Title :
Closed-form Cramér-Rao lower bounds for CFO and phase estimation from turbo-coded square-QAM-modulated signals
Author :
Bellili, Faouzi ; Methenni, Achref ; Affes, Sofiene
Author_Institution :
INRS-EMT, Montreal, QC, Canada
Abstract :
We consider the problem of joint phase and carrier frequency offset (CFO) estimation from turbo-coded square-QAM modulated signals. We derive for the first time the closed-form expressions for the exact Cramér-Rao lower bounds (CRLBs) of this estimation problem. In particular, we introduce a new recursive process that enables the construction of arbitrary Gray-coded square-QAM constellations. Some hidden properties of such constellations will be revealed and carefully handled in order to decompose the likelihood function (LF) into the sum of two analogous terms. This decomposition makes it possible to carry out analytically all the statistical expectations involved in the Fisher information matrix (FIM). The new analytical CRLB expressions corroborate the previous attempts to evaluate the underlying perfromance bounds empirically. In the low-to-medium signal-to-noise ratio (SNR) region, the CRLB for code-aided (CA) estimation lies between the bounds for completely blind [non-data-aided (NDA)] and completely data-aided (DA) estimation schemes, thereby highlighting the coding gain potential in CFO and phase estimation. Most interestingly, in contrast to the NDA case, the CA CRLBs start to decay rapidly and reach the DA bounds at relatively small SNR thresholds. The derived bounds are also valid for LDPC-coded systems and they can be evaluated in the same way when the latter are decoded using the turbo principal.
Keywords :
Gray codes; frequency estimation; matrix decomposition; maximum likelihood decoding; modulation coding; parity check codes; phase coding; phase estimation; quadrature amplitude modulation; recursive estimation; turbo codes; CA estimation; CFO estimation; CRLB expression; DA estimation; FIM decoding; Fisher information matrix; LDPC coded system; LF decomposition; arbitrary Gray-coded square QAM constellation; carrier frequency offset estimation; closed-form Cramer-Rao lower bound; code-aided estimation; data-aided estimation; likelihood function; low-to-medium SNR region; phase estimation; recursive process; signal-to-noise ratio; statistical expectation; turbo-coded square QAM modulated signal; Estimation; Phase shift keying; Quadrature amplitude modulation; Signal to noise ratio; Synchronization; Turbo codes; Wireless communication; Carrier phase shift; Cramér-Rao lower bound (CRLB); Gray mapping; carrier frequency offset (CFO); code-aided (CA); extrinsic information; square QAMs; turbo/LDPC codes;
Conference_Titel :
Global Communications Conference (GLOBECOM), 2014 IEEE
Conference_Location :
Austin, TX
DOI :
10.1109/GLOCOM.2014.7037447