This technical report is the supporting document of our proposed approach basedon a neural network for joint multichannel reduction of echo, reverberation and noise [1]. First, werecall the model of the proposed approach. Secondly, we express the vectorized computation of echocancellation and dereverberation. Thirdly, we detail the complete derivation of the update rules.Fourthly we describe the computation of the ground truth targets for the neural network usedin our approach. Fifthly we detail the variant of the proposed approach where echo cancellationand dereverberation are performed in parallel. Sixthly we describe the variant of the proposedapproach where only echo cancellation is performed. Then we specify the recording and simulationparameters of the dataset, we detail the computation of the estimated early near-end componentsand we recall the baselines. Finally we give the results after each filtering step and providesestimated spectrogram examples by all the approaches.