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We investigate the spectral efficiency of the multiple-input, multiple-output (MIMO)-driven non-orthogonal multiple access (NOMA)-based cognitive radio (CR) networks. We first investigate the spectrum sensing performance of a MIMO-CR network by employing the blindly combined energy detection (BCED) scheme. We derive expressions for the average achievable throughput in MIMO-NOMA CR networks with imperfect spectrum sensing using the BCED technique. Through Monte Carlo simulations and numerical techniques, we show the the spectral efficiency achieved due to MIMO-NOMA in CR networks is better as compared to the MIMO-based orthogonal multiple access (MIMO-OMA) CR networks.