Wireless communication is one of the most rapid growing technology. To support new services demanding high data rate, the system design requires sophisticated signal processing at the transmitter and receiver. The signal processing techniques include Fast Fourier Transform (FFT), Inverse Fast Fourier Transform (IFFT) computation, Maximal Ratio Receive Combining (MRRC) scheme, Peak-to-Average Power Ratio (PAPR) reduction techniques, resource allocation algorithms, optimization algorithms, detection algorithms and assignment algorithms to name a few. These signal processing techniques makes wireless communication system computationally complex leading to performance limitation. In this work we implemented some of the mentioned signal processing techniques under Graphics Processing Unit (GPU) environment to harness the parallel implementation. The huge computational capabilities of GPU have been used to reduce the execution time of complex systems. Modern wireless communication heavily relies on FFT and IFFT computation. This research work attempts to address implementation of FFT and IFFT through High Performance Computing (HPC) with GPU. PAPR is another area which requires high computational complexity. Here, it is also evaluated on GPU architecture. In Orthogonal Frequency Division Multiple Access (OFDMA) downlink system, allocation of resource to user at Base Station (BS) demand computational efficient algorithm to fulfill the user’s data rate requirement. Hence, this thesis proposes Resource Allocation and Subcarrier Assignment (RASA) algorithm for multi-core architectures with Open Multiprocessing (OpenMP) support. Further in this thesis, subcarrier assignment problem using well know Hungarian algorithm is analyzed and implemented on Compute Unified Device Architecture (CUDA). Strong computational advantages are observed in parallel implementation of above problems in the area of wireless communication applications. Hence GPU based HPC can provide the promising solution for complex wireless systems. The findings have been extensively evaluated through computer simulation with GPU processor.