Spatial Division Multiplexing Systems Research Articles

Post-FEC performance evaluation of optical SDM systems with mode-dependent loss

This work is focused on the bit error rate (BER) performance of spatial division multiplexing (SDM) systems over an optical channel with mode-dependent loss or gain (collectively referred to in this paper as MDL). When the latter is non-negligible, the BER has a random nature that introduces the outage probability as an important performance metric for the system design and also impacts on the selection of a forward-error correction (FEC) scheme. In MDL-impaired SDM systems, the pre-FEC BER is a random variable whose probability density function (PDF) and coding gain depend on the signal-to-noise ratio (SNR) at the receiver input. Hence, the common and simple approach of adding a coding gain factor to the pre-FEC BER to obtain the post-FEC BER is not adequate, and numerical simulations are needed. In this paper, we simulate and analyze the performance in terms of post-FEC BER for two proposals of applying low-density parity check (LDPC) FEC encoder/decoder in a SDM system MDL-impaired and an optimal linear multiple input multiple output (MIMO) receiver. In the first one, the LDPC is applied independently to each mode, and in the second one, the LDPC is applied among all SDM modes. Simulation results indicate that the first proposal outperforms the second. Simplifications in the log-likelihood ratio (LLR) computations have also been considered.

BER analysis of an optimum MIMO linear receiver in optical SDM systems with mode-dependent loss.

Multiple-input multiple-output (MIMO) receivers designed to optimize the minimum mean square error (MMSE) are a common choice in coherent optical communication systems based on spatial division multiplexing (SDM). This kind of receivers naturally integrate both MIMO equalization and matched filtering functions. However, when the optical channel exhibits significant mode-dependent loss (MDL) and/or mode-dependent gain (MDG), the impact of inter-symbol interference (ISI) and crosstalk that arise, even using an ideal MIMO MMSE linear receiver, is barely analyzed. Moreover, due to the random nature of the MDL/MDG model, the resulting ISI, crosstalk, and bit error rate (BER) also become random variables and, hence the system performance is more unpredictable. In this paper, we first evaluate the residual distortion (ISI and crosstalk) after the MIMO receiver and then we study the validity of assuming it as an additional Gaussian noise term independent of the channel noise. Next, the probability density distribution (PDF) of the BER is analyzed, from both an analytical perspective and numerical simulations. For the latter, we use a single-carrier 2-PAM (pulse amplitude modulation) system, with pulse shaping, and the MIMO MMSE receiver implementation by means of a MIMO fractionally-spaced equalizer (FSE). We carry out simulations of the system under different conditions of MDL/MDG level and signal to noise ratio (SNR), measured at the receiver input. Additionally, we address possible fits of the BER PDF to known closed-form distributions, among which the Generalized Extreme Value (GEV) family of distributions is selected, and polynomial functions are proposed that relate the system parameters with the GEV PDF parameters. Finally, we present contour maps of BER according to a giving target of system outage probability (OP) that depend on the MDL/MDG and SNR conditions.

Matched Filtering for MIMO Coherent Optical Communications with Mode-Dependent Loss Channels.

The use of digital signal processors (DSP) to equalize coherent optical communication systems based on spatial division multiplexing (SDM) techniques is widespread in current optical receivers. However, most of DSP implementation approaches found in the literature assume a negligible mode-dependent loss (MDL). This paper is focused on the linear multiple-input multiple-output (MIMO) receiver designed to optimize the minimum mean square error (MMSE) for a coherent SDM optical communication system, without previous assumptions on receiver oversampling or analog front-end realizations. The influence of the roll-off factor of a generic pulse-amplitude modulation (PAM) transmitter on system performance is studied as well. As a main result of the proposed approach, the ability of a simple match filter (MF) based MIMO receiver to completely eliminate inter-symbol interference (ISI) and crosstalk for SDM systems under the assumption of negligible MDL is demonstrated. The performance of the linear MIMO fractionally-spaced equalizer (FSE) receiver for an SDM system with a MDL-impaired channel is then evaluated by numerical simulations using novel system performance indicators, in the form of signal to noise and distortion ratio (SNDR) loss, with respect to the case without MDL. System performance improvements by increasing the transmitter roll-off factor are also quantified.

