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This paper introduces a new maximum likelihood (ML) solution for thecode-aided (CA) timing recovery problem in square-QAM transmissions andderives, for the very first time, its CA Cram\'er-Rao lower bounds (CRLBs) inclosed-form expressions. By exploiting the full symmetry of square-QAMconstellations and further scrutinizing the Gray-coding mechanism, we expressthe likelihood function (LF) of the system explicitly in terms of the codebits' \textit{a priori} log-likelihood ratios (LLRs). The timing recovery taskis then embedded in the turbo iteration loop wherein increasingly accurateestimates for such LLRs are computed from the output of the soft-inputsoft-output (SISO) decoders and exploited at a per-turbo-iteration basis inorder to refine the ML time delay estimate. The latter is then used to betterre-synchronize the system, through feedback to the matched filter (MF), so asto obtain more reliable symbol-rate samples for the next turbo iteration. Inorder to properly benchmark the new CA ML estimator, we also derive for thevery first time the closed-form expressions for the exact CRLBs of theunderlying turbo synchronization problem. Computer simulations will show thatthe new closed-form CRLBs coincide exactly with their empirical counterpartsevaluated previously using exhaustive Monte-Carlo simulations. They will alsoshow unambiguously the potential performance gains in time synchronization thatcan be achieved owing to the decoder assistance. Moreover, the new CA MLestimator almost reaches the underlying CA CRLBs, even for small SNRs, therebyconfirming its statistical efficiency in practice. It also enjoys significantimprovements in computational complexity as compared to the most powerfulexisting ML solution, namely the combined sum-product andexpectation-maximization (SP-EM) algorithm.

Time Synchronization of Turbo-Coded Square-QAM-Modulated Transmissions: Code-Aided ML Estimator and Closed-Form Cram\'er-Rao Lower Bounds