Weight sharing has been the key feature of convolutional neural networks. The success of weight sharing in addressing machine learning problems lies in its ability to force the neural network to detect common `local' features across an image by applying the same weights across all input samples (pixels). As a result, weight sharing leads to many benefits such as lesser data for training and lower risk of overfitting the data. However, these advantages are more relevant to machine learning problems than those in signal processing. We therefore study weight sharing for LMS type algorithms so that we can analyse its effect on their properties that are more useful to signal processing tasks. Rigorous analysis of our proposed LMSM algorithm demonstrates that weight sharing leads to better convergence properties and enhanced capability to cope with a large number of channels in terms of both computational complexity and stability. Simulation studies support our approach on weight sharing, especially in scenarios as massive as 256 x 256 MIMO systems
