In this paper joint effect of transmitter and receiver IQ imbalance under insufficient and sufficient cyclic prefix (CP) is studied. The case of insufficient CP length leads to increase in the rate of symbol transmission, on the other hand it causes inter-symbol-interference. Morever, existence of IQ imbalance in the transmitter and receiver causes distortion in the received signals. So this problem leads to increase of bit error rate. To compensation of this effect and other impairments, simultaneously, per-tone equalization (PTEQ) structure implementation is necessary. Regarding to topology of this structure and required high length filters, the system computations will be very high, even using simplest adaptive algorithms. In this work to reduce the computational burden, an adaptive algorithm based on selective coefficient updating (SCU) has been presented. In addition, to increase of the convergence speed of adaptive algorithms,wavelet packet transform (WPT) is applied to branches of PTEQ structure in second stage. Then SCU method based on the rate of wavelet papcket entropy has been used. It must be mentioned that in this method not only computational complexity has been reduced but also bit error rate has been improved. In the third stage, the combination of both SCU and data selective updating (DSU) to increase of convergence speed and to reduce of computational complexity have been derived. Simultaneous using of two DSU and SCU methods besides WPT, is suitable for compensation ofchannel effect and IQ imbalance. Simulation results show that this algorithm not only causes considerably reduction on amount of calculations, but also have better performance.