A joint pre- and post-equalization scheme is proposed for an optical intensity modulation and direct detection (IM/DD) system. At the transmitter, a linear feed-forward pre-equalizer with just two, three, or four filter taps is suggested to limit the transmitter's complexity and to allow the use of multi-level modulation. Finally, this concept is combined with a zero-forcing post-equalizer at the receiver. By utilizing numerical optimization to design the multi-level signals, the intersymbol-interference originating from the channel is mitigated pre-equalizer taps, a reduction of 3 % in received power compared to a conventional zero-forcing design is achieved. The equalization scheme is tailored for an optical IM/DD system. Therefore, the specific power constraints of such a setup are taken into account in the equalizer design process. In contrast to existing research, the approach is tested for a multi-mode fiber system, which is affected by increased inter-symbol interference due to modal dispersion. The simulation results show that by shifting a small portion of the equalization complexity to the transmitter side, the required optical power to reach a bit-error rate of 10(-3) is reduced by 7.3% for zero-forcing and 6.8% for minimum mean square error post-equalizers. the noise increase by the post-equalizer is reduced by 6.9 % when including the pre-equalizer with just two filter taps. Compared to an equalization scheme that solely relies on a zero-forcing post-equalizer, the suggested joint pre- and post-equalization scheme is able to improve the bit-error rate performance by an average of 7.15 %. A testbed experiment with a 250 m multi-mode fiber channel and a data rate of 2.5 Gbps operating at 1550 nm confirms these simulation results.

In optical communication, the higher-order modulation (HOM) schemes have attracted a lot of attention as they provide higher data rates within a defined bandwidth. Due to shot noise, the received data is affected by different noise variances depending upon the received power levels. In such systems, an equidistant constellation is not always optimal. Therefore, a geometric constellation shaping (GCS) approach is proposed. The purpose of this contribution is to investigate the potential of GCS with pulse amplitude modulation (PAM) to improve the bit-error rate (BER) performance. Moreover, this work aims to identify the conditions, e.g. the constellation size, where the GCS enhances the performance of an intensity modulated and direct detected (IM/DD) system. The GCS is realized with the aid of nonlinear optimization. In the analyzed scenarios, the simulation results show that GCS is not beneficial in terms of the BER performance for low constellation sizes. In contrast, GCS for high constellation sizes can significantly improve the BER. The experimental measurement results suggest that GCS can be advantageous.

In short reach intensity modulated and direct detected (IM/DD) optical multiple-input multiple-output (MIMO) systems linear equalization strategies are commonly applied. However, the square-law detector inherently is a non-linear system element. This work investigates this discrepancy and shows for which laser types and under which mode coupling conditions baseband linearity applies for the first time. Based on a system model that integrates a multitude of aspects, e.g. the phase state of each fiber mode and mode coupling, it is shown that the received signal consists of a linear component and one that can be considered as interference. The simulation and measurement results highlight that only MIMO setups with weak and no mode cross-talk can be considered as linear. Systems with high mode cross-talk are impaired by significant interference, resulting in a highly degraded bit-error rate performance.

The profound understanding of time-variance in an intensity modulation and direct detection system is required for the transmitter and receiver design. In this contribution, two methods for analyzing this time-variance are studied when transmitting through an multi-mode fiber (MMF) channel in conjunction with mode-selective launching. The first method involves the camera-based measurement of the near field intensity profile at the MMF end-face. Secondly, a repeated measurement of the channel's impulse response is performed using a least squares channel estimation. By introducing a vibration to the MMF it is shown that both methods are able to detect these frequencies and their occurring harmonics when calculating the Doppler spectrum. However, compared to the DC component the vibration frequency amplitudes are negligibly small. Therefore, the channel can be assumed as time-invariant in the measured span of a few seconds, benefiting decision-aided adaptive signal processing.

The exploitation of the spatial domain with the concept of multiple-input multiple-output (MIMO) is a promising approach to further improve the cost efficiency in fiber-optic communications. Historically, the first optical MIMO systems utilized multi-mode couplers for the purpose of mode multiplexing (MUX) and demultiplexing (DEMUX). However, their high insertion losses and asymmetries demand for alternative components. Nowadays, next to optical couplers, photonic lanterns have become considerably more attractive offering low insertion losses and being able to excite individual modes. Therefore, they are in the focus of this contribution. A setup of 6-port photonic lanterns is evaluated by measurements and compared with other multiplexing components. The measurement results and the simulated bit-error rate performances highlight that photonic lanterns are well-suited for optical MIMO communications.

