For wireless communications system, Orthogonal Frequency Division Multiplexing (OFDM) is a widely applied technique. This system also enables simple filtration or equalization by cyclic prefix insertion. The sensitivity of single-carrier systems to carrier frequency offset (CFO) is much lesser than that of OFDM systems. In present OFDM standards, such as IEEE802.11a/g or DVB-T, preamble (or pilots) is used to estimate and compensate the carrier frequency offset (CFO) and channel impulse response. There is a considerable problem i.e. the residual carrier frequency offset still destroys the orthogonality of the received OFDM signals after the CFO estimation and compensation. This situation further worsens the bit error rate of OFDM systems during the equalization process. In this research work, an equalized OFDM system over AWGN noise by using 16, 64, 128 and 256 QAM is designed. The designed system is modified by using QAM mapping at transmitter and receiver ends. Also, normalization of transmission bits and de-normalization of received bits is done for decreasing BER and SER. Performance analysis of designed OFDM architecture with ZF equalization is performed by using four efficient modulation indexes (16, 64, 128 and 256) with M-QAM modulation. Whole analysis is implemented over OFDM model with AWGN noise. Here the OFDM architecture is used to reduce noise (can be inter-symbol interference) which is the most important loss or attenuation in optical signals, thus mapping and equalization (filtering) is performed. After implementation of proposed method, we have evaluated the performance of the same by using Symbol Error Rate (SER) and Bit Error Rate (BER). These parameters are calculated and plotted with respect to input SNR. MATLAB R2013a has been used as an implementation platform using generalized MATLAB toolbox and wireless communication tool box.