  In this paper, we present the ergodic sum secrecy rate (ESSR) analysis of an
underlay spectrum sharing non-orthogonal multiple access (NOMA) system. We
consider the scenario where the power transmitted by the secondary transmitter
(ST) is constrained by the peak tolerable interference at multiple primary
receivers (PRs) as well as the maximum transmit power of the ST. The effect of
channel estimation error is also taken into account in our analysis. We derive
exact and asymptotic closed-form expressions for the ESSR of the downlink NOMA
system, and show that the performance can be classified into two distinct
regimes, i.e., it is dictated either by the interference constraint or by the
power constraint. Our results confirm the superiority of the NOMA-based system
over its orthogonal multiple access (OMA) based counterpart. More
interestingly, our results show that NOMA helps in maintaining the secrecy rate
of the strong user while significantly enhancing the secrecy performance of the
weak user as compared to OMA. The correctness of the proposed investigation is
corroborated through Monte Carlo simulation.
