QR factorization equalisation scheme for mode devision multiplexing transmission in fibre optics

Optical communication systems play a major role in handling worldwide Internet traffic. Internet traffic has been increasing at a dramatic rate and the current optical network infrastructure may not be able to support the traffic growth in a few decades. Mode division multiplexing is introduced as a new emerging technique to improve the optical network capacity by the use of the light modes as individual channels. One of the main issues in MDM is mode coupling which is a physical phenomenon when light modes exchange their energy between each other during propagation through optical fiber resulting in inter-symbol interference (ISI). Many studies based on Least Mean Square (LMS) and Recursive Least Square (RLS) have taken place to mitigate the mode coupling effect. Still, most approaches have high computational complexity and hinders high-speed communication systems. Blind equalisation approach does not need training signals, thus, will reduce the overhead payload. On the other hand, QR factorization shows low computational complexity in the previous research in the radio domain. The combination of these two concepts shows significant results, as the use of low complexity algorithms reduces the processing needed to be done by the communication equipment, resulting in more cost effective and smaller equipment, while having no training signal saves the bandwidth and enhances the overall system performance. To the best knowledge of the researcher, blind equalisation based on QR factorization technique has been not used in MDM equalisation to date. The research goes through the four stages of the design research methodology (DRM) to achieve the purpose of the study. The implementation stage is taken two different simulators has been used, the first one which is the optical simulator is used to collect the initial optical data then, MATLAB is used to develop the equalisation scheme. The development starts with the derivation of the system’s transfer function (H) to be used as the input to the developed equalizer. Blind equalisation based on QR factorization is chosen as a way to introduce an efficient equalization to mitigate ISI by narrowing the pulse width. The development stages include a stage where the channel estimation is taken place. Statistical properties based on the standard deviation (STD) of the powers of the input and output signals has been used for the blind equalisation’s channel estimation part. The proposed channel estimation way has the ability in estimating the channel with an overall mean square error (MSE) of 0.176588301 from the initial transmitted signal. It is found that the worst channel has an MSE of 0.771365 from the transmitted signal, while the best channel has and MSE of 0.000185 from the transmitted signal. This is done by trying to avoid the issues accompanied with the development of the previous algorithms that have been utilized for the same goal. The algorithm mentioned in the study reduces the computational complexity problem which is one of the main issues that accompany currently used tap filter algorithms, such as (LMS) and (RLS). The results from this study show that the developed equalisation scheme has a complexity of O(N) compared with O(N2) for RLS and at the same time, it is faster than LMS as its calculation CPU time is equal to 0.005242 seconds compared with 0.0077814 seconds of LMS. The results are only valid for invertible and square channel matrices

Algorithms and Subsystems for Next Generation Optical Networks

This thesis investigates algorithms and subsystems for digital coherent optical networks to alleviate system requirements and enable spectrally efficient systems. Spectral shaping of individual channel is investigated to mitigate backreflections in bi-directional Passive Optical Network (PON) enabling more than 1000 users operating at 10 Gbit/s. It is then shown that temporal delay skews, caused by misalignment in the coherent receiver, induce a large penalty for Nyquist filtered signals. An adaptive 4×4 equaliser is developed to compensate the imperfections dynamically. This is subsequently demonstrated experimentally with Polarisation Division Multiplexed (PDM) Quadrature Phase Shift Keying (QPSK) and 16-level Quadrature Amplitude Modulation (QAM). Furthermore, a modified blind equaliser is designed to adaptively compensate for unknown amount of Chromatic Dispersion (CD). The equaliser is demonstrated experimentally using 10.7 GBd PDM-QPSK transmission over 5,200 km. To simplify the computational complexity of the equalisers a multiplier free update scheme is explored in simulations. Optical frequency combs are investigated as phase and frequency synchronised sub- carrier sources for Dense Wavelength Division Multiplexing (DWDM) systems. The effect of phase synchronisation between sub-channels of a superchannel is examined in simulations without showing performance deviation when no additional optical or digital processing is applied. Afterwards, the transmission performance of two generation techniques implementing 400 Gbit/s superchannels, utilising PDM-16QAM, is evaluated. Although, the average performance of the two combs is identical subchannel fluctuations are observed due to uneven spectral profile. Carrier Phase Estimation (CPE) is explored for both single channel and superchannels systems. An equaliser interleaved with CPE, is explored for PDM-64QAM with minor improvement. Alternatively, Digital Coherence Enhancement (DCE) allowed the detection of 6 GBd PDM-64QAM with a 1.4 MHz linewidth laser, an order of magnitude improvement in linewidth tolerance. Finally, a joint CPE across a comb superchannel is demonstrated with a factor of 5 tolerance improvement

