Low-complexity Equalization Research Articles

Low complexity equalization in coherent optical communication based on Fermat number transform.

In order to reduce the power consumption of digital signal processing (DSP) in a coherent optical communication system, a low complexity equalization scheme in DSP flow of a 400 Gb/s DP-16QAM system has been proposed. This scheme is based on Fermat number transform (FNT), which sequentially performs static equalization (SE) and dynamic equalization (DE) in the transform domain. For different distances, the proposed scheme finds the optimal solution under the condition that transform length and data bit width are mutually restricted under different transmission distances while achieving low complexity and optimal performance. The experimental results show that the adopted transform-domain equalization (TrDE) scheme has much lower computational complexity than the traditional frequency-domain equalization (FDE) and time-domain equalization (TDE) nearly without any performance loss. In the 80, 160, and 240 km scenarios, the number of multiplier is reduced by more than 72%, and the advantage becomes more obvious as the transmission capacity increases.

UAMP-Based Equalization for Dual Pulse Shaping Transmission Systems

Dual pulse shaping (DPS) transmissions enable the use of A/D and D/A converters with half of the symbol rate, alleviating the requirement of high speed conversion devices in wideband millimeter wave communications. In this letter, we focus on DPS equalization and propose a unitary approximate message passing (UAMP) based equalization technique. Two DPS transmission schemes are considered, and by exploiting the special structure of the system transfer matrix, two low-complexity equalizers are developed with the fast Fourier transform (FFT). Simulation results show that significant performance gains can be achieved by the UAMP-based equalizers, compared to the conventional DPS equalizer.

Mitigating Clipping Distortion in Multicarrier Transmissions Using Tensor-Train Deep Neural Networks

Multicarrier transmissions, such as orthogonal frequency/chirp division multiplexing (OF/CDM), offer high spectral efficiency and low complexity equalization in multipath fading channels at the cost of high peak-to-average power ratio (PAPR). High peak powers can occur randomly and may drive the power amplifier (PA) into saturation, resulting in non-linear distortion. In this work, we propose a novel tensor-train (TT) deep neural network (DNN) architecture combined with soft clipping to reduce the PAPR to a deterministic level and minimize in-band distortion, while also satisfying spectral mask constraints. The proposed solution requires modifications only at the transmitter and there is no loss of spectral efficiency. Employing the TT decomposition allows for significant reduction in parameters. Results show that the proposed solution allows for significant reduction in PAPR with minimal performance loss. Furthermore, an upper bound for the PAPR is also derived which allows for the prediction of the required input power back off (IBO) without extensive simulations and trial-and-error.

Low-complexity equalizers and applications

Equalizers for audio signal processing play an important role in microphones, mixing systems, mastering processors, monitor loudspeakers, and consumer devices such as smart tablets, smart phones, wireless headphones, and hearing devices. We will introduce low-complexity filter designs for equalizers based on first- and second order recursive filters. Low-complexity filter design means having the lowest number of parameters and design equations for first- and second-order difference equation realizing prescribed filter transfer functions such as low-pass, high-pass, band-pass, and all-pass filters. Based on these basic filters, we derive all-pass realizations of these standard filters and then apply them to design parametric low- and high-frequency shelving filters and peak filters. These last two versions of weighting filters are based on three parameters, namely, the cut-off or center frequency, the bandwidth or Q factor, and the gain in dB for a low-, mid-, or high frequency band and are, therefore, named parametric equalizers. These parametric equalizers' PEQs occur in a channel-strip of a mixing console and are an integral part of the mixing process. We will describe several further applications of PEQs for amp and loudspeaker modeling, headphone equalization and head-related transfer function modeling, and audio coding. All applications allow a low-complexity filter design, parameter update, and efficient recursive filter implementations with much lower complexity compared to non-recursive filters.

