COMPARATIVE ANALYSIS OF ML AND MAP DETECTORS FOR PAM CONSTELLATIONS IN AWGN CHANNEL

Slobodan Aca Vlajkov, Aleksandra Ž Jovanović, Zoran H Perić

DOI Number
https://doi.org/10.2298/FUEE2002217V
First page
217
Last page
226

Abstract


In this paper we perform a comparative performances analysis of “maximum a posteriori” (MAP) and “maximum likelihood” (ML) detectors for one-dimensional constellation in the adaptive white Gaussian noise (AWGN) channel. More precisely, error probabilities per symbol for the aforementioned detectors are compared for the case when the pulse amplitude modulation (PAM) constellation with the equidistant and non-equiprobable constellation points is used as one-dimensional constellation. We perform analysis for different distributions of the constellation point probabilities and different values of the signal-to-noise ratio (SNR). The analysis indicates which detector can be adequate choice for the certain distribution of constellation point probabilities and the SNR. Besides this, for the straightforward performance assessment of the MAP detector we derive a formula for the symbol error probability. Our analysis also points out that the nonuniform distribution of the constellation points probabilities does not necessarily improve the symbol error probability. With the aim to decrease the symbol error probability we propose a method for defining constellation point probabilities. The presented results show that PAM constellation designed by utilizing the method we propose significantly outperforms the conventional PAM constellation in terms to the symbol error probability.


Keywords

PAM constellation, AWGN channel, ML detector, MAP detector, symbol error probability

Full Text:

PDF

References


J. G. Proakis, Digital communications, McGraw-Hill Science, 2001.

P. Ivaniš, D. Drajić, Introduction to Information Theory and Coding (In Serbain), Akademska misao, 2018.

A. Alvarado, E. Agrell, F. Brannstrom, "Asymptotic comparison of ML and MAP detectors for multidimensional constellations", IEEE Transactions on Information Theory, vol. 64, no. 2, pp. 1231–1240, 2018.

M. Ivanov, F. Brannstrom, A. Alvarado, et al., "On the exact BER of bit-wise demodulators for one-dimensional constellations", IEEE Transactions on Communications, vol. 61, no. 4, pp. 1450–1459, 2013.

H. Kuai, F. Alajaji, G. Takahara, "Tight error bounds for nonuniform signaling over AWGN channels", IEEE Transactions on Information Theory, vol. 46, no. 7, pp 2712–2718, 2000.

L. Wei, I. Korn, "Optimal M-amplitude shift keying/quadrature amplitude shift keying with non-equal symbol probabilities", IET Communications, vol. 5, no. 6, pp 745–752, 2011.

L. Wei, "Optimized M-ary orthogonal and bi-orthogonal signaling using coherent receiver with non-equal symbol probabilities", IEEE Communications Letter, vol. 16, no. 6, pp 793–796, 2012.

I. Korn, J. P. Fonseka, S. Xing, "Optimal binary communication with nonequal probabilities", IEEE Transactions on Communications, vol. 51, no. 9, pp 1435–1438, 2003.

V. Ipatov, "Comments on Optimal binary communication with nonequal probabilities", IEEE Transactions on Communications, vol. 55, no. 1, pp. 231, 2007.

Z. H. Perić, "Nonlinear transformation of one-dimensional constellation points in order to error probability decreasing", Facta Universitatis, Series: Electronics and Energetics, vol. 11, no. 3, pp. 291–299, 1998.

Z. H. Perić, M. S. Bogosavljević, "Performance of nonuniform PAM constellations for Gaussian channel", Electronics and Electrical Engineering, vol. 52, no. 3, pp. 27–30, 2004.

Z. H. Perić, N. Milošević, A. Ž. Jovanović, et al., "Design of piecewise uniform PAM constellation", In Proceedings of the XII International SAUM Conference on Systems, Automatic Control and Measurements, Niš, Serbia, November 2014, pp. 109–111.

Z. H. Perić, A. Ž. Jovanović, S. A. Vlajkov, "Comparative analysis of various PAM constellations", In Proceedings of the XIII International SAUM Conference on Systems, Automatic Control and Measurements, Niš, Serbia, November 2016, pp. 27-30, 2016.

I. B. Djordjevic, A. Ž. Jovanovic, Z. H. Peric, T. Wang, "Optimized vector-quantization-based signal constellation design (OVQ-SCD) for multidimensional optical transport", In Proceedings of thd CLEO: Science and Innovations, San Jose, California United States, June 8-13, 2014.

I. B. Đorđević, A. Ž. Jovanović, Z. H. Perić, T. Wang, "Multidimensional optical transport based on optimized vector-quantization-inspired signal constellation design", IEEE Transactions on Communications, vol. 62, no. 9, pp. 3262–3273, 2014.

I. B. Đorđević, A. Ž. Jovanović, M. Cvijetić, Z. H. Perić, "Multidimensional vector quantization-based signal constellation design enabling beyond 1 Pb/s serial optical transport networks", IEEE Photonics Journal, vol. 5, no. 4, 2013.

S. A. Vlajkov, A. Ž. Jovanović, Z. H. Perić, "Approach in companding-quantisation-inspired PAM constellation design", IET Communications, Vol. 12, No. 18, pp. 2305–2314, 2018.


Refbacks

  • There are currently no refbacks.


ISSN: 0353-3670 (Print)

ISSN: 2217-5997 (Online)

COBISS.SR-ID 12826626