Adaptive schemes and analysis for blind beamforming with insufficient cyclic prefix in single carrier-frequency division multiple access systems

When the duration of the cyclic prefix (CP) is shorter than that of the channel impulse response in single carrier-frequency division multiple access systems, inter-symbol interference and inter-carrier interference will degrade the system performance. Previously, one solution of this problem while considering the effect of carrier frequency offsets (CFOs) and the co-channel interference is a blind received beamforming scheme based on eigenanalysis in a batch mode. As the capability in suppressing the multipath signal with the delay larger than the CP length has not previously been analysed theoretically for the scheme, the theoretical analysis regarding the capability in suppressing the long-delayed multipath signal is provided in this study. The analysis provided in this study is also utilised to design an adaptive processing scheme. The adaptive algorithm is developed to find the beamforming weight vector updated on a per symbol basis without using reference signals. The proposed adaptive algorithm reduces the computational complexity of and shows competitive performance under the insufficient CP, the CFOs, the co-channel interference and the time-varying scenarios. The simulation results reveal that the proposed adaptive algorithm provides better performance than the previously proposed algorithm.