Multi-input Multi-output Equalization Research Articles

Ant-colony optimization-based multi-input multi-output (ACO-MIMO) equalization for low-complexity mode-division multiplexing (MDM) processing

In mode-division multiplexing (MDM) systems, the computational complexity of the multi-input multi-output (MIMO) equalization module is a critical obstacle to practical development. The step size μ and the number of taps K are key parameters in the equalization algorithm, influencing the performance of finite impulse response (FIR) equalizers, including convergence speed and output signal quality. To alleviate the computational burden of locating the optimal μ-K combination, we propose two ant colony optimization (ACO) -based MIMO equalization schemes: the fixed ACO-MIMO and the random ACO-MIMO, corresponding to two optimization strategies. These schemes expedite the initialization process of both parameters. Subsequently, we conduct experiments to evaluate their performance in a 3-mode recirculating-loop transmission system. Our findings demonstrate that, compared to conventional schemes, such as genetic algorithm (GA) and steepest descent algorithm (SDA), the proposed ACO-MIMO schemes significantly reduce the number of calls to the equalization algorithm for locating optimal μ-K combination by up to 42.74% and 80.63%, reducing the complexity of the whole MIMO equalization for MDM systems. And the resulting hit-rate Phit for the optimal μ-K combination reaches up to 99.34%. Moreover, the ACO-MIMO schemes exhibit stable performance across different data collected from various round-trips, confirming the robust operation for the long-haul MDM transmission. Finally, we investigate the performance disparity between the two proposed ACO-MIMO schemes through bit-error-rate (BER) distribution, concluding that under a large dataset with various BER distributions, the performance of both schemes is essentially equivalent.

Recent Advances in DSP Techniques for Mode Division Multiplexing Optical Networks with MIMO Equalization: A Review

This paper provides a technical review regarding the latest progress on multi-input multi-output (MIMO) digital signal processing (DSP) equalization techniques for high-capacity fiber-optic communication networks. Space division multiplexing (SDM) technology was initially developed to improve the demanding capacity of optic-interconnect links through mode-division multiplexing (MDM) using few-mode fibers (FMF), or core-multiplexing exploiting multicore fibers (MCF). Primarily, adaptive MIMO filtering techniques were proposed to de-multiplex the signals upon different modes or cores, and to dynamically compensate for the differential mode group delays (DMGD) plus mode-dependent loss (MDL) via DSP. Particularly, the frequency-domain equalization (FDE) techniques suggestively lessen the algorithmic complexity, compared with time-domain equalization (TDE), while holding comparable performance, amongst which the least mean squares (LMS) and recursive least squares (RLS) algorithms are most ubiquitous and, hence, extensively premeditated. In this paper, we not only enclose the state of the art of MIMO equalizers, predominantly focusing on the advantage of implementing the space–time block-coding (STBC)-assisted MIMO technique, but we also cover the performance evaluation for different MIMO-FDE schemes of DMGD and MDL for adaptive coherent receivers. Moreover, the hardware complexity optimization for MIMO-DSP is discussed, and a joint-compensation scheme is deliberated for chromatic dispersion (CD) and DMGD, along with a number of recent experimental demonstrations using MIMO-DSP.

6.4 Tb/s (32 [formula omitted] 200 Gb/s) WDM direct-detection transmission with twin-SSB modulation and Kramers–Kronig receiver

We experimentally demonstrate 6.4 Tb/s wavelength division multiplexed (WDM) direct-detection transmission based on Nyquist twin-SSB modulation over 25 km SSMF with bit error rates (BERs) below the 20% hard-decision forward error correction (HD-FEC) threshold of 1.5 × 10−2. The two sidebands of each channel are separately detected using Kramers–Kronig receiver without MIMO equalization. We also carry out numerical simulations to evaluate the system robustness against I/Q amplitude imbalance, I/Q phase deviation and the extinction ratio of modulator, respectively. Furthermore, we show in simulation that the requirement of steep edge optical filter can be relaxed if multi-input–multi-output (MIMO) equalization between the two sidebands is used.

Fast convergent frequency-domain MIMO equalizer for few-mode fiber communication systems

