A new implementation of complex number multiplier using RB representations

Redundant binary (RB) representation is one of the signed-digit number systems originally introduced by Avizienis, which provides carry-propagation-free addition. Since the multiplication of two numbers is generally performed by the addition of partial products, the carry-propagation-free feature of the RB arithmetic can be used to design high-speed multipliers and multiply-and-accumulate units. Complex number arithmetic computations are one of the key arithmetic components in modern digital communication and optical systems. Complex number multiplication plays a unique role in these applications. In this paper, a new implementation of the complex-number multiplier based on a Redundant Binary (RB) representation is presented. With the proposed algorithms, the complex number multiplication is reduced to parallel RB multiplications. The implementation result on Xilinx FPGAs is presented in the paper compared to other methods. The proposed complex number multiplier is used in our proposed high-performance Complex Arithmetic Signal Processor.