Improved bounds for timing estimation jitter

Application of a detection theory (DT) bound to the symbol timing recovery problem is developed. It is shown that this bound is particularly well suited to the symbol synchronization problem and provides useful information in a wide variety of situations. The Cramer-Rao (CR) aid DT bounds are compared for this application. In order to fully assess the comparative usefulness of the two bounds, a different form of the CR bound that is more applicable to the symbol timing problem than the usual statement of the CR bound is derived. This modification of the CR bound appears neither to have been suggested nor noted before. It is shown that the DT bound yields useful results for signaling pulses with jump discontinuities and for small signal-to-noise ratios (SNRs). The DT bound provides information about the variation in performance achievable for different symbol sequences. In contrast the CR bound gives no useful information about any of these three cases