In this contribution a novel method for determining the power coupling coefficients between mode groups for arbitrary devices under test in a multi-mode system is presented. It is based on impulse response measurements and is used to evaluate the power coupling between mode groups for a multi-mode fusion coupler and a 1 km graded-index multi-mode fiber (MMF) at 1327 nm operating wavelength. The obtained coefficients highlight that a lot of power coupling between mode groups takes place in the studied fusion coupler. In contrast, when transferring through the 1 km MMF the majority of the incident power stays in the samemode group. Based on the obtained power coupling coefficients, impulse responses for a (2x2) multiple-input multiple-output (MIMO) transmission are simulated and the corresponding bit-error rate (BER) performance for different parameter configurations is studied. The simulation setup includes single-mode fiber (SMF) to MMF splices aligned with different radial eccentricities for mode specific excitation and multi-mode fusion couplers for mode multiplexing and demultiplexing. Comparing the SMF to MMF launch eccentricities shows that an offset of 15 micrometer paired with the centric launch shows the best BER results in the analyzed configuration.

Multiple-input multiple-output (MIMO) systems can be considerably afflicted by uncertainty and numerical errors from various sources at different stages in the modeling and simulation process. In this paper, we perform a verification and validation analysis of the process for frequency selective MIMO systems and establish the respective current verification degree for the subtasks. Our special focus is on the stage of channel estimation, for which we show in detail how the verification degree can be improved using methods with result verification and analyse the uncertainty using Monte-Carlo and interval techniques. However, we also touch upon the stages of channel simulation and power allocation from the same point of view.

The profound understanding of mode coupling in spatial multiplexed optical systems is required for performance optimization purposes. In this contribution different optical coupler technologies are compared with respect to their bit-error rate (BER) performance as multiplex devices in a (2x2) multiple-input multiple-output (MIMO) environment. Therefore, the power coupling coefficients between mode groups for all testbed components are determined at 1327 nm with a method based on impulse response measurements. This method and its refinements are presented in this work. By taking the obtained power coupling coefficients, the MIMO impulse responses are simulated and the corresponding BER performance for different launch parameters is studied. The simulation setup includes single-mode fiber (SMF) to multi-mode fiber (MMF) splices aligned with different radial eccentricities for mode group specific excitation, different multi-mode couplers for mode multiplexing, a 1 km OM4 grade MMF and a multi-mode fusion coupler for demultiplexing. Here, the setup with the customized fusion coupler shows the best BER results in comparison to other coupler technologies. In addition, the optimal choice of the SMF to MMF launch eccentricity highly depends on the implemented coupler technology. Particularly, deviations of 2 mu m from the optimal launch setup can lead to a tenfold increase in the BER. It is noteworthy, that the optimal setup does not always include the center launch condition.

Interference in frequency-selective multiple-input multiple-output (MIMO) systems can be removed by applying a block-transmission description based on spatio-temporal vector coding and using singular value decomposition (SVD). In this contribution a newly developed SVD algorithm for polynomial matrices (PMSVD) is analyzed and compared to the commonly used SVD-based MIMO equalization. Since the PMSVD processing results in independent single-input single-output layers exhibiting a frequency-selective characteristic, a simple zero forcing equalizer or an optimal Viterbi detector is applied in this work so as to remove the occurring inter-symbol interferences. The PMSVD orthogonalization is compared with the conventional SVD in terms of the achievable spectral efficiencies, showing that there is no loss applying PMSVD over SVD processing. In addition, the bit-error rate performances in different channel scenarios are evaluated and optimized by applying combined bit and power allocation schemes. One scenario involves the measured specific impulse responses of a (2×2) optical MIMO channel, consisting of a 1.4 km multi-mode fiber, optical fusion couplers for mode multiplexing and demultiplexing when operating at a wavelength of 1576 nm. The computer simulation results show that the PMSVD could be an alternative signal processing method compared to conventional SVD-based approaches in frequency-selective MIMO channels.

In the fiber-optic telecommunication community space division multiplex, synonymously referred to as optical multiple-input multiple-output (MIMO), is a potential candidate to overcome the imminent capacity crunch. The concept of transmitting parallel data streams on different optical modes of a few-mode or multi-mode fiber is in the focus of this work. Thus, different approaches for mode-selective excitation, mode multiplexing and demultiplexing are presented. This includes a completely new approach in this field based on digital mirror devices (DMDs) which benefits from its high flexibility when it comes to pattern generation and its theoretical low insertion loss of around -1.27 dB. However, the blazed grated structure of the micromirror array (MMA) makes it complex to find the optimal coupling conditions. This work shows an intuitive solution for that problem. In addition to the DMDs, photonic lanterns and optical fusion couplers combined with offset splices are studied with respect to their optical MIMO suitability.

