Cognitive Radio is considered as a promising technology to address the paradox of spectrum scarcity and spectrum under-utilization. It has to operate in different bands under various data rates and combat adversary channel conditions. Therefore, Cognitive Radio needs an adaptive physical layer which has to be supported by a reconfigurable baseband processing platform. In this paper, we propose an Multiprocessor System-on-Chip (MPSoC) platform to fulfill the requirements of reconfigurability, speed and energy efficiency. The key element on this platform is the Montium tile processor. To support adaptive DSP algorithms for Cognitive Radio on this platform is our main interest. This paper discusses several key algorithms for Cognitive Radio baseband processing and the implementation on the Montium based reconfigurable platform.