Finite Impulse Response Equalizer Research Articles

End-to-end optimization of optical communication systems based on directly modulated lasers

The use of directly modulated lasers (DMLs) is attractive in low-power, cost-constrained short-reach optical links. However, their limited modulation bandwidth can induce waveform distortion, undermining their data throughput. Traditional distortion mitigation techniques have relied mainly on the separate training of transmitter-side pre-distortion and receiver-side equalization. This approach overlooks the potential gains obtained by simultaneous optimization of the transmitter (constellation and pulse shaping) and receiver (equalization and symbol demapping). Moreover, in the context of DML operation, the choice of laser-driving configuration parameters such as the bias current and peak-to-peak modulation current has a significant impact on system performance. We propose, to our knowledge, a novel end-to-end optimization approach for DML systems, incorporating the learning of bias and peak-to-peak modulation current to the optimization of constellation points, pulse shaping, and equalization. The simulation of the DML dynamics is based on the use of the laser rate equations at symbol rates between 15 and 25 Gbaud. The resulting output sequences from the rate equations are used to build a differentiable data-driven model, simplifying the calculation of gradients needed for end-to-end optimization. The proposed end-to-end approach is compared to three additional benchmark approaches: the uncompensated system without equalization, a receiver-side finite impulse response equalization approach, and an end-to-end approach with learnable pulse shape and nonlinear Volterra equalization but fixed bias and peak-to-peak modulation current. The numerical simulations on the four approaches show that the joint optimization of bias, peak-to-peak current, constellation points, pulse shaping, and equalization outperforms all other approaches throughout the tested symbol rates.

Low-complexity reconfigurable FIR lowpass equalizers for polynomial channel models

This paper introduces realizations of a reconfigurable finite-impulse-response (FIR) filter for simultaneous equalization and lowpass filtering. The main advantage of the proposed solutions is computational complexity reduction compared to existing solutions for a given performance, which leads to reduced hardware complexity. The proposed structures employ properties of both a variable bandwidth (VBW) filter and a variable equalizer (VE) with variable coefficients. The overall transfer function of the proposed reconfigurable lowpass equalizer (RLPE) is a weighted linear combination of fixed subfilters where the weights are directly determined by the bandwidth and one or several parameters of the channel needed to be equalized. The paper provides design procedures based on minimax optimization and introduces a fast design method for the filter with several variable parameters that can substantially decrease the design time. Filter order estimation expressions as well as complexity expressions are presented for all proposed realizations. Design examples include comparison of the RLPE structures and a common approach of using a regular FIR equalization filter requiring online redesign when the bandwidth or channel characteristics are changed. It is shown that the number of general multiplications can be reduced up to 91% using the proposed RLPE.

Digital Finite Impulse Response Equalizer for Nonlinear Frequency Response Compensation in Wireless Communication

Signal distortion can occur when the gain or attenuation of a component changes non-linearly with frequency, which is referred to as nonlinear frequency response. Common communications components such as filters, amplifiers, and mixers can lead to nonlinear frequency responses, which can cause errors in transmitting and receiving. This article outlines the design and demonstration of a static and dynamic finite impulse response (FIR) digital equalizer circuit. Using predistortion topology with a coupled feedback loop, the adaptive Least-Mean Square (LMS) algorithm was implemented. The FIR filter was simulated in MATLAB and Vivado and then implemented onto an Eclypse Z7 Field Programmable Gate Array (FPGA) evaluation board. Simulations showed that the custom RTL module gave the same frequency response that was produced in MATLAB calculations. The filter was able to dynamically equalize the frequency responses of different nonlinear boards that were used as the devices under test (DUT). Measurements showed that the equalizer was able to compensate for system distortion from 0.2 to 0.8 Nyquist frequency. The phase response remained relatively linear across the band of interest, with a group delay flatness less than 10 ns.

