Cramer-Rao Lower Bounds of DOA Estimates from Square QAM-Modulated Signals

• Published in: IEEE transactions on communications 2011-06, Vol.59 (6), p.1675-1685
• Main Authors: Bellili, F, Hassen, S B, Affes, S, Stephenne, A
• Format: Article
• Language: English
• Subjects: Antennas; Applied sciences; Arrays; Detection, estimation, filtering, equalization, prediction; Direction of arrival estimation; DOA estimation; Estimates; Estimation; Exact sciences and technology; Exact solutions; Gaussian; Information, signal and communications theory; Lower bounds; Mathematical analysis; Modulation; Modulation, demodulation; Offsets; QAM signals; Quadrature amplitude modulation; Quadratures; Radiocommunications; Signal and communications theory; Signal to noise ratio; Signal, noise; stochastic Cramer-Rao lower bound (CRLB); Stochastic processes; Studies; Systems, networks and services of telecommunications; Telecommunications; Telecommunications and information theory; Transmission and modulation (techniques and equipments); UCA; ULA
• ISSN: 0090-6778; 1558-0857
• DOI: 10.1109/TCOMM.2011.050211.100036A

In this paper, we derive for the first time analytical expressions for the inphase/quadrature (I/Q) non-data-aided (NDA) Cramér-Rao lower bounds (I/Q NDA CRLBs) of the direction of arrival (DOA) estimates from square quadrature amplitude (QAM)-modulated signals corrupted by additive white circular complex Gaussian noise (AWCCGN) with any antenna configuration. Yet the main contribution embodied by this paper consists in deriving for the first time analytical expressions for the NDA Fisher information matrix (FIM) and then for the stochastic CRLB of the NDA DOA estimates in the case of square QAM-modulated signals. It will be shown that in the presence of any unknown phase offset (i.e., non-coherent estimation), the ultimate achievable performance on the NDA DOA estimates holds almost the same irrespectively of the modulation order. However, the NDA CRLBs obtained in the absence of the phase offset (i.e., coherent estimation) vary, in the high SNR region, from one modulation order to another.