This paper proposes novel Bayesian learning approaches for sparse channel estimation in a multi-user millimeter-wave massive multiple-input multiple-output underlay cognitive radio system. The intelligent reflecting surfaces (IRS)-aided secondary network adopts a two-phase transmission protocol comprising of silent and estimation phases. During the silent phase, the secondary base station(SBS) captures primary network pilot transmissions to estimate the cascaded channel between primary users and the SBS. Next, the estimation phase considers two pilot design policies with an inherent estimation accuracy and spectral efficiency trade-off, for cascaded channel estimation with respect to the secondary users, IRS, and SBS. Further, the associated hybrid and marginalized Cramér-Rao bounds are developed to benchmark the efficacy of proposed estimation schemes. Simulation results demonstrate the superior performance of the proposed approaches in comparison to existing compressed sensing methods such as orthogonal matching pursuit and subspace multi-user joint channel estimation.

Intelligent reflecting surface (IRS)-aided millimeter wave (mmWave) systems are potential contenders for large scale deployment in 5G and beyond communication. Owing to the passive nature of IRS systems, the acquisition of accurate channel state information in bandwidth constrained scenarios becomes a highly challenging task. This work leverages the inherent sparsity associated with cascaded channels of IRS mmWave systems to develop novel sparse Bayesian learning (SBL)-based channel estimation algorithms. The underlying row-wise temporal correlation of the effective angular domain sparse channel matrix is first theoretically demonstrated followed by the development of the temporal SBL channel estimation approach. Further, utilizing the scaling property of cascaded channels for multiple users, low complex variants of the proposed SBL solutions are developed. Simulation results demonstrate significant improvement of the proposed SBL schemes over existing techniques.