3GPP TR 38.901 CDL, Doppler Spread & Coherence Time Calculator
Max Doppler Shift ($f_{d,\max}$):
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50% Coherence Time ($T_{c, 50\%} \approx \frac{9}{16\pi f_d}$):
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Geometric Coherence Time ($T_c \approx \sqrt{\frac{9}{16\pi f_d^2}}$):
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MIMO Spatial Correlation ($\rho_{\text{spatial}}$):
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Understanding 3GPP TR 38.901 CDL & Doppler Effects
The Clustered Delay Line (CDL) model in 3GPP TR 38.901 extends traditional 2D TDL models into full 3D space, incorporating Azimuth and Elevation Angles of Arrival and Departure (AoA, ZoA, AoD, ZoD) for 5G NR Massive MIMO evaluation.
Maximum Doppler Shift & Coherence Time Formulas
Maximum Doppler shift ($f_{d,\max}$) depends directly on the relative velocity ($v$), speed of light ($c$), and carrier frequency ($f_c$):
- $$f_{d,\max} = \frac{v}{c} f_c$$
- $$\text{50\% Coherence Time Bound: } T_{c, 50\%} \approx \frac{9}{16\pi f_{d,\max}}$$
Spatial Antenna Correlation ($\rho_{\text{spatial}}$)
For an omnidirectional 2D propagation environment, spatial correlation between uniform linear array (ULA) elements spaced by $\Delta d / \lambda$ follows the zeroth-order Bessel function of the first kind:
- $$\rho_{\text{spatial}} = J_0\left(2\pi \frac{\Delta d}{\lambda}\right)$$