Decision-directed Equalization Research Articles

Timing Recovery and Adaptive Equalization for Discrete Multi-Tone Signalling in Wireline Applications

This paper proposes a discrete multi-tone timing-recovery system with adaptive equalization for ultra-high-speed wireline applications. It combines frequency-domain clock recovery with decision-directed equalization to improve receiver performance while eliminating the need for pilot carriers, thereby increasing spectral efficiency. Compared to a conventional pilot-carrier-based technique employing four pilot carriers and a 32-point FFT, this approach improves phase-error sensitivity by 3.6 times, tracking bandwidth by 1.7 times, increases the jitter tolerance slope by <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"> <tex-math notation="LaTeX">$20dB$ </tex-math></inline-formula> per decade at low frequency, and removes residual equalization error, resulting in an overall data-rate increase of 27%. The concept is validated at the system-level and gate-level through synthesis in an FPGA. A convergence analysis of both the adaptive equalizer and clock synchronization shows the system’s ability to mitigate error propagation and remain synchronized in the presence of impairments. Finally, we highlight the system’s ability to trade-off clock convergence versus phase error sensitivity. Either parameter can be adjusted by 15 times, optimizing the receiver over a broad range of signal conditions.

180 Gb/s PAM8 Signal Transmission in Bandwidth-Limited IMDD System Enabled by Tap Coefficient Decision Directed Volterra Equalizer

In this paper, we have explored the feasibility of 8-level pulse amplitude modulation (PAM8) format for realizing beyond 100 Gb/s transmission in a bandwidth-limited intensity modulation and direct-detection (IMDD) system. Generally, Volterra equalizer is a practical algorithm which can be used in bandwidth-limited system to combat the linear and nonlinear impairments. However, we observe that the performance of Volterra equalizer would be restricted by a phenomenon of level-dependent equalized effect, especially in low optical signal-to-noise ratio case. To cope with this problem, a tap coefficient decision directed Volterra equalizer (TDD-Volterra) with multiple sets of tap coefficients is proposed. The optimal set of tap coefficients is selected according to the decision results of input symbols before equalization. By this means, the TDD-Volterra is effective for overcoming the level-dependent equalized effect. By using the proposed TDD-Volterra, 180 Gb/s PAM8 signal is successfully transmitted over 2 km standard single mode fiber in an IMDD system with the 10-dB bandwidth of 17.5 GHz for the first time. The achieved bit error rate (BER) value is below the 7% overhead hard-decision forward error correction threshold of $3.8\times 10 ^{-3}$ . Moreover, the performance comparison among decision-directed least-mean square equalizer, Volterra Equalizer, and TDD-Volterra are analyzed in this paper. The experimental results show that compared to the conventional Volterra equalizer, the algorithm complexity of TDD-Volterra is decreased by over 50% for achieving a given BER value. Our research may provide a solution for beyond 100 Gb/s short-reach applications using bandwidth-limited electro-optical components.

Testing different Channel Estimation Techniques in Real-Time Software Defined Radio Environment

In modern wireless communication to maximize spectral efficiency and to minimize the bit error rate OFDM (Orthogonal frequency-domain multiplexing) is used. OFDM is used broadly in networks using various protocols, including wireless vehicular environment IEEE 802.11p, IEEE 802.16d/e Wireless Metropolitan Area Networks, Long-Term Evolution 3GPP networks and IEEE 802.11a/g/n Wireless Local Area Networks. The main challenges involved when using OFDM for wireless communications are short channel-coherence bandwidth and the narrow coherence time, and both have a major effect on the reliability and latency of data packet communication. These properties increase the difficulty of channel equalization because the channel may change drastically over the period of a single packet. Spectral Temporal Averaging is an enhanced decision-directed channel equalization technique that improves communication performance (as far as the frame delivery ratio (FDR) and throughput) in typical channel conditions. This paper reports tests of Spectral Temporal Averaging channel equalization in an IEEE 802.11a network, compared with other channel equalization techniques in terms of the FDR in a real-time environment. Herein, a software defined Radio (SDR) platform was used for estimating the channel. This proves that the system can provide over 90% of delivery ratio at 25 db of Signal to Noise Ratio (SNR) for various digital modulation techniques. For this purpose, an experimental setup consisting of software-defined radio, Universal Software Radio Peripheral (USRP) N210 along with wide bandwidth daughter board as hardware and GNU radio is used.

