Calculating gain of multiple antenna system
I've never heard of radars using thousands of antennas before but the reasons for antenna diversity is well known. Several antennas can increase the probability that, no-matter what direction a transmission is arriving, and no-matter how that transmission is polarized, it will be received correctly. 

This usually means, for each antenna, an amplifier and demodulator i.e. it can be quite complex and there is no apparent multiplication of antenna gain. In fact, depending on the mechanical configuration of the antenns, there can be a reduction in gain for each antenna due to the proximity of the other antennas.