A novel approach to robust radar detection of range-spread targets

This paper proposes a novel approach to robust radar detection of range-spread targets embedded in Gaussian noise with unknown covariance matrix. The idea is to model the useful target echo in each range cell as the sum of a coherent signal plus a random component that makes the signal-plus-noise hypothesis more plausible in presence of mismatches. Moreover, an unknown power of the random components, to be estimated from the observables, is inserted to optimize the performance when the mismatch is absent. The generalized likelihood ratio test (GLRT) for the problem at hand is considered. In addition, a new parametric detector that encompasses the GLRT as a special case is also introduced and assessed. The performance assessment shows the effectiveness of the idea also in comparison to natural competitors.Comment: 28 pages, 8 figure

Design of Customized Adaptive Radar Detectors in the CFAR Feature Plane

The paper addresses the design of adaptive radar detectors with desired behavior, in Gaussian disturbance with unknown statistics. Specifically, based on detection probability specifications for chosen signal-to-noise ratios and steering vector mismatch levels, a methodology for the design of customized constant false alarm rate (CFAR) detectors is devised in a suitable feature plane obtained from two maximal invariant statistics. To overcome the analytical and numerical intractability of the resulting optimization problem, a novel general reduced-complexity algorithm is developed, which is shown to be effective in providing a feasible solution (i.e., fulfilling a constraint on the probability of false alarm) while controlling the behavior under both matched and mismatched conditions, so enabling the design of fully customized adaptive CFAR detectors

Design of Robust Radar Detectors Through Random Perturbation of the Target Signature

The paper addresses the problem of designing radar detectors more robust than Kelly's detector to possible mismatches of the assumed target signature, but with no performance degradation under matched conditions. The idea is to model the received signal under the signal-plus-noise hypothesis by adding a random component, parameterized via a design covariance matrix, that makes the hypothesis more plausible in presence of mismatches. Moreover, an unknown power of such component, to be estimated from the observables, can lead to no performance loss, under matched conditions. Derivation of the (one-step) GLRT is provided for two choices of the design matrix, obtaining detectors with different complexity and behavior. A third parametric detector is also obtained by an ad-hoc generalization of one of such GLRTs. The analysis shows that the proposed approach can cover a range of different robustness levels that is not achievable by state-of-the-art with the same performance of Kelly's detector under matched conditions

