Low-cost designs of rectangular to polar coordinate converters for digital communication

This paper presents several architectural designs of rectangular-to-polar coordinate conversion (RPC) for digital communication systems. Given a two-dimensional (2-D) vector (x, y) , the key operation in the RPC is to calculate the arctangent value φ = tan^-1( y / x) and the vector length ρ = √x² + y². We propose three multi-stage architectures for the design of the RPC, targeting for different precision requirements. The RPC operation can be considered as finding a rotation to align the given vector along the x axis. Such a rotation can be decomposed into three sub-rotations, each implemented by ROM-based multiplication-addition, linear approximation, or CORDIC micro-rotations. The major design consideration is how to partition the rotation angle and how to choose the proper architecture to minimize the total area cost. Implementation results show that the best architectural design is highly depends on the precision requirement.