Performance Study of a Near Maximum Likelihood Code-Aided Timing Recovery Technique

Abstract

International audienceIn this paper, we propose a new code-aided (CA) timing recovery algorithm for various linear constant modulus constellations based on the Maximum Likelihood (ML) estimator. The first contribution is the derivation of a soft estimator expression of the transmitted symbol instead of its true or hard estimated value which is fed into the timing error detector (TED) equation. The proposed expression includes the Log-Likelihood Ratios (LLRs) obtained from a turbo decoder. Our results show that the proposed CA approach achieves almost as good results as the data-aided (DA) approach over a large interval of SNR values while achieving a higher spectral efficiency. We also derive the corresponding CA Cramer Rao Bounds (CRB) for various modulation orders. Contrarily to former work, we develop here the CRB analytical expression for different M-PSK modulation orders and validate them through comparison to empirical CRB obtained by Monte Carlo iterations. The proposed CA estimator realizes an important gain over the non data-aided approach (NDA) and achieves a smaller gap when compared to its relative CA CRB, especially at moderate SNR values where modern systems are constrained to work

Near MAP Dynamical Delay Estimator and Bayesian CRB for Coded QAM Signals

“…Then, in practice, hard estimatesâ k of the transmitted symbols are computed at the receiver and replace a k in (25); this is called the NDA mode. In a coded system, we can take advantage of the decoder soft output to provide smoother and more accurate estimate of a k as it was proposed in [7], [8] for the on-line timing loop. We can similarly replace a k by the soft symbolã k in (25) for the smoothing off-line procedure and obtain an off-line CA mode.…”

“…These techniques take advantage of the decoder soft output to reduce the estimator error in the timing recovery [7]- [15] as well as in the carrier frequency and the phase synchronization process [16], [17]. In [7], [8], the authors deal with the time synchronization problem for a constant time delay and they suggest to use a CA TED derived from the Maximum Likelihood (ML) estimator. The theoretical performance analysis is rather difficult for CA estimation techniques and has rarely been evaluated in the literature so that CA timing recovery techniques are often evaluated by simulations.…”

“…Closed form expressions of the CRB have been derived in [21] for CA carrier frequency and phase offset estimation for turbo-coded Square-QAM modulated signals. However, to the best of our knowledge, for the timing recovery problem, the CRB has been evaluated for DA [22], NDA [23] and CA [7], [8] only for a constant delay.…”

An identification technique for the co-frequency mixed communication signals based on cumulants

“…Given (17), (18), and (20), the moments M pq of the over-sampled data when the two signals are BPSK modulated and ω 1 = ω 2 can be obtained as (21).…”

“…That means the signal bandwidth and the timing information should be estimated if prior knowledge is not available. However, the accurate estimation of these parameters is quite difficult under low signal-to-noise ratio (SNR) condition [15][16][17][18].…”