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Adaptation Behavior of Pipelined Adaptive Filters

Adaptation Behavior of Pipelined Adaptive Filters. Prakash Khanikar Varun Gopalakrishna. Adaptive Filters. Coefficients updated at each iteration until they converge To minimize the difference between filter output and desired signal Adaptation processes based on minimization criteria

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Adaptation Behavior of Pipelined Adaptive Filters

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  1. Adaptation Behavior of Pipelined Adaptive Filters Prakash Khanikar Varun Gopalakrishna ECE 734 - Spring 2004

  2. Adaptive Filters • Coefficients updated at each iteration until they converge • To minimize the difference between filter output and desired signal • Adaptation processes based on minimization criteria • LMS (Least Mean Squares) • RLS (Recursive Least Squares) ECE 734 - Spring 2004

  3. Adaptive Filters • LMS update based on instantaneous sample value of the tap input vector and error signal • RLS update based on all past available information • Ensemble averaging (LMS) vs. Time based averaging (RLS) • RLS has a much faster convergence rate than LMS • Attained at the expense of an increase in computational complexity ECE 734 - Spring 2004

  4. Pipelining approach • Recursive and adaptive filters difficult to pipeline due to long feedback loops • Look ahead computation could be used but not practical for IC implementations • Substantial hardware saving by use of relaxed look ahead transformation • To reduce computational complexity, there is also a need to investigate systolic arrays ECE 734 - Spring 2004

  5. Relaxed Look Ahead • Based on approximating the algorithms obtained via look-ahead • Sacrifice of the equivalence between serial and pipelined algorithms at expense of convergence characteristics • Smaller hardware overhead making attractive for VLSI implementation • Higher throughput with power-area tradeoff • Higher clock speed ECE 734 - Spring 2004

  6. Exponentially weighted RLS algorithm α*(n) k(n) d*(n) uH(n) z-1 I ∑ + w(n-1) w(n) ECE 734 - Spring 2004

  7. ECE 734 - Spring 2004

  8. Stability Issues • Stability of the pipelined recursive realizations • Sensitive to the filter coefficients ECE 734 - Spring 2004

  9. Systolic array Implementation • Input data is not consumed in traditional pipelining approaches • QRD-RLS algorithm • Good numerical properties • Can be mapped to a coarse grain pipelining systolic array • Highly suitable for VLSI implementation • Systolic architecture based on QRD-RLS algorithm using the Givens rotation ECE 734 - Spring 2004

  10. Conclusions • Use of techniques and algorithms like pipelining, systolic array mapping towards efficient implementation of adaptive filters • Faster implementation (higher clock speed) without hardware overhead • Immediate Goals • To exploit inherent parallelism through block/parallel processing techniques • To propose an efficient systolic array architecture for the RLS algorithm ECE 734 - Spring 2004

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