Accurate Calculation of Bit Error Ratios in Optical Fiber Communications Systems

自从掺铒光纤放大器的发明和长距离光纤通信系统的出现以来，通常不可能准确地计算误码率(BERS)。光纤传输线中的非线性是这一困难的最终来源。信号和噪声之间的非线性相互作用会显著影响接收器之前的噪声分布，从而使简单的分析方法失效。同时，人们必须计算的低位误码率-在某些情况下在10-15数量级-使得标准的蒙特卡罗模拟变得不实用。传输非线性还导致图案相关性以及接收的标记和间隔中的扩展，这不是由于噪声引起的，并且必须被考虑。在波分复用(WDM)系统中，数以千计的比特可以相互作用，因此很难准确地计算码型依赖关系。此外，准确地对接收机进行建模是至关重要的，包括接收机引起的码间干扰，并且必须能够考虑前向纠错和信号处理的影响。在过去的几年中，PI已经开发了一套能够解决所有这些问题的理论工具，并使BER的准确计算变得触手可及。对于这些问题中的每一个，他们至少开发了两种不同的方法，一种是确定性的，一种是统计学的，这两种方法在大部分情况下是非常一致的，并且相互自我验证。然而，要在实际环境中测试这些方法，验证在某些环境中可能有用的简化方法，并在实验中验证结果，还需要大量的进一步发展。该提议的智力优势在于他们采用了主要应用于理想化环境的复杂数学工具，并将它们发展成有效的计算方法，可以用于在具有显著复杂性的真实世界实验系统中计算BER。拟议研究的广泛影响在于其潜在的实质性影响信息技术及其教育特征。他们预计，在进一步开发后，这些工具将影响系统设计，降低开发和系统成本，并鼓励创新。通过与实验的仔细比较，他们预计这些工具将为这些复杂系统的工作原理提供新的见解。PIS制定的这些方法将在密歇根大学教授的课程和他们在外部教授的短期课程中传播，以及在出版物中传播。数学系学生和工程系学生之间的跨学科互动是该提案的一个主要特点。研究生研究助理将执行大部分拟议工作，作为其教育的一部分，与代表人数不足的群体进行接触是该提议的另一个关键特点。

0400535MenyukSince the invention of the erbium-doped fiber amplifier and the advent of long-haul optical fiber communications systems, it has not been possible in general to accurately calculate the bit error ratios (BERs). Nonlinearity in the optical fiber transmission line is the ultimate source of this difficulty. Nonlinear interactions between the signal and the noise can significantly affect the noise distribution prior to the receiver, invalidating simple analytical approaches. At the same time, the low BERs that one must calculate -on the order of 10 -15 in some cases - make standard Monte Carlo simulations impractical.Transmission nonlinearity also leads to pattern dependences and a spread in the received marks and spaces that is not due to noise and must be taken into account. In wavelength-division-multiplexed (WDM) systems, thousands of bits can interact, so that accurately accounting for the pattern dependences is difficult.Additionally, it is critically important to model the receiver accurately, including receiver-induced intersymbol interference, and one must be able to take into account the impact of forward error correction and signal processing.In the past few years, the PIs have developed a set of theoretical tools that are capable of addressing all these issues and have put the accurate calculation of BERs within reach. For each of these issues, they have developed at least two different methods, one deterministic and one statistical, that are in excellent agreement for the most part and are mutually self-validating. However, considerable further development is needed to test these methods in practical contexts, to validate reduced approaches that might be useful in certain contexts, and to validate results experimentally.The intellectual merit of the proposal resides in their taking sophisticated mathematical tools that have been applied primarily to idealized settings and developing them into effective computational methods that can be used to calculate BERs in real-world experimental systems with significant complexity.The broad impacts of the proposed research lie in its potential to substantially impact information technology and in its educational features. They expect that after further development, these tools will impact system design, lowering both development and systems costs and encouraging innovation. By careful comparison to experiments, they expect these tools to provide new insights into how these complex systems work. These methods that the PIs develop will be disseminated in courses taught at UMBC and short courses that they teach externally, as well as in publications. Interdisciplinary interactions between students in Mathematics and students in Engineering is a key feature of the proposal. Graduate research assistants will carry out most of the proposed work as part of their education, and outreach to under-represented groups is another key feature of the proposal.