≈ 1 𝐵 𝐷 = 1 330 =   

      𝑇𝑐  =  3 ms    If the vehicle moving toward the base station the shifted frequency can be calculated as  𝑓 𝑐 ′ =   𝑓 𝑐 +   𝑓 𝑑   𝑓 𝑐 ′ =  1850MHz + 165.47 Hz