Elsevier

Signal Processing

Volume 47, Issue 1, November 1995, Pages 41-54
Signal Processing

An investigation on number of signals whose directions-of-arrival are uniquely determinable with an electromagnetic vector sensor

https://doi.org/10.1016/0165-1684(95)00098-4Get rights and content

Abstract

We first study a theorem on the relationship among linear dependence of steering vectors, correlation among signals, and the number of signals whose DOAs are uniquely determinable, which was derived by Wax and Ziskind (1989) and Nehorai et al. (1991) for a class of scalar-sensor arrays. We then extend the theorem to include all scalar-sensor arrays, as well as vector-sensor arrays receiving polarized signals. We further generalize the first part of the theorem to include vector-sensor arrays receiving general signals (which can be polarized, partially polarized or unpolarized). Subsequently, we show that the DOAs of twouncorrelated signals can be uniquely determined with one electromagnetic vector sensor, regardless of the states of polarization. However, it may be impossible to determine uniquely the DOAs of twofully correlated signals. Finally, we establish a relationship between uniqueness in measurements and uniqueness in MUSIC estimates.

Zusammenfassung

Zunächst untersuchen wir ein Theorem zum Zusammenhang zwischen der linearen Abhängigkeit von Steeringvektoren, der Korrelation von Signalen und der Signalanzahl, deren Ankunftsrichtungen eindeutig bestimmbar sind; das Theorem wurde von Wax und Ziskind (1989) sowie Nehorai et al. (1991) für eine bestimmte Klasse von Skalarsensor-Feldern hergeleitet. Dann erweitern wir das Theorem so, daβ alle Skalarsensor-Arrays eingeschlossen werden sowie Vektorsensor-Felder, diepolarisierte Signale empfangen. Weiterhin verallgemeinern wir den ersten Teil des Theorems, um Vektorsensor-Arrays mit einzubeziehen, welcheallgemeine Signale empfangen (die polarisiert, teilweise polarisiert oder unpolarisiert sein können). Im Anschluβ daran zeigen wir, daβ die Einfallsrichtungen zweierunkorrelierter Signale eindeutig mit Hilfe eines elektromagnetischen Vektorsensors unabhängig vom Polarisationszustand bestimmt werden können. Es kann jedoch unmöglich sein, die Ankunftsrichtungen zweiervollständig korrelierter Signale eindeutig zu bestimmen. Schlieβlich stellen wir eine Beziehung zwischen Eindeutigkeit der Messung und Eindeutigkeit der MUSIC-Schätzung her.

Résumé

Nousétudions d'abord un théorème concernant la relation entre la dépendance linéaire de vecteurs de direction, la corrélation entre les signaux, et le nombre de signaux dont les DOA sont déterminables de manière unique, qui fut dérivépar Wax et Ziskind (1989) et Nehorai et al. (1991) pour une classe de réseaux de senseurs scalaires. Nousétendons ensuite le théorème, afin d'inclure tous les réseaux de senseurs scalaires, y compris les réseaux de senseurs scalaires recevant des signauxpolarisés. Nous généralisons encore la première partie du théorème pour inclure les réseaux de senseurs vectoriels recevant des signauxgénéraux (qui peuventeˆtre polarisés, partiellement polarisés ou non polarisés). En conséquence, nous démontrons que les DOA de deux signauxnon corrélés peuventeˆtre univoquement déterminées avec un senseur vectorielélectromagnétique, quels que soient lesétats de polarisation. Toutefois, il peuteˆtre impossible de déterminer univoquement les DOA de deux signauxtotalement corrélés. Finalement, nousétablissons une relation entre l'unicitédans les mesures et l'unicitédans les estimées MUSIC.

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