A Generalized Two-Dimensional FFT Precoded Filter Bank Scheme With Low Complexity Equalizers in Time-Frequency Domain

A Generalized Two-Dimensional FFT Precoded Filter Bank Scheme With Low Complexity Equalizers in Time-Frequency Domain

Low-Complexity Chromatic Dispersion Equalization FIR Digital Filter for Coherent Receiver

This paper proposes a novel and efficient low-complexity chromatic dispersion equalizer (CDE) based on finite impulse response (FIR) filter architecture for polarization-multiplexed coherent optical communication systems. The FIR filter coefficients are optimized by weights to reduce the energy leakage caused by the truncation effect, and then quantization is used uniformly to reduce the number of real number additions and real number multiplications by utilizing the diversity of the quantized coefficients. Using Optisystem 15 to build a coherent optical communication system for simulation and experimental demonstration, the results show that after the filter coefficients are optimized by weights. Compared with the time-domain chromatic dispersion equalizer (TD-CDE), the proposed design has a lower bit error rate (BER) and better equalization effect. When the transmission distance is 4000 km and the system quantization stages M = 16, the multiplication operation and addition operations reduce computing resources by 99% and 43%, and the BER only increases by 5%. Compared with frequency-domain chromatic dispersion equalizer (FD-CDE), widely used in long-distance communication, the multiplication operation reduces computing resources by 30%. The proposed method provides a new idea for high-performance CDE in long-distance coherent optical communication systems.

A low-complexity orthogonal time frequency space modulation method for underwater acoustic communication

Compared with the orthogonal frequency division multiplexing (OFDM) modulation, the orthogonal time frequency space(OTFS) modulation has a lower peak-to-average power ratio. It can effectively resist the time selective fading caused by the Doppler effect and has significant performance advantages over doubly dispersive channels. However, the conventional OTFS linear minimum mean square error (LMMSE) method has a high complexity and is not easy to process in real time. In order to solve this problem, we propose a low-complexity equalization algorithm with infinite norm constraints based on the optimal coordinate reduction. The equalization algorithm not only obtains the optimal solution through a certain number of iterations and avoids direct matrix inversion but also equalizes infinite norm constraints to improve the symbol detection performance gains. At the same time, the OTFS delay-Doppler channel matrix we utilize is sparse and the two-norm squares of each column vector equally reduces the complexity of optimal coordinate descent. Finally, the simulation in the underwater acoustic communication scenario we designed verify the effectiveness of the proposed equalization algorithm. The simulation results show that the performance of the proposed equalization algorithm is close to that of the LMMSE method, while its low complexity is ensured.

PDL and CD insensitive low complexity equalizer for short reach coherent systems.

We propose a polarization dependent loss (PDL) and chromatic dispersion (CD) insensitive, low-complexity adaptive equalizer (AEQ) for short-reach coherent optical transmission systems. The AEQ contains a 1-tap butterfly finite impulse response (FIR) filter and two N-tap FIR filters. It first performs polarization demultiplexing using the 1-tap filter, of which the coefficients are obtained based on Stokes space. Then it mitigates the inter-symbol interference (ISI) using the two N-tap finite impulse response (FIR) filters and adjust the filter's coefficients by utilizing constant modulus algorithm (CMA). Through theoretical and experimental analysis, we verify that this proposed AEQ can perform robust polarization demultiplexing when PDL and CD exists. Besides, our proposed AEQ has faster convergence speed compared with recently proposed AEQs. In addition, it reduces the number of multipliers and thus reduce the computational complexity of conventional butterfly filter structure AEQ. And this proposed AEQ suffers little bit error ratio loss compared with the conventional AEQ. Due to the low-complexity and robustness to PDL and CD, this proposed AEQ is well-suited for future low-cost short-reach optical communication system.

Low-complexity equalizer with a hybrid decision scheme for 50 Gb/s/λ PAM4-PON using a low-cost 10 G receiver.

In this Letter, we experimentally demonstrate a 50Gb/s/λ four-level pulse amplitude modulation-based passive optical network system with a 10 G class receiver. A memory polynomial equalizer (MPE) combined with a decision feedback equalizer (DFE) is applied to eliminate channel distortions in the system. To further improve the performance of the MPE-DFE, for the first time, to the best of our knowledge, a low-complexity hybrid decision scheme (HDS) is proposed, which consists of single-symbol decision (SSD) and multi-symbol decision (MSD). The SSD is exactly the conventional hard decision based on minimum Euclidean distance, whereas MSD is based on a simplified maximum likelihood detection principle with M-algorithm. In terms of complexity, MSD requires 19.1% more multiplications than SSD, but the symbol number of MSD only accounts for less than 20% of the total signal frame when the received optical power is greater than -27dBm. Experimental results show that the proposed MPE-DFE with HDS achieves a 0.7 dB and 1.3 dB sensitivity gain compared with conventional SSD, and up to 35.4 dB and 31.4 dB link power budget, regarding the forward error correction threshold of 10-2 and 10-3, respectively.

