Novel Structures for Cyclic Convolution Using Improved First-Order Moment Algorithm

This paper first presents a decomposition scheme to reduce the computation time and make the first-order moment-based cyclic convolution well suited for hardware implementation. By decomposing the fixed convolution kernel into similar subparts and using their preprocessing results as control signals, each subpart of cyclic convolution can be calculated with a basic computing substructure. Due to the flexibility of decomposition, a trade-off between computation time and hardware complexity exists. And for a pair of fixed decomposition coefficients, the similarity among subparts leads to the time-efficient structure and the area-efficient structure for cyclic convolution without limitation on the convolution length N and the word length L. Since the basic computing substructure only contains a simple control module, several circularly right-shift registers and N accumulation units, there is no requirement for multipliers and large memory. Comparisons in terms of area-delay product, area-time product and power consumption with the existing memory-based structures have been made to demonstrate the efficiency and effectiveness of the proposed structures. Using the same metrics, the comparison results further show significant improvement of the proposed designs over the previous first-order moment-based structure.