Enhanced Finite Impulse Response Equalizer with Activity Detection Guidance and Tap Decoupling Techniques

Enhanced Finite Impulse Response Equalizer with Activity Detection Guidance and Tap Decoupling Techniques

A 12.5-Gb/s Near-Ground Transceiver Employing a MaxEye Algorithm-Based Adaptation Technique

A 12.5-Gb/s complete near-ground transceiver is demonstrated. The output stage of the transmitter (TX) employs 2-tap finite-impulse response equalization (EQ) and also performs ac-coupled EQ for an additional EQ. A continuous-time linear equalizer (CTLE) on the receiver (RX) side compensates for the channel attenuation. Based on the maximum eye algorithm, the peaking gain of CTLE is adaptively controlled to track a time-variant environment, such as PVT variations. Each TX and RX is implemented with clocking circuits: a differential PLL, and a dual-loop clock and data recovery circuit. The proposed transceiver is fabricated in a 45-nm CMOS process, and the entire TX and RX, respectively, consume 92 and 138 mW under a 1.2-V supply while operating at 12.5 Gb/s.

A 25mW Highly Linear Continuous-Time FIR Equalizer for 25Gb/s Serial Links in 28-nm CMOS

Thanks to the high flexibility in matching the channel frequency response and the compatibility with simple adaptation techniques, Finite Impulse Response (FIR) filters enhance the equalization performances of high-speed wireline receivers. This paper presents a 25-Gb/s FIR equalizer in 28-nm CMOS. The impact of filter noise and distortion, crucial aspects for an analog implementation, is discussed. A thorough system analysis, aimed at deriving the specifications for circuits design, suggests four taps, with a tap-to-tap delay in the range 0.5-1 UI, as optimal compromise among complexity (hence power dissipation) and equalization performances. To keep high SNR, a new all-pass stage is proposed to realize a delay line suitable for high-speed operation while being able to accommodate large input signal amplitude. Measurements are shown at 25 Gb/s for both Non Return to Zero (NRZ) and Pulse Amplitude Modulation (PAM)-4 signals. With a core power dissipation of 25 mW from 1-V supply, the proposed FIR filter recovers 20- and 9-dB channel loss for NRZ and PAM-4, respectively, with horizontal eye openings of 50% and 30%. Compared with the previously reported FIR filters for wireline links at comparable speed, the proposed realization achieves excellent equalization performance with the best power efficiency of 1 mW/Gb/s.

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.

ICI-Free Equalization in OFDM Systems with Blanking Preprocessing at the Receiver for Impulsive Noise Mitigation

In this letter, we consider the problem of equalizing finite-impulse response (FIR) channels in orthogonal frequency-division multiplexing (OFDM) systems, which employ at the receiver a blanking nonlinearity to mitigate impulsive noise (IN). By exploiting the frequency redundancy associated with the presence of OFDM virtual carriers, we design a frequency-domain linear FIR equalizer that compensates for the intercarrier interference (ICI) generated by nonlinear preprocessing. Monte Carlo computer simulations, carried out assuming a Middleton Class A model for the IN, allows one to assess the error probability performance of the proposed equalizer.

Blind Equalization in OFDM Systems by Channel Shortening and Channel Diversity Exploitation

We propose two alternative approaches for blind channel shortening to design time domain finite impulse response equalizer (TDE) in multicarrier single input, multiple output systems. The first approach we utilize the constant envelop of the transmitted signal called constant modulus (CM). Second approach is based on decision directed algorithm, where we update time domain equalizer using decision directed cost function. These cost function have been widely studied for single carrier systems, implementing them in multicarrier scenario is of great importance. Simulations shows they outperform classical multicarrier equalization by restoration of redundancy (MERRY) and Carrier nulling algorithm (CNA) that utilizes redundancies inherent in carriers in terms of bit error rate. General Terms Channel equalization algorithms in wireless communication.

Performance Evaluation of Neuro ITI Canceller for Two-Dimensional Magnetic Recording by Shingled Magnetic Recording

A neuro intertrack interference canceller (neuro-ITIC) is proposed to diminish the influences of ITI and jitter-like medium noise for two-dimensional magnetic recording (TDMR) by shingled magnetic recording. The bit error rate (BER) performance of a low-density parity-check coding and iterative decoding system including a generalized partial response class-I channel with the neuro-ITIC is also obtained via computer simulation using a read/write channel model under TDMR specifications of 4 Tb/in , and it is compared to those for a two-dimensional neural network equalizer (2D-NNE) and an ITI canceller (ITIC) with a one-dimensional finite impulse response equalizer (1D-FIRE). It is clarified that the BER performance for the neuro-ITIC is far superior to those for the 2D-NNE and the ITIC with the 1D-FIRE.

