Nonlinear Equalization through a Volterra Filter

  • Description

    OFDM is a modulation format that can be advantageously used in access systems as it provides increased spectral efficiency, enhanced equalization capabilities and flexible bandwidth allocation compared to single-carrier modulation schemes. While baseband transmission is rather tolerant to the nonlinear behavior of the transmission channel, OFDM requires a highly linear transmission channel. One of the main contributors for channel nonlinearity is chirp-GVD interaction, which leads to subcarrier-to-subcarrier intermixing interferences (SSII) after detection.
    SSII can be mitigated through equalization of the received signal by nonlinear filtering [1]. One type of nonlinear filter is the Volterra filter. In order to train filter coefficients, a known training sequence is sent by the transmitter; the Volterra filter coefficients are then trained using the LMS algorithm to reduce the error at the output of the filter [2].

  • Typical Results

    This application example demonstrates SSII mitigation by means of a Volterra filter. The laser is directly modulated using DMT (real-valued OFDM), while direct detection is performed at the receiver. The 9-Gbaud signal is composed of 32 subcarriers, each modulated with 16QAM, and includes 12,5% cyclic prefix resulting in a net signal rate of 31,5 Gbit/s. As fiber length is 40 km, modulation index is set at 25% guaranteeing enough optical power at the receiver.
    Three runs of the setup are performed: in the first run the Volterra filter is off, in the second run it adapts its coefficients, and in the final run the filter is active. For each run, a different transmitted signal is used. Figure 1 shows the error signal at the output of the filter. Figure 2 shows transmitted and received spectra for the final run with and without filter. The SSII can be observed in the 10 GHz-17 GHz range. The BER of all subcarriers are reported in Figure 3 for the cases with and without the filter. Figure 4 and 5 show the constellation of 32 subcarriers before and after the filter.

  • Further Information

    Keywords: OFDM, access networks, Volterra, Equalization, Direct Modulation, Direct detection, chirp-GVD interaction

    Similar demonstrations are available in VPItransmissionMaker Optical Systems and on the VPIphotonics Forum.

    [1] W. Yan, B. Liu, L. Li, Z. Tao, T. Takahara, and J. C. Rasmussen, 'Nonlinear Distortion and DSP-based Compensation in Metro and Access Networks using Discrete Multi-tone' in ECOC (2012), paper Mo.1.B.2.
    [2] N. André, K. Habel, H. Louchet, A. Richter, 'Equalization Techniques for High-speed OFDM-based Access Systems Using Direct Modulation and Direct Detection' in ICTON (2013)

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