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| Main Authors: | , , , |
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| Format: | Preprint |
| Published: |
2026
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| Subjects: | |
| Online Access: | https://arxiv.org/abs/2605.29364 |
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Table of Contents:
- Ongoing demand for radio spectrum by commercial wireless services has steadily increased pressure on the frequency bands traditionally reserved for radar. This paper addresses the joint problem of designing non-contiguous radar transmission spectra and estimating the range profile from the resulting reduced measurement set. Transmission spectra are constructed using a Marginal Fisher Information (MFI) criterion that removes blocks of frequencies contributing least to estimation accuracy. To process the underdetermined signals acquired from the resulting sparse measurement vector, an iterative Reduced-Rank Minimum Mean-Square Error (RRMMSE) estimator is proposed. The estimator starts with a single-target hypothesis and grows the active target subspace one range bin at a time, updating the a~priori target covariance matrix in each iteration using both the largest estimated reflection coefficient and its posterior error variance. This avoids inversion of the full $M{\times}M$ covariance matrix that would be required by a one-step MMSE and concentrates the rank of the estimator on the support of significant scatterers. The Bayesian Cramér--Rao Lower Bound (CRLB) on the per-bin reflection coefficient is derived for the non-contiguous spectrum measurement model, and the computational complexity of the proposed estimator is shown to scale as $\Order(G^2 M K^2)$, where $G$ is the number of detectable scatterers, $M$ is the number of range bins, and $K$ is the number of preserved spectral samples. Simulations using $50\%$ and $75\%$ spectrally occupied MFI-designed spectra confirm that the algorithm recovers sparse range profiles with Mean-Square Error (MSE) close to the fully filled baseline when the number of significant scatterers is not larger than the rank of the sparse sensing matrix.