Adaptive Blind Postdistortion and Equalization of System Impairments for a Single-Channel Concurrent Dual-Band Receiver

Concurrent dual-band receivers use fewer RF components to flexibly receive signals in the dual bands. To further reduce the number of components, a compact concurrent dual-band receiver architecture has been demonstrated in this paper. It employs only a single down-conversion channel to down-convert the dual-band signals simultaneously. The down-converted signal is a relatively narrowband signal without the wide gap between the two bands. Hence, slower analog-to-digital converters can be adopted in the subsequent circuits to digitize the received signal. Due to the nonlinearity of the low-noise amplifier, there might be noticeable nonlinearity distortion and memory effects in the received dual-band signals. To ensure high signal quality, a blind postdistortion algorithm is proposed to cancel out the nonlinearity distortion in the two received signals adaptively. Subsequently, the blind finite-impulse response equalizers for each band are built based on the modified constant modulus algorithm and the decision-directed equalization method. In addition, the nonideal wireless channel response is also able to be compensated using the proposed algorithm. Experimental results have shown perfect postcompensation performances of the overall algorithms in the dual bands.

Performance comparison between packet and continuous data transmission using two adaptive equalizers in shallow water

Transmitted signals are markedly affected by sea surface and bottom boundaries in shallow water. The time variant reflection signals from such boundaries characterize the channel as a frequency-selective fading channel and cause intersymbol interference (ISI) in underwater acoustic communication. A channel-estimate-based equalizer is usually adopted to compensate for the reflected signals under this kind of acoustic channel. In this study, we apply two approaches for packet and continuous data transmission of the quadrature phase shift keying (QPSK) system. One is the use of a two-dimensional (2D) rotation matrix in a non-frequency-selective channel. The other is the use of two equalizers of types — the feed forward equalizer (FFE) and decision-directed equalizer (DDE) — with a normalized least mean square (NLMS) algorithm in a frequency-selective channel. The percentage improvement of packet transmission is notably better than that of continuous transmission.

An Optimized Combination of Frequency Domain Adaptive Equalizers

In order to overcome the defects of the high computational loads and selecting the threshold of mean square error (MSE) for time domain decision-directed constant modulus blind equalization algorithm (DD+CMA), a frequency domain parallel decision multi-modulus blind equalization algorithm based on frequency domain MMA(FMMA) and frequency domain LMS (FLMS) algorithm is proposed. The proposed algorithm is composed of the FMMA and FLMS, and the FMMA and FLMS run automatically in soft switching parallel manner. In running process, it is not necessary to selecting the threshold of the MSE. Moreover, the computational loads can be reduced by circular convolution in the frequency domain signals instead of linear one of the time domain signals. Simulation results show that performance of the proposed algorithm outperforms the FLMS and the FMMA algorithm.

A Feedforward Partial Phase Noise Mitigation in the Time-Domain using Cyclic Prefix for CO-OFDM Systems

We propose a blind feedforward phase noise mitigation method in the time-domain for a coherent optical orthogonal frequency division multiplexing (CO-OFDM) systems. By exploiting the redundancy of the cyclic prefix (CP), the proposed scheme acquires the overall phase noise difference information during an OFDM block and attempts to mitigate the phase noise in the time domain using a linear approximation. The proposed algorithm mitigates common phase error (CPE) and inter-carrier-interference (ICI) due to phase noise simultaneously, improving the system performance, especially when decision-directed equalizers are used. The simulation results demonstrate the effectiveness of the proposed feedforward phase noise mitigation approach in time domain.

Steepest-descent method-based adaptive frequency domain equalizer in coherent optical orthogonal frequency division multiplexing with quadrature phase shift keying modulation

An adaptive frequency domain equalizer (A-FDE) in quadrature phase shift keying-coherent optical-orthogonal frequency division multiplexing (QPSK-CO-OFDM) system is proposed in this paper. A-FDE uses steepest descent method to search the optimal equalization parameters. And through applying the adaptive control factor (ACF) to monitor the state of A-FDE, the interference from phase noise (PN) and chromatic dispersion (CD) can be mitigated. The numerical simulation shows that the performance of A-FDE has a remarkable improvement on combating PN and CD comparing with the conventional decision-directed equalizer (DDE). And the A-FDE can achieve the forward-error-correction (FEC) threshold in noisier scenario. Furthermore, because the calculation of ACF only bases on valid data instead of pilot symbols (PSs), A-FDE has low PS overhead merit.

