Decomposition of Complex Multipliers Using Polynomial Encoding

We present a new method for complex multiplication. The method relies on encoding 2n-bit complex numbers (n-bit real part and n-bit imaginary) as polynomials of degree 7 in the ring of polynomials modulo x8— 1 with n/4-bit coefficients. Complex multiplication can then be performed with an 8-point cyclic convolution plus some conversion overhead and, with care, this can be done without introducing any errors. The technique is suitable for designs using systolic arrays.