The application of compressed sensing (CS) theory to non-orthogonal multiple access (NOMA) systems has been investigated recently. As described in this paper, we propose a quality-of-service (QoS)-aware, low-complexity, CS-based user selection and power allocation scheme with adaptive resource block selection for downlink NOMA systems, where the tolerable interference threshold is designed mathematically to achieve a given QoS requirement by being relaxed to a constrained l1 norm optimization problem. The proposed scheme adopts two adaptive resource block (RB) selection algorithms that assign proper RB to user pairs, i.e. max-min channel assignment and two-step opportunistic channel assignment. Simulation results show that the proposed scheme is more effective at improving the user rate than other reference schemes while reducing the required complexity. The QoS requirement is approximately satisfied as long as the required QoS value is feasible.