A Soft-Switching Blind Equalization Scheme via Convex Combination of Adaptive Filters

Blind equalizers avoid the transmission of pilot sequences, allowing a more efficient use of the channel bandwidth. Normally, after a first rough equalization is achieved, it is necessary to switch these equalizers to a decision-directed (DD) mode to reduce the steady-state mean-square error (MSE) to acceptable levels. The selection of an appropriate MSE threshold for switching between the blind and the DD modes is critical to obtain a good overall performance; however, this is not an easy task, since it depends on several factors such as the signal constellation, the communication channel, or the signal-to-noise ratio. In this paper, we propose an equalization scheme that adaptively combines a blind and a DD equalizers running in parallel. The combination is itself adapted in a blind manner, and as a result the overall scheme can automatically switch between the component filters, avoiding the need to set the transition MSE level a priori. The performance of our proposal is illustrated both analytically and through an extensive set of simulations, where we show its advantages with respect to existing hard- and soft-switching equalization schemes.

Generation and detection of 240-Gb/s PDM-64QAM using optical binary synthesizing approach and phase-folded decision-directed equalization

We present new generation and detection methods for high symbol-rate 64-ary quadrature amplitude modulation (64QAM). The 64QAM signal is created by tandem in-phase/quadrature (I/Q) modulators driven by electrical binary signals. The first I/Q modulator, which has four drive arms (i.e. a dual-drive I/Q modulator), yields 16QAM with an offset at the 1st quadrant of the complex plane. Subsequently, the second modulator switches this 16QAM signal over four quadrants via the typical quadrature phase-shift-keying (QPSK) modulation scheme, hence the desired 64QAM is generated. To mitigate the impacts of transmitter imperfections, we also propose a phase-folded decision-directed (PF-DD) linear equalizer at the receiver. Using these new techniques, we experimentally demonstrate the 120- and 240-Gb/s polarization-division-multiplexed (PDM) return-to-zero (RZ) 64QAM systems. The required optical signal-to-noise ratio (OSNR) for a bit-error rate (BER) of 2.4x10(-2) is measured at 20.2 or 23 dB, respectively, which is ~3.5 dB off the theoretical limit.

Experimental Study of a novel adaptive decision-directed channel equalizer in 28 GBaud RGI-DP-CO-OFDM transport systems

We report and experimentally investigate the performance of an adaptive decision-directed channel equalizer (ADDCE) in reduced-guard-interval dual-polarization coherent-optical orthogonal-frequency-division-multiplexing (RGI-DP-CO-OFDM) transport systems. ADDCE retrieves an estimation of the phase noise value after an initial decision making stage by extracting and averaging the phase drift of all OFDM sub-channels. Moreover, it updates the channel transfer matrix on a symbol-by-symbol basis. We experimentally compare the performance of the ADDCE and the conventional equalizer (CE) combined with maximum-likelihood (ML) phase noise compensation and inter-subcarrier-frequency-averaging (ISFA) algorithms. The study is conducted at 28 GBaud for RGI-DP-CO-OFDM systems with quadrature-phase-shift-keying (QPSK) and 16 quadrature amplitude modulation (16-QAM) formats. Using ADDCE, zero-overhead laser phase noise compensation is accomplished and the overhead due to training symbol (TSs) insertion is significantly reduced. In addition, ADDCE offers a superior performance over the CE in the presence of synchronization timing errors and residual chromatic dispersion (CD). We also achieve a longer transmission distance than when using the CE. At a forward-error-correction (FEC) threshold of 3.8 × 10−3, using a cumulative overhead of less than 2.6%, transmission distances of 5500 km and 400 km were achieved for the cases of QPSK and 16-QAM RGI-DP-CO-OFDM, respectively.

