Multi-constraint Gerchberg-Saxton iteration algorithms for linearizing IM/DD transmission systems

Abstract

Chromatic dispersion-enhanced signal-signal beating interference (SSBI) considerably affects the performance of intensity-modulation and direct-detection (IM/DD) fiber transmission systems. For recovering optical fields from received double sideband signals after propagating through IM/DD transmission systems, Gerchberg-Saxton (G-S) iterative algorithms are promising, which, however, suffers slow convergence speeds and local optimization problems. In this paper, we propose a multi-constraint iterative algorithm (MCIA) to extend the Gerchberg-Saxton-based linearized detection. The proposed technique can accelerate the convergence speed and realize nonlinear-equalization-free detection. Based on the data-aided iterative algorithm (DIA) and the decision-directed data-aided iterative algorithm (DD-DIA), the proposed technique reuses redundant bits from channel coding to not only correct decision errors but also enforce the constraints on the task function to further accelerate the whole optical field retrieval processing. Simulation results show that, compared with the DD-DIA, the MCIA reduces the received optical power (ROP) by about 1.5-dB for a 100-Gb/s over 50-km SSMF PAM-4 signal transmission at the symbol error rate (SER) of 2×10−2. For a 100-Gb/s over 400-km SSMF transmission system, just 30 MCIA iterations is needed, which is 30% reduction in iteration count compared with the DD-DIA. For further increased transmission capacities, the MCIA can improve the SER by two orders of magnitude compared with the conventional IA. To validate the effectiveness of the MCIA, we also conduct experiments to transmit 92-Gb/s PAM-4 signals over 50-km IM/DD fibre systems. We find that the MCIA has a 1-dB ROP improvement compared with the DD-DIA. Compared with Volterra nonlinear equalization, the BERs of the MCIA with a simple linear equalizer are reduced by more than one order of magnitude with only 52 MCIA iterations.

Error-Controlled Iterative Algorithms for Digital Linearization of IMDD-Based Optical Fibre Transmission Systems

“…Based on the Gerchberg-Saxton (G-S) algorithm for the 2Dimage construction of X-ray diffraction [20], the phase retrieval of 1D signals was developed for CD pre-compensation [21], [22] or post-compensation [23] for improving signal transmission capacities or reaches of non-return-to-zero on-off keying (NRZ-OOK)-encoded IMDD systems [22], [23] and even quadrature phase shift keying (QPSK)-encoded coherent systems [24]. To further improve the capacity versus reach performances of IMDD transmission systems, a decisiondirected data-aided iterative algorithm (DD-DIA) [25] and a multi-constraint iterative algorithm (MCIA) [26] have recently been reported, which support ≥100 Gb/s 4-level pulse amplitude modulation (PAM4) IMDD transmission over ≥50 km SMFs. Compared with the DD-DIA, the MCIA reduces the required number of iterations and symbol error rate because redundant bits associated with forward error correction (FEC) are reused to reduce decision errors of the PAM symbols in the iterations.…”

“…In addition, in the MCIA the use of FEC in the iterations may cause a large latency. Furthermore, the power and optical signal-to-noise ratio (OSNR) penalties compared with the optical back-to-back (OBTB) systems were not discussed in [25], [26].…”

Gerchberg-Saxton Based Finite Impulse Response Filter for Electronic Dispersion Compensation in IM/DD Transmission: Experimental Demonstration

“…However, under direct detection, the optical phase is lost and complexvalued compensation of CD used in coherent systems could not be adopted. In an effort to compensate the CD-induced linear power fading penalty in IM/DD transmission, a phaseretrieval iterative algorithm, known as Gerchberg-Saxton (GS) algorithm was introduced theoretically, and demonstrated experimentally [1]- [8]. In all prior implementations of the GS algorithm in the context of IM/DD transmission, a number of real-time iterations on the incoming information bearing waveform was required, which increase both the hardware complexity and power consumption of the EDC circuit.…”

Gerchberg-Saxton Based Finite Impulse Response Filter for Electronic Dispersion Compensation in Intensity-Modulation/Direct-Detection Transmission

“…A 56 Gb/s PAM4 was transmitted over 80 km of SMF with only 5 iterations of the modified GS algorithm and a FIR noise shaping filter [23]. A multi-constraint version of the GS algorithm has also been recently reported [20]. In almost all demonstrations of the GS algorithm in IM/DD, dynamic real-time iterations are performed on the data or pilot symbols and additional equalization is needed at the receiver to combat residual ISI.…”