A Jointly Gaussian (JG) equalizer is derived for turbo equalization based on an augmented real matrix representation of channel model and a Gaussian approximation of the received symbol sequence. Using matrix inversion lemma and Cholesky decomposition, a low-complexity implementation of JG equalizer is also presented. The simulation results and complexity comparison confirm that turbo equalization with JG equalizer has a better performance and a lower complexity than the existing turbo equalization with linear minimum mean squared erro.r equalizer. A Jointly Gaussian (JG) equalizer is derived for turbo equalization based on an augmented real matrix representation of channel model and a Gaussian approximation of the received symbol sequence. Using matrix inversion lemma and Cholesky decomposition, a low-complexity implementation of JG equalizer is also presented. The simulation results and complexity comparison confirm that turbo equalization with JG equalizer has a better performance and a lower complexity than the existing turbo equalization with linear minimum mean squared erro. r equalizer.