Gerchberg-Saxton Based FIR Filter for Electronic Dispersion Compensation in IM/DD Transmission Part I: Theory and Simulation

Abstract

<p>Intensity-modulation and direct-detection (IM/DD) systems deployed for short reach optical fiber links require electronic dispersion compensation (EDC) at the transmitter and/or electronic equalization at the receiver. Under direct detection, the optical phase is lost and complex-valued compensation of chromatic dispersion (CD) used in coherent systems could not be adopted. The utilization of the iterative Gerchberg-Saxton (GS) algorithm for EDC in IM/DD systems, has been demonstrated in theory and experiment, through treating the amplitude at the transmitter and the phase prior-to the direct detection receiver as a degree of freedom. In this article, three GS approaches for CD compensation in IM/DD systems using finite impulse response (FIR) filters are described and demonstrated. The first two approaches are closely related and rely on a cascaded FIR structure, while the third approach offers a novel non-iterative solution for EDC in IM/DD systems. In this solution, a feed-forward static digital FIR filter is designed and optimized using the Gerchberg-Saxton algorithm for transmitter CD pre-compensation. This is achieved through decoupling of pattern dependent and modulation format dependent aspects of transmission from the GS iterations by setting the target amplitude at the receiver to single impulse at the center of the time-window. With every successive iteration an impulse response for the CD pre-compensation filter emerges and is used to set the FIR tap weights. It is also demonstrated that the same optimum taps weight can be obtain analytically by applying the frequency-domain fiber transfer function to the iterations of the GS algorithm under the assumptions of small-signal analysis. The FIR filter is implemented using a non-recursive tapped delay line structure with an 8-bit finite-precision arithmetic. An adaptive $T$-spaced feed-forward equalizer (FFE) is utilized at the receiver for compensating residual CD. It is shown, as an example, that a 56 Gb/s non-return to zero (NRZ) on-off keying (OOK) signal could be transmitted over 80 km of single mode fiber (SMF) with a chirp-free single drive Mach-Zehnder modulator (MZM) and a 417-tap FIR filter operating at 2 sample-per-symbol with the bit error ratio (BER) below the hard-decision forward error correction (FEC) limit of $3.8 \times 10^{-3}$. Enabling a 21-tap post-FFE, reduces the BER to a 1 dBQ margin below the FEC limit.</p> <p><br></p>