Neural detection of QAM signal with strongly nonlinear receiver

doi:10.1016/S0925-2312(98)00044-7

Neurocomputing

Volume 21, Issues 1–3, 6 November 1998, Pages 159-171

https://doi.org/10.1016/S0925-2312(98)00044-7 Get rights and content

Abstract

Neural receiver structures have been developed for adaptive discrete-signal detection in telecommunication applications. Neural networks combined with conventional equalizers improve the performance especially in compensating for nonlinear distortions. These distortions may result, for instance, from nonlinear amplification implemented for reducing the power consumption. In this paper, the behavior of the neural receiver in multipath channel with additive white Gaussian noise has been investigated. The transmitted signal is quadrature amplitude modulated (QAM). A receiver structure based on self-organizing map (SOM) is compared with a conventional decision feedback equalizer (DFE).

Introduction

Nonlinear distortions of signal constellation decrease the performance of a transmission system. These nonlinearities can arise from both the transmission and receiver end of the transmission channel. The amplifiers might decrease the modulation peak values. In our earlier studies, we have shown how the effect of nonlinear distortions of the transmitter can be diminished using self-organizing maps in the receiver 5, 6, 10, 11. In this study, we concentrate on nonlinear distortion of the receiver end.

Receiver end nonlinearities can be due to an uncontrollable shift of the operation point 1, 2, 3, 7, 8, or the signal is fed through a nonlinear amplifier on purpose. Such an amplifier can be used to cut off amplitude peak values and thus save power. The power consumption has a direct influence on the size of the required battery, for example, in mobile telephones. We have to consider receiver structures which are using less power than the structures used nowadays in order to further decrease the size of portable phones. Naturally, the nonlinear distortion degrades the performance of an equalizer as compared to conventional structures with undistorted decision levels. This study investigates the possibility to achieve less degradation than with conventional equalizer structures. Also, it is expected that the neural methods might be more robust, i.e., that they might be less sensitive to parameter variations which may occur due to aging, temperature variations and alike. Finally, we have to decide how much power can be saved without harmful loss in performance.

Section snippets

System model

The receiver model with real signals is depicted in Fig. 1. The intermediate frequency (IF) signal R(t) with carrier frequency f_c enters the first bandpass filter. The purpose of this filter is to clean out noise and unwanted signals outside the band of the wanted signal. The bandpass signal can be represented as $R(t)= Re {r(t) e^{jω_{c}t}},$ where r(t) is the complex envelope of the received signal.

The signal is then amplified in the IF-amplifier having a nonlinear characteristic curve. This curve can be

Nonlinear amplifier

The nonlinearity in the amplifier is an instantaneous functional correspondence $f (x)$ between input x and output y. Preferred function is logarithmic or some approximation to that. In practice, most of the amplifiers have a logarithmic characteristic curve. In this paper, $f (x)= 10^{0.1g} log_{10} (1+ax) log_{10} (1+a)$ is considered as a possible characteristic curve of the amplifier. Here g is the amount of nonlinear distortion in dBs and a is a curvature parameter. The above $f (x)$ fulfills the following

Approximating a logarithmic curve

The characteristic curve of a nonlinear amplifier is approximated using a fifth order polynomial as described in Section 3. Decay of the amplifier is 3 or 6 dB in the peak amplitude values of signal constellation. The data vectors x and y used in the least-squares sense curve fitting were $x=[−1−b,−1,−1+b,−s/2,−0.1, 0.1, s/2, 1−b, 1, 1+b],$ $y=[−s−d,−s,−s+d,−s/2,−0.1, 0.1, s/2, s−d, s, s+d],$ where b=0.25, $s(g)= 10^{0.1g}$ and $d=(s(g)−s(g_{0}))b/(1−s(g_{0})).$ The idea is to define a group of curves using the maximum decay g₀

Equalizers

In this paper, the main interest is in an equalizer structure in which a decision feedback equalizer and a self-organizing map [6]have been combined. The structure shown in Fig. 4 is used to compensate for the nonlinearities. The output of DFE is fed into SOM. The SOM is used as an adaptive decision device. When a QAM modulated signal is used, the in-phase and quadrature components of the signal make up a two-dimensional SOM input vector. The SOM is initialized to a square grid of the same size

Simulations

In the simulations, both 16-QAM and 64-QAM have been used. The channel model has been one or two-path. The transfer functions were correspondingly H(z)=1 and H(z)=1−0.2z⁻¹. There has been no interfering signal. The SOM size is 4×4 in 16-QAM and 8×8 in 64-QAM. The RBF basis function width is fixed to 13 after a few preliminary tests. The first 40 input vectors are used as RBF centers and the weights are adjusted using the whole pilot sequence. The simulations have been run 20 or 50 times on each

Conclusion

The simulation results are quite promising. It is obvious that an adaptive method, such as SOM or other neural equalizer, increases the robustness of the receiver when a nonlinear amplifier forms an essential part of the demodulator chain. Both the decay of the amplifier and the amount of levels in modulation have an effect on the performance of the equalizer. Neural equalizers are less disturbed by a small shift of operation point, but if the shifts toward the origin are larger, DFE

Acknowledgements

The study has been financed by NOKIA Mobile Phones and the Technology Development Centre Finland (TEKES) which is gratefully acknowledged. Similarly the reviewers are acknowledged for their remarks and comments.

Kimmo Raivio received his M.Sc. degree from Helsinki University of Technology, Finland, in 1990. He got his Licentiate degree in computer science from Helsinki University of Technology in 1993 and currently he is a Ph.D. student at the Laboratory of Computer and Information Science, Helsinki University of Technology. He holds two patents, has published papers in international conferences and journals. His research interests include neural networks and their applications in telecommunications,

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Jukka Henriksson graduated 1970 (Diploma Engineer) from Helsinki University of Technology (HUT). He got his Licentiate degree in 1980 and Doctor degree in 1985 from the same university, both with high honours. He worked in Communications Laboratory of HUT from 1969 to 1984. He joined Nokia Telecommunications 1984 and has been since 1986 in Nokia Research Center (NRC). He was nominated as Research Fellow of NRC (in the area of propagation, modulation and coding) in 1994. He has been active in modulation studies, diversity reception and other areas of radio propagation in fixed radio links. He has worked also within TV transmission (EUREKA HDTV and digital TV) and some other areas of radio transmission like neural detection of digital signals.

Dr. Henriksson holds several (about 12) patents and has published papers in national and international forums. He was granted the Nokia Award in 1990 for achievements within digital communications, especially radio links. He is a senior member of IEEE and a member of the Finnish Society of Electronic Engineers (EIS).

Olli Simula received his Dr. Tech. degree in computer science from Helsinki University of Technology, Finland, in 1979. He is currently Professor of Computer Science and Engineering at the Laboratory of Computer and Information Science, Helsinki University of Technology. Dr. Simula is the author of a number of journal and conference papers and book chapters on digital signal processing, image analysis, and neural computing. He is editor of two conference proceedings in image analysis and artificial neural networks. His research interests include digital signal processing, neural networks and their applications in process monitoring, modeling, and analysis, and intelligent methods in telecommunications, especially neural receiver structures and adaptive resource management methods.

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Neural detection of QAM signal with strongly nonlinear receiver

Abstract

Introduction

Section snippets

System model

Nonlinear amplifier

Approximating a logarithmic curve

Equalizers

Simulations

Conclusion

Acknowledgements

Signal Process.

Channel equalization using adaptive complex radial basis function networks

IEEE J. Selected Areas Commun.

Neural Networks: a Comprehensive Foundation

Self-Organizing Maps