  The novel active simultaneously transmitting and reflecting surface (ASTARS)
has recently received a lot of attention due to its capability to conquer the
multiplicative fading loss and achieve full-space smart radio environments.
This paper introduces the ASTARS to assist non-orthogonal multiple access
(NOMA) communications, where the stochastic geometry theory is used to model
the spatial positions of pairing users. We design the independent
reflection/transmission phase-shift controllers of ASTARS to align the phases
of cascaded channels at pairing users. We derive new closed-form and asymptotic
expressions of the outage probability and ergodic data rate for ASTARS-NOMA
networks in the presence of perfect/imperfect successive interference
cancellation (pSIC). The diversity orders and multiplexing gains for
ASTARS-NOMA are derived to provide more insights. Furthermore, the system
throughputs of ASTARS-NOMA are investigated in both delay-tolerant and
delay-limited transmission modes. The numerical results are presented and show
that: 1) ASTARS-NOMA with pSIC outperforms ASTARS assisted-orthogonal multiple
access (ASTARS-OMA) in terms of outage probability and ergodic data rate; 2)
The outage probability of ASTARS-NOMA can be further reduced within a certain
range by increasing the power amplification factors; 3) The system throughputs
of ASTARS-NOMA are superior to that of ASTARS-OMA in both delay-limited and
delay-tolerant transmission modes.
