Hardware implementation of trigonometric functions with application to digital communications

Abstract

Trigonometric functions can be implemented in hardware by using efficient shift-and-add based algorithms such as CORDIC (Coordinate Rotation Digital Computer) and BKM (Bajard Kla Muller; initials of inventors of the BKM algorithm). Although the CORD IC algorithm is more complex to implement than BKM, it is generally preferred due to the fact that BKM requires more pre-computed table elements. CORDIC is useful in applications where cost is a priority. This algorithm may be used to generate carriers for digital modulation schemes. The CORDIC algorithm is also ideal since it computes Sine and Cosine at the same time and hence two carriers in quadrature can be generated concurrently, with the same algorithm. This algorithm is therefore useful to implement digital carriers for BPSK (Binary Phase Shift Keying), QPSK (Quadrature Phase Shift Keying) and QAM (Quadrature .Amplitude Modulation) modulation schemes. This Final Year Project is focused on the hardware implementation of the CORD IC algorithm in VHDL (Very-High-Speed Integrated Circuits Hardware Description Language), in order to generate trigonometric functions. These functions are then used as a part of a larger design to develop a carrier generation block for modulation schemes. The second part of the project focuses on the application of such functions for BPSK, QPSK, QAM-16 and QAM-256 implementations. The VHDL modules developed in this project are portable across many implementation technologies both for FPGAs (Field Programmable Gate Array) and ASICs (Application Specific Integrated Circuit). One must remember that communication devices are becoming an essential part of every electronic device, and hence issues of compactness and efficiency of algorithms to be implemented in hardware, are crucial when implementing hardware-based digital communication schemes.