Improving Interference Cancellation in Spatial Division Multiplexing Using a Combination of the Channel Coding and QR-Successive Interference Cancellation

This paper introduces QR-SIC detector to minimize the probability of error comparing to SDM system. Spatial-division-multiplexing (SDM) system is a multiple-inputs-multiple-outputs (MIMO) system used to increase data transmission rate in modern communication systems. The major disadvantage of SDM system is the interference between the received symbols. In this paper, a new trans-receiver architecture for SDM system is introduced. This receiver uses a Successive-Interference-Cancellation (SIC) detector based on QR-decomposition of the channel matrix and a Forward-Error- Correction (FEC) channel code. The proposed architecture merges the interference cancellation process in QR-SIC detector and the forward error correction process in the channel decoder. The feedback symbols in the QR-SIC detector are the output symbols from the channel decoder after they are re-encoded and re-modulated and more robust. The new architecture minimizes the probability of error in the demodulated symbols more than the conventional SDM receiver. If the conventional SDM receiver needs 100 MWATT transmitted power the proposed system needs only 64 MWATT transmitted power. So The new architecture of the SDM receiver can save up to 36% of the transmitted signal power used with the conventional SDM receiver. At BER of 10-4, the convolution codes of code rates 3/4, 1/2, and 1/4 achieve coding gains of 15 dB, 24 dB, and 30 dB with respect to the uncoded 4-antennas SDM receiver. the proposed SDM receiver at BER of 10-4 is 2dB, 1.5 dB, and 0.9 dB better than the BER performance of the conventional coded SDM receiver at the same code rates and the same number of antenna. The enhancement in the BER performance of the proposed SDM receiver increases as the code gain of the used code. This increase in the power efficiency and bandwidth comes at the expense of an increase in the receiver complexity and latency

Robust ICA based mode demultiplexing

In this paper, we present a mode demultiplexing algorithm based on robust independent component analysis (ICA) in electrical domain. Multi-mode fiber (MMF) based spatial division multiplexing system is modeled as a behavioral model. Different modes can carry the data to increase the system capacity with the proposed algorithm. In the system, two orthogonal frequency division multiplexing (OFDM) signals are modulated on two modes by two vertical cavity surface emitting lasers (VCSEL) and then coupled into the MMF with an optical coupler. Two channel signals are separated by the proposed robust ICA mode demultiplexing algorithm after photodetectors at the receiver side. The OFDM signals can be demodulated successfully after the separation. Compared with a single mode transmission in MMF, the transmission performance of two mode channels is not degraded significantly with the proposed mode demultiplexing algorithm. Our results show that the proposed algorithm can carry out the modes demultiplexing successfully and the cross-talk between modes can be reduced or be negligible after processing. It also demonstrates a new application of ICA algorithm in the electrical time-domain mode demultiplexing.

Repeater Power Conversion Efficiency in Submarine Optical Communication Systems

In power-limited trans-oceanic submarine systems, the electrical-to-optical (E/O) power conversion efficiency determines the amount of optical signal power generated by repeaters, which governs the cable capacity. In contrast to conventional submarine systems, recent single mode fiber spatial division multiplexing (SDM) systems operate at a lower channel power and support a larger number of optical fibers. Moreover, pump sharing technology is used in SDM systems to enhance cable capacity and system reliability, where a group of pump lasers are combined to feed a group of fiber pairs. The repeater E/O power conversion efficiency is directly related with cable capacity, as well as capacity per power and cost per capacity analysis. Therefore, it is important to understand the characteristics of repeater E/O efficiency. We developed a model to analyze the repeater E/O efficiency in submarine SDM systems. Experimental measurement data of pump lasers and numerical simulation results of Erbium doped fiber amplifiers (EDFAs) were used as input information to the model to analyze repeater E/O efficiency in various system designs. Based on the E/O efficiency model results, we investigated cable capacity using the Gaussian noise (GN) model. Moreover, cable capacity per power was calculated and compared based on three different power metrics: (i) electrical supply power, (ii) pump optical power and (iii) EDFA output power. With the aid of the repeater E/O efficiency model, one can analyze the efficiency of submarine systems using the direct metric of cable capacity per electrical supply power.

