Deep MMSE Estimation for Data Detection

This letter develops minimum mean-squared error (MMSE) estimators based on deep neural networks for data detection. Since the optimal MMSE is analytically intractable, researchers usually resort to linear MMSE approximations, which often incur performance degradation. To overcome this loss, we develop a near-optimal estimator by exploiting the Donsker-Varadhan representation of mutual information (MI) and the recently discovered derivative relationship between MI and MMSE. The near-optimal MMSE estimator can be computed with a deep neural network (NN). We can train the NN using the mini-batches of input and output samples. We validate this estimator using two examples where the closed-from MMSE is available. We then use this estimator to design an end-to-end communication system. We compare this setup with several conventional techniques and show promising performance.