Mean acquisition time analysis of fixed-step serial search algorithms

In this paper, mean acquisition time (MAT) analysis of fixed-step serial search (FSSS) algorithms is presented. First, it is shown that the MAT of an FSSS algorithm can be obtained from that of a conventional serial search (CSS) algorithm after a certain mapping of the uncertainty region. Then, a generic formula for the MAT of FSSS algorithms is derived, which is valid for both dense and sparse channel environments. In addition, MAT formulas for high signal-to-noise ratio scenarios, for large uncertainty regions, and for dense channels are obtained as special cases of the generic solution. Finally, simulation results are presented to verify the analysis and to investigate the factors that affect the optimal step size for FSSS algorithms.