GSFAP adaptive filtering using log arithmetic for resource-constrained embedded systems

Adaptive filters are widely used in digital signal processing for such applications as system identification, noise cancellation, and in areas such as digital communication systems. Traditionally, small resource-constrained embedded systems have used the least computationally intensive filter adaptive algorithms based on least mean squares (LMS).The power-normalized version (NLMS) is typical example. More complex adaptive algorithms, such as recursive least squares (RLS), are usually too computationally expensive for implementation in small embedded systems.Our work deals with a floating-point-like implementation of the Gauss-Seidel fast affine projection (GSFAP) algorithm and shows that FPGAs are a highly suitable platform for more computationally intensive adaptive algorithms. FAP based algorithms are characterized by better adaptation properties than NLMS with only a slightly higher complexity, providing some compromise between the slow convergence of NLMS and the computational complexity of RLS.We present the design of an optimized core which implements GSFAP. To reduce the resource requirements we use logarithmic arithmetic, rather than conventional floating point, within the custom core. Our design makes effective use of the pipelined logarithmic addition units, and takes advantage of the very low cost of logarithmic multiplication and division.The resource requirements of the resulting GSFAP core are slightly higher than the requirements for the corresponding NLMS core. However, experiments show that GSFAP has adaptation properties much superior to NLMS which is demonstrated on a noise/echo cancellation example.