A Root-MUSIC-Like Direction Finding Method for Cyclostationary Signals
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A Root-MUSIC-Like Direction Finding Method for Cyclostationary Signals Pascal Charge´ LESIA, DGEI, INSA Toulouse, 135 Avenue de Rangueil, 31077 Toulouse Cedex 4, France Email: [email protected]
Yide Wang ´ IREENA/SETRA, Ecole Polytechnique de l’Universit´e de Nantes, La Chantrerie, 44306 Nantes, France Email: [email protected] Received 4 December 2003; Revised 2 June 2004 We propose a new root-MUSIC-like direction finding algorithm that exploits cyclostationarity in order to improve the directionof-arrival estimation. The proposed cyclic method is signal selective, it allows to increase the resolution power and the noise robustness significantly, and it is also able to handle more sources than the number of sensors. Computer simulations are used to show the performance of the algorithm. Keywords and phrases: array processing, direction finding, MUSIC, cyclostationary signals.
1.
INTRODUCTION
The aim of this paper is the estimation of the direction-ofarrival (DOA) of impinging signals in the telecommunications systems area, where almost all signals exhibit the cyclostationarity property [1]. The cyclostationarity has been first introduced into array processing by Gardner [2]. We can find in the literature several algorithms (see [1]) that exploit cyclostationarity to improve the performances of the conventional methods. Instead of using the correlation matrix as in the conventional methods, these algorithms require the estimation of the cyclic correlation matrix that reflects the cyclostationarity of incoming signals, assuming they have baud rates and/or are carrier modulated signals as they would be in radar and radio communication applications. Recently, an extended cyclic MUSIC algorithm has been proposed in [3] that provides a rather good estimation performance. In [4] an extended root-MUSIC (extension of the rootMUSIC [5]) algorithm has been proposed in the noncircular source case. In this paper, we propose a new extended cyclic direction finding method that allows to select desired signals and to ignore interferences, by exploiting the cyclostationarity property of the signals of interest (SOI). The proposed method is inspired from the extended root-MUSIC method [4], and then is restricted to linear uniformly spaced arrays. But it has the distinct advantage over [3] in that it does not require a search over parameter space. Instead, our algorithm here
requires calculation of the roots of a polynomial, which is a simple process and has low computation cost. 2.
DATA MODEL
In this paper, we consider a uniform linear array of L antennas. Suppose there are K electromagnetic waves impinging on the array from angular directions θk , k = 1, . . . , K. The incident waves are assumed to be plane waves, as generated from far-field point sources. Furthermore, the signals are assumed to be narrowband. In our study, we assume that Kα sources emit cyclostationary signals with cycle frequency α (with Kα ≤ K). In the following, we consider that s(t) contains only the Kα signals that exhibit cy
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