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Knowledge of the basic characteristics of the wall is especially important for the proper function of through-wall radars (TWR). In this paper, we introduce an estimation method that can provide the unknown wall parameters in real time. Our algorithm is based on a modified version of common midpoint processing, a technique adopted from geophysics. Using this method, it is possible to estimate the thickness and the permittivity of the wall from time-delay-only measurements performed at several different transceiver-receiver separations. Time-delay estimation (TDE) of echoes backscattered from the wall at each antenna separation is performed entirely in the frequency domain by a subspace super-resolution method. Our TDE approach is capable of resolving overlapping echoes reflected from the wall even in the case of only one snapshot of the measured data, suboptimal calibration possibilities, imperfect deconvolution of the measurement system, and limited radar bandwidth. The performance of our estimation algorithm is verified by simulations, and we also present the results for two real brick walls measured by using the time-domain technique. The estimated wall parameters can be utilized for improving the accuracy of real-time locating and tracking of moving humans by TWR.