The Design of the NLMS Adaptive Filters Using the Fast-Division Approximation with CSD Encoded Divisors

The computational bottleneck of an NLMS algorithm is the division. This brief presents a division approximation method by encoding the divisor in a canonical signed digit (CSD) form. With the CSD-encoded divisor, we can easily approximate the division by multiplication. This approximation can be made fast. The corresponding percent error will be at most 11.11%. Such percent error has a tiny impact on the performance of the NLMS adaptive filters. The experiment of designing a 16-tap FIR NLMS adaptive filter with the proposed division approximation on an FPGA platform shows that the throughput rate is increased by 136% without any significant performance penalty compared with the NLMS adaptive filter using the conventional SRT division.