Quater-imaginary base for complex number arithmetic circuits

Arithmetic operations involving complex numbers are widely used in the signal processing functions in the physical layer of modern wireless and wireline communication systems, electronic instrumentation and control systems. With the ever increasing throughput requirements of such systems, the power consumption of the hardware realization is increasing beyond the allowed budget. Arithmetic circuits based on binary numeral system that have been optimized rigorously over the past few decades are currently being used for the computation involving complex numbers. In this paper, we present the potential of arithmetic circuits for complex number computations based on the Quater-imaginary (QI) base numeral system to reduce power consumption. We show that for a simple multiplier implementation in the QI base, the savings in power and area consumption could be up to 40% when synthesized in 28nm TSMC standard cell technology node.