Periodogram-based derivation of first-order power spectral density from remote sensing of the ocean surface by HF-Doppler radar

In the Ph.D. thesis of Gill, the author determines the power spectral density per unit area by finding the auto-correlation of the received voltage assuming a certain number of scatters, and then taking its Fourier transform. Here, we instead find the power spectral density using Welch's periodogram approach, where we take the Fourier transform of the expression for the received voltage, and equate the power spectral density to the expected value of the squared-magnitude of this transform. This simplifies the analysis, and leads to new insights about the first-order Bragg peaks.