Conditional negating booth multiplier

Abstract

An angle rotator performs angle rotation of an input complex signal in the complex plane according to an angle θ. The angle rotator includes a coarse stage rotation and a fine stage rotation. The two specific amounts of rotation are obtained directly from the original angle, without performing iterations as are performed by known CORDIC-type methods. The coarse stage rotation is performed using truncated approximations for the cosine θM and the sine θM, where θM is a radian angle that corresponds to a most significant word (MSW) of the input angle θ. The fine stage rotation is performed using one or more error values that compensate for approximations and quantization errors associated with the coarse stage rotation. By partitioning the rotation into coarse and fine rotation stages, a two stage structure is obtained that requires much less hardware than a single-stage rotator, without sacrificing angle precision. This can occur because the two-stage rotator stores pre-computed cosine θM and the sine θM values in a small lookup table (e.g. memory device) for fast retrieval. Furthermore, the angle rotator consolidates all operations into a small number of reduced-size multipliers, enabling the use of efficient multiplier implementations, such as Booth encoding, thereby yielding a smaller and faster overall circuit. When higher precision is desired, more accurate results can be attained simply by increasing the wordlength and the multiplier size, without significantly increasing overall circuit latency.

Description

CROSS-REFERENCE TO RELATED APPLICATIONS [0001] This application is a continuation of U.S. Non-Provisional application Ser. No. 09 / 698,246, filed Oct. 30, 2000, which claims the benefit of U.S. Provisional Application No. 60 / 162,391, filed on Oct. 29, 1999, all of which are incorporated herein by reference. [0002] U.S. Non-Provisional application Ser. No. 09 / 698,249, filed Oct. 30, 2000, entitled, “Apparatus and Method for Rectangular-to-Polar Conversion” of common assignee is related to the parent application and is herein incorporated by reference in its entirety.STATEMENT REGARDING FEDERALLY-SPONSORED RESEARCH AND DEVELOPMENT [0003] This invention was made with Government support under grant no. MIP 9632698 awarded by the National Science Foundation. The U.S. Government has certain rights in this invention.BACKGROUND OF THE INVENTION [0004] 1. Field of the Invention [0005] The present invention is related to digital signal processing and digital communications. More specifically t...

AI Technical Summary

Benefits of technology

[0018] By partitioning the rotation into coarse and fine rotation stages, a two stage structure is obtained that requires much less hardware than a single stage rotator, without sacrificing angle precision. This can occur because the two stage rotator stores pre-computed cosine θM and the sine θM values in a small lookup table (e.g. memory device) for fast retrieval. This same lookup table can be reused by a phase rotator for carrier recovery, in systems wherein both subsystems are present. Furthermore, the angle rotator consolidates all operations into a small number of reduced-size multipliers, enabling the use of efficient multiplier implementations, such as Booth encoding, thereby yielding a smaller and faster overall circuit. When higher precision is desired, more accurate results can be attained simply by increasing the wordlength and the multiplier size, without increasing overall circuit latency. Further efficiency in implementation can be achieved by exploiting certain opportunities presented by Booth encoding methods in relation to the angle rotator's special “two-butterfly” structure.

Problems solved by technology

This symbol rotation can seriously degrade system performance.

Moreover, changing the phase of the sampling clock 114 would cause jitter.

As for the digital video broadcasting system (DVB) systems, the most challenging of all DVB transmissions is the one used in terrestrial channels (DVB-T) due to the presence of strong echoes which characterize the propagation medium.

The discussion, however, extends to a general problem of Cartesian-to-polar conversion, which is encountered in many communication applications.

However, this method is likely to result in a large coefficient memory.

To design low-cost modems, a large coefficient memory is undesirable.

Although this approach achieves reasonable performance, the hardware complexity grows rapidly as the number of samples used to calculate each new sample is increased for better accuracy.

Thus, the critical data path gets longer as N increases, thereby creating a limitation on the achievable data rate.

There are three issues that are to be considered in evaluating an interpolation scheme: 1) accuracy of interpolation, 2) complexity of implementation and 3) latency.

Images