Aki Happonen

DSP implementation of Cholesky decomposition

Both the matrix inversion and solving a set of linear equations can be computed with the aid of the Cholesky decomposition. In this paper, the Cholesky decomposition is mapped to the typical resources of digital signal processors (DSP) and our implementation applies a novel way of computing the fixed-point inverse square root function. The presented principles result in savings in the number of clock cycles. As a result, the Cholesky decomposition can be incorporated in applications such as 3G channel estimator where short execution time is crucial

GSM channel estimator using a fixed-point matrix inversion algorithm

This paper presents a fixed-point matrix inversion implementation of a linear minimum mean square error (LMMSE) channel estimator for GSM receivers. The matrix inversion algorithm uses Cholesky decomposition implemented by a reconfigurable processing element. The fixed-point word length analysis is based on the bit error rate (BER) simulations using standard GSM channel models: TU, HT, and RA. The obtained results are compared to floating point matrix inversion results. Our simulations show that 16 bits fixed-point implementation of matrix inversion in LMMSE estimator gives equal BER performance compared to floating point matrix inversion. The condition number of involved matrices in LMMSE estimator varies depending on the channel model. This variation affects the word length requirements of the matrix inversion engine.

Low-complexity Inverse Square Root Approximation for Baseband Matrix Operations

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.

Processing Element for Reciprocal and Reciprocal Square Root

Our topic is reciprocal and reciprocal square root and we propose processing element without iterations. Implementation is based on look-up tables and computation in logarithm domain. Simulation results and implementation complexity for 16 bits input operand with fixed point and floating point output formants are presented. Two truncation methods, LSB and half LSB, for output are presented and their impact to output error is discussed. Relative error for reciprocal is less than 5% for floating point output format.

Ad-hoc Networks Extending Wireless Broadband Coverage and Capacity for Mobile Internet Usage

The number of wireless Internet users is expected to increase rapidly within the next few years resulting in a huge increase in the number of bits transferred between wireless devices and networks. When looking at current mobile networks, they have mainly been designed for optimized delivery of voice calls and not for broadband data. Although mobile networks are evolving, we expect there to be a need for complementary solutions for providing wireless Internet access. Thus we introduce an ad-hoc networking solution using WiFi short range radio technology for extending cellular wireless broadband coverage and capacity into places where it is most urgently needed; densely populated areas and indoors. We further propose connecting the ad-hoc networking solution to the operators total access offering. As a result, wireless users may enjoy an easy to use, good quality, secure and robust service offering when entering the wireless Internet era, and access providers are equipped with tools to utilize complementary access technologies in places where they suit best. Operators arc able to make efficient use of their existing investments and open new service concepts and business models with mobile Internet domain use cases evolution. Also end users become an essential part of business ecosystem by providing content, services and access to other users.

ON IMPLEMENTATION ASPECTS OF UPLINK MC-CDMA MULTI-USER DETECTION

This paper considers the implementation of multi-user detector in MC-CDMA receivers using fixed-point matrix inversion algorithms. The fixed-point word length analysis is based on the matrix condition number analysis and residual errors. The obtained bit error results have been compared to floating point matrix inversion results.