Cramer-Rao bound on timing recovery of linearly modulated signals with no ISI

A new Cramér–Rao lower bound for symbol timing recovery of linearly modulated (quadrature amplitude modulation) signals is presented. Contrary to some other works on the subject, the transmitted data is assumed to be unknown at the receiver. The bound is derived from a likelihood function that includes the symbol randomness. For large number of symbols, the bound is achievable at any signal-to-noise ratio. The separation of symbol timing recovery and phase recovery schemes is investigated using the new results. It is shown that the separation of these operations causes a degradation of less than 0.3 dB compared to joint phase and timing recovery. The bound is derived for symbol shaping limited to a single symbol length (i.e., no intersymbol interference.) Simulations for longer pulse shapes demonstrate that the new results provide better performance prediction than other known techniques.