Timing Estimation Based on Higher Order Cyclostationarity for Faster-Than-Nyquist Signals

Abstract

Faster-than-Nyquist (FTN) transmission is a promising technique to increase spectral efficiency at fixed constellation size. However, traditional timing synchronization algorithms mostly rely on the eye diagram opening after matched-filtering (e.g., Gardner, zero-crossing). Such approaches are thus unsuitable in presence of FTN-induced intersymbol interference. In this paper, we first show that FTN signals exhibit cyclostationarity at the lth-order (l > 2) according to their bandwidth and symbol period. Then, we derive non-data-aided timing offset estimators from the cyclic temporal cumulant function. Besides its relevance for strong FTN scenarios, the proposed solution is also robust to frequency and phase offsets.

The Evolution of Faster-Than-Nyquist Signaling

“…While the family of CE schemes designed for FTN signaling was reviewed in Section VI-A, a diverse range of other estimation issues such as carrier phase estimation and synchronization designed for FTN signaling were considered in [157][158][159][160][161][162][163][164][165] and [166][167][168][169][170][171], respectively. To elaborate, in [170], a timing synchronization scheme based on exploiting the higher-order cyclostationarity of FTN signaling was proposed. The robustness of this scheme against frequency offsets was characterized in a simple AWGN channel.…”

“…López et al [170] Proposed a timing synchronization scheme based on the higher-order cyclostationarity of FTN signaling. 2021…”

Optimal Pilot Sequences for Timing Estimation in Faster-Than-Nyquist Systems

“…e j2π( f T s − k K )l d f . (19) For large K, the Dirichlet kernel in (19) can be approximated by a 1/T s -periodic Dirac comb which yields (9) and completes the proof.…”

“…Theorem 1 connects asymptotically the eigendecomposition of G H ξ G ξ to the frequency response of the pulse-channel function, characterized by its support (−B/2; B/2). A restriction to ρ ≥ 1/2 (i.e., at most 100 % excess bandwidth), limits the sum in (9) to its zeroth and first terms:…”

“…In a non-data-aided (NDA) approach, traditional synchronization techniques mostly rely on IPI-free observations or on second-order cyclostationarity [7]; both are obviously unsuited to FTN signals. To overcome this issue, a non-linear least squares method has been proposed for carrier-frequency-offset estimation [8]; higher-order cyclostationarity can be used to build timing estimators, even though the observation length quickly becomes prohibitive as the density gets significant [9].…”