CRB Solving For Two-Hop MIMO Collaborative Systems Based On Nested PARAFAC Model

In two-hop MIMO collaborative systems, a nested PARAFAC model is constructed at the destination node to facilitate joint channel and symbol estimation using the BALS algorithm. This paper derives a closed-form expression for the Cramer-Rao Bound (CRB) for the channel by vectorizing and stacking the received signals, and analyzes the computational complexity using the Slepian-Bangs formula. The nested PARAFAC model enhances channel state information (CSI) estimation by integrating multi-dimensional signal information. The CRB closure expression is derived by employing complex matrix derivation rules and properties of the multivariate joint Gaussian distribution. Simulation results illustrate the CRB performance for both hops and highlight the computational complexity involved.