In modern 5G user equipments (UEs), the power amplifier (PA) contributes significantly to power consumption during uplink transmissions, especially in cell-edge scenarios. While reducing power backoff can enhance PA efficiency, it introduces nonlinear distortions that degrade signal quality. Existing solutions, such as digital pre-distortion, require complex feedback mechanisms for optimal performance, leading to increased UE complexity and power consumption. Instead, in this study we explore digital post-distortion (DPoD) techniques, which compensate for these distortions at the base station, leveraging its superior computational resources. In this study, we conduct an comprehensive study concerning the challenges and advantages associated with applying DPoD in time-domain, frequency-domain, and DFT-s-domain. Our findings suggest that implementing DPoD in the time-domain, complemented by frequency-domain channel equalization, strikes a good balance between low computational complexity and efficient nonlinearity compensation. In addition, we demonstrate that memory has to be taken into account regardless of the memory of the PA. Subsequently, we show how to pose the complex-valued problem of nonlinearity compensation in a real Hilbert space, emphasizing the potential performance enhancements as a result. We then discuss the traditional Volterra series and show an equivalent kernel method that can reduce algorithmic complexity. Simulations validate the results of our analysis and show that our proposed algorithm can significantly improve performance compared to state-of-the-art algorithms.