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Quasi-Optimal and Optimal Estimates of the Amplitude of the Unlocalized Signal


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DOI: https://doi.org/10.15866/iremos.v13i4.17445

Abstract


This paper focuses on the synthesis and the analysis of the algorithms for estimating the amplitude of a free-form video pulse with the unknown moments of appearance and disappearance, since such algorithms are expected to provide overcoming the prior parametrical uncertainty. Hardware and/or software implementations as well as performance of quasi-likelihood, maximum likelihood, and quasi-optimal estimation algorithms are also tested. One of the objectives of this paper is to find the closed analytical expressions for the biases and the variances of the introduced estimates, their accuracy increasing with signal-to-noise ratio. In order to obtain the quasi-likelihood estimate of the amplitude, instead of the unknown moments of appearance and disappearance, their expected values are used. It allows designing a measurer that is simply implemented technically. However, in this case, the loss in accuracy of the resulting estimate still occurs due to the difference between the expected and the real time parameters of a pulse. In order to improve the accuracy of the estimate, the adaptive maximum likelihood algorithm can be applied though it is rather complex in terms of technical implementation. In this paper, the quasi-optimal amplitude estimation algorithm that helps to develop both effective and technically simpler implemented measurer is proposed. It is not optimal, but its characteristics coincide with the corresponding characteristics of the adaptive maximum likelihood estimate under the big signal-to-noise ratio, as confirmed by the results of statistical simulation. The influence of prior ignorance of the time parameters on the quality of the signal amplitude estimate is also determined.
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Keywords


Maximum Likelihood Method; Quasi-Optimal Reception; Free-From Video Pulse; Estimated Signal Amplitude; Moments of Appearance and Disappearance; Local Markov Approximation Method; Bias of Estimate; Variance of Estimate

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References


D. Middleton, An Introduction to Statistical Communication Theory (Wiley-IEEE Press, 1996).

S.M. Kay, Fundamentals of Statistical Signal Processing, Volume I: Estimation Theory (Prentice Hall, 1993).

H.L. van Trees, K.L. Bell, Z. Tian, Detection, Estimation, and Modulation Theory. Part I. Detection, Estimation and Filtering Theory (Wiley, 2013).

V.I. Tikhonov, Optimal Signal Reception [in Russian] (Radio i Svyaz', 1983).

E.I. Kulikov, A.P. Trifonov, Signal Parameter Estimation against Hindrances [in Russian] (Sovetskoe Radio, 1978).

Z. Wu, B. Lankl, Coded Pulse-Amplitude-Modulation for Intensity-Modulated Optical Communications, 11th International ITG Conference on Systems, Communications and Coding (SCC 2017), pp. 1-5, Hamburg, Germany, February 2017.

M.T. Dabiri, S.M.S. Sadough, M.A. Khalighi, Differential Pulse-Amplitude Modulation Signalling for Free-Space Optical Communications, IET Optoelectronics, Vol. 13 (Issue 4):155-160, August 2019.
https://doi.org/10.1049/iet-opt.2018.5112

Z. Zhao, A. Yang, P. Guo, Q. Tan, X. Xin, A Modulation Format Identification Method Based Signal Amplitude Sorting and Ratio Calculation, Optics Communications, Vol. 470 (Article number 125819):1-7, September 2020.
https://doi.org/10.1016/j.optcom.2020.125819

S. Nandi, D. Kundu, Estimation of Parameters in Random Amplitude Chirp Signal, Signal Processing, Volume 168 (Article number 107328):1-29, March 2020.
https://doi.org/10.1016/j.sigpro.2019.107328

C. Wang, X. Liu, B. Fan, Estimation Method for Weak Sinusoidal Amplitude in Alpha Noise, 12th International Conference on Signal Processing (ICSP 2014), pp. 46-51, Hangzhou, China, October 2014.
https://doi.org/10.1109/icosp.2014.7014967

K. Czuszynski, J. Ruminski, A. Polinski, A. Bujnowski, Estimation of the Amplitude of the Signal for the Active Optical Gesture Sensor with Sparse Detectors, 9th International Conference on Human System Interactions (HSI 2016), pp. 483-489, Portsmouth, United Kingdom, 2016.
https://doi.org/10.1109/hsi.2016.7529678

S. Zheng, X. Pan, A. Zhang, Y. Jiang, W. Wang, Estimation of Echo Amplitude and Time Delay for OFDM-Based Ground-Penetrating Radar, IEEE Geoscience and Remote Sensing Letters, Vol. 12 (Issue 12):2384-2388, December 2015.
https://doi.org/10.1109/lgrs.2015.2478279

R.G. McKilliam, A. Pollok, W. Cowley, I.V.L. Clarkson, B.G. Quinn, Carrier Phase and Amplitude Estimation for Phase Shift Keying Using Pilots and Data, IEEE Transactions on Signal Processing, Vol. 62 (Issue 15):3976-3989, August 2014.
https://doi.org/10.1109/tsp.2014.2332976