Digital signal processing for coherent optical fibre communications

In this thesis investigations were performed into digital signal processing (DSP) algorithms for coherent optical fibre transmission systems, which provide improved performance with respect to conventional systems and algorithms. Firstly, an overview of coherent detection and coherent transmission systems is given. Experimental investigations were then performed into the performance of digital backpropagation for mitigating fibre nonlinearities in a dual-polarization quadrature phase shift keying (DP-QPSK) system over 7780 km and a dual-polarization 16- level quadrature amplitude modulation (DP-QAM16) system over 1600 km. It is noted that significant improvements in performance may be achieved for a nonlinear step-size greater than one span. An approximately exponential relationship was found between performance improvement in Q-factor and the number for required complex multipliers. DSP algorithms for polarization-switched quadrature phase shift keying (PS-QPSK) are then investigated. A novel two-part equalisation algorithm is proposed which provides singularity-free convergence and blind equalisation of PS-QPSK. This algorithm is characterised and its application to wavelength division multiplexed (WDM) transmission systems is discussed. The thesis concludes with an experimental comparison between a PS-QPSK transmission system and a conventional DP-QPSK system. For a 42.9 Gb/s WDM system, the use of PS-QPSK enabled an increase of reach of more than 30%. The resultant reach of 13,640 km was, at the time of publication, the longest transmission distance reported for 40 Gb/s transmission over an uncompensated link with standard fibre and optical amplification

Digital Signal Processing for Optical Communications and Coherent LiDAR

Internet data traffic within data centre, access and metro networks is experiencing unprecedented growth driven by many data-intensive applications. Significant efforts have been devoted to the design and implementation of low-complexity digital signal processing (DSP) algorithms that are suitable for these short-reach optical links. In this thesis, a novel low-complexity frequency-domain (FD) multiple-input multiple-output (MIMO) equaliser with momentum-based gradient descent algorithm is proposed, capable of mitigating both static and dynamic impairments arising from the optical fibre. The proposed frequency-domain equaliser (FDE) also improves the robustness of the adaptive equaliser against feedback latencies which is the main disadvantage of FD adaptive equalisers under rapid channel variations. The development and maturity of optical fibre communication techniques over the past few decades have also been beneficial to many other fields, especially coherent light detection and ranging (LiDAR) techniques. Many applications of coherent LiDAR are also cost-sensitive, e.g., autonomous vehicles (AVs). Therefore, in this thesis, a low-cost and low-complexity single-photodiode-based coherent LiDAR system is investigated. The receiver sensitivity performance of this receiver architecture is assessed through both simulations and experiments, using two ranging waveforms known as double-sideband (DSB) amplitude-modulated chirp signal and single-sideband (SSB) frequency-modulated continuous-wave (FMCW) signals. Besides, the impact of laser phase noise on the ranging precision when operating within and beyond the laser coherence length is studied. Achievable ranging precision beyond the laser coherence length is quantified

Blind adaptive equalization for QAM signals: New algorithms and FPGA implementation.

Adaptive equalizers remove signal distortion attributed to intersymbol interference in band-limited channels. The tap coefficients of adaptive equalizers are time-varying and can be adapted using several methods. When these do not include the transmission of a training sequence, it is referred to as blind equalization. The radius-adjusted approach is a method to achieve blind equalizer tap adaptation based on the equalizer output radius for quadrature amplitude modulation (QAM) signals. Static circular contours are defined around an estimated symbol in a QAM constellation, which create regions that correspond to fixed step sizes and weighting factors. The equalizer tap adjustment consists of a linearly weighted sum of adaptation criteria that is scaled by a variable step size. This approach is the basis of two new algorithms: the radius-adjusted modified multitmodulus algorithm (RMMA) and the radius-adjusted multimodulus decision-directed algorithm (RMDA). An extension of the radius-adjusted approach is the selective update method, which is a computationally-efficient method for equalization. The selective update method employs a stop-and-go strategy based on the equalizer output radius to selectively update the equalizer tap coefficients, thereby, reducing the number of computations in steady-state operation. (Abstract shortened by UMI.) Source: Masters Abstracts International, Volume: 45-01, page: 0401. Thesis (M.A.Sc.)--University of Windsor (Canada), 2006