On Structure-Criterion Switching Control for Self-Optimized Decision Feedback Equalizer Vladimir R. Krstić, Member, IEEE, Nada Bogdanović Institute “Mihajlo Pupin” Belgrade, Serbia This work was supported by the Ministry of Education, Science and Technological Development of the Republic of Serbia; the project of technological development TR 32037, 2011-2017. IcETRAN 2017 5-8 Jun, 2017. Kladovo-SERBIA

IcETRAN 2017, Kladovo-SERBIA Presentation outlines: Non data-aided adaptive Decision Feedback Equalization (blind DFE) Self-optimized DFE scheme: some topics of the DFE blind activation Soft-DFE equalizer: structure, criteria and operation control problems Innovated structure-criterion switching control Simulation results: the Soft-DFE convergence achievements Conclusions and Soft-DFE convergence animations IcETRAN 2017, Kladovo-SERBIA

IcETRAN 2017, Kladovo-SERBIA Data-aided adaptive equalizer: baseband model The adaptive equalizer is a system (channel) identifier. To estimate unknown channel transfer function a conventional equalizer utilizes a known train sequence (preamble). IcETRAN 2017, Kladovo-SERBIA

IcETRAN 2017, Kladovo-SERBIA Blind Decision Feedback Equalizer (DFE): basic structure Blind DFE includes: - FFF – feedforward FIR filter, - FBF – feedback FIR ilter, - Blind coefficients adaptation criterion/algorithm - Data slicer or some sort of soft data detection - Convergence-control monitor commonly based on the output mean square error (MSE) The major drawback of blind DFE is the error propagation phenomenon caused by the absence of any kind of preamble. IcETRAN 2017, Kladovo-SERBIA

IcETRAN 2017, Kladovo-SERBIA Self-optimized DFE scheme: the solution of blind DFE that “skips” the error propagation effects: SO-DFE scheme diminishes the error propagation effects optimizing both the structure and the optimization criterion according to convergence state: - in the blind operation mode the SO-DFE transforms itself into the cascaded linear equalizer to open the signal constellation enough and than - transforms itself back into the non-linear decision-directed structure. IcETRAN 2017, Kladovo-SERBIA

IcETRAN 2017, Kladovo-SERBIA A practical realization of the SO-DFE concept: Soft-DFE equalizer b) a) c) The Soft-DFE performs adaptation through three operation modes combining JEM (Joint Entropy Maximization), CM (Constant Modulus) and MMSE (Minimum Mean Square Error) criteria: a) blind mode, b) soft transition mode and c) tracking mode. To switch operation modes the Soft-DFE monitors the convergence state estimating the output MSE and using the fixed MSE threshold levels. IcETRAN 2017, Kladovo-SERBIA

IcETRAN 2017, Kladovo-SERBIA Problem definition The structure-criterion switching problem is analyzed through two steps: inadequacy of the current MSE estimation method effects of the fixed MSE threshold levels on the equalizer convergence. The current solution: to decide optimal switching Soft-DFE estimates the output MSE exploiting efficiency of the FSE-CMA equalizer recovering the kurtosis statistic of the given signal constellation. IcETRAN 2017, Kladovo-SERBIA

IcETRAN 2017, Kladovo-SERBIA The current solution: the illustration of the fixed MSE threshold TL1 effects on the Soft-DFE convergence behavior. The three typical scenarios of Soft-DEF structure-criterion switching from the blind to the soft decision-directed operation mode for the 64-QAM signal. The fixed threshold level TL1=8.13 dB is selected as an optimal. IcETRAN 2017, Kladovo-SERBIA

IcETRAN 2017, Kladovo-SERBIA The new MSE estimation method combining the fixed threshold MSETL with the whitener a posteriori error which is a result of the received signal whitening using the JEM stochastic gradient algorithm. IcETRAN 2017, Kladovo-SERBIA

IcETRAN 2017, Kladovo-SERBIA The innovated on line structure-criterion switching control from blind to soft-transition mode: the monitor estimates MSEB,n and compares it with the time variable threshold MSETLV. Parameters K (integer, K>1) and S mostly depend on the given signal. IcETRAN 2017, Kladovo-SERBIA

IcETRAN 2017, Kladovo-SERBIA Simulation results The m-QAM system simulator includes: the signal constellation source, transmitter and receiver band-pass filters, multipath channel model and Soft-DFE . The performance results are given in the terms of PDF of the blind mode duration time, MSE convergence characteristics and ESI index obtained as the ratio between the successful equalizations and the total number of Monte Carlo runs. IcETRAN 2017, Kladovo-SERBIA

IcETRAN 2017, Kladovo-SERBIA Probability density function histograms of the blind mode time duration obtained with 16-QAM and 64-QAM signals for TLF-fixed and TLV variable threshold cases. IcETRAN 2017, Kladovo-SERBIA

IcETRAN 2017, Kladovo-SERBIA Convergence characteristics obtained with 16-QAM (left) and 64-QAM (right) signals. Table: ESI [%] obtained for 10000 runs. Channel Mp-A Mp-C Mp-E 16-QAM ESI: TLF 99.92 99.87 98.94 ESI: TLV 99.94 99.90 99.20 64-QAM 100 99.50 98.40 99.66 98.10 IcETRAN 2017, Kladovo-SERBIA

Conclusions and Soft-DFE convergence animations The new structure-criterion switching control combines the fixed MSE term with the whitener’s a posteriori error . The MSE estimation method combines the fourth-order statistic of the FSE-CMA equalizer and the pre-whitener’s second order statistic. Effectively, the switching controls behaves as a control with time variable threshold. The method is computationally cost effective because uses the already existing whitener’s a posteriori errors. The new method speeds the equalizer’s convergence rate and indicates higher robustness regarding the received signal non-stationarity. The method can be adapted for different type blind equalizes performing the received signal prewhitening. IcETRAN 2017, Kladovo-SERBIA

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Thank you for attention IcETRAN 2017, Kladovo-SERBIA