Multi-Gigabit Spatial-Division Multiplexing Transmission Over Multicore Plastic Optical Fiber

Today, we are evident to the revolution of the automotive industry and its demand for high bandwidth sensor fusion. Multiple high bandwidth sensors are connected, generating tremendous amount of data to be transferred in real-time in harsh environment, i.e., multi-gigabit intra-vehicle networks. Plastic optical fiber (POF) is an attractive medium for these multi-gigabit intra-vehicle networks due to its inherent EM compatibility, galvanic isolation, low weight, high tolerance to mechanical vibrations, low bending loss, and easy handling. However, commercial off-the-shelf PMMA based POFs are bandwidth-length product limited. Here, we suggest increasing the spectral efficiency using spatial-division multiplexing (SDM). In this article, we have experimentally demonstrated a low cost and eye-safe 3 × 3 multiple-input multiple-output (MIMO) SDM system over a 15 meters multicore (MC) POF using commercial optical components, e.g., RC-LEDs and Si-PIN photodiodes. A 3 × 1 spot-based cores coupler spatial multiplexer was developed to couple the optical components with the MC-POF. This system achieved raw data rates of 1.5 Gb/s and 2.4 Gb/s using offline-processed MIMO equalization. The proposed system enables a flexible and scalable optical MIMO system that can meet the requirements of the automotive industry.

Nonlinear Distortion Cancellation in Spatial Division Multiplexing System Based on RZ-Coded PCTWs Technique

spatial division multiplexing (SDM) system has been considered as promising systems due to its ability to transport a higher bit rate for longer transmission distance. However, nonlinear phase noise (NPN (degrades SDM system performance. In this paper, we propose return-to-zero (RZ)-coded phase-conjugated twin waves (PCTWs) to improve the effectiveness of nonlinear distortion cancellation in the SDM system. In this approach, the PCTWs are modulated by m-array quadrature amplitude modulation (mQAM) then RZ encoded. After that, RZ-mQAM PCTWs are co-propagated over two fibres links. The received signals are superimposed to suppress the NPN. An analytical model that characterizes the performance of spatial-multiplexed (SM) RZ-coded PCTWs scheme is developed. Moreover, we numerically investigate the system performance with 4QAM format at 20Gsymbol/s rate. The results display that the performance is substantially better for the proposed scheme. Transmission reaches of both 4QAM PCTWs and RZ-4QAM PCTWs schemes are extended by 77.8% and 100%, respectively, in contrast with the 4QAM scheme.

Stability of Ince-Gaussian beams in elliptical core few-mode fibers.

A comparative stability analysis of Ince-Gaussian and Hermite-Gaussian modes in elliptical core few-mode fibers is provided to inform the design of spatial division multiplexing systems. The correlation method is used to construct crosstalk matrices that characterize the spatial modes of the fiber. Up to six low-order modes are shown to exhibit about -20 dB crosstalk. The crosstalk performance of each mode set is found to be similar. However, a direct comparison between modes of equal Gouy phase shift, a parameter that ensures identical beam quality, and phase at the detector, demonstrates better relative power transmission for Ince-Gaussian beams. This result is consistent with the natural modes supported by a 100m elliptical core fiber for which a mode ellipticity of ϵ=2 was found to be optimal. The relative power difference is expected to be magnified over longer fiber lengths in favor of Ince-Gaussian modes.

Real-time 100 Gbps/λ/core NRZ and EDB IM/DD transmission over multicore fiber for intra-datacenter communication networks.

A BiCMOS chip-based real-time intensity modulation/direct detection spatial division multiplexing system is experimentally demonstrated for both optical interconnects. 100 Gbps/λ/core electrical duobinary (EDB) transmission over 1 km 7-core multicore fiber (MCF) is carried out, achieving KP4 forward error correction (FEC) limit (BER < 2E-4). Using optical dispersion compensation, 7 × 100 Gbps/λ/core transmission of both non-return-to-zero (NRZ) and EDB signals over 10 km MCF transmission is achieved with BER lower than 7% overhead hard-decision FEC limit (BER < 3.8E-3). The integrated low complexity transceiver IC and analog signal processing approach make such a system highly attractive for the high-speed intra-datacenter interconnects.

Time-domain characteristics of ultrafast transverse mode switching based on Si nanowires.

We investigate the potential of an ultrafast transverse mode switch based on silicon on insulator (SOI) platform for the switching applications in the spatial division multiplexing (SDM) systems. The impact of waveguide geometry, operation wavelength, pulse width of the pump and probe waves, as well as the temporal delay between the pulses are discussed with a special focus on the temporal switching windows of the switch. The optimized switching performances are further applied to a switching node in a hybrid optical time division-multiplexing (OTDM) and SDM system. The switching energy of the Si-based switch is shown to be potentially smaller than that of the Si3N4 based integration platform.

