This work investigates a multi-user, multi-antenna uplink wireless system, in which multiple users transmit signals to a base station. Prior research has explored the potential for linear growth in spectral efficiency by employing multiple transmit and receive antennas. This gain depends heavily on the quality of channel state information and the number of uncorrelated antennas. However, spatial correlations, arising from closely-spaced antennas and channel aging effects -- stemming from the difference between the channel state at pilot and data time instances -- can substantially counteract these benefits, and degrade the transmission rate, especially in non-stationary environments. To address these challenges, this work introduces a real-time beamforming framework to compensate for the spatial correlation and channel aging effects. First, a channel estimation scheme leveraging temporal channel correlations and considering mobile device velocity and antenna spacing is developed. Subsequently, an expression approximating the average spectral efficiency -- which depends on pilot spacing, pilot and data powers, and beamforming vectors -- is obtained. By maximizing this expression, optimal parameters are identified. Numerical results demonstrate the effectiveness of the proposed approach compared to prior works. Interestingly, the optimal pilot spacing remains unaffected by large-scale channel parameters and the velocities of interfering users. The impact of interference components also diminishes with an increasing number of transmit antennas.