I'm currently working on DOA estimation using ML. Let me give a brief overview before I ask my query. Firstly incoming signals are transformed into a matrix of complex numbers. The size depends on the number of sensors and signals. After further performing mathematical steps, we find the covariance matrix and take the upper traingular values(excluding the diagonal elements). These final complex values from the covariance matrix corresponding to each theta is fed into an ML model for predictions.
I noticed that we get directional information when we use both- complex numbers and just the imaginary of those complex numbers. That is the model is able to estimate the correspoding theta.
However, when we just feed the real part of the complex numbers, the model performs very poorly and is unable to estimate the direction.
I was hoping to get clarity on what exactly the real and imaginary part signify and how do I explain that the imaginary part has directional information and real doesn't. Is there any mathematical explanation?