Optimal Step-Size Mechanism for Stochastic Gradient Algorithm Applied to CDMA Receiver in Multipath Fading Channels

This paper investigates the optimal step-size mechanism for a stochastic gradient (SG) based direct sequence (DS-) code division multiple access (CDMA) receiver under the influence of the multiple access interference (MAI) and intersymbol interference (ISI) in multi-path environments by utilizing a simple stochastic model. The convergence of the derived optimal step-size sequence is verified analytically. The learning curve is applied to analyze and compare the speed of convergence and residual mean-squared error (MSE) for the fixed and time-varying step-size sequence methodologies. Simulations show that the receiver utilizes the derived optimal step-size sequence not only has faster convergent speed and smaller MSE, but also is robustly to different multi-path channels.