Pilotless timing recovery for baseband multicarrier modulation

Sampling Frequency Error Estimators for PRIME v1.4 systems

“…For the sake of simplicity, SN R k = SN R. As seen, the proposed estimator attains the CRB in almost the whole SNR range. On the contrary, while the estimator in [9] is also efficient for ∆n = 1 ppm (curves are indistinguishable), for ∆n = 100 ppm the proposed one outperforms it at a reduced computational complexity.…”

“…2 depicts the variance of (8) computed by means of simulations for ∆n = 1 ppm and ∆n = 100 ppm, the variance in (9), referred to as theoretical, and the CRB. The simulated variance of the classical estimator in [9] is also depicted for comparison. For the sake of simplicity, SN R k = SN R. As seen, the proposed estimator attains the CRB in almost the whole SNR range.…”

Timing error estimation for baseband multicarrier modulation

“…A general closed form for the CRLB for any constellation size is not achievable. In this case, an MCRLB can be resorted, as stated in [11], whose expression is…”

“…In [11], an estimator based on a weighted sum of the estimations provided by each subchannel individually is proposed, where the weights are calculated to minimize the mean square error (MSE) of the estimation. ‡ The resultant expression iŝ…”

“…In the case of xDSL applications, no carrier frequency exists and hence, exclusive and more accurate and efficient methods for timing error estimation can be considered. Among the scarce work published on this specific matter, Reference [11] is worth pointing out, where a decision-directed timing error estimator is proposed based on a linear combination of individual estimations obtained from each DMT subchannel. In this study, the modified Cramer-Rao lower bound (CRLB) for the problem under study is outlined and three estimators are considered: the estimator proposed in [11], the decision-directed maximum likelihood (ML) estimator and a new estimator consistent on a modification of the ML estimator.…”