Space-Time Coding Schemes for MDL-Impaired Mode-Multiplexed Fiber Transmission Systems

Spatial division multiplexing (SDM) holds out the prospects of increasing the capacities of optical fiber transmission links, especially with the recent achievements in the design of few-mode fibers and few-mode optical amplifiers. However, these systems are impaired by the capacity-limiting mode dependent loss (MDL) arising from imperfections in the optical fiber and inline components. Optical solutions were suggested to reduce, yet not completely remove, the accumulated MDL in the link through the use of strong coupling fibers and mode scramblers. Inspired by our previous study on mitigating polarization dependent loss (PDL), we present space-time (ST) coding schemes to mitigate MDL in mode-multiplexed optical transmission systems. We show, for the first time, that the combination of redundancy-free ST coding solutions with inline mode scrambling and optimal maximum-likelihood (ML) detection can completely absorb the SNR penalties induced by the MDL. The performance was assessed through simulations of three- and six-mode multiplexed systems where MDL levels up to 10 dB were observed. However, given the increased computational complexity of the suggested ML-decoded ST schemes, we present two reduced-complexity ST solutions offering a near-optimal performance. The first one consists in using a sub-optimal decoder and the second is a multiblock ST coding approach that can be scaled up for larger SDM systems.

Achievable information rates calculation for optical OFDM few-mode fiber long-haul transmission systems.

We propose a method to estimate the lower bound of achievable information rates (AIRs) of high speed orthogonal frequency-division multiplexing (OFDM) in spatial division multiplexing (SDM) optical long-haul transmission systems. The estimation of AIR is based on the forward recursion of multidimensional super-symbol efficient sliding-window Bahl-Cocke-Jelinek-Raviv (BCJR) algorithm. We consider most of the degradations of fiber links including nonlinear effects in few-mode fiber (FMF). This method does not consider the SDM as a simple multiplexer of independent data streams, but provides a super-symbol version for AIR calculation over spatial channels. This super-symbol version of AIR calculation algorithm, in principle, can be used for arbitrary multiple-input-multiple-output (MIMO)-SDM system with channel memory consideration. We illustrate this method by performing Monte Carlo simulations in a complete FMF model. Both channel model and algorithm for calculation of the AIRs are described in details. We also compare the AIRs results for QPSK/16QAM in both single mode fiber (SMF)- and FMF-based optical OFDM transmission.

Multicasting in a spatial division multiplexing system based on optical orbital angular momentum

We report multicasting data from a single orbital angular momentum (OAM) spatial channel onto multiple OAM channels of equally spaced OAM charge numbers. The designed sliced phase patterns for multicasting are loaded on the spatial light modulator. By optimizing the design of the phase pattern, the power of multicasted OAM channels can be equalized. We experimentally demonstrate multicasting five and seven OAM channels from a single-input OAM channel carrying a 100 Gbit/s quadrature phase-shift keying (QPSK) data stream.

A High Throughput Configurable SDR Detector for Multi-user MIMO Wireless Systems

Spatial division multiplexing (SDM) in MIMO technology significantly increases the spectral efficiency, and hence capacity, of a wireless communication system: it is a core component of the next generation wireless systems, e.g. WiMAX, 3GPP LTE and other OFDM-based communication schemes. Moreover, spatial division multiple access (SDMA) is one of the widely used techniques for sharing the wireless medium between different mobile devices. Sphere detection is a prominent method of simplifying the detection complexity in both SDM and SDMA systems while maintaining BER performance comparable with the optimum maximum-likelihood (ML) detection. On the other hand, with different standards supporting different system parameters, it is crucial for both base station and handset devices to be configurable and seamlessly switch between different modes without the need for separate dedicated hardware units. This challenge emphasizes the need for SDR designs that target the handset devices. In this paper, we propose the architecture and FPGA realization of a configurable sort-free sphere detector, Flex-Sphere, that supports 4, 16, 64-QAM modulations as well as a combination of 2, 3 and 4 antenna/user configuration for handsets. The detector provides a data rate of up to 857.1 Mbps that fits well within the requirements of any of the next generation wireless standards. The algorithmic optimizations employed to produce an FPGA friendly realization are discussed.