오차 제곱 가중치기반 랩 계수 갱신을 적용한 동시 등화기

동시 등화는 통신 채널을 블라인드 등화 시 수렵 특성 개선에 유용하다. 그러나 동시 등화는 등화기가 정상상태에 수렴한 후에도 동시 적응을 계속함으로써 성능 개선이 제한적이다. 본 논문에서는 동시 등화의 수렴 특성과 함께 정상상태 성능을 개선하기 위해, 가변 수렴상수와 가중치기반의 탭 계수 갱신을 적용하는 새로운 동시 등화 기법을 제안한다. 제안하는 동시 vsCMA+DD 등화는 가변 수렴상수 CMA(variable step-size CMA: vsCMA)와 판정의거 (decision-directed: DD) 알고리즘의 오차 신호를 사용하여 가중치를 산출하고, 이를 이용하여 두 등화기를 각각 가중 갱신한다. 제안 방법은 vsCMA에 의해 CMA의 오차 성능을 개선하고, 가중치기반의 탭 계수 갱신에 의해 수렴 속도와 정상상대 성능을 개선하였다. 모의실험을 통해 제안 방식의 성능 개선을 검증하였다. For blind equalization of communication channels, concurrent equalization is useful to improve convergence characteristics. However, the concurrent equalization will result in limited performance enhancement by continuing concurrent adaptation with two algorithms after the equalizer converges to steady-state. In this paper, to improve the convergence characteristics and steady-state performance of the concurrent equalization, proposed is a new concurrent equalization technique with variable step-size parameter and weight-based tap coefficients update. The proposed concurrent vsCMA+DD equalization calculates weight factors using error signals of the variable step-size CMA (vsCMA) and DD (decision-directed) algorithm, and then updates the two equalizers based on the weights respectively. The proposed method, first, improves the error performance of the CMA by the vsCMA, and enhances the steady-state performance as well as the convergence speed further by the weight-based tap coefficients update. The performance improvement by the proposed scheme is verified through simulations.

Performance Evaluation of Phase Estimation Algorithms in Equalized Coherent Optical Systems

We assess the performance of a coherent optical system employing a phase estimation algorithm combined with a least mean square decision-directed equalizer in a feedback configuration and compare it to the constant modulus algorithm with an independent carrier phase estimation approach for 16-quadratic-amplitude-modulation transmission. Both series and parallel implementations are discussed. Hardware issues regarding a recursive implementation of the estimation filter are also reported.

Blind Equalization and Carrier Phase Recovery in a 16-QAM Optical Coherent System

Blind equalization and carrier phase recovery in a simulated 14 Gbaud 16-QAM optical coherent system are investigated. Equalization techniques to compensate for linear transmission impairments are presented using the constant modulus algorithm (CMA), the recursive least-squares (RLS)-CMA, and the radius directed equalization (RDE). With 7 T/2-spaced taps, the RDE and the RLS-CMA can compensate up to 1000 ps/nm of CD in the 16-QAM coherent system with performances comparable to the decision-directed (DD) equalizer. We show that the RDE is a promising technique for blind equalization in a 16-QAM coherent system with lower complexity than the RLS-CMA. Blind carrier phase recovery is investigated in a decision-directed-mode. We show that the blind carrier phase recovery algorithm can recover the Square-16-QAM constellation for laser beat linewidths of DeltanuTs ~ 10-4 in a polarization-multiplexed (POLMUX) 16-QAM coherent system with the RDE algorithm giving better overall performance than the CMA when compensating for CD and differential group delay (DGD). Finally, the dynamical characteristics of the equalizers to track endless polarization rotations are discussed. With the adaptation parameters optimized, the equalizers can track angular rate of rotation ~ 105 rad/s.

Space–Time Adaptive Decision-Directed Equalizer Based on NLMS-Like Affine Projection Algorithm Using Iterative Hyperplane Projection

This paper introduces a space-time decision feedback equalizer whose coefficients are recursively renewed on the basis of the modified affine projection algorithm (APA). Despite its effectiveness against a rank-deficiency problem, the complexity of the conventional APA utilizing the sample matrix inversion is considerable. Furthermore, the shift invariance property could not be exploited in the case of a space-time decision-directed equalizer (STDE) application. To overcome such challenges, this paper introduces an APA employing a hyperplane projection scheme to reduce computational complexity without any degradation in its convergence characteristic and tracking capability. The performance of the proposed equalization methodology is verified by showing its superior bit error rate behaviors, fast convergence property, and reduced computational complexity by performing adaptive STDE under the single-input-multiple-output wireless multipath fading channel.

