Efficiency of four fed patch antenna

There is four fed patch for circular pol (see Attachments) simulated in CST. When 1 port is excited the S31 is about -4dB, S21=S41=-13dB, S11=-15dB. It means that total efficiency of antenna is less than 60%, because ~40% of power return to the port 3. When all ports simultaneous excitation are performed the efficiency more than 95%.
Why efficiency calc doesn't connected with S-parameters? Do you have some articles or books about the problem? Thanks.

I will start by saying that your numbers sounds too bad. Coupling mechanisms for such structures are: radiation and due to surface waves, however in a passable design results should be much better.
May I ask what is the distance between the patches and GND? Is your design optimal?

Radiation efficiency is defined by the amount of power that is radiated divided by the acceptable power, where the acceptable power is the difference between the input power and reflected power.
The reason behind this 'weird' definition is that when you design an antenna you can separate between two causes:
a. Antenna matching.
b. How good my antenna acts like an antenna - efficiency.

My explanation: For simultaneous excitation, the transmission from 1 to 3 looks like port 3 reflection to the software. Then it is not "loss" for an efficiency calculation.

Why do you have 4 feeds instead of 2?

I Agree with your comments. I related to radiation efficiency for a single port antenna, which is not the case here.

4 feeds is use to obtain good axial ratio, phase center stability, rad. pattern in hemisphere, because it is GNSS antenna (f1~1230 MHz, f2=1560 MHz). Below the power and efficiency vs frequency is presented.
1 port is excited:

4 ports are excited:

?power outgoing all ports? contains reflected and transmited to other port power.
An efficiency calculation takes ?power outgoing all ports? into account

Calculation was performed by combining 3d farfield, but when real devider was used in model, the efficiency results have been the same.