Title :
Evaluation of Cramer-Rao Bounds for Phase Estimation of Coded Linearly Modulated Signals
Author :
Nan Wu ; Hua Wang ; Hongjie Zhao ; Huafeng Liu ; Jingming Kuang
Author_Institution :
Sch. of Inf. & Electron., Beijing Inst. of Technol., Beijing, China
Abstract :
The evaluation of Cramer-Rao Bounds (CRBs) for phase estimation of coded linearly modulated signals are difficult due to the intractable expectations of the likelihood function with respect to coded symbols. In this paper, we propose two methods towards this end. The first one is a semi-analytical method for coded QPSK signals. Based on Gaussian approximation of extrinsic information, the expression of CRB is derived in terms of signal-to-noise ratio (SNR) and the mean of extrinsic information in closed form. For high-order modulations, e.g., 16QAM signal, we propose a numerical method based on multidimensional Gauss-Hermite Quadrature (GHQ). It is shown that, without suffering from the linearization error, the results of numerical method by GHQ outperform the semi-analytical results, and the former are consistent with that of the Monte Carlo simulations for systems with different codes and numbers of decoding iterations.
Keywords :
Monte Carlo methods; approximation theory; decoding; iterative methods; modulation coding; phase estimation; quadrature amplitude modulation; quadrature phase shift keying; 16QAM signal; Cramer-Rao bounds; Gaussian approximation; Monte Carlo simulations; SNR; coded QPSK signals; coded linearly modulated signals; coded symbols; decoding iterations; high-order modulations; intractable expectations; likelihood function; linearization error; multidimensional Gauss-Hermite quadrature; phase estimation; semianalytical method; signal-to-noise ratio; Cramer-Rao bounds; Iterative decoding; Monte Carlo methods; Phase estimation; Phase shift keying;
Conference_Titel :
Vehicular Technology Conference (VTC Spring), 2014 IEEE 79th
Conference_Location :
Seoul
DOI :
10.1109/VTCSpring.2014.7022915