Stochastic blind equalization based on PDF fitting using Parzen estimator

This work presents a new blind equalization approach that aims to force the probability density function (pdf) at the equalizer output to match the known constellation pdf. Quadratic distance between pdf's is used as the cost function to be minimized. The proposed method relies on the Parzen window method to estimate the data pdf and is implemented by a stochastic gradient descent algorithm. The kernel size of the Parzen estimator allows a dual mode switch or a soft switch between blind and decision-directed equalization. The proposed method converges faster than the constant modulus algorithm (CMA) working at the symbol rate, with a similar computational burden, and reduces the residual error of the CMA in multilevel modulations at the same time. A comparison with the most common blind techniques is presented.

Performance analysis of error propagation effects in the dfe for atsc dtv receivers

The paper analyzes the error propagation phenomenon in the decision feedback equalizer (DFE) for the receivers of Advanced Television Systems Committee (ATSC) digital television (DTV) and presents the performance upper-limits of the DFE by comparing various error propagation cases and the no-error propagation case. As one approach to the performance limit, we consider a blind DFE, adopting a trellis decoder with a trace-back depth of 1 as a decision device. Through simulation, we show how much the DFE performance in ATSC DTV receivers is affected by error propagation. We found that while blind equalization is preferable to decision-directed (DD) equalization at signal-to-noise ratio (SNR) values less than 18 dB, DD equalization is superior to blind equalization at SNR values greater than 18 dB. In addition, symbol error rate curves quantitatively show that the performance difference in the DFE caused by error propagation becomes clearer at the trellis decoder following the DFE. The analysis results presented are very informative for developing equalization algorithms for ATSC DTV receivers.

Recursive least-squares backpropagation algorithm for stop-and-go decision-directed blind equalization

Stop-and-go decision-directed (S-and-G-DD) equalization is the most primitive blind equalization (BE) method for the cancelling of intersymbol-interference in data communication systems. Recently, this scheme has been applied to complex-valued multilayer feedforward neural network, giving robust results with a lower mean-square error at the expense of slow convergence. To overcome this problem, in this work, a fast converging recursive least squares (RLS)-based complex-valued backpropagation learning algorithm is derived for S-and-G-DD blind equalization. Simulation results show the effectiveness of the proposed algorithm in terms of initial convergence.

Decision-directed frame-synchronous adaptive equalization filtering of a speech signal by implementing a hidden Markov model

For equalizing a speech signal constituted by an observed sequence of successive input sound frames, which speech signal is liable to be affected by disturbances, the speech signal is modelled by means of a hidden Markov model and, at each instant t: equalization filters are constituted in association with the paths in the Markov sense at instant t; at least a plurality of the equalization filters are applied to the frames to obtain, at instant t, a plurality of filtered sound frame sequences and an utterance probability for each of the paths respectively associated with the equalization filters applied; the equalization filter corresponding to the most probable path in the Markov sense is selected; and the filtered frame supplied by the selected equalization filter is selected as the equalized frame.

Performance of a Multiple-Antenna Multiple-Equalizer System for a CDMA Indoor Wireless System

A multiple-antenna multiple-equalizer (MAME) system for interference suppression in some code-division multiple-access (CDMA) indoor wireless systems is investigated. The MAME system offers enhanced interference suppression capabilities over existing approaches under certain conditions and can thus increase system capacity. The details of the MAME system are discussed and the unique features of this work as compared with many other studies on space-time processing are explained using spectral correlation and diversity domain concepts. The effects of the number of antennas, tap spacing of the equalizers, spectral correlation, and diversity domains are discussed using simulation results. Adaptation performance results are also presented and a recently proposed quasi-Newton algorithm is recommended for use in the MAME system. Decision-directed equalization results are also studied under various conditions and bit-error rate results are presented. Simulation results illustrate that the MAME system can offer enhanced interference suppression capabilities in CDMA indoor wireless systems.