Low computational complexity channelisation algorithm for multi-standard software defined radio receiver

Abstract

This work focuses on achieving a low complexity channelisation algorithm for these two algorithms for any frequency \change[Friend]{bands}{band} whether low or high, exploring three approaches in developmental sequence based on different computational rationales.

The first approach involves the development of two algorithms described as Hybrid Generalised Discrete Fourier Transform (HGDFT) and Hybrid Farrow (HFarrow) Channelisation Algorithms. These developments involve hybridising frequency response masking techniques and coefficient decimating filter with either the modulated GDFT or modulated Farrow filter. These methods efficiently reduce the computational complexity to some extent.

The second approach focuses on improving the performance of HGDFT and HFarrow algorithms using different digital number systems, implemented on parallel distributed arithmetic architecture. The digital number representations used are: Parallel Distributed Arithmetic Based Residual Number System (PDA-RNS), Parallel Distributed Arithmetic Based Canonical Signed Residual Number System (PDA-CSRNS), and Parallel Distributed Arithmetic Based Common Sub-expression Elimination Method (PDA-CSE). These approaches resulted in significantly fewer filter coefficients as well as a reduction in the number of multipliers and adders used. Thus, the computational complexities of HGDFT and HFarrow improved remarkably when optimised with the parallel distributed arithmetic and number systems.

However, the filter's passband ripples and the stop band attenuation degrade in performances due to the rounding of the continuous filter coefficients. A Genetic Algorithm (GA) was introduced to optimise the performances of the hybrid filter. Results obtained showed better filter structures with lower computational complexities.

The third approach uses the multi-rate, multi-stage method to reduce computational capability of the HGDFT and HFarrow channelisation algorithms. The large number of filter coefficients in HGDFT and HFarrow were factored into different stages. These relaxed the filter specifications and resulted in more reduced computational complexities.