Motivated by the recent interest in single-mode semiconductor optical amplifiers and multimode erbium-doped fiber amplifiers, we present a unified, comprehensive treatment of the effect of polarization- and mode-dependent gain (PDG and MDG) on the capacity of ultra-long-haul transmission systems. We study the problem using simulations of a multisection model, including the effects of PDG or MDG and polarization mode dispersion (PMD) or modal dispersion. We also analytically derive exact expressions for the capacity distribution of PDG-impaired single-mode systems. In agreement with previous work, we find that PDG and MDG cause fluctuations in capacity, which reduces average capacity and may cause outage. We show that the multimode systems studied, with at least $D = 14$ spatial/polarization modes, have sufficient modal diversity and frequency diversity to strongly suppress capacity fluctuations and reduce outage probability so that the outage capacity approaches the average capacity. We show that single-mode systems, by contrast, inherently provide low modal and frequency diversity, making them more prone to outage. To alleviate this problem, frequency diversity can be increased by artificially inserting PMD. Finally, we quantify the PDG/MDG requirements of optical amplifiers to ensure that the average capacity is close (within a 1-2 dB effective SNR loss) to the theoretical optimum. We show that these PDG/MDG requirements are stringent, especially considering the minimum-mean-square error linear equalizers implemented in typical multiple-input multiple-output receivers.

中文翻译：

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偏振和模式相关增益对超长途系统容量的影响

由于最近对单模半导体光放大器和多模掺铒光纤放大器的兴趣，我们对偏振和模式相关增益（PDG 和 MDG）对超长光纤容量的影响进行了统一、综合的处理。 - 远距离传输系统。我们使用多节模型的模拟来研究该问题，包括 PDG 或 MDG 和偏振模式色散 (PMD) 或模式色散的影响。我们还通过分析推导出 PDG 受损单模系统容量分布的精确表达式。与之前的工作一致，我们发现 PDG 和 MDG 会导致容量波动，从而降低平均容量并可能导致中断。我们展示了研究的多模系统，至少有 $D = 14$ 空间/极化模式，具有足够的模态多样性和频率多样性，能够强烈抑制容量波动，降低停电概率，使停电容量接近平均容量。我们表明，相比之下，单模系统固有地提供低模态和频率多样性，使它们更容易中断。为了缓解这个问题，可以通过人为插入 PMD 来增加频率分集。最后，我们量化了光放大器的 PDG/MDG 要求，以确保平均容量接近（在 1-2 dB 有效 SNR 损失内）接近理论最佳值。我们表明这些 PDG/MDG 要求是严格的，特别是考虑到在典型的多输入多输出接收器中实现的最小均方误差线性均衡器。