Al-Dwairi, M., Skopin, D., Detection and Demodulation of AM Signals Using Two Dimensional Spectral Surface, (2017) International Review on Computers and Software (IRECOS), 12 (4), pp. 185-190.
https://doi.org/10.15866/irecos.v12i4.14709

Perov, A., Noise Immunity Analysis of LocataNet Navigation Receiver, (2018) International Review of Aerospace Engineering (IREASE), 11 (3), pp. 127-137.
https://doi.org/10.15866/irease.v11i3.14581

O.V. Chernoyarov, M.M. Shahmoradian, M. Marcokova, Y.E. Korchagin, Secrecy of communications in data transmission by impulses with unknown moments of appearance and disappearance, International Journal of Engineering, Transactions A: Basics, Vol. 32 (Issue 4):548-554, April 2019.
https://doi.org/10.5829/ije.2019.32.04a.12

A.P. Trifonov, Y.E. Korchagin, P.A. Kondratovich, Estimation of the Appearance and Disappearance Times of Unknown-amplitude Signals, Radiophysics and Quantum Electronics, Vol. 55 (Issue 6):413-428, June 2012.
https://doi.org/10.1007/s11141-012-9378-9

C.C. Heyde, Quasi-Likelihood and Its Application: A General Approach to Optimal Parameter Estimation (Springer-Verlag, 1997).

V.I. Mudrov, V.L. Kushko, Methods of Measurements Processing. Quasi-Likelihood Estimates [in Russian] (Radio i Svyaz', 1983).

M.I. Gryaznov, M.A. Gurevich, M.A. Ryabinin, Pulse Parameter Measurements [in Russian] (Radio i Svyaz', 1991).

O.V. Chernoyarov, Y.E. Korchagin, A.A. Makarov, A.N. Glushkov, The Duration Estimate of the Missing Signal with the Unknown Amplitude, International Journal of Applied Engineering Research, Vol. 12 (Issue 19): 8548-8555, October 2017.

A.P. Trifonov, Y.E. Korchagin, Joint Estimates of the Parameters of a Signal with Unknown Moments of Appearance and Disappearance, Izvestiya Vysshikh Uchebnykh Zavedenij. Radioelektronika, Vol. 43 (Issue 5):34-43, May 2000.

O.V. Chernoyarov, Y.A. Kutoyants, A.P. Trifonov, On Misspecifications in Regularity and Properties of Estimators, Electronic Journal of Statistics, Vol. 12 (Issue 1):80-106, January 2018.
https://doi.org/10.1214/17-ejs1385

A.P. Trifonov, Y.E. Korchagin, O.V. Chernoyarov, B.I. Shakhtarin, Detection of Radio Signals That Appear and Disappear at Unknown Moments, Journal of Communications Technology and Electronics, Vol. 60 (Issue 4):375-385, April 2015.
https://doi.org/10.1134/s1064226915040130

A.P. Trifonov, Y.E. Korchagin, M.V. Trifonov, O.V. Chernoyarov, Estimate of the Moments of Appearance and Disappearance of a Radio Signal with Unknown Initial Phase, Wulfenia, Vol. 22 (Issue 9):105-116, September 2015.
https://doi.org/10.12988/ams.2014.47588

O.V. Chernoyarov, A.V. Zakharov, A.P. Trifonov, A.V. Salnikova, A.A. Makarov, The Common Approach to Calculating the Characteristics of the Signal Parameters Joint Estimates Under the Violation of the Decision Statistics Regularity Conditions, Engineering Letters, Vol. 28 (Issue 2):492-503, May 2020.

A.S. Terent’yev, Probability Distribution of a Time Location of an Absolute Maximum at the Output of a Synchronized Filter, Radiotekhnika i Elektronika, Vol. 13 (Issue 4):652-657, April 1968.

E.B. Dynkin, Theory of Markov Processes (Dover Publications Inc., 2006).

M.I. Yadrenko, Spectral Theory of Random Fields (Springer, 1983).

Vorotova, A., Medvedev, M., Soloviev, V., Finaev, V., Statistical Data Processing of Two Mobile Objects Behavior in Random Environments Using Simulation Modeling Method, (2019) International Review of Automatic Control (IREACO), 12 (4), pp. 182-191.
https://doi.org/10.15866/ireaco.v12i4.17319

O.V. Chernoyarov, E.A. Lysina, M. Marcokova, B.I. Shakhtarin, Modeling of Random Processes Transformations Exemplified by the Software Implementation of the Algorithms for the Processing of the Random Pulse Against Correlated Interferences, 2015 International Conference on Simulation, Modelling and Mathematical Statistics (SMMS2015), pp. 169-180, Chiang Mai, Thailand, 2015.


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