Power domain non-orthogonal multiple access (PD-NOMA) with successive interference cancellation (SIC) on the receiver side has drawn great attention recently as a promising multiple-access scheme for next-generation (5G) mobile-communication systems. PD-NOMA utilizes the power domain for user multiplexing, which allows users to share resources to increase the system spectral efficiency, so as to improve system throughput. In this paper, we introduce an PD-NOMA application scenario, i.e., supporting group communication in public safety network. Because of the power-difference requirements of users in the PD-NOMA system, for the group communications, the number of users who can share these resources is limited; and the cryptographic keys thus cannot be distributed to user equipment efficiently. To solve this problem, we investigate combining PD-NOMA and spatial multiplexing technologies to meet the demand for high spectral efficiency. That is, we present a scheme for combining PD-NOMA with space shift keying (SSK) modulation, namely PD-NOMA-SSK, to help meet the demand for high spectral efficiency by exploiting the additional spatial domain. At the same time, we also suggest that the system throughput can be further enhanced by using PD-NOMA-SSK with multi-input multi-output (MIMO) multiplexing technology. The simulation results confirm the validity of the proposed schemes by comparing them with the conventional SSK and MIMO multiplexing schemes.