# Adaptive Pre/Post-Compensation of Cascade Filters in Coherent Optical Transponders
## 1 Introduction  
The deployment of optical switches, such as reconfigurable optical add drop multiplexing (ROADM), was a key milestone in enabling all-optical transmission, as illustrated in Figure 1a, from source to destination in a dense wavelength division multiplexing (DWDM) network. They offer great advantages for service providers such as simplification of network planning and provisioning, reduction in infrastructure cost and lower power consumption (no electrical to optical, and vice-versa, conversion required). Each optical link is split into sections called spans. The latter is characterized by the position of ROADM nodes. The length of fiber per span is in the range of 80 to 160 km depending on the amplification technology used [1]. With flexibility being a requirement in current and future optical networks, ROADMs, which are made using Liquid-Crystal on Silicon (LCOS) [2] or Micro-Electro Mechanical Systems (MEMS) [3] with optical switch fabric, allow control to be done per wavelength both in terms of routing and attenuation. \"Broadcast and Select\" and \"Route and Select\" are two main switching architectures based on ROADMs discussed in [4]. ROADMs, acting like filters with limited passband bandwidth, are critical limitations in fixed-grid optical networks [5]. They introduce colored noise to the signal while affecting both the amplitude and the phase of the propagated stream of optical pulses. The system impact of concatenated filtering on 28 Gigabaud (Gbaud), using dual-polarization (DP) 8 QAM constellation, was discussed in [6]. Both passband bandwidth-narrowing and ripples are discussed in [7]. As the signal travels from the source to destination on an all-optical link, the aforementioned effects accumulated the signal passes through a series of cascaded ROADMs. This introduces dispersion and spectral clipping which are impairments that lead to performance degradation. Currently deployed ROADMs have fixed-bandwidths of 50 and 100 GHz per wavelength. Deployment of next-generation flexible-bandwidth, enabling flex-grid networks, with a granularity of 6.25 GHz is under-way [8]. Temperature also impacts the frequency response of the Electro-Optics (EO) at the transmitter and receiver which, along with the effects of the ROADMS, causes an overall filtering effect that must be compensated for to minimize SNR penalty. To compensate for the filtering frequency-dependent loss, as illustrated in Figure 1b, the authors of [9; 10] discussed applying a pre-compensation at the Tx of a 10G optical transponder. It is assumed that the transfer function (TF) of the channel is measured and available to use. In [11; 12], authors studied the impact of pre-compensation, using finite impulse response (FIR) filters at the digital to analog converter (DAC), of the narrowing of bandwidth due to gridless ROADMs. The method assumes the knowledge of the number of ROADMs in the link and the center frequency offset. In [13], the authors introduced new hardware (HW) block, a trellis decoder, at the end of the Rx processing chain. The solution requires extra processing and cause higher power consumption. In [14], the authors suggested using external optical wave-shapers at the edge of the DWDM link. The concept is similar to the Dispersion Slope Compensation module, described in [15], that deals with compensating for chromatic dispersion per span along the link. However, besides the cost, maintenance and power consumption of new modules in link, the shapers have to be programmed for initial deployment. which makes network planning more burden but will lack continuous track of changes in transferring frequency response due to temperature or drift in center frequency when MEMS' mirrors ages. In [16], time-domain hybrid modulation is used to reduce the gap between the R-OSNR of regular M-QAM constellations, therefore provides flexible line-rate transmission.