  Recent studies have demonstrated the superiority of non-orthogonal multiple
access (NOMA) over orthogonal multiple access (OMA) in cooperative
communication networks. In this paper, we propose a novel half-duplex
cooperative asynchronous NOMA (C-ANOMA) framework with user relaying, where a
timing mismatch is intentionally added in the broadcast signal. We derive the
expressions for the individual throughputs of the strong user (acts as relay)
which employs the block-wise successive interference cancellation (SIC) and the
weak user which combines the symbol-asynchronous signal with the
interference-free signal. We analytically prove that in the C-ANOMA systems
with a sufficiently large frame length, the strong user attains the same
throughput to decode its own message while both users can achieve a higher
throughput to decode the weak user's message compared with those in the
cooperative NOMA (C-NOMA) systems. Besides, we obtain the optimal timing
mismatch when the frame length goes to infinity. Furthermore, to exploit the
trade-off between the power consumption of base station and that of the relay
user, we solve a weighted sum power minimization problem under quality of
services (QoS) constraints. Numerical results show that the C-ANOMA system can
consume less power compared with the C-NOMA system to satisfy the same QoS
requirements.
