Massive multiple-input-multiple-output (MIMO) is a key enabler for obtaining higher data rates in the next generation wireless technology. While it has the power to transform cellular communication, with potential for spatial diversity and multiplexing, a bottleneck that often gets overlooked is the fronthaul capacity. The fronthaul link that connects a massive MIMO Remote Radio Head (RRH) and carries in-phase and quadrature (IQ) samples to the Baseband Unit (BBU) of the base station can throttle the network capacity/speed if appropriate data compression techniques are not applied, particularly in the uplink. This paper proposes an iterative technique for fronthaul load reduction in the uplink for massive MIMO systems utilizing the convolution structure of the received signals. The proposed algorithm provides compression ratios of about 30- 50×. This work provides extensive analysis of the performance of the proposed method for a plethora of practical scenarios and constraints, such as different channel parameters and models, receive antenna correlation, and under imperfect channel information. It also discusses the numerical convergence and complexity of the proposed algorithm and compares the performance against other existing compression techniques. © 2023 IEEE.