The Cramer-Rao bound for phase estimation from coded linearly modulated signals
- 21 May 2003
- journal article
- Published by Institute of Electrical and Electronics Engineers (IEEE) in IEEE Communications Letters
- Vol. 7 (5) , 207-209
- https://doi.org/10.1109/lcomm.2003.812168
Abstract
In this letter, we express the Cramer-Rao bound (CRB) for carrier phase estimation from a noisy linearly modulated signal with encoded data symbols, in terms of the marginal a posteriori probabilities (APPs) of the coded symbols. For a wide range of classical codes (block codes, convolutional codes, and trellis-coded modulation), these marginal APPs can be computed efficiently by means of the Bahl-Cocke-Jelinke-Raviv (BCJR) algorithm, whereas for codes that involve interleaving (turbo codes and bit interleaved coded modulation), iterated application of the BCJR algorithm is required. Our numerical results show that when the BER of the coded system is less than about 10/sup -3/, the resulting CRB is essentially the same as when transmitting a training sequence.Keywords
This publication has 9 references indexed in Scilit:
- The true Cramer-Rao bound for phase-independent carrier frequency estimation from a PSK signalPublished by Institute of Electrical and Electronics Engineers (IEEE) ,2004
- The impact of the observation model on the Cramer-Rao bound for carrier phase and frequency synchronizationPublished by Institute of Electrical and Electronics Engineers (IEEE) ,2004
- Cramer-Rao lower bounds for QAM phase and frequency estimationIEEE Transactions on Communications, 2001
- The geometry of turbo-decoding dynamicsIEEE Transactions on Information Theory, 2000
- On the true and the modified Cramer-Rao bounds for the estimation of a scalar parameter in the presence of nuisance parametersIEEE Transactions on Communications, 1998
- Near optimum error correcting coding and decoding: turbo-codesIEEE Transactions on Communications, 1996
- Phase and frequency estimation for PSK packets: bounds and algorithmsIEEE Transactions on Communications, 1996
- The modified Cramer-Rao bound and its application to synchronization problemsIEEE Transactions on Communications, 1994
- Optimal decoding of linear codes for minimizing symbol error rate (Corresp.)IEEE Transactions on Information Theory, 1974