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Project on
ALE USING FLMS ALGORITHM Prepared by :
Mr Prabhash K Singh (Communication System,12531012)
Mr. Sreekanth CB (Communication System,12531014)
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BLMS(Block Least Mean Square)
• Incoming data sequence is sectioned into
blocks using serial to parallel converter.
• Block of input data are applied to FIR filter one
block at a time.
• Adaptation of filter proceeds on a block by
block basis rather than sample by sample
basis as in conventional LMS algorithm.
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FLMS(Fast Least Mean Square)
• BLMS requires both linear convolution and linearcorrelation in its implementation.
• FFT provides powerful tool for faster convolutionand faster correlation.
• A frequency domain implementation of BLMS willbe more efficient.
• FLMS is the frequency domain implementation of
BLMS• Computationally more efficient than Block-
LMS(more than 15 times).
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FLMS Algorithm
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Algorithm continued…..
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ALE Using FLMS Algorithm
• Generate a signal of the forms(n) = A sin(2πf1n/Fs) + B sin(2πf2n/Fs)Fs = sampling Frequency
• A noise w(n) is added to the signal to produce the noisy signald(n) = s(n) + w(n)
• The noise is a white uniformly distributed sequence with zeromean. The SNR of this signal should about -7 dB. The desired signal( or primary signal) is d(n). The reference signal is d(n−1) and isapplied to the input of an N-tap FIR filter that produces the outputy(n), which should be the estimate of the signal. Use the LMSalgorithm for adaptation. Choose N and the step size appropriately
for good results.
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Part one:
• Experiment with different block lengths of
L=100, 200, 400, 800, and 1000. Discuss the
effect of the block length on convergence, if
any. How does the computational change with
the block length? Using SNR=10
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Fig 1: Block length=100
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Fig 2: Block length=200
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Fig 3: Block length=400
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Fig 4: Block length=800
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Fig 5: Block length=1000
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• Effect of Block length on convergence:
when block length increases
1. convergence didn’t happen. To maintainconvergence we have to decrease the step
size.
2. computational complexity decreases for
same number of iterations
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• Optimal choice is block length = filter length,its computationally more efficient.
• When
block length < filter length-advantage of reduced processing delay
-still more efficient than conventional LMS.
block length > filter lengththere is redundant operations in adaptive
process
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Part 2: FLMS v/s LMS
• FLMS is computationally more efficient.
• FLMS converges at a faster rate than LMS.
•
Convergence rate of FLMS can be furtherimproved by assigning different step size for
each weight.
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Part 3:
• In the FLMS, contiguous blocks of data are
used. One variantion is to use partially
overlapping blocks in order to gain convergent
speed. Use overlaps of L/4, L/2 and 3L/4 andrepeat your experiments Discuss the
performance of the algorithm.
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• As overlapping between block elements
increases their convergence is also faster.
• But need more computation is involved.
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!!! THANK YOU !!!