Future space missions require reliable architectures with higher performance and lower power consumption. Exploring new architectures worthy of undergoing the expensive and time-consuming process of radiation hardening is critical for this endeavor. Two such architectures are the Texas Instruments KeyStone II octal-core processor and the ARM® Cortex®-A53 (ARMv8) quad-core CPU. DSPs have been proven in prior space applications, and the KeyStone II has eight high-performance DSP cores and is under consideration for potential hardening for space. Meanwhile, a radiation-hardened quad-core ARM Cortex-A53 CPU is under development at Boeing under the NASA/AFRL High-Performance Spaceflight Computing initiative. In this paper, we optimize and evaluate the performance of batched 1D-FFTs, 2D-FFTs, and the Complex Ambiguity Function (CAF). We developed a direct memory-access scheme to take advantage of the complex KeyStone architecture for FFTs. Our results for batched 1D-FFTs show that the performance per Watt of KeyStone II is 4.5 times better than the ARM Cortex-A53. For CAF, our results show that the KeyStone II is 1.7 times better.