Mode Subset Selection and Feedback for Low Complexity Equalization in DWDM MMF Links

Multiplexing through multimode fibers (MMFs) has been known to increase data rates significantly. However, mode dependent losses cause some modes to not offer optimal performance. Only a subset of modes identified by the receiver to be used for transmission can be fed back to the transmitter for lowering complexity. However, feeding back subsets for all WDM channels requires huge feedback burden. In this letter, we show that the best subsets for some wavelengths can be reused across neighbouring WDM channels without much loss of performance. Simulations reveal that reusing mode subsets across channels yields high rates with limited feedback burden.

Efficient equalisers for OFDM and DFrFT-OCDM multicarrier systems in mobile E-health video broadcasting with machine learning perspectives

Recently, the orthogonal frequency-division multiplexing (OFDM) system has become an appropriate technique to be applied on the physical layer in various requests, mainly in wireless communication standards, which is the reason to use OFDM within mobile wireless medical applications. The OFDM with cyclic prefix (CP) can compensate lacks for the time-invariant multi-path channel effects using a single tap equaliser. However, for mobile wireless communication, such as the use of OFDM in ambulances, the Doppler shift is expected, which produces a doubly dispersive communication channel where a complex equaliser is needed. This paper proposes a low-complexity band LDLH factorisation equaliser to be applied in mobile medical communication systems. Moreover, the discrete fractional Fourier transform (DFrFT) is used to improve the communication system’s performance over the OFDM. The proposed low-complexity equaliser could improve the OFDM, and the DFrFT-orthogonal chirp-division multiplexing (DFrFT-OCDM) system’s performance, as illustrated in the simulation results. This proves that the recommended system outperforms the standard benchmark system, which is an essential factor as it is to be applied within mobile medical systems.

Dual Pulse Shaping Transmission and Equalization for High-Speed Wideband Wireless Communication Systems

Analog-to-digital and digital-to-analog conversion devices for signals with very large bandwidth are not always available due to technical or cost issues. This limits the realization of very high data-rate digital communication systems. In this paper, we propose a dual pulse shaping (DPS) transmission scheme, which can achieve full Nyquist rate transmission with only a half of the sampling rate for each of the two data streams. Two classes of ideal complementary Nyquist pulses are formulated assuming raised-cosine (RC) pulse shaping. The condition for cross-symbol interference (CSI) free transmission is derived and validated for the proposed pulses. Structures of the DPS transmitter and receiver are described and low-complexity equalization techniques tailored to DPS are proposed. With DPS, a millimeter wave system with commercially available and affordable data conversion devices is exemplified for achieving high-speed low-cost wireless communications. Simulation results with two sets of practical dual spectral shaping pulses are provided. The results verify the effectiveness of the proposed scheme, with comparison to the benchmark conventional Nyquist pulse shaping system.

Low Complexity Equalization of Orthogonal Chirp Division Multiplexing in Doubly-Selective Channels.

Orthogonal Chirp Division Multiplexing (OCDM) is a modulation scheme which outperforms the conventional Orthogonal Frequency Division Multiplexing (OFDM) under frequency selective channels by using chirp subcarriers. However, low complexity equalization algorithms for OCDM based systems under doubly selective channels have not been investigated yet. Moreover, in OCDM, the usage of different phase matrices in modulation will lead to extra storage overhead. In this paper, we investigate an OCDM based modulation scheme termed uniform phase-Orthogonal Chirp Division Multiplexing (UP-OCDM) for high-speed communication over doubly selective channels. With uniform phase matrices equipped, UP-OCDM can reduce the storage requirement of modulation. We also prove that like OCDM, the transform matrix of UP-OCDM is circulant. Based on the circulant transform matrix, we show that the channel matrices in UP-OCDM system over doubly selective channels have special structures that (1) the equivalent frequency-domain channel matrix can be approximated as a band matrix, and (2) the transform domain channel matrix in the framework of the basis expansion model (BEM) is a sum of the product of diagonal and circulant matrices. Based on these special channel structures, two low-complexity equalization algorithms are proposed for UP-OCDM in this paper. The equalization algorithms are based on block LDL factorization and iterative matrix inversion, respectively. Numerical simulations are finally proposed to show the performance of UP-OCDM and the validity of the proposed low complexity equalization algorithms. It is shown that when the channel is doubly selective, UP-OCDM and OCDM have similar BER performance, and both of them outperform OFDM. Moreover, the proposed low complexity equalizers for UP-OCDM both show better BER performance than their OFDM counterparts.

