The Square Kilometre Array (SKA) will be the biggest radio telescope ever built, with unprecedented sensitivity, angular resolution, and survey speed. This paper explores the de-sign of a custom architecture for the central signal processor (CSP) of the SKA1-Low, the SKA's aperture-array instrument consisting of 131,072 antennas. The SKA1-Low's antennas receive signals between 50 and 350 MHz. After digitization and preliminary processing, samples are moved to the CSP for further processing. In this work, we describe the challenges in building the CSP, and present a first quantitative study for the implementation of a custom hardware architecture for processing the main CSP algorithms. By taking advantage of emerging 3D-stacked-memory devices and by exploring the design space for a 14-nm implementation, we estimate a power consumption of 14.4 W for processing all channels of a sub-band and an energy efficiency at application level of up to 208 GFLOPS/W for our architecture.