Our solution is to use the Nasa DSN (Deep Space Network) to communicate with a SNS (SolarNet Satellite) positioned in an orbit around the sun in between Earth's and Mars' orbits. The satellite will act as a relay between the two planets in the case Mars is blinded by the sun.

While simulating one possible orbit we found out that by using a single satellite there will be a complete blindness period anyway (even if not that often), given by an opposition of the satellite and Earth/Mars, and the Solar Conjunction of Mars and Earth.

A more reliable solution would involve the use of multiple sats in the same orbit, so that they give a form of redundancy, completely avoiding the comms blindness problem.

Communication between Earth-SNS1-Mars and vice-versa could be achieved by using NASA’s DSN. Messages could be sent from Earth to the DSN by using its standard communication protocol, and then, by using UHF, the message could be delivered to destination, through SNS1 (SolarNet Satellite 1). This type of communication can also be used as a redundancy method while communicating in non-conjunction periods.  

By using multiple satellites the bandwidth could be increased by using all the satellites as different paths to reach destination, merging their bandwidhts, despite the latency loss. In fact the latency will be the one of the longest path.