This paper investigates the waveform design problem of wideband cognitive radar for the detection of extended targets in which the knowledge of target impulse response and interference is imprecise. We resort to a maximin approach to design the waveform that is robust to the model uncertainties, i.e., we optimize the waveform to maximize the worst-case signal to interference plus noise ratio (SINR) over the uncertainty region. We show that the maximin waveform design problem can be formulated into a convex optimization problem. Results indicating the robustness of the proposed method are provided via numerical simulations.

In this study, parameter identifiability in array shape self‐calibration in colocated multiple‐input multiple‐output radar is addressed under a deterministic framework. In contrast to the random model used in the previous analysis, some distinct identifiability conditions are established through deriving and then analysing the Cramér–Rao bound on self‐calibration accuracy of antenna positions using far‐field targets whose directions of arrival and scattering coefficients are initially unknown. It is proved that at least three non‐collinear targets are needed to precisely self‐calibrate the positions of antennas of arbitrary geometry when there exist a position reference and a direction reference . The sole exception is an actually linear array for which self‐calibration is impossible.

We consider the problem of angle-robust joint transmit waveform and receive filter design for colocated multiple-input multiple-output (MIMO) radar, in the presence of signal-dependent interferences. The design problem is cast as a max-min optimization problem to maximize the worst-case output signal-to-interference-plus-noise-ratio (SINR) with respect to the unknown angle of the target of interest. Based on rank-one relaxation and semi-definite programming (SDP) representation of a nonnegative trigonometric polynomial, a cyclic optimization algorithm is proposed to tackle this problem. The effectiveness of the proposed method is illustrated via numerical examples.

The statistical angular resolution limit (RL) of two closely-spaced point sources in array processing is analyzed based on the framework of hypothesis test. For the first time, the general case where neither the source signals nor the parameters of interest are known under both the null hypothesis and the alternative is considered. Using the theory of misspecified model, the asymptotic distribution of the twice log-generalized-likelihood-ratio statistic under the alternative hypothesis is derived. It is shown to be non-central chi-squared distributed with degrees of freedom equal to the difference in dimensionality of the parameters under both hypotheses, and non-centrality parameter closely related to the Kullback-Leibler divergence of the probability density functions under both hypotheses. The information-theoretic-criteria-based model order selection rules are adopted and a novel detection-based RL is derived. The Cramér-Rao bound (CRB)-based RL is also derived for comparison. It is observed that the detection-based RL and the CRB-based RL are fundamentally different in such general case. Numerical simulations verify the theoretical results.

In array shape self-calibration where the sensor position errors and source locations are both unknown, the identifiability of the unknowns is a fundamental problem. Previously, using an approximate hybrid Cramér-Rao bound (HCRB), it was found that under the assumption of small random errors, a nominally linear array is impossible to self-calibrate, but a nominally non-linear array is possible to self-calibrate with three noncollinear far-field sources. In this letter, both small and large random errors are considered, thus the crucial small-error approximation has to be dropped. An accurate HCRB is then derived using fully the prior information about the errors. The accurate HCRB proves that if it is tight, a perturbed nominally linear array is possible to self-calibrate. The larger the sensor position errors, the easier the self-calibration. This is important because of the wide application of linear array. Moreover, two noncollinear far-field sources are sufficient to self-calibrate an array of arbitrary nominal shape.

In this paper, we consider the statistical angular resolution limit (ARL) on resolving two closely-spaced point sources in array processing based on the framework of hypothesis testing. A more general formulation of the linearized hypothesis test is proposed and a new analytical expression of the ARL is derived. The result is more general and its superiority over previous work is verified via numerical simulations. For the first time, we also investigate the case of two identical sources where a second-order approximation is necessary. Numerical simulations show that the theoretical result agrees with the Cramér-Rao bound (CRB) criterion-based ARL with regard to the relation between the resolution limit and the signal-to-noise-ratio (SNR).

In this letter, we analyze the convergence rate of loaded sample matrix inversion (LSMI) algorithm in amplitude heterogeneous clutter environment. The probability density function of output signal to interference and noise ratio loss (SINR Loss) is derived. Then we give an approximate expression of average SINR loss. Compared with the case where samples used for estimation of covariance matrix of cell under test (CUT) are independent and identically distributed (i.i.d.) with the snapshot of CUT, if the clutter to noise ratio (CNR) of the training samples is larger than that of CUT, the convergence rate of LSMI is faster and output SINR is higher; conversely, the convergence rate of LSMI is slower and SINR is lower. Simulation validates the theoretical analysis.

Based on Stein's lemma, we use relative entropy as a measure of error exponent to study detection performance of Neyman Pearson (NP) detectors for both multiple-input multiple-output (MIMO) radar and phased array radar. In high signal-to-noise ratio (SNR) region, we introduce the concept of diversity order to get insights of results. In low SNR region, we give instructive approximations for analytical results of relative entropy. Finally, we use relative entropy measure to study the problem of choosing the number of transmitters and receivers for MIMO radar.

A novel noise subspace based method is applied to the minimum localization system using time-of-arrival (TOA) measurements from three base stations (BS). Since the distance measurement between the mobile station (MS) and the BS bears analogy to the multidimensional similarity (MDS) between their coordinates, we express the MS coordinate as the linear combination of the BSs' coordinates, where the weight vector lies in the noise subspace of the MDS matrix. It is proved that this weight vector is the area coordinate of the MS when the triangle formed by the three BSs serves as the reference frame. Because the dimension knowledge of the localization problem is utilized to estimate the noise subspace and to mitigate the errors in TOA measurements, the proposed method is superior to the ordinary linear localization method in most of the enhanced quadrants of the area coordinates system.

The traditional CFAR processors are based on the sliding-window concept, which have substantial performance degradation under nonhomogeneity. Owing to temporal processing and the exploitation of the local homogeneity of the map cell, the clutter-map procedure acquires enhanced robustness with little CFAR losses. In this paper, a Gaussian biparametric clutter-map constant false alarm rate (GBCM-CFAR) processor is proposed which merges the clutter-map technique and noncoherent integration together. It can approximately achieve CFAR independent of the original clutter distribution. The performance in the presence of fast point targets is assessed, in the examples of Weibull and lognormal clutter, in order to elicit the effect of the system parameters. Its performance is close to that of the optimum Neyman-Pearson detector with little CFAR losses in homogeneous environments. It is also suitable to deal with the nonhomogeneous situation.