Space division multiplexing using few-mode fibers has been extensively explored to sustain the continuous traffic growth. In few-mode fiber optical systems, both spatial and polarization modes are exploited to transmit parallel channels, thus increasing the overall capacity. However, signals on spatial channels inevitably suffer from the intrinsic inter-modal coupling and large accumulated differential mode group delay (DMGD), which causes spatial modes de-multiplex even harder. Many research articles have demonstrated that frequency domain adaptive multi-input multi-output (MIMO) equalizer can effectively compensate the DMGD and demultiplex the spatial channels with digital signal processing (DSP). However, the large accumulated DMGD usually requires a large number of training blocks for the initial convergence of adaptive MIMO equalizers, which will decrease the overall system efficiency and even degrade the equalizer performance in fast-changing optical channels. Least mean square (LMS) algorithm is always used in MIMO equalization to dynamically demultiplex the spatial signals. We have proposed to use signal power spectral density (PSD) dependent method and noise PSD directed method to improve the convergence speed of adaptive frequency domain LMS algorithm. We also proposed frequency domain recursive least square (RLS) algorithm to further increase the convergence speed of MIMO equalizer at cost of greater hardware complexity. In this paper, we will compare the hardware complexity and convergence speed of signal PSD dependent and noise power directed algorithms against the conventional frequency domain LMS algorithm. In our numerical study of a three-mode 112 Gbit/s PDM-QPSK optical system with 3000 km transmission, the noise PSD directed and signal PSD dependent methods could improve the convergence speed by 48.3% and 36.1% respectively, at cost of 17.2% and 10.7% higher hardware complexity. We will also compare the frequency domain RLS algorithm against conventional frequency domain LMS algorithm. Our numerical study shows that, in a three-mode 224 Gbit/s PDM-16-QAM system with 3000 km transmission, the RLS algorithm could improve the convergence speed by 53.7% over conventional frequency domain LMS algorithm.

ICI Mitigation for Dual-Carrier Superchannel Transmission Based on m-PSK and m-QAM Formats

We propose an intercarrier interference (ICI) mitigation scheme for dual-carrier superchannel transmission. Using the modified decision directed least mean square (DD-LMS) based multi-input multi-output (MIMO) processing, we can simultaneously realize both polarization division demultiplexing and ICI mitigation for PDM-m-PSK and PDM-m-QAM formats. Thanks to the innovative modification of frequency-shift operation, the MIMO equalization enables synchronous output of dual-carrier signals with robust performance against frequency offset, laser phase noise, as well as polarization mode dispersion (PMD). The experimental back-to-back transmission of PDM-16QAM signal has 8.3-dB OSNR improvement using the proposed MIMO processing. Three dual-carrier 160-Gb/s PDM-16QAM superchannels within 25-GHz grid are experimentally transmitted over 640-km standard single-mode fiber (SSMF), leading to net spectral efficiency of 5.7b/s/Hz.

Joint digital signal processing of Nyquist-wavelength division multiplexing superchannel with group detection

To relax the limited sampling rate of an analog-to-digital converter (ADC) and to reduce the complexity of conventional fiber-optical superchannel coherent detection, we propose and demonstrate a joint digital signal processing (DSP) technique of Nyquist-wavelength division multiplexing superchannel with group detection. At the receiver side, three Nyquist-spaced channels with 12.5 Gbaud polarization multiplexing-quadrature phase shift keying signals are group detected with a sampling rate per channel of 1.33 times over the normal sampling rate. A modified carrier separation technique is then put forward to retrieve the high-frequency interference component of both the designated channel and its adjacent channels, which can subsequently be used to recover the designated channel with new constant modulus algorithm-based joint multiinput-multioutput equalizers. The results show that the proposed group detection and joint DSP algorithm can simultaneously improve the transmission performance and reduce the complexity of both the transmitter and receiver, regardless of bandwidth restrictions from the waveshaper, ADC module, and coherent receiver.

Linear Propagation Effects in Mode-Division Multiplexing Systems

In this paper, we review linear propagation effects in a multimode fiber (MMF) and their impact on performance and complexity in long-haul mode-division multiplexing (MDM) systems. We highlight the many similarities to wireless multi-input multioutput (MIMO) systems. Mode-dependent loss and gain (MDL), analogous to multipath fading, can reduce average channel capacity and cause outage in narrowband systems. Modal dispersion (MD), analogous to multipath delay spread, affects the complexity of MIMO equalization, but has no fundamental effect on performance. Optimal MIMO transmission uses a basis of the Schmidt modes, which may be obtained by a singular value decomposition of the MIMO channel. In the special case of a unitary channel (no MDL), an optimal basis is the set of principal modes, which are eigenvectors of a group delay operator, and are free of signal distortion to first order. We present a concatenation rule for the accumulation of MD along a multisection link. We review mode coupling in MMF, including physical origins, models, and regimes of weak and strong coupling. Strong mode coupling is a key to overcoming challenges in MDM systems. Strong coupling reduces the group delay spread from MD, minimizing the complexity of MIMO signal processing. Likewise, it reduces the variations of loss and gain from MDL, maximizing channel capacity. In the strong-coupling regime, the statistics of MD and MDL depend only on the number of modes and the variance of accumulated group delay or loss/gain, and can be derived from the eigenvalue distributions of certain Gaussian random matrices.

