MCRB and MSE Analysis for Parameter Estimation in AFDM-ISAC Systems

Affine frequency division multiplexing (AFDM) is a promising waveform for integrated sensing and communication (ISAC). In AFDM systems, the complex gains, delays, and Doppler shifts are commonly estimated from the AFDM symbols carrying pilots and data simultaneously. In practice, however, the unknown data symbols and data-pilot coupling interference may render the estimator mismatched to the true signal model. In this paper, we systematically characterize the parameter-estimation performance of AFDM-ISAC systems under practical model misspecification. The main contributions are threefold. First, we extend the Cramér-Rao bound (CRB) for a general observation model that treats the data symbols as unknown, which generalizes existing AFDM CRB analyses and serves as the matched benchmark for the subsequent analysis. Second, we identify two practical sources of misspecification, namely a covariance mismatch caused by insufficient pilot-data isolation and a combined covariance-and-mean mismatch caused by sequential single-target estimation, and derive the corresponding misspecified CRB (MCRB). Third, we characterize the pseudotrue parameters under different levels of prior knowledge, analyze the resulting estimation bias, and establish a lower bound (LB) on the mean square error (MSE). Simulation results validate the derived bounds and show that, under model misspecification, the CRB is overly optimistic while the MCRB and LB faithfully characterize the achievable accuracy. The comparison further reveals how these bounds vary with the pilot length and pilot power, providing useful guidance for pilot configuration.