Modeling of Writing Process for Two-Dimensional Magnetic Recording and Performance Evaluation of Two-Dimensional Neural Network Equalizer

Modeling of a simple writing process considering intergranular exchange fields and magnetostatic interaction fields between grains is studied for two-dimensional magnetic recording (TDMR). A new designing method of a two-dimensional neural network equalizer with a mis-equalization suppression function (2D-NNEMS) for TDMR is also proposed. The bit-error rate (BER) performance of a low-density parity-check coding and iterative decoding system with the designed 2D-NNEMS is obtained via computer simulation using a read/write channel model employing the proposed writing process under TDMR specifications of 4 Tb/in <sup xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">2</sup> , and it is compared with those for one- and two-dimensional finite impulse response equalizers (FIREs). It is clarified that the BER performance for the designed 2D-NNEMS is far superior to those for the FIREs.

Correcting the Effects of Mismatches in Time-Interleaved Analog Adaptive FIR Equalizers

Analog discrete-time finite-impulse-response (FIR) filters have been used as equalizers in digital communication receivers. For high speed applications, an FIR equalizer can be implemented using parallel sample-and-holds (S/Hs) and time-interleaved equalizer channels. Mismatches among the parallel S/Hs degrade the equalizer performance. This paper addresses mismatches of DC offsets, gain errors, sample-time errors, and bandwidths in the S/Hs. It is shown that having a different set of adapted coefficients in each equalizer channel can reduce the effects of mismatches. Simulation results are presented for different communication channels.

A study on modeling of the writing process and two-dimensional neural network equalization for two-dimensional magnetic recording

A simple writing process considering magnetic clusters due to exchange coupling between grains is studied for two-dimensional magnetic recording. The bit error rate (BER) performance of a low-density parity-check coding and iterative decoding system with a two-dimensional neural network equalizer (2D-NNE) that can diminish the influences of jitter-like medium noise and inter-track interference is obtained using a read/write channel model based on the proposed writing process, and it is compared with those for one- and two-dimensional finite impulse response equalizers (FIREs). It is clarified that the BER performance for the 2D-NNE is far superior to those for the FIREs.

Method of Designing an Infinite Impulse Response Equalizer for Magnetic Recording Channels

A finite impulse response (FIR) equalizer is practically employed in conjunction with the Viterbi detector for data detection process in magnetic recording channels. However, the FIR equalizer with a large number of taps is required at high density storage channels. It is well-known that an infinite impulse response (IIR) filter with a small number of taps can closely approximate such an FIR filter. In this paper, we present three methods of designing the IIR equalizer for magnetic recording channels. Results indicate that, when the number of equalizer taps is small (e.g., 3 taps) and the normalized recording density is high, the IIR equalizer designed based on the minimum mean-squared error approach performs much better than the FIR equalizer, especially in longitudinal recording channels.

Read/Write Channel Modeling and Two-Dimensional Neural Network Equalization for Two-Dimensional Magnetic Recording

An accurate medium modeling method of discretized granular medium with non-magnetic grain boundaries using a discrete Voronoi diagram is proposed for two-dimensional magnetic recording. A simple closed-form representation of a double-shielded reader sensitivity function is also proposed for modeling the reading process. Moreover, a two-dimensional neural network equalizer (2D-NNE) is proposed to mitigate the influence of intertrack interference and jitter-like medium noise. The bit-error rate performance of partial response class-I maximum likelihood (PR1ML) system with the 2D-NNE is obtained by computer simulation based on the proposed read/write channel model. The performance is far superior to that of PR1ML system with a two-dimensional finite impulse response equalizer.

Wavelet—Artificial Neural Network Receiver for Indoor Optical Wireless Communications

The multipath-induced intersymbol interference (ISI) and fluorescent light interference (FLI) are the two most important system impairments that affect the performance of indoor optical wireless communication systems. The presence of either incurs a high optical power penalty and hence the interferences should be mitigated with suitable techniques to ensure optimum system performance. The discrete wavelet transform (DWT) and the artificial neural network (ANN)-based receiver to mitigate the effect of FLI and ISI has been proposed in the previous study for the ON-OFF keying (OOK) modulation scheme. It offers performance improvement compared to the traditional methods of employing a high-pass filter and a finite impulse response equalizer. In this paper, the investigation of the DWT-ANN-based receiver for baseband modulation techniques including OOK, pulse position modulation, and digital pulse interval modulation is reported. The proposed system is implemented using digital signal processing board and results are verified by comparison with simulation data.

