  Integrated Sensing and Communications (ISAC) surpasses the conventional
frequency-division sensing and communications (FDSAC) in terms of spectrum,
energy, and hardware efficiency, with potential for greater enhancement through
integration of non-orthogonal multiple access (NOMA). Leveraging these
advantages, a multiple-input multiple-output NOMA-ISAC framework is proposed in
this paper, in which the technique of signal alignment is adopted. The
performance of the proposed framework for both downlink and uplink is analyzed.
1) The downlink ISAC is investigated under three different precoding designs: a
sensing-centric (S-C) design, a communications-centric (C-C) design, and a
Pareto optimal design. 2) For the uplink case, two scenarios are investigated:
a S-C design and a C-C design, which vary based on the order of interference
cancellation between the communication and sensing signals. In each of these
scenarios, key performance metrics including sensing rate (SR), communication
rate (CR), and outage probability are investigated. For a deeper understanding,
the asymptotic performance of the system in the high signal-to-noise ratio
(SNR) region is also explored, with a focus on the high-SNR slope and diversity
order. Finally, the SR-CR rate regions achieved by ISAC and FDSAC are studied.
Numerical results reveal that in both downlink and uplink cases, ISAC
outperforms FDSAC in terms of sensing and communications performance and is
capable of achieving a broader rate region, clearly showcasing its superiority.
