Study on High-Speed Magnitude Approximation for Complex Vectors

Abstract: High-speed magnitude approximation algorithms for complex vectors are discussed intensively. The perfor-mance and the convergence speed of these approximation algorithms are analyzed. For the polygon fitting algorithms, theapproximation formula under the least mean square error criterion is derived. For the iterative algorithms, a modifiedCORDIC (coordinate rotation digital computer) algorithm is developed. This modified CORDIC algorithm is proved to bewith a maximum relative error about one half that of the original CORDIC algorithm. Finally, the effects of the finiteregister length on these algorithms are also concerned, which shows that 9 to 12-bit coefficients are sufficient for practicalapplications.