Range Information and Amplitude-phase Information for Multi-carrier Radar Systems

This paper considers the problem of information extraction for single target with complex additive white Gaussian noise in general multi-carrier radar systems based on the range information (RI) and amplitude-phase information (API). First, the total information of the systems can be formulated as the mutual information (MI) between the receiving signals and jointly the range vector and amplitude-phase vector. Second, the total MI is the sum of the RI and the API, where the API is dependent on RI. Meanwhile, the expressions of RI and the API are derived in a constant reflection coefficient scenario. Furthermore, a closed-form approximation of RI is obtained in high signal to noise ratio (SNR), which is proportional to the root mean square bandwidth, SNR and detection time. The variance for range estimation is identical to the Cramér-Rao bound (CRB) and approximation results in high SNR. Numerical simulations are presented to validate the proposed theory, and shown the maximum likelihood estimation result is equivalent to the theoretical results and approximation in high SNR.