Robust FIR equalization for time-varying communication channels with intermittent observations via an LMI approach

The optimal design of finite impulse response (FIR) filters for equalization/deconvolution is investigated in this paper. Two practical yet challenging constraints are incorporated into the modeling of the equalization system: (1) The parameters of the communication channel model are arbitrarily time-varying within a polytope with finite known vertices; (2) at the received end, the received signal is usually intermittent due to network-induced packet dropouts which are modeled by a stochastic Bernoulli distribution. Under the stochastic theory framework, a robust design method for the FIR equalizer is proposed such that the equalization system can achieve the prescribed energy-to-peak performance even it is subject to uncertainties, external noise, and data missing. Sufficient conditions for the existence of the equalizer are derived by a set of linear matrix inequalities (LMIs). An illustrative design example demonstrates the design procedure and the effectiveness of the proposed method.

Convolutive-Error-Measure Analysis for Inverse Filtering and Minimum Total-Model-Order Determination Subject to Positive-Definiteness

To the best of our knowledge, there exists no explicit formulation of the exact <i xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">L</i> <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">2</sub> convolutive error for any arbitrary filter (system) and the corresponding truncated inverse filter. In addition, the approach to determine the minimum total-model-order of the inverse filter subject to the maximum allowable <i xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">L</i> <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">2</sub> convolutive error is also in demand. In this paper, we first derive the general formula of the <i xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">L</i> <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">2</sub> convolutive error measure with respect to the filter coefficients. According to this new error measure function, we design an optimal inverse finite impulse response (FIR) filter given the fixed model orders to achieve the minimum convolutive error. Then, we propose a new algorithm to determine the minimum total-model-order of the appropriate truncated inverse filter to achieve a specified convolutive error based on the discrete filled function approach. The numerical evaluation is demonstrated for a tradeoff between the total-model-order and the system performance, e.g., the bit error rate (BER) for a communication receiver compensated by an FIR equalizer.

Adaptively Combined FIR and Functional Link Artificial Neural Network Equalizer for Nonlinear Communication Channel

This paper proposes a novel computational efficient adaptive nonlinear equalizer based on combination of finite impulse response (FIR) filter and functional link artificial neural network (CFFLANN) to compensate linear and nonlinear distortions in nonlinear communication channel. This convex nonlinear combination results in improving the speed while retaining the lower steady-state error. In addition, since the CFFLANN needs not the hidden layers, which exist in conventional neural-network-based equalizers, it exhibits a simpler structure than the traditional neural networks (NNs) and can require less computational burden during the training mode. Moreover, appropriate adaptation algorithm for the proposed equalizer is derived by the modified least mean square (MLMS). Results obtained from the simulations clearly show that the proposed equalizer using the MLMS algorithm can availably eliminate various intensity linear and nonlinear distortions, and be provided with better anti-jamming performance. Furthermore, comparisons of the mean squared error (MSE), the bit error rate (BER), and the effect of eigenvalue ratio (EVR) of input correlation matrix are presented.

Krylov Subspace Algorithms and Circulant-Embedding Method for Efficient Wideband Single-Carrier Equalization

Wider bandwidth allows higher data rate by transmitting narrower pulses. However, doing so would also increase the discrete channel memory length. For single-carrier communication systems this results in higher computational burden at the receiver. We are concerned with single-carrier nonblock transmission schemes with receiver oversampling, as they can provide higher spectral efficiency than block transmission schemes in the presence of large delay spreads. We first propose a simple finite-impulse-response (FIR) equalizer that is based on the circulant-embedding (CE) method and analyze its performance by investigating the relationship between solutions of various finite-dimensional models and the original infinite-dimensional problem. We show that under proper conditions the CE FIR equalizer converges exponentially fast to the IIR equalizer. We then focus on the conjugate gradient (CG) algorithm as an efficient means for equalization that is specifically well suited for dealing with large-delay-spread channels. We discuss the importance of stopping the iterations for the CG algorithm at the right time in the presence of noise and present several reliable low-cost stopping criteria. It turns out that the CG algorithm equipped with appropriate stopping criteria can outperform MMSE equalizers. Since both the CE and the CG methods can be efficiently implemented via fast Fourier transforms, equalization complexity is only in the order of N log(N) for N data symbols. Several numerical experiments demonstrate the performance of the proposed methods.