How can I generate a cross spectrum? HFSWR

I have two sets of data (V1 and V2), each is an array of 4096 by 512 complex voltages (raw). I have already applied windowing, range processing and doppler processing leading to the generation of the range-Doppler map.

Now I wish to calculate the cross spectrum V12 using V1 and V2. Where should I start? Can I use the equation below? And if I were to use the said equation, do the parameters FFT(B) and FFT(A) correspond to the ouput of my Doppler processing? What does N^2 mean? • The cross-spectrum is defined as the Fourier transform of the cross-covariance (or cross-correlation if the means of both stochastic processes are zero). – Tendero Feb 22 '18 at 14:48
• Your question is unanswerable. The cross-spectrum cannot be obtained from the individual power spectra of the two signals because it depends on the joint properties of the signals, not their individual properties that determine their individual power spectra. – Dilip Sarwate Feb 22 '18 at 16:08
• The question, as asked, cannot be answered: there is no way. As Dilip says, information is lost when calculating the individual power spectra. If you have the original data (it's not clear to me that you do), then you can calculate the cross-spectra directly from that. – Peter K. Feb 22 '18 at 19:01
• It sounds like you perhaps want a complex ambiguity function. Could you elaborate on how the data was acquired – Stanley Pawlukiewicz Feb 27 '18 at 4:15
• @StanleyPawlukiewicz The data is taken from a high frequency surface wave radar. There are 512 pulses for each integration time and for each pulses 4096 complex samples were taken, resulting to a 4096 by 512 complex voltages. – colladsky Feb 27 '18 at 5:26