Table of Contents
ISRN Signal Processing
Volume 2011, Article ID 615934, 8 pages
Research Article

Low-Complexity Inverse Square Root Approximation for Baseband Matrix Operations

1Department of Computer Systems, Tampere University of Technology, P.O. Box 553, 33101 Tampere, Finland
2Nokia Multimedia Imaging, Nokia Devices R&D, Nokia, Visiokatu 1, 33720 Tampere, Finland
33GP/DSE, ST-Ericsson, Hermiankatu 1 B, 33720 Tampere, Finland
4Nokia Devices R&D, Nokia, Elektroniikkatie 3, 90570 Oulu, Finland

Received 8 December 2010; Accepted 11 January 2011

Academic Editors: E. D. Übeyli and E. Salerno

Copyright © 2011 Perttu Salmela et al. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.


Baseband functions like channel estimation and symbol detection of sophisticated telecommunications systems require matrix operations, which apply highly nonlinear operations like division or square root. In this paper, a scalable low-complexity approximation method of the inverse square root is developed and applied in Cholesky and QR decompositions. Computation is derived by exploiting the binary representation of the fixedpoint numbers and by substituting the highly nonlinear inverse square root operation with a more implementation appropriate function. Low complexity is obtained since the proposed method does not use large multipliers or look-up tables (LUT). Due to the scalability, the approximation accuracy can be adjusted according to the targeted application. The method is applied also as an accelerating unit of an application-specific instruction-set processor (ASIP) and as a software routine of a conventional DSP. As a result, the method can accelerate any fixed-point system where cost-efficiency and low power consumption are of high importance, and coarse approximation of inverse square root operation is required.