I think, this talks about the power Pt...where it is deifned as P = v^2 divided by R

https://1drv.ms/i/c/4286f33e519f4694/IQBlaFlBKoh0R7GmuKspNvC4AZ2g8EmaJGX065kYJZNQ8yU?e=G9TVdL

integration based only on magnitude

integration of both magnitude and phase

angular distance from the peak centre(boresight) to the first null

(https://soaneemrana.org/onewebmedia/INTRODUCATION%20TO%20RADAR%20SYSTEM%20BY%20MERRIL,%20I%20SKLOINK%20(4).pdf)

https://youtu.be/SYkUli9-o1I?si=VcnI6pe1zGrYIaiy

\(\theta \) (Theta) and \(\phi \) (Phi): These are the angular coordinates in a 3D spherical system. \(\theta \) represents the elevation angle (up/down) and \(\phi \) represents the azimuth angle (left/right). They specify the exact direction in space relative to the antenna. \(E(\theta, \phi)\): This is the Electric Field Vector (measured in Volts per meter). It describes how strong the electrical force of the radio wave is in a given direction \((\theta, \phi)\). Because radio waves oscillate, \(E\) contains complex numbers to account for phase. \(\vert{}\vert{} \dots \vert{}\vert{}^2\): This represents taking the squared magnitude (absolute value squared) of that complex electric field. \(P(\theta, \phi)\): This is the Radiation Intensity or Power Pattern. It represents the power per unit solid angle (Watts per steradian) flowing out into that specific direction.

Correlate the received signal with a template of the expected signal, That operation is the matched filter.

Instead of processing signals directly at the final RF frequency, systems often convert them to a convenient intermediate frequency called the IF