The initial process of identifying any available base station (BS) by a user equipment (UE) that wants to communicate is termed as cell search. To ensure a reliable communication, any UE has to be synchronized with the BS both in time and frequency domains. Cell search process is said to be complete once cell ID associated with long-term evolution (LTE) BS is decoded successfully. This paper presents a series of cell search and synchronization algorithms, which efficiently estimated time and frequency offsets as well as cell ID. The synchronization signals present in LTE, namely, primary synchronization signal (PSS) and secondary synchronization signal, that carry cell ID are critically exploited in the algorithms. The aforementioned algorithms are classified into two modules, namely, module I and module II, based on their computation complexity. In module I, a cyclic prefix (CP)-based maximum likelihood (ML) estimator is employed to obtain a coarse estimate of time and fractional frequency offset; however, the estimates are refined using synchronization signals. A joint estimation of timing, integer frequency offset (IFO), and PSS ID (sector ID) is carried out in module II. Both the modules operate on the cross-correlation approach of PSS with the received signal for obtaining timing and sector ID. IFO as a part of module II is detected from a finite hypotheses set using synchronization signals. Extensive simulations are carried out on a time-varying frequency-selective channel to analyze the performance of the algorithms. © 2017, The Author(s).