How does using double antennas (one with delay) and adding their output help the SNR?
As mentioned by Barry, this has got to do with beamforming. 

If you consider what occurs when a signal hits the two antennas, as shown in the following figure:



The signal received by the antennas will have a time delay between the antennas. This time delay is related to the angle theta that the signal is arriving from. 

When adding the signals together at the output, due to the time delay (if there is one) between elements, when the signals are added together there is destructive interference:



This serves as an attenuation of the signals coming from that direction. If the signal arrives from zero degrees there is no time delay and the signals add constructively. Alternatively it is possible to aim the array of signals by introducing a time delay to cancel the time delay introduced due to the geometry of the sensors. For narrowband signals this is done by introducing phase delays. 

So by having multiple sensors and adding them together you are creating a spatial filter, getting better quality signals from a specific direction even if there is interference signals of the same frequencies (so long as they come from a different direction). 

This is what a typical beamformer response pattern looks like: