In communication receivers, the gain and phase inbalance between the inphase and quadrature (I&Q) channels can cause serious degradation in receiver performance. Consider the problem of jointly estimating the four parameters of the received I&Q signals: the amplitude imbalance, the DC offset for each channel, and the phase onsets between the I&Q channels. Using a Fourier series expansion of the received data, the equations for least square estimation based on the measured I&Q data in a loop back mode are derived. The estimated parameters are then used for the correction of the data and the improvement of the BER performance. Examples are given for the compensation of amplitude and phase imbalance in a QPSK receiver and higher order modulation.