MIMO-OFDM/OCDM low-complexity equalization under a doubly dispersive channel in wireless sensor networks

In this article, three novel systems for wireless sensor networks based on Alamouti decoding were investigated and then compared, which are Alamouti space–time block coding multiple-input single-output/multiple-input multiple-output multicarrier modulation (MCM) system, extended orthogonal space–time block coding multiple-input single-output MCM system, and multiple-input multiple-output system. Moreover, the proposed work is applied over multiple-input multiple-output systems rather than the conventional single-antenna orthogonal chirp division multiplexing systems, based on the discrete fractional cosine transform orthogonal chirp division multiplexing system to mitigate the effect of frequency-selective and time-varying channels, using low-complexity equalizers, specifically by ignoring the intercarrier interference coming from faraway subcarriers and using the LSMR iteration algorithm to decrease the equalization complexity, mainly with long orthogonal chirp division multiplexing symbols, such as the TV symbols. The block diagrams for the proposed systems are provided to simplify the theoretical analysis by making it easier to follow. Simulation results confirm that the proposed multiple-input multiple-output and multiple-input single-output orthogonal chirp division multiplexing systems outperform the conventional multiple-input multiple-output and multiple-input single-output orthogonal frequency division multiplexing systems. Finally, the results show that orthogonal chirp division multiplexing exhibited a better channel energy behavior than classical orthogonal frequency division multiplexing, thus improving the system performance and allowing the system to decrease the equalization complexity.

Low-complexity equalization scheme for suppressing FFE-enhanced in-band noise and ISI in 100 Gbps PAM4 optical IMDD system.

The commonly used feed-forward equalizer (FFE) in an intensity modulation and direct-detection (IMDD) system is seriously restrained by the enhanced in-band noise in the high-frequency region. In this Letter, a low-complexity equalization scheme including FFE, post-filter (PF), and a newly designed interference cancellation (IC) algorithm is proposed to cope with the FFE-enhanced noise and serious inter-symbol interference (ISI) simultaneously. In our experiment, the achieved bit error rate value of 100 Gb/s optical double-sideband (ODSB) four-level pulse amplitude modulation (PAM4) signal transmission over 10 km standard single-mode fiber (SSMF) can go below the 20% overhead soft-decision forward error correction threshold of ${2.7} \times {{10}^{ - 2}}$2.7×10-2 when the FFE is replaced by the proposed equalizer. Even a 100 Gb/s optical single-sideband (OSSB) PAM4 signal can be successfully transmitted over 80 km SSMF. The results show that the proposed ${\rm FFE}+{\rm PF}+{\rm IC}$FFE+PF+IC algorithm can effectively suppress the FFE-enhanced noise and ISI with a quite low increase in complexity. Moreover, compared to the joint FFE, PF, and maximum likelihood sequence detection (MLSD) algorithm, the proposed ${\rm FFE}+{\rm PF}+{\rm IC}$FFE+PF+IC algorithm has 1.2 dB and 0.4 dB power penalties after 10 km SSMF in ODSB and 80 km SSMF in OSSB cases, respectively. However, the complexity of this IC algorithm is approximately 3% that of the MLSD.

A Low-Complexity Equalizer for Video Broadcasting in Cyber-Physical Social Systems Through Handheld Mobile Devices

In Digital Video Broadcasting-Handheld (DVB-H) devices for cyber-physical social systems, the Discrete Fractional Fourier Transform-Orthogonal Chirp Division Multiplexing (DFrFT-OCDM) has been suggested to enhance the performance over Orthogonal Frequency Division Multiplexing (OFDM) systems under time and frequency-selective fading channels. In this case, the need for equalizers like the Minimum Mean Square Error (MMSE) and Zero-Forcing (ZF) arises, though it is excessively complex due to the need for a matrix inversion, especially for DVB-H extensive symbol lengths. In this work, a low complexity equalizer, Least-Squares Minimal Residual (LSMR) algorithm, is used to solve the matrix inversion iteratively. The paper proposes the LSMR algorithm for linear and nonlinear equalizers with the simulation results, which indicate that the proposed equalizer has significant performance and reduced complexity over the classical MMSE equalizer and other low complexity equalizers, in time and frequency-selective fading channels.

