GSPT-AS-based Neural Network Design

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GSPT-AS-based Neural Network

Design

Presenter: Kuan-Hung Chen

Adviser: Tzi-Dar Chiueh

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Outline

• Motivation

• GSPT-AS LMS Algorithm

• Power Amplifier Model

• Predistortor Architecture

• Simulation Results and Complexity Analysis

• Conclusions

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Motivation

• Initial simulation results show that the GSPT-based

neural network cannot converge.

• The reason is that the magnitude of all weights will

have approximately the same order if only the sign of the updating term is taken for weight updating.

• So, it is reasonable that the magnitude of the

updating term should be taken into account.

 It is straightforward to apply the GSPT-AS LMS algorithm, that takes the magnitude of the updating term into account, to the weight updating in the neural network.

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Basic Structure of an LMS

Adaptive Filter

z-1 z-1 z-1 z-1 z-1 z-1 z-1 z-1 w₀ w₁ w₂ w₃ _ + e[n] d[n] μ y[n] x[n] 0 linear filter

coefficient updating block

] [ ] [ ] [ ] 1 [ ] [ ] [ ] [ ] [ ] [ ] [ 3 0 i n x n e μ n w n w n y n d n e i n x n w n y i i i i           





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GSPT LMS Algorithm

• Reduce the complexity of both linear filter and the

coefficient updating block in an adaptive filter

1 0 , 0 ] [ ] [ , ] [ 0 ] [ ] [ , ] [ 0 ] [ ] [ , ] [ ] 1 [ ] [ ] [ ] [ ] [ ] [ ] [ 1 0                         



  N k k n x n e if n w k n x n e if n w k n x n e if n w n w n y n d n e k n x n w n y k k k k N k k

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GSPT-AS LMS Algorithm

• Q(z) represents a power-of-2 value which is closest

to z but not larger than z and g is the group size.

   





        1 0 , 1 ] [ , ] [ , ] [ 0 ] [ , ] [ 1 ] [ , ] [ , ] [ ] 1 [ 0 ] [ ] [ , 1 0 ] [ ] [ , 1 ] [ 1 ] [ ] [ , 0 1 ] [ ] [ , 1 ] [ ] [ log 1 ] [ ] [ ] [ ] [ , ] [ ] [ ] [ , , 2 1 0                                                 _ _ _ _      



  N k n s m n m if n w n m if n w n s m n m if n w n w k n x n e if k n x n e if n s k n x Q n e Q μ if k n x Q n e Q μ if k n x Q n e Q μ g floor n m n y n d n e k n x n w n y k k m k k k k k m k k k k N k k

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Coefficient Updater for

GSPT-AS LMS

AS LMS

• Based on the magnitude of the updating term, we c

hoose the proper updating unit to receive the carry in/borrowin signal. linear filter carryout borrowout carryin borrowin

Updating term decision block

μ x[n-k] e[n] b₆ updating unit reset b₇ b₈ b₉ updating unit reset b₁₀ b₁₁ b₃ updating unit reset b₄ b₅ b₀ updating unit reset b₁ b₂

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Power Amplifier Model

• To simulate a solid-state power amplifier, the

following model is used for the AM/AM conversion:

• The AM/PM conversion of a solid-state power

amplifier is small enough to be neglected.

• A good approximation of existing amplifiers is

obtained by choosing p in the range of 2 to 3.

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Transfer Function of AM/AM

Conversion

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64-QAM Constellations

Distorted by PA Model

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Predistortor Architecture

(a) Learning Architecture SSPA NN || || I + jQ Angle NN I + jQ SSPA Polar to Rectangular (b) Predistortion Architecture + -|| -|| || ||

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Neural Network Structure

• The neural network structure used is a MLP with

one hidden layer.

• The input layer has 1 neuron and 1 bias neuron.

• The hidden layer has 10 neurons and 1 bias neuron. • The output layer has 1 neuron.

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Backpropagation Algorithm

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GSPT-AS-based Backpropaga

tion Algorithm

• Let Q(z) represent a power-of-2 value which is

closest to z but not larger than z.

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Simulation Results (1)

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Simulation Results (2)

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64-QAM Constellation with G

SPT-AS-based Predistortion

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Floating-Point Scheme vs.

GSPT-AS-based Scheme

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Complexity Analysis

Fixed-point GSPT-AS Output calculation Multiplication 2  N 2  N Addition 2  N + 1 2  N + 1 f() N N ---Weight updating Multiplication 5  N 0 Addition 4  N + 1 N Power-of-2 Addition 0 5  N Round-to-power-of-2 0 3  N + 2

GSPT-AS coeff. updater 0 3  N + 1

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Conclusions

• A low-complexity GSPT-AS-based neural network p

redistortor for nonlinear PA has been designed and simulated.

• Simulation results show that the GSPT-AS-based n

eural network predistortor can achieve very close p erformance to the floating-point neural network pr edistortor with much lower complexity.

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Reference

1. C. N. Chen, K. H. Chen, and T. D. Chiueh, “Algorithm and Arch itecture Design for a Low-Complexity Adaptive Equalizer,” in

Proc. of IEEE ISCAS ‘03, 2003, pp. 304-307.

2. R. V. Nee and R. Prasad, OFDM Wireless Multimedia Commun ications, Artech House, 2000.

3. F. Langlet, H. Abdulkader, D. Roviras, A. Mallet, and F. Casta nié, “Adaptive Predistortion for Solid State Power Amplifier u sing Multi-layer Perceptron,” GLOBECOM ’01. IEEE, Vol. 1, 2 5-29 Nov. 2001, pp. 325-329.