radar system designers

Abstract: This paper proposes a progressive Bayesian multiple-input multiple-output (MIMO) sensing framework for multiple targets over multiple stages. We consider a practical yet challenging scenario where the targets' angles are unknown and random parameters to be estimated, while the targets' reflection coefficients are unknown nuisance parameters. With an initial prior probability density function (PDF) for the targets' angles, we progressively update the prior PDF for each sensing stage as the posterior PDF obtained from the previous stage, based on which Bayesian transmit beamforming optimization is performed to minimize the sum posterior Cramér-Rao bound (PCRB) in estimating the targets' angles and Bayesian sensing is performed with the help of new observations in this stage. To analytically characterize the intractable and high-dimensional posterior PDF with low complexity, we propose a variational Bayesian inference based approach which derives a surrogate posterior PDF in closed form with only polynomial complexity over the number of targets, in sharp contrast to existing numerical calculation approaches with exponential complexity. Numerical results validate the efficacy of our proposed framework in progressively refining sensing performance.

Abstract: We study the expected aperiodic autocorrelation sidelobes of random communication symbols transmitted through a unitary modulation matrix. We consider proper sub-Gaussian constellations, namely those with fourth absolute moment $μ_4<2$ and zero pseudo-variance, including the commonly used uniform square quadrature amplitude modulation (QAM) and uniform phase-shift keying (PSK) constellations. For every prescribed lag, we determine the exact minimum expected sidelobe level (ESL) and a unitary modulation attaining it by applying a normalized inverse discrete Fourier transform (IDFT) separately on each chain of sample indices spaced by that lag. The full orthogonal frequency division modulation (OFDM) modulation attains this minimum if and only if the lag divides the block length $N$. Combining this criterion with the complete characterization of the minimizers at lag one, we show that a unitary modulation minimizes the ESL simultaneously over the first $r$ positive lags, called the prefix $\{1,\ldots,r\}$ with $1\le r<N$, if and only if every lag in that prefix divides $N$. In particular, simultaneous optimality over all positive lags is impossible for $N\ge 3$. We also prove that OFDM globally minimizes the partial expected integrated sidelobe level (EISL), defined as the sum of the ESLs over a selected subset of positive lags, for every such prefix. This also resolves the full EISL conjecture when $r=N-1$.

Abstract: We present Schur-Neural KF (SN-KF), a learning-based correction to the extended Kalman filter (EKF) that preserves the probabilistic conditioning interpretation of the EKF. The method perturbs the predictive state-measurement cross-covariance and the Cholesky factor of the measurement noise covariance so that the resulting joint predictive covariance is always positive semidefinite. The positive semidefiniteness is ensured by a Schur complement-based parametrization. We instantiate the parametrization with a recurrent neural architecture whose matrix outputs are modulated by amplitude gates. We prove that incorporating a measurement does not increase the filter's state uncertainty, and show that no measurement can induce an arbitrarily large state correction relative to its statistical surprise. We also present a perturbative analysis suggesting SN-KF's structural strength in the data-scarce regime. We provide two numerical experiments to illustrate the practical benefits of SN-KF. In a two-radar experiment, enforcing Schur-consistency provides a much broader failure-free hyperparameter region and reduces RMSE for small training subsets, consistent with our theoretical analysis in the data-scarce regime. In the unicycle experiment, SN-KF achieves the best precision, recall, false alarm rate, and gated RMSE under innovation-based sensor-fault rejection.

Abstract: Finite-aperture near-field sensing leads to a super-resolution geometry fundamentally different from the translation-invariant Fourier setting. In the Fresnel regime, wavefront curvature introduces a range-dependent quadratic aperture phase, so distinguishability is governed by incomplete quadratic exponential sums of the form \( \sum_{n=0}^{N_r-1} a_n e^{i(ω_1 n+ω_2 n^2)} \), rather than by angular separation alone. We develop a deterministic recovery theory for sparse measures with ranges on a finite grid and continuous angles, and introduce a support-uniform quadratic-phase aperture criterion replacing classical minimum separation. Under this criterion, total-variation minimization exactly recovers every sparse measure in the admissible support class, uniformly over all nonzero complex amplitudes. The proof develops nonasymptotic support-uniform bounds for finite quadratic sums and combines them with a gauged Hermite dual certificate controlling interpolation, local curvature, and off-support leakage. We further construct a finite-harmonic Bessel-Vandermonde lift with explicit truncation error. In the far-field limit, the quadratic phase disappears and the theory reduces to Fourier-type angular super-resolution.