# High-Speed, High-Performance DQPSK Optical Links with Reduced Complexity VDEE Equalizers
## 1 Introduction  
Due to the rapid evolution of cloud services, traffic demand is growing dramatically every year in every network segment. Especially in core optical networks, this demand necessitates adaptation of high-speed channels in a power efficient and economically viable way. Transporting traffic at high bit rates, such as 100 Gbit/s, may become challenging as various impairments manifest themselves [1]. Combating those impairments is cumbersome and power consuming, hence, the preferred solution choices are not obvious in network segments that are sensitive to cost and power consumption, like in metropolitan area networks [2] and inter-data center networks [3]. Typically, these segments are subject to unpredictable traffic changes and all distortions vary in a nondeterministic way. Optical transport technologies optimized for such network applications with direct detection (DD) techniques gain an increasing number of supporters due to the adaptivity and low complexity offered by optical and electronic transmission technologies used to compensate for linear and nonlinear impairments [4]. Chromatic dispersion (CD) is the prevailing linear impairment that causes intersymbol interference (ISI) [2]. Distortion compensation techniques have been made readily available with optical and electronic means [5; 6; 7]. Optical compensators are usually based on dispersioncompensating fiber (DCF) placed along the optical transmission system, while electronic ones are usually based on equalizers. Optical compensating techniques are rigid as far as the amount of the CD they mitigate implying that its value is known in advance. Electronic equalizers [5; 8], on the other hand, are utilized adjustably after signal detection and can additionally compensate part of the PMD [6]. Equalization methods can be performed by a maximum likelihood sequence estimation (MLSE) method [6] or on the use of non-linear decision feedback filters for mitigating ISI in optical communication systems. Equalization methods based on recursive Volterra nonlinear filters have been proposed [7; 9], noting however, that the use of Volterra equalizers still becomes cumbersome when the ISI extends more than a few symbols. In high data rate systems, signal distortions caused by intersymbol interference increase proportionally to the square of the data rate, hence, the performance of the transmission system is very sensitive to the possible residual dispersion at the receiver. Optical dispersion compensation can only compensate for specific values of chromatic dispersion, however, in dynamic multi-channel network segments dispersion is not always known in advance. As discussed in [2] optical transmission systems can benefit from a combination of rigid DCF with adaptive equalization at the receiver where residual dispersion is adjustably compensated after signal detection. In this paper, we investigate the performance of the conventional non-return to zero differential quaternary phase shift keying (NRZ-DQPSK) optical link that comprises an optical channel with standard single mode and dispersion compensating fiber and various receiver configurations that combine single-ended receivers and joint reduced complexity Volterra-type equalizers [2; 10; 11]. For the first time, to our knowledge, the scope of the investigation takes advantage of the linear dependency among the electrical signals (constructive/destructive and in-phase/quadrature) at the receiver side, to further reduce the complexity of proposed equalizers, allowing for numerically sound and viable implementation configurations. The proposed partially-joint single-ended digital equalization schemes for the DQPSK signaling utilize a triplet out of the quartet of electrical signals (constructive/destructive and in-phase/quadrature) available at the single ended receiver, for equalization, and eventually the detection of the transmitted bit streams. As a result a 25% reduction of the computational cost compared to the fully-deployed joint counterpart is achieved.