Lms algorithm FOR NON-STATIONARY INPUTS FOR THE PIPELINED IMPLEMENTATION OF ADAPTIVE ANTENNAS

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• Lms algorithm FOR NON-STATIONARY INPUTS FOR THE
  PIPELINED IMPLEMENTATION OF ADAPTIVE
  ANTENNAS
•  
• Prof.Yu Hen Hu Arjun Arunachalam
• Department of Electrical and Computer
  Engineering
• University Of Wisconsin-Madison
• E-mail arunacha_at_cae.wisc.edu
• ECE-734 Spring 2002

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ABSTRACT

•  
• In this project, a modified LMS algorithm has
  been proposed which is capable of handling
  non-stationary inputs. The algorithm is then
  modified for the pipelined implementation of
  adaptive antennas which have higher throughput .A
  number of recently proposed Approximation
  techniques when applied to standard LMS algorithm
  can result in instability due to a change in the
  functionality of the algorithm and thus careful
  calibration of step size and depth of pipelining
  is needed. This project also studies the issues
  involved with the various approximations
  techniques used to reduce the overhead involved
  when the look-ahead technique is applied to a
  standard LMS algorithm.

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Structure of an Adaptive Filter

• U(N) Y(N)
• 
  D(N)

Transversal Filter With weights W (n)
Adaptive Weight Control Mechanism
?
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Equations governing the Behavior of a pipelined
Adaptive Filter

• Pipelined LMS
• Computation
• For n0,1,2,3n
• E (n)D (n)-W (n-M) hU (n)
• W (n1)W (n-M) ? ?E (n-I) U (n-I) This is a
  look ahead only if the error and input are wide
  sense stationary else this cannot be look-ahead.
• Note This approximation Applicable for
  Stationary Inputs only
• Different LMS has been proposed for
  non-stationary inputs in the report.

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Approximation Technique for Stationary LMS

• Replace the summation
• ??E (n-I) U (n-I) I1,2M
• With the Expression
• ? M E (n)U (n).
• This Stabilizes the pipelined implementation of
  an adaptive filter.approximation techniques such
  as RLA technique change the functionality of the
  LMS algorithm which may cause extreme instability
  necessitating the need for proper selection of
  step size and pipeline depth etc.

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• The aim of the simulations above was
• 1.To show that the approximations introduced were
  just as effective as RLA if not better in
  pipelining an adaptive LMS filter.
• 2.To show that without the additional hardware
  overhead, we can still obtain the same accuracy
  of an RLA approximation and also ensure a greater
  range of pipeline depths.
• 3.I did not want to make drastic changes in the
  functionality of the algorithm and yet obtain
  significant pipelining depths.
•  
• Results
• 1.I achieved the same accuracy of an RLA
  approximation and in some cases the accuracy is
  better.
• 2.The depth of pipeline can be more for this
  approximation
• 3.We can see that for a pipeline depth of 20,
  instability seems to be creeping in but the
  algorithm still is very accurate.
• 4.The additional hardware overhead is not
  involved and the change is functionality is not
  as drastic as in RLA.
•  
•  

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Non Stationary LMS-Changes introducedto the
original algorithm

• 1.Forgetting Factor
• 2.Epoch Length for staggered Update of the
  weights.

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• Results and analysis
•  the aim of the NON-LMS simulations was
•  1.To pipeline a non-stationary input LMS
  algorithm and then test its stability
•  2.To change the epoch length and test for
  various pipeline depths.
•   Results
•  The non-stationary algorithm looks a lot more
  stable at greater pipeline depths than the
  stationary algorithm. Also, for greater pipeline
  depths for a fixed epoch length, the algorithm
  takes a long time to converge. Therefore, we can
  vary the epoch length or the pipeline depth in
  order to ensure faster convergence. Therefore, a
  balance between the throughput and convergence
  time should be theyre depending on the type of
  application for which we use the filter.
• When we reduce the epoch length, the incoming
  data is broken up into smaller blocks and takes a
  longer time to converge. This can be seen by
  comparing the plots of the learning curve for
  pipelining depth of 5 but with epoch lengths of
  10 and 7 respectively. Therefore, we need to
  reduce the pipeline depth in order to reduce the
  convergence time. Therefore, for a pipeline depth
  of 3 as shown above, the convergence time is much
  lower. The conclusion is that depending on the
  application we need to strike a balance between
  the depth of pipelining and the epoch length.

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Conclusion and Discussion

• These courses provided me with the knowledge base
  to pursue this work.
• I believe a lot more work can be done with
  adaptive filters to ensure faster computation for
  a variety of different applications. For example,
  changing epoch lengths for different can ensure
  faster computation for a much higher depth of
  pipeline. I believe that the work that needs to
  be done with adaptive filters needs to be more
  application specific.
•  This project is an implementation type project
  undertaken by one person.
• ARJUN ARUNACHALAM
•