Effect of Mode Coupling on Signal Processing Complexity in Mode-Division Multiplexing

Mode-division multiplexing systems employ multi-input multi-output (MIMO) equalization to compensate for chromatic dispersion (CD), modal dispersion (MD) and modal crosstalk. The computational complexity of MIMO equalization depends on the number of modes and on the group delay (GD) spread arising from CD and MD. Assuming the strong-coupling regime, in which the total system length far exceeds the correlation length of modal fields, we quantify the GD spread arising from MD, showing that it can be reduced significantly by mode coupling. We evaluate the computational complexity of various MIMO single-carrier equalizers, considering separate or combined equalization of CD and MD, in the time or frequency domain. We present numerical examples for the optimally designed graded-index depressed-cladding fibers supporting D=6, 12, 20 or 30 modes in two polarizations. Assuming a 2000-km system length, a 1-km correlation length, and a combined CD+MD frequency-domain equalizer, the complexity (in complex multiplications per two-dimensional symbol) is a factor 1.4, 1.7, 2.2, 2.8 times higher for D=6, 12, 20, 30 than for polarization-multiplexed systems in standard single-mode fiber (D=2).

Demodulation and multi-input multi-output equalization for mode division multiplexing system using a novel few-mode fiber

In order to solve the mode crosstalk in a mode division multiplexing (MDM) transmission system, we design and fabricate a novel few-mode fiber (FMF) with high mode differential group delay (MDGD) that ensure that all supporting modes can transmit through the FMF independently. Then, we propose a cascaded multi-input multi-output (MIMO) delay equalization method, in order to further suppress the mode crosstalk from the mode division multiplexer/demultiplexer (MUX/DeMUX) and improve the transmission distance and spectrum efficiency of MDM system. Our simulation results verify that the cascaded MIMO delay equalization method together with the novel FMF can effectively mitigate the mode crosstalk of MDM transmission. Compared with the traditional MIMO equalization method, our proposed equalization method can be successfully applied to the QPSK signal transmission through the FMF with large MDGD, while no obvious increase of computation complexity is observed. Our results show that for a 40 Gbps two-mode division multiplexing system, the Q factor can be improved by 1.7 dB after 40 km FMF transmission using the proposed cascaded MIMO equalization method. Therefore, all those results are very conducive to the next-generation high capacity fiber-optic transmission.

Blind MIMO equalization with optimum delay using independent component analysis

AbstractBlind space–time equalization of multiuser time‐dispersive digital communication channels consists of recovering the users' simultaneously transmitted data free from the interference caused by each other and the propagation effects, without using training sequences. In scenarios composed of mutually independent non‐Gaussian i.i.d. users' signals, independent component analysis (ICA) techniques based on higher‐order statistics can be employed to refine the performance of conventional linear detectors, as recently shown in a code division multiple access environment (Signal Process 2002; 82:417–431). This paper extends these results to the more general multi‐input multi‐output (MIMO) channel model, with the minimum mean square error (MMSE) as conventional equalization criterion. The time diversity introduced by the wideband multipath channel enables a reduction of the computational complexity of the ICA post‐processing stage while further improving performance. In addition, the ICA‐based detector can be tuned to extract each user's signal at the delay which provides the best MMSE. Experiments in a variety of simulation conditions demonstrate the benefits of ICA‐assisted MIMO equalization. Copyright © 2004 John Wiley & Sons, Ltd.

Finite-length MIMO equalization using canonical correlation analysis

We propose finite-length multi-input multi-output (MIMO) equalization methods for "smart" antenna arrays using the statistical theory of canonical correlations. We show that the proposed methods are related to maximum likelihood (ML) reduced-rank channel and noise estimation algorithms in unknown spatially correlated noise as well as to several previously developed equalization schemes.

FIR channel-shortening equalizers for MIMO ISI channels

Finite-length delay-optimized multi-input multi-output (MIMO) equalizers that optimally shorten the impulse response memory of frequency-selective MIMO channels are derived. The MIMO equalizers are designed to minimize the average energy of the error sequence between the equalized MIMO channel impulse response and an MIMO target impulse response (TIR) with shorter memory. Two criteria for optimizing the MIMO TIR are analyzed and compared. The presented analytical framework encompasses a multitude of previously-studied finite-length equalization techniques.

Bounds on SIMO and MIMO Channel Estimation and Equalization with Side Information

Constrained Cramer-Rao bounds are developed for convolutive multi-input multi-output (MIMO) channel and source estimation in additive Gaussian noise. Properties of the MIMO Fisher information matrix (FIM) are studied, and we develop the maximum rank of the unconstrained FIM and provide necessary conditions for the FIM to achieve full rank. Equality constraints on channel and signal parameters provide a means to study the potential value of side information, such as training symbols (semi-blind case), constant modulus (CM) sources, or known channels. Nonredundant constraints may be combined in an arbitrary fashion, so that side information may be different for different sources. The bounds are useful for evaluating the performance of SIMO and MIMO channel estimation and equalization algorithms. We present examples using the constant modulus blind equalization algorithm. The constrained bounds are also useful for evaluating the relative value of different types of side information, and we present examples comparing semi-blind, constant modulus, and known channel constraints. While the examples presented are primarily in the communications context, the CRB framework applies generally to convolutive source separation problems.