  Semi-grant-free (Semi-GF) non-orthogonal multiple access (NOMA) enables
grant-free (GF) and grant-based (GB) users to share the same resource blocks,
thereby balancing the connectivity and stability of communications. This letter
analyzes ergodic rates of Semi-GF NOMA systems. First, this paper exploits a
Semi-GF protocol, denoted as dynamic protocol, for selecting GF users into the
occupied GB channels via the GB user's instantaneous received power. Under this
protocol, the closed-form analytical and approximated expressions for ergodic
rates are derived. The numerical results illustrate that the GF user (weak NOMA
user) has a performance upper limit, while the ergodic rate of the GB user
(strong NOMA user) increases linearly versus the transmit signal-to-noise
ratio.
