The behavior of a two element antenna system within a mobile phone where one antenna has a particular slot configuration, designed to reduce the mutual coupling of the two antennas at a particular frequency corresponding to the length of the slot and the ground and feed placement, is analyzed and measured. This particular set of antenna geometries can create a large group delay at certain frequencies, significantly increasing the isolation between the two antennas. A large group delay can reduce the mutual coupling between two antenna by over 25 dB compared to a non-optimized system. By reducing the mutual coupling, the radiation efficiency increases by 20-30%. This paper analyzes the two antenna system within a mobile phone where the first antenna is GSM + 3G and the second antenna is 4G where the 4G frequency band directly overlaps with the 3G frequency band.