LTE is the brand name for emerging and developed technologies that comprise the existing 3G and 4G networks. The LTE specification provides downlink peak rates of at least 100 Mbps, and uplink of at least 50 Mbps. LTE supports scalable carrier bandwidths, from 1.4 MHz to 20 MHz and supports both frequency division duplexing (FDD) and time division duplexing (TDD). LTE has now been commercialized and is already being used by some of the mobile carriers. The high data rates promised by LTE have made it the current sought after technology. One interesting challenge in the physical layer of LTE is how the mobile unit immediately after powering on, locates a radio cell and locks on to it. This thesis, presents how the mobile unit establishes this connection with the strongest cell station in vicinity. To do this, the mobile unit has to overcome the challenges of estimating the channel to communicate with the cell site and frequency synchronization. Also, multiple mobile units communicate to the same receiver and from various distances. Hence, it is up to the mobile to synchronize itself appropriately to the base stations. LTE uses two signals, the Primary Synchronization Signal and the Secondary Synchronization Signal sequentially to determine which of the available cell sites a mobile would lock in to. This thesis simulates using MATLAB, the mobile cell search procedure, the challenges associated with it as discussed here and the solutions.