Pozicione igre na grafovima

\section*{Abstract} We study Maker-Breaker games played on the edges of the complete graph on $n$ vertices, $K_n$, whose family of winning sets \cF consists of all edge sets of subgraphs $G\subseteq K_n$ which possess a predetermined monotone increasing property. Two players, Maker and Breaker, take turns in claiming $a$, respectively $b$, unclaimed edges per move. We are interested in finding the threshold bias b_{\cF}(a) for all values of $a$, so that for every $b$, b\leq b_{\cF}(a), Maker wins the game and for all values of $b$, such that b>b_{\cF}(a), Breaker wins the game. We are particularly interested in cases where both $a$ and $b$ can be greater than $1$. We focus on the \textit{Connectivity game}, where the winning sets are the edge sets of all spanning trees of $K_n$ and on the  \textit{Hamiltonicity game}, where the winning sets are the edge sets of all Hamilton cycles on $K_n$. Next, we consider biased $(1:b)$ Avoider-Enforcer games, also played on the edges of $K_n$. For every constant $k\geq 3$ we analyse the $k$-star game, where Avoider tries to avoid claiming $k$ edges incident to the same vertex. We analyse both versions of Avoider-Enforcer games, the strict and the monotone, and for each provide explicit winning strategies for both players. Consequentially, we establish bounds on the threshold biases f^{mon}_\cF, f^-_\cF and f^+_\cF, where \cF is the hypergraph of the game (the family of target sets). We also study the monotone version of $K_{2,2}$-game, where Avoider wants to avoid claiming all the edges of some graph isomorphic to $K_{2,2}$ in $K_n$.   Finally, we search for the fast winning strategies for Maker in Perfect matching game and Hamiltonicity game, again played on the edge set of $K_n$. Here, we look at the biased $(1:b)$ games, where Maker's bias is 1, and Breaker's bias is $b, b\ge 1$.\section*{Izvod} Prou\v{c}avamo takozvane Mejker-Brejker (Maker-Breaker) igre koje se igraju na granama kompletnog grafa sa $n$ \v{c}vorova, $K_n$, \v{c}ija familija pobedni\v{c}kih skupova \cF obuhvata sve skupove grana grafa $G\subseteq K_n$ koji imaju neku monotono rastu\'{c}u osobinu. Dva igra\v{c}a, \textit{Mejker} (\textit{Pravi\v{s}a}) i \textit{Brejker} (\textit{Kva\-ri\-\v{s}a}) se smenjuju u odabiru $a$, odnosno $b$, slobodnih grana po potezu. Interesuje nas da prona\dj emo grani\v{c}ni bias b_{\cF}(a) za sve vrednosti pa\-ra\-me\-tra $a$, tako da za svako $b$, b\le b_{\cF}(a), Mejker pobe\dj uje u igri, a za svako $b$, takvo da je b>b_{\cF}(a), Brejker pobe\dj uje. Posebno nas interesuju slu\v{c}ajevi u kojima oba parametra $a$ i $b$ mogu imati vrednost ve\'cu od 1. Na\v{s}a pa\v{z}nja je posve\'{c}ena igri povezanosti, gde su pobedni\v{c}ki skupovi  grane svih pokrivaju\'cih stabala grafa $K_n$, kao i igri Hamiltonove konture, gde su pobedni\v{c}ki skupovi grane svih Hamiltonovih kontura grafa $K_n$. Zatim posmatramo igre tipa Avojder-Enforser (Avoider-Enforcer), sa biasom $(1:b)$, koje se tako\dj e igraju na granama kompletnog grafa sa $n$ \v{c}vorova, $K_n$. Za svaku konstantu $k$, $k\ge 3$ analiziramo igru $k$-zvezde (zvezde sa $k$ krakova), u kojoj \textit{Avojder} poku\v{s}va da izbegne da ima $k$ svojih grana incidentnih sa istim \v{c}vorom. Posmatramo obe verzije ove igre, striktnu i monotonu, i za svaku dajemo eksplicitnu pobedni\v{c}ku strategiju za oba igra\v{c}a. Kao rezultat, dobijamo gornje i donje ograni\v{c}enje za grani\v{c}ne biase f^{mon}_\cF, f^-_\cF i f^+_\cF, gde \cF predstavlja hipergraf igre (familija ciljnih skupova). %$f^{mon}$, $f^-$ and $f^+$. Tako\dj e, posmatramo i monotonu verziju $K_{2,2}$-igre, gde Avojder \v{z}eli da izbegne da graf koji \v{c}ine njegove grane sadr\v{z}i graf izomorfan sa $K_{2,2}$. Kona\v{c}no, \v{z}elimo da prona\dj emo strategije za brzu pobedu Mejkera u igrama savr\v{s}enog me\v{c}inga i Hamiltonove konture, koje se tako\dj e igraju na granama kompletnog grafa $K_n$. Ovde posmatramo asimetri\v{c}ne igre gde je bias Mejkera 1, a bias Brejkera $b$, $b\ge 1$

Adaptive Radar Detection in Heterogeneous Clutter-dominated Environments

In this paper, we propose a new solution for the detection problem of a coherent target in heterogeneous environments. Specifically, we first assume that clutter returns from different range bins share the same covariance structure but different power levels. This model meets the experimental evidence related to non-Gaussian and non-homogeneous scenarios. Then, unlike existing solutions that are based upon estimate and plug methods, we propose an approximation of the generalized likelihood ratio test where the maximizers of the likelihoods are obtained through an alternating estimation procedure. Remarkably, we also prove that such estimation procedure leads to an architecture possessing the constant false alarm rate (CFAR) when a specific initialization is used. The performance analysis, carried out on simulated as well as measured data and in comparison with suitable well-known competitors, highlights that the proposed architecture can overcome the CFAR competitors and exhibits a limited loss with respect to the other non-CFAR detectors