Mean Doppler frequency shift is obtained by which technique?

Mean Doppler frequency shift is obtained by which technique?

• A. Zero-crossing detector
• B. Phase quadrature
• C. Fast Fourier transform
• D. Autocorrelation

Answer: (D)

The mean Doppler frequency shift is extracted from how a Doppler-shifted signal correlates with itself over time. If the received signal has a dominant Doppler tone, in complex baseband it looks like a rotating phasor e^{j2π fD t}. The autocorrelation R(τ) = E[x(t) x*(t+τ)] then behaves as R(τ) ∝ e^{j2π fD τ}. Its phase grows linearly with lag τ at a rate of 2π fD, so the Doppler frequency fD equals (1/2π) times the slope of the autocorrelation phase with respect to τ. Practically, you compute the sample autocorrelation for small lags, unwrap the phase, and estimate the slope. That slope is the mean Doppler frequency shift. This approach is robust because it leverages correlation to suppress noise and focuses on the steady phase rotation caused by Doppler. Other methods exist—zero-crossings are more sensitive to noise, phase-quadrature requires coherent phase tracking, and FFT-based methods aim for the full spectrum and then take a mean via spectral metrics—but autocorrelation directly ties the phase progression to frequency, giving a clean estimate of the mean Doppler shift.

The mean Doppler frequency shift is extracted from how a Doppler-shifted signal correlates with itself over time. If the received signal has a dominant Doppler tone, in complex baseband it looks like a rotating phasor e^{j2π fD t}. The autocorrelation R(τ) = E[x(t) x*(t+τ)] then behaves as R(τ) ∝ e^{j2π fD τ}. Its phase grows linearly with lag τ at a rate of 2π fD, so the Doppler frequency fD equals (1/2π) times the slope of the autocorrelation phase with respect to τ. Practically, you compute the sample autocorrelation for small lags, unwrap the phase, and estimate the slope. That slope is the mean Doppler frequency shift.

This approach is robust because it leverages correlation to suppress noise and focuses on the steady phase rotation caused by Doppler. Other methods exist—zero-crossings are more sensitive to noise, phase-quadrature requires coherent phase tracking, and FFT-based methods aim for the full spectrum and then take a mean via spectral metrics—but autocorrelation directly ties the phase progression to frequency, giving a clean estimate of the mean Doppler shift.