On the application of the Cramer-Rao and detection theory bounds to mean square error of symbol timing recovery

A modified Cramer-Rao bound is derived that takes account of the fact that the symbol timing estimate is restricted to a finite interval of one symbol duration. A detection theory bound is also applied to the symbol timing problem. Results obtained using the Cramer-Rao and detection theory bounds are compared. It is shown that the detection theory bound is superior to the traditionally used Cramer-Rao bound. In particular, the detection theory bound gives useful results for sharp pulse shapes and shows a dependence of the mean square error on the data sequence. It also yields meaningful results for small signal-to-noise ratios.>