Beamformer gain and array gain/directivity index

Hello all I am studying array processing in which beam forming is an essential part. I have some basic related to beam former gain & array gain (AG) or directivity index(DI):

1. What is a relation of AG and DI with Beam former gain? 2. Are there any adaptive beam formers which can provide an SNR improvement as compared to conventional beam former (e.g. delay & sum beam former) with same type of input? If yes, can we quantify these improvements e.g. in terms of SNR dB?

Any help is greatly appreciated.

Thanks