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For orthogonal frequency division multiplexing (OFDM), cyclic prefix (CP) should be longer than the length of channel impulse response, resulting in a loss of bandwidth efficiency. In this paper, we describe a new technique to restore the cyclicity of the received signal when the CP is not sufficient for OFDM systems. The proposed technique efficiently restores the cyclicity of the current received symbol by adding the weighted next received symbol to the current received symbol. Iterative CP reconstruction (CPR) procedure, based on the residual intersymbol interference cancellation (RISIC) algorithm, is analyzed and compared to the RISIC. In addition, we apply the CPR method to Alamouti space-time block coded (STBC) OFDM system. It is shown that in the STBC OFDM, tail cancellation as well as cyclic reconstruction of the CPR procedure should be repeated. The computational complexities of the RISIC, the proposed CPR, the RISIC with STBC, and the proposed CPR with STBC are analyzed and their performances are evaluated in multipath fading environments. We also propose an iterative channel estimation (CE) method for OFDM with insufficient CP. Further, we discuss the CE method for the STBC OFDM system with the CPR. It is shown that the CPR technique with the proposed CE method minimizes the loss of bandwidth efficiency due to the use of CP, without sacrificing the diversity gain of the STBC OFDM system.