In cyclic prefix (CP)-based transmission systems, if the time duration of the cyclic extension is shorter than the channel impulse response duration, this degrades system performance due to introducing inter-symbol interference (ISI) and inter-carrier interference (ICI). In this thesis, we propose a blind beamforming algorithm for single carrier frequency division multiple access (SC-FDMA) systems under insufficient CP scenarios. Besides, we also consider the effects of carrier frequency offsets (CFO) in the processing schemes. The simulation results are presented here by employing the SC-FDMA uplink signal model to illustrate the efficacy of the proposed algorithms.