Current radar signal processors (RSPs) lack either performance or flexibility. Custom soft-core processors exhibit potential in high-performance signal processing applications, yet remain relatively unexplored in research literature. In this paper, we use an iterative design methodology to propose a novel soft-core streaming processor architecture. The datapaths of this architecture are arranged in a circular pattern, with multiple operands simultaneously flowing between switching multiplexers and functional units each cycle. By explicitly specifying instruction-level parallelism and software pipelining, applications can fully exploit the available computational resources. The proposed architecture exceeds the clock cycle performance of a commercial high-end digital signal processor (DSP) processor by an average factor of 14 over a range of typical operating parameters in an RSP application.