Non-orthogonal multiple access (NOMA) has the potential to enhance spectrum efficiency (SE) in 5G and other upcoming networks. Utilizing cognitive radio (CR) and multiple access techniques might potentially enhance spectral efficiency (SE). The combination of NOMA’s network-oriented multi-access capabilities with the CR network (CRN) is expected to usher in a new era of efficient communication. This study improves the SE of the NOMA power domain (PD) in the downlink (DL) by employing uncooperative cognitive radio networks (UCCRNs). If the primary user (PU) cannot receive data on the dedicated channel owing to noise or interference, this approach is anticipated to be advantageous. Two network topologies were suggested, each having a bandwidth (BW) of 110 MHz and using quadrature phase shift keying (QPSK). Additionally, 8 × 8, 16 × 16, and 32 × 32 Multiple-Input Multiple-Output (MIMO) topologies are employed, each varying in terms of transmit powers, user distances, and power placement coefficients. Performance studies also consider channel instability and successive interference cancellation (SIC). The channels that experience fading are characterized by Rayleigh fading and exhibit frequency selectivity. MATLAB computes the model’s SE. The SE performance of 8 × 8, 16 × 16, and 32 × 32 MIMO NOMA is 32.8, 53, and 71% better than the standard NOMA model. Additionally, UCCRN 8 × 8, 16 × 16, and 32 × 32 MIMO NOMA improve SE performance by 41, 59, and 73% compared to the standard NOMA model. Employing MIMO technology greatly enhances SE. The derived equations correspond to the results of the Monte Carlo simulations, validating our discoveries.