In around the corner radar, particle filter tracking can help to improve the estimation accuracy of a Non-Line of Sight target position. However, in case of using one single receiving antenna, the measurement model only contains multipath delay information. Due to the lack of information in the model, particles corresponding to ambiguous positions can be assigned high weight values. This can leads the particle cloud to diverge from the actual target trajectory and requires several time steps to converge on it again. In this work, our proposed solution consists in exploiting additional Direction-of Arrival information provided by an array of receiving antennas in the particle filter framework. By simulation and experimentation, we will show that the proposed solution allows to solve the aforementioned problem, and thus achieves better localization results compared to single antenna-based tracking as well as non-tracking localization algorithm.

In the state-of-the-art, the Probability of False Alarm (PFA)- threshold relationship for the popular Matched Filter (MF) is often derived assuming that unknown non-linear parameters lie on a grid. However, these parameters vary continuously in practice. This is known as the off-grid case. In this article, an asymptotic PFA-threshold relationship for the popular Matched Filter is derived in the off-grid case under complex white Gaussian noise hypothesis using expected Euler characteristics. This asymptotic relationship fits very well with corresponding Monte-Carlo trials in the moderate to low PFAregime.

The electromagnetic congestion due to the continuous growth of spectral demand has been skyrocketing for the past years. Joint radar-communication systems are, thus, attracting attention as they can alleviate spectrum occupancy by using the same bandwidth to perform both applications. In this context, a cooperative radar-communication system, which is a specific category that uses communication codes to both transmit information and perform radar missions, can be considered. Continuous phase-modulated (CPM) codes are considered in this article in order to generate high-resolution radar images from airborne radar. Since mitigating the sidelobe level energy is essential for good image quality, we resort here to optimized mismatched filters (MMFs). A fast algorithm is proposed to minimize the computational time of these filters. Simulated data are generated, as well as resynthesized synthetic aperture radar (SAR) images, and reconstructed from real chirp-based data using CPM codes and MMFs. Their performance is evaluated using different comparison tools and shows that the use of mismatched filtering and different messages embedded in the phase of each transmitted code provides enhanced image quality.

Off-grid targets are known to induce a mismatch that dramatically impacts the detection probability of the popular Normalized Matched Filter. To overcome this problem, the unknown target parameter is usually estimated through a Maximum Likelihood strategy resulting in a GLRT detection scheme. While the test statistic for the null hypothesis is well known in the on-grid case, the off-grid scenario is more involved and, to the best of our knowledge, no such theoretical result is available. This paper fills this gap by proposing such an expression under circular compound Gaussian noise with known covariance matrix thanks to a geometrical approach.

In classical detection framework, the parameter space is usually discretized, so that in reality received parameter dependent signals are never perfectly aligned with the signal model under test: it leads to the off-grid signal mismatch. In a Gaussian adaptive context (i.e. the noise covariance is unknown), Kelly GLRT and AMF detectors are well established techniques that can suffer severe performance degradation in presence of this kind of mismatch. We propose here to use adaptive subspace detectors to solve this issue, a suitable subspace (that coincides with the Discrete Prolate Spheroidal Sequences basis when the signal model is that of sinusoids in noise) is proposed that offers robust performance. The interest lies in the fact that such detectors are really easy to implement and we are able to derive their analytic performance.

A new lower bound is proposed in this article. Like Levenshtein bound, it relates to the maximum correlation value (autocorrelation and cross-correlation) a set of sequences can achieve. The novelty introduced here is that each sequence is associated with a mismatched filter. The proposed bound is inspired from Levenshtein's, holds for any set of unimodular sequences and can be applied in both aperiodic and periodic cases. It appears that the obtained expression does not deviate a lot from the (matched) Levenshtein, which indicates that the use of a mismatched filter will not guarantee much better sidelobe performance, as the number fo sequences is significant, contrary to the popular belief.

In this letter, we consider the robustness of the mismatched filter in presence of off-grid target. Since for an off-grid target, the received sampled signal differs from the on-grid signal, the mismatched filter as optimized in the literature is not optimal anymore, and in particular may present a deteriorated sidelobe level. We propose here a general optimization program enabling to get an optimal mismatched filter-with respect to the integrated sidelobe level (ISL)-within the resolution cell. We detail then the resulting solution in two particular radar cases, namely a Doppler steering vector and a linear chirp signal. In both cases, the proposed solution involves the discrete prolate spheroidal sequences. Simulation results show that this solution indeed provides the best ISL in the resolution cell.

This paper deals with lower bounds on aperiodic correlation of sequences. It intends to solve two open questions. The first one is on the validity of the Levenshtein bound for a set of sequences other than binary sequences or those over the roots of unity. Although this result could be a priori extended to polyphase sequences, a formal demonstration is presented here, proving that it does actually hold for these sequences. The second open question is on the possibility to find a bound tighter than Welch's, in the case of a set consisting of two sequences M = 2. By including the specific structure of correlation sequences, a tighter lower bound is introduced for this case. Besides, this method also provides in the cases M = 3 and M = 4 a tighter bound than the up-to-now tightest bound provided by Liu et al.

This article examines the problem of tracking NLOS targets by exploiting multipath information measured by an urban around-the-corner radar. Due to the non linearity relationship between target position and multipath delays and the complexity of the multipath measurement model, a particle filter is considered. It samples separately the target state (po-sition and velocities) and the multipath amplitudes thanks to an appropriate importance density function. GLRT particle filter, a special case of the proposed particle filter, is shown to provide the most efficient localization results. Simulations demonstrate the ability of the particle filter to correctly estimate the target location and the improvement of localization performance compared to a multipath localization algorithm without tracking.

The irreducible binary cyclic codes of even dimension, introduced by Delsarte and Goethals in 1970, constitute a parametric class with three parameters. We show that these codes and their duals are either proper or not good for error detection.