In this work, we develop a new method for the maximum Doppler Spread (DS), the Angular Spread (AS) and the mean Angle of Arrival (AoA) estimation in a Rayleigh channel with a Single Input Multiple Output (SIMO) system using an Uniform Linear Array (ULA) at the receiver. We also consider a macro-cell environment. In this paper, the cross-correlation matrix is defined for the Laplacian angular distribution and their derivatives are used to estimate the three parameters. Simulation results show that, our proposed algorithm outperforms the Auto-Correlation Function (ACF) based approach developed in [1] for the maximum DS estimation. For the mean AoA and the AS estimation, our approach offers lower Root Mean Square Error (RMSE) than the Spread Root MUSIC (SRM) estimator [2].