Low-Complexity Equalization of MIMO-OSDM

Orthogonal signal-division multiplexing (OSDM) is an attractive alternative to conventional orthogonal frequency-division multiplexing (OFDM) due to its enhanced ability in peak-to-average power ratio (PAPR) reduction. Combining OSDM with multiple-input multiple-output (MIMO) signaling has the potential to achieve high spectral and power efficiency. However, a direct channel equalization in this case incurs a cubic complexity, which may be expensive for practical use. To solve the problem, low-complexity per-vector and block equalization algorithms of MIMO-OSDM are proposed in this paper for time-invariant and time-varying channels, respectively. By exploiting the channel matrix structures, these algorithms have only a linear complexity in the transformed domain. Simulation results demonstrate their validity and the related performance comparisons.

An efficient adaptive equalization architecture for high-speed coherent PON systems

Algorithmic and architectural options and tradeoffs between performance and complexity/power dissipation are imperative to be considered in the transfer of coherent technology from long-haul transmission to passive optical network (PON) application. In this work, a novel low-complexity equalization architecture cascaded two frequency domain equalizers (FDEQs) and one 1-tap 2 × 2 butterfly equalizer is proposed targeting PON applications. FDEQ is designed to handle link chromatic dispersion (CD) and the imperfection of transceiver frequency response. The 1-tap 2 × 2 butterfly equalizer is introduced to realize polarization demultiplexing. A simplified FDEQ tap coefficient calculation method is designed. The performance of the proposed equalization architecture is experimentally verified by a 32-GBaud dual-polarization (DP) Nyquist-QPSK system over 20-km standard single-mode fiber (SSMF) transmission. With the proposed method, the number of hardened multipliers for field-programmable gate array (FPGA) realization is reduced by ∼90% compared with conventional 2 × 2 butterfly equalizer, at the expense of 0.5 dB receiver sensitivity.

Low-Complexity Equalization of Orthogonal Signal-Division Multiplexing in Doubly-Selective Channels

Orthogonal signal-division multiplexing (OSDM) is a generalized modulation scheme to bridge the gap between orthogonal frequency-division multiplexing (OFDM) and single-carrier frequency-domain equalization. It allows significantly more flexibility in system design; however, over doubly-selective channels, it suffers from a special signal distortion structure, namely inter-vector interference, which is analogous to inter-carrier interference in conventional OFDM. To analyze its effect, in this paper, the complex exponential basis expansion model (CE-BEM) is used to approximate the doubly-selective channel. We show that the composite channel matrix of OSDM systems is cyclically block banded in this case, and the blocks in its main band can be further diagonalized. By exploiting this unique matrix structure, low-complexity block and serial OSDM equalization algorithms are then proposed. These two equalization algorithms are based on block LDLH factorization and block iterative matrix inversion, respectively, both of which are implemented in a transformed domain to avoid direct inversion of large matrices. In addition, a CE-BEM channel estimation method is designed for OSDM systems, which uses frequency-shifted Chu sequences as pilots to ease the computation. Numerical simulations are finally provided to justify the validity of our channel equalization and estimation algorithms.

Low-complexity blind in-phase/quadrature imbalance compensation and field-programmable gate array realization for coherent receivers

Receiver in-phase/quadrature (I / Q) imbalance caused by imperfect analog receiver front end can rapidly degrade system performance in a coherent optical transmission system. These imbalances, including I / Q gain and phase imbalance, become increasingly important when higher symbol rate, higher modulation order, and low roll-off pulse shape are used. Here, a low-complexity blind equalization algorithm, cascaded phase, and gain imbalance equalizers, is designed to mitigate these interferences. Furthermore, a field-programmable gate array hardware realization with 128-parallel processing units is performed to demonstrate the proposed algorithm in a 32-GBaud 16-quadrature amplitude modulation off-line transmission experiment. Based on the obtained results, the proposed blind I / Q imbalance compensation algorithm can provide very good compensation performance with low logic element consumption, which is more suitable for high order and high baud rate transmission system.