Ambiguity function and Cramer-Rao bounds for standard and new modified Costas signals

Nadjah Touati (1) , Charles Tatkeu (1) , Thierry Chonavel (2, 3) , Yassin El Hillali (4, 5) , Atika Rivenq (4, 5)

1 IFSTTAR/COSYS/LEOST - Laboratoire Électronique Ondes et Signaux pour les Transports
2 SC - Département Signal et Communications
3 Lab-STICC_TB_CID_TOMS
4 IEMN-DOAE - Institut d’Électronique, de Microélectronique et de Nanotechnologie - Département Opto-Acousto-Électronique - UMR 8520
5 COMNUM - IEMN - COMmunications NUMériques - IEMN

The Cramer-Rao bound (CRB) gives a lower variance bound that an estimator can achieve. Presented is a mathematical approach to estimate it for specific radar signals, namely Costas signals and their modified versions. The modified versions design consists in widening Costas frequency hops and replacing rectangular pulses with other waveforms (namely linear frequency modulated pulses, phase codes and other Costas codes). The calculation is based on approximations of the ambiguity function (AF) around the mainlobe. The CRBs are then derived based on relationships between the AF and these bounds.

Mots clés: RADAR SIGNAL PROCESSING; FUNCTION APPROXIMATION; SPREAD SPECTRUM RADAR; ESTIMATION THEORY

Mots clés: EMETTEUR; RADAR; ONDE; MESURES DOPPLER

Domaines: Traitement du signal et de l'image [eess.SP]; Réseaux et télécommunications [cs.NI]; Intelligence artificielle [cs.AI]; Electronique

Nadjah Touati, Charles Tatkeu, Thierry Chonavel, Yassin El Hillali, Atika Rivenq. Ambiguity function and Cramer-Rao bounds for standard and new modified Costas signals. Electronics Letters, 2015, 51, p1497-1499. ⟨10.1049/el.2015.1092⟩. ⟨hal-01213613⟩