Mobile communication technology evolved rapidly over the last few years due to increasing demands such as accessing Internet services on mobile phones with a better quality of the offered services. In order to fulfil this, wireless telecommunication industry worked hard and defined a new air interface for mobile communications which enhances the overall system performance by increasing the capacity of the system along with improving spectral efficiencies while reducing latencies. For this, two technologies, called Worldwide Interoperability for Microwave Access (WiMAX) and Third Generation Partnership Project Long Term Evolution (3GPP LTE), emerged with an aim of providing voice, data, video and multimedia services on mobile phones at high speeds and cheap rates. In this thesis, we have conducted a detailed comparative study between WiMAX and 3GPP LTE by focusing on their first two layers, i.e. Physical and MAC layer. The comparison specifically includes system architecture, radio aspects of the air interface (such as frequency band, radio access modes, multiple access technologies, multiple antenna technologies and modulation), protocol aspects of the air interface (in terms of protocol architecture, modulation and frame structure), mobility and Quality of Service (QoS). We have also given a brief comparative summary of both technologies in our thesis. In the thesis, we investigated the LTE uplink and performed link level simulations of Single Carrier Frequency Domain Equalization (SC-FDE) and Single Carrier Frequency Division Multiple Access (SC-FDMA) in comparison with Orthogonal Frequency Division Multiplexing (OFDM). The comparison has been in terms of Signal-to-Noise Ratio (SNR) and Symbol Error Rate (SER). In order to verify the theoretical results, we simulated the Peak to Average Power Ratio (PAPR) of SC-FDMA system in comparison with OFDMA. We also simulated the capacity of Multiple Input Multiple Output (MIMO) systems in comparison with Single Input Single Output (SISO) systems. The simulation was performed on a PC running MATLAB 7.40 (R2007a). The operating system used in the simulation was Microsoft Windows Vista.