Broadband single carrier modulated signals experience severe multipath distortion scrambling & ISI when propagating through physical medium. Correcting the distortion with channel equalization is the foremost task of the detector. Prior information about the transmitted signals in the form of channel decoder feedback can significantly enhance equalization accuracy. An algorithm that iteratively performs channel decoding and equalization with prior information is generally denoted turbo-equalizer. Turbo-Equalizer uses prior information & the principle of interference cancellation by MMSE criterion. Here we have tested Adaptive Turbo Equalization with least Mean Square Algorithm (LMS) & modified normalized LMS algorithm & Turbo-Decoding with a Log-Map. Consequently the Mean Square Error analysis, Stability analysis and convergence analysis are provided and its shown if the system is sparse, then the system will converge faster for a given total asymptotic MSE, though the choice of initialization is important. Here all the Implementation concepts have been verified in MATLAB platform and evaluation of the proposal is presented. The measurement for the performance is displayed as bit error rates (BER) in comparison to SNR of the Channel.