Two antenna method - dB or dbi?

In measuring the gain of a YAGI with a Network analyser S12 parameters, I used the exact same YAGI for both send and receive antennas. After balancing the equation and subtracting cable and free space losses, should my resulting gain be in dB or dBi? can I say it is in dBi? but explain why because my reference antenna is not isotropic but rather the same YAGI.
is there such notation as dB(with reference to the same antenna)?

there is technically no such thing as plain "dB" when referring to antenna gain.
It has to be related to something else its meaningless. The 2 primary used references are dBd = gain relative to a dipole
and the one you have stated dBi = gain relative to an isotropic radiator.

I would expect that you would have to start with that baseline to know the performance of the yagi in question so that you can define its overall effect in the link budget of the system.

Dave

Yes - and more than that: The term "free space loss" and it's calculation is based on the characteristic of an isotropic radiating antenna. The antenna has, of course, no such thing as "gain". It can only focus it's power - if compared with an isotropic characteristic.
However, you can compare two antennas and express the difference in "dB".

Thank you for your responses, however, What I need is for someone to help me with a concrete answer. I have measured the received power from a YAGI antenna, transmitted from an identical YAGI. How do you express this power received? it has to be dB because there is no dipole involved.

On the other hand, if it is expressed in dB, then how do you convert dB to dBi?

Thanks

If you like to express power in logarithmic scale it is always dBm or dbW. This is because it must be referenced to a certain value. For example, dBm means: dB more than 1 mW and dBW means: db more than 1W.

Dear robertobolanos;
I think Friis equation helps youFriis transmission equation - Wikipedia, the free encyclopedia
Since you use identical antennas Gt and Gr is the same. You shoul have known about also Pt and Pr from your measurments.
Hope helps

Use one of the Yagi antenna as a reference (doesn't matter its gain, and you don't have to know it).
Use a dipole antenna working on the same frequency as the Yagi antennas, placed on the same polarity (vertical or horizontal).
Measure the level in dBm with this setup (Yagi and Dipole).
Replace the dipole antenna with the second Yagi, and measure the level in dBm.
The difference in dB between the two measurements is the gain in dBd (referenced to dipole) of the second Yagi antenna.
Can do the same thing to find the gain of the first Yagi.