For reducing the switching frequency between the radio frequency (RF) chain and transmit antennas, a class of new sparse space shift keying modulation (SSSK) schemes are presented. This new class is proposed to simplify hardware implementation, through carefully designing the spatial constellation mapping pattern. Specifically, different from traditional space shift keying modulation (SSK), the proposed SSSK scheme utilizes more time slots to construct a joint design of time and spatial domain SSK modulation, while maintaining the special structure of single RF chain. Since part of the multi-dimension constellations of SSSK concentrate the energy in less time slots, the RF-switching frequency is effectively reduced due to the sparsity introduced in the time domain. Furthermore, through theoretical analysis, we obtain the closed-form expression of the bit error probability for the SSSK scheme, and demonstrate that slight performance gain can be achieved compared to traditional SSK with reduced implementation cost. Moreover, we integrate transmit antenna selection (TAS) to achieve considerable performance gain. Finally, simulation results confirm the effectiveness of the proposed SSSK scheme compared to its traditional counterpart.