A document by Abdullah S. Karar . Click on the document to view its contents.

Short-reach fiber optical links employing intensity modulation (IM) at the transmitter (Tx) and direct detection (DD) at the receiver (Rx), suffer from linear and nonlinear sources of impairments due to the interaction of chromatic dispersion (CD) with DD. In this article, joint electronic dispersion compensation (EDC) at the Tx, using two distinct Gerchberg-Saxton (GS) based approaches, and at the Rx, using a functional link neural network (FLNN) equalizer is demonstrated for IM/DD transmission. The first Tx approach utilizes the modified iterative GS algorithm, which partially mitigate linear and nonlinear sources of inter-symbol interference (ISI). The second Tx pre-EDC approach only pre-compensates for the linear power fading effect through implementing a GS based finite impulse response (FIR) filter. At the Rx, a T/2-spaced or T-spaced adaptive post-feed forward equalizer (FFE) is employed to fully compensate residual chromatic dispersion prior to attempting nonlinear equalization. Furthermore, a Volterra nonlinear equalizer (VNLE) is introduced to benchmark the performance and complexity of the FLNN, Subsequently, either a FLNN or a VNLE are utilized for nonlinear system identification and subsequent post-equalization mitigating uncompensated nonlinear sources of ISI. The FLNN nonlinear taps resulting from the functional expansion block are optimized using the  recursive least square (RLS) algorithm. The Tx-FIR and Rx-FLNN enable 112 Gbit/s non-return to zero (NRZ) on off keying (OOK) transmission over 20 km of single mode fiber (SMF) and 112 Gbit/s 4- level pulse-amplitude modulation (PAM-4) transmission over 10 km of SMF. It is shown that the use of Tx pre-EDC reduces the complexity of the required equalization at the Rx. In addition, the FLNN was found to offer a 74% reduction in computational complexity relative to the third-order VNLE.

Intensity-modulation and direct-detection (IM/DD) transmission over short-reach optical fiber links, require electronic dispersion compensation (EDC) at the transmitter and/or electronic equalization at the receiver. Recently, the iterative Gerchberg-Saxton (GS) algorithm was demonstrated for EDC in IM/DD systems, through treating the amplitude at the transmitter and the phase prior-to the direct detection receiver as a degree of freedom. In Part I of this work, three GS approaches using finite impulse response (FIR) filters for EDC in IM/DD systems are demonstrated. The first two are closely related and rely on a cascaded FIR structure, while the third offers a novel noniterative EDC solution using a single GS optimized static FIR filter. This is achieved through decoupling pattern dependent aspects of transmission from the GS iterations by targeting a single impulse at the DD receiver. With every successive iteration an impulse response for the GS filter emerges and sets the FIR tap weights. It is also demonstrated that closed-form analytical expressions for the GS filter impulse response can be obtained through small-signal frequency-domain analysis. The FIR filter is simulated using 8-bit finite-precision arithmetic. An adaptive T spaced post feed-forward equalizer (FFE) is utilized for mitigating residual chromatic dispersion. It is shown, that a T/2-spaced pre-EDC FIR filter with 417 taps can support 56 Gb/s non-return-to-zero (NRZ) on-off keying (OOK) transmission over 80 km of single mode fiber (SMF) with a chirp-free Mach-Zehnder modulator (MZM). Part II of this work, presents experimental demonstration of the non-iterative GS FIR filter proposed and simulated in this article.

In this article, the first experimental demonstration of a non-iterative electronic dispersion compensation (EDC) solution implemented at the transmitter using a finite impulse response (FIR) filter optimized with the Gerchberg-Saxton (GS) algorithm, is presented, for intensity-modulation and direct- detection (IM/DD) systems. The theoretical framework for the GS FIR filter and preliminary simulations have been presented in Part I of this work. Here, the performance of the GS FIR filter is compared to that of the iterative GS algorithm in the transmissions of 56-Gb/s on-off keying (OOK) over 80 km of single mode fiber (SMF) with a post feed-forward equalizer (FFE) for combating residual inter-symbol interference (ISI). Furthermore, the influence of the pulse shape (raised cosine or rectangular) and modulation format (return-to-zero (RZ) or non- return-to-zero (NRZ)) on the measured bit error ratio (BER) is experimentally investigated, while changing the number of FIR taps, the number of post-FFE taps, and the number of post-FFE samples-per-symbol. It is shown that within the range of the target digital extinction ratios (DERs) for which the original iterative GS algorithm offers benefit, both analytical and numerical methods for calculating the optimum FIR taps, outlined in Part I of this work, produce similar BER performance as predicted. To that end, the former method is extended, here, through a non-recursive frequency response formula, which offers insight into the action of the GS filter with different pulse shaping and enables the derivation of the explicit GS impulse response. It is also shown that rectangular RZ pulse shaping exploits the full benefit of GS filtering through a uniform spectrum, enabling a BER below the 7% hard-decision forward error correction (HD-FEC) limit, with a 641-tap T/2-spaced pre-EDC FIR filter and a 3-tap adaptive T-spaced post-FFE.