This paper explores an overlapped-multiple-input multiple-output (MIMO) antenna architecture and a spectrum sharing algorithm via null space projection (NSP) for radar-communications coexistence. In the overlapped-MIMO architecture, the transmit array of a collocated MIMO radar is partitioned into a number of subarrays that are allowed to overlap. Each of the antenna elements in these subarrays have signals orthogonal to each other and to the elements of the other subarrays. The proposed architecture not only improves sidelobe suppression to reduce interference to communications system, but also enjoys the advantages of MIMO radar without sacrificing the main desirable characteristics. The radar-centric spectrum sharing algorithm then projects the radar signal onto the null space of the communications system's interference channel, which helps to avoid interference from the radar. Numerical results are presented which show the performance of the proposed waveform design algorithm in terms of overall beampattern and sidelobe levels of the radar waveform and finally shows a comparison of the proposed system with existing collocated MIMO radar architectures.