Joint Pre- and Post-Equalization with Higher-Order Modulation Formats in SDM-Based Optical MIMO Systems

Abstract

The multiple-input and multiple-output (MIMO) technology is a promising area of research to cope up with the demands of higher data rates and capacity. In the optical communication domain, the combination of space-division multiplexing (SDM) with higher-order modulation (HOM) formats over an optical MIMO system actively addresses these challenges. By allowing multi-level signaling with limited increment in the transmitter’s complexity, a jointly designed pre- and post-equalization (PPE) for an optical MIMO system with a multi-mode fiber (MMF) link is proposed. Cost-effectiveness of the system is incorporated by utilizing intensity modulation/direct detection (IM/DD) with HOM formats such as pulse-amplitude modulation (PAM) schemes. With the aid of a numerical optimization algorithm, the proposed joint-PPE filter coefficients are optimized with respect to the MMF channel and the transmit power constraint. In contrast to existing research on the single-mode fiber (SMF) based optical systems, the effectiveness of the proposed joint-PPE filter is analyzed on an MMF link, which is considerably degraded by the modal dispersion. In the analyzed experimental scenario, the proposed joint-PPE scheme confirms to be beneficial as compared to the post-equalization only (PE-only) in terms of bit-error rate (BER) performance. Furthermore, the required average received optical power to reach a BER 10−4 by the joint-PPE scheme is improved by 2 dB with comparison to the minimum mean-squared error (MMSE) PE-only.

Joint-Transceiver Equalization Technique over a 1.4 km Multi-Mode Fiber Using Optical MIMO Technique in IM/DD Systems

“…Similarly, an enhancement of ≈2.58 dB in the P r gain is achieved by the joint-PPE using PAM-2 format. Despite using a longer MMF channel with twice the bit-rate compared to [19], the improvement of ≈0.65 dB and ≈0.84 dB in the P r gains at 10 −4 BER is still accomplished. Additionally, with the improved numerical optimization of the PPE taps, an enhancement of nearly two folds in the required Pr gain at 10 −4 BER is attained using PAM-2 constellation compared to [23].…”

“…The characteristics of t n are that the zero-duality gap is achieved between the primal and the dual problems when t n → 0, ∀n . By combining (19), ( 20) and ( 21), the final optimization problem is defined as…”

“…However, a linear MMSE-based equalizer is selected because of comprehensive implementation, simple realization and analytical traceability [3,18]. Additionally, a further boost in the system performance is evident in the presence of a transceiver equalization compared to the equalization applied either at the transmitter or the receiver [14,15,19]. According to the literature, the zero-forcing (ZF) principle is commonly adapted for the design of the pre-equalizer.…”

“…Additionally, the performance evaluation of these pre-and post-equalization (PPE) schemes is validated either on the single-input and single-output (SISO) system model or over an SMF fiber [16,17,21,22]. Although the PPE schemes are reported in [14,15,19,23], the experimental comparison with conventional PPE schemes using a longer MMF and higher data rate needs to be investigated. Moreover, addressing the lower convergence rate to achieve the optimal design of PPE coefficients is crucial [19,23].…”

“…Although the PPE schemes are reported in [14,15,19,23], the experimental comparison with conventional PPE schemes using a longer MMF and higher data rate needs to be investigated. Moreover, addressing the lower convergence rate to achieve the optimal design of PPE coefficients is crucial [19,23]. This research gap limits the feasible use of a pre-equalizer on the transmitter side due to high complexity.…”