Simultaneous Symbol Timing and Frame Synchronization for Phase Shift Keying

We develop an estimator of time offset (or time-of-arrival) of a transmitted communications signal that contains both pilot symbols, known to the receiver, and data symbols, unknown to the receiver. We focus on signalling constellations that have symbols lying on the complex unit circle, such as M-ary phase shift keying (M-PSK). We describe an algorithm for computing the estimator that requires O(L log L) operations in the worst case, where L is the number of transmitted symbols. Our estimator integrates information from the pilot symbols more effectively than popular estimators from the literature that usually split estimation into two subproblems called symbol timing and frame synchronisation. Our estimator combines these subproblems into a single operation, that of estimating time offset. We hypothesise that our estimator will be statistically more accurate. Monte-Carlo simulations support this hypothesis.

[1]  Yik-Chung Wu,et al.  Unified analysis of a class of blind feedforward symbol timing estimators employing second-order statistics , 2006, IEEE Transactions on Wireless Communications.

[2]  Moisés Simões Piedade,et al.  A new ML-based data-aided feedforward symbol synchronizer for burst-mode transmission , 2000, 2000 IEEE International Symposium on Circuits and Systems. Emerging Technologies for the 21st Century. Proceedings (IEEE Cat No.00CH36353).

[3]  William F. Egan,et al.  Phase-Lock Basics , 1998 .

[4]  Heinrich Meyr,et al.  Digital filter and square timing recovery , 1988, IEEE Trans. Commun..

[5]  Erdal Panayirci,et al.  A new approach for evaluating the performance of a symbol timing recovery system employing a general type of nonlinearity , 1996, IEEE Trans. Commun..

[6]  Andrew J. Viterbi,et al.  Nonlinear estimation of PSK-modulated carrier phase with application to burst digital transmission , 1983, IEEE Trans. Inf. Theory.

[7]  H. V. Trees.  Detection, Estimation, And Modulation Theory , 2001 .

[8]  Luc Vandendorpe,et al.  A Theoretical Framework for Iterative Synchronization Based on the Sum–Product and the Expectation-Maximization Algorithms , 2007, IEEE Transactions on Signal Processing.

[9]  P. Vaidyanathan.  Multirate Systems And Filter Banks , 1992 .

[10]  Kenneth M. Mackenthun,et al.  A fast algorithm for multiple-symbol differential detection of MPSK , 1994, IEEE Trans. Commun..

[11]  L. Mordell,et al.  Diophantine equations , 1969 .

[12]  I. Vaughan L. Clarkson,et al.  Carrier Phase and Amplitude Estimation for Phase Shift Keying Using Pilots and Data , 2013, IEEE Transactions on Signal Processing.

[13]  Wim Sweldens.  Fast block noncoherent decoding , 2001, IEEE Communications Letters.

[14]  Thomas H. Cormen,et al.  Introduction to algorithms [2nd ed.] , 2001 .

[15]  I. Vaughan L. Clarkson,et al.  Noncoherent least squares estimators of carrier phase and amplitude , 2013, 2013 IEEE International Conference on Acoustics, Speech and Signal Processing.

[16]  James V. Krogmeier,et al.  Real time implementation of a symbol timing recovery algorithm for a narrowband wireless modem , 1998, Proceedings of the 1998 IEEE International Conference on Acoustics, Speech and Signal Processing, ICASSP '98 (Cat. No.98CH36181).

[17]  D. Anderson,et al.  Algorithms for minimization without derivatives , 1974 .

[18]  Erchin Serpedin,et al.  An alternative blind feedforward symbol timing estimator using two samples per symbol , 2003, IEEE Trans. Commun..

[19]  Heinrich Meyr,et al.  Digital communication receivers - synchronization, channel estimation, and signal processing , 1997, Wiley series in telecommunications and signal processing.

[20]  Umberto Mengali,et al.  Feedforward ML-based timing estimation with PSK signals , 1997, IEEE Communications Letters.

[21]  J. Massey,et al.  Optimum Frame Synchronization , 1972, IEEE Trans. Commun..

[22]  Luc Vandendorpe,et al.  On Maximum-Likelihood Timing Synchronization , 2007, IEEE Transactions on Communications.

[23]  L.R. Rabiner,et al.  Interpolation and decimation of digital signals—A tutorial review , 1981, Proceedings of the IEEE.

[24]  Patrick Robertson.  Optimal Frame Synchronization for Continuous and Packet Data Transmission , 1995 .

[25]  Luc Vandendorpe,et al.  Code-Aided Turbo Synchronization , 2007, Proceedings of the IEEE.

[26]  P. Nielsen.  Some Optimum and Suboptimum Frame Synchronizers for Binary Data in Gaussian Noise , 1973, IEEE Trans. Commun..

[27]  Heidi Steendam,et al.  Low-SNR limit of the Cramer-Rao bound for estimating the time delay of a PSK, QAM, or PAM waveform , 2001, IEEE Communications Letters.

[28]  Seung Joon Lee.  A new non-data-aided feedforward symbol timing estimator using two samples per symbol , 2002, IEEE Commun. Lett..

[29]  William H. Press,et al.  Numerical recipes in C , 2002 .

[30]  Umberto Mengali,et al.  The modified Cramer-Rao bound and its application to synchronization problems , 1994, IEEE Trans. Commun..

[31]  Ronald L. Rivest,et al.  Introduction to Algorithms , 1990 .