Polynomial singular value decomposition (PSVD) plays a very important role in broadband multiple-input multiple-output (MIMO) systems. One of its applications lies in the decoupling of MIMO convolutive mixing channel matrix in order to recover the transmitted signals corrupted by the channel interference (CI) at the receiver. In this paper, a novel algorithm, known as multiple shift second order sequential best rotation (MS-SBR2), is proposed to compute the approximate PSVD of the broadband MIMO channel matrix. Experimental examples, including a measured (2 × 2) optical MIMO channel impulse response using the multi-mode fiber (MMF) testbed, are presented to examine the proposed algorithm. Bit error rate (BER) performances are evaluated among different transmission schemes. In addition, power allocation (PA) schemes are investigated to further optimize the BER performance.

The multiple-input multiple-output (MIMO) concept is of high interest in fiber-optic communication since it is able to overcome the capacity limits of current transmission systems. In this work different receiver-side interference compensation techniques are studied in a spatially multiplexed fiber-optic transmission through 0.5 km multi-mode fiber with a gross bit-rate of 5 Gbps using intensity modulation and direct detection. Broadband successive interference cancellation (SIC) and broadband zero forcing (ZF) equalization are compared as electronic interference compensation methods in a (2×2) MIMO transmission. The results show that ordered SIC can significantly improve the transmission quality compared to the ZF equalization approach in the studied testbed configuration. Also, spatial filtering as an interference reduction technique is studied with respect to its effect on the bit-error rate (BER) performance, showing that in the analyzed channel scenario the use of such a filter is beneficial. Using a spatial filter improves the mode group separation at the receiver and hence reduces the MIMO signal processing complexity.

The multiple-input multiple-output (MIMO) technology has attracted a lot of interest in the optical fiber community: MIMO allows higher data rates with no loss regarding bandwidth and transmit power. The inherent interferences within a MIMO system call for appropriate signal processing strategies. Polynomial schemes such as polynomial matrix singular value decomposition (PMSVD) have attracted the research interest since they do not require any block transmission compared with schemes such as spatio-temporal vector coding (STVC). In comparison to SVD-based STVC schemes, where the whole MIMO system is transferred into a number frequency nonselective non-interfering single-input single-output (SISO) systems, PMSVD transfers the MIMO system into independent SISO layers exhibiting a frequency-selective characteristic. In this work optimal power allocation solutions in PMSVD-assisted optical MIMO systems with layer-based zero-forcing equalization are investigated. As shown by our computer simulations and testbed measurements, optimal power allocation (PA) leads to the best BERs at the cost of a high complexity compared to suboptimal PA solutions. However, as highlighted by our simulation results, suboptimal PA schemes seem to be a good alternative for achieving nearly optimum bit-error rate (BER) at a significantly lower complexity.

In this work silicon multi-segment photo detectors are analyzed for their suitability as mode demultiplexing devices in multi-mode multiple-input multiple-output (MIMO) transmissions. Therefore, different chips are characterized with respect to their local responsivities and segment's bandwidths. The fiber alignment and packaging process of the detector are presented. By using a two-segment detector a (2x2) MIMO transmission over 1 km multi-mode fiber at 850 nm operating wavelength is formed and characterized by its specific impulse responses as well as the bit-error rate performance capabilities. The results show that multi-segment detectors are suited for simple and efficient mode demultiplexing in a multi-mode MIMO system.

In this contribution an optical (4x4) multi-mode MIMO (multiple-input multiple-output) system using two (2x4) fusion star couplers for mode multiplexing and demultiplexing and transmitting over 2 km OM4 multi-mode fiber (MMF) is constructed. The characterization of this MIMO system is performed by measuring the 16 specific channel impulse responses at an operating wavelength of 1326 nm. Furthermore, the measured spatial power distribution shows the spatial diversity of the different excited mode groups. Based on the receive signal energy of the individual single-input single-output (SISO) channels the port configuration of the underlyingMIMO system has been established. Finally, the bit error rate (BER) performance is evaluated and compared to lower order MIMO systems while using the same physical setup. The results show that the fusion star couplers are well-suited for the task of mode multiplexing.

Polynomial matrix singular value decomposition (PMSVD) plays a very important role in broadband multiple-input multiple-output (MIMO) systems. It can be used to decompose a broadband MIMO channel matrix in order to recover the transmitted signals corrupted by the channel interference (CI) at the receiver. In this contribution newly developed singular value decomposition (SVD) algorithm for polynomial matrices are analyzed and compared in the application of decomposing optical MIMO channels. The bit-error rate (BER) performance is evaluated and optimized by applying bit and power allocation schemes. For our simulations, the specific impulse responses of the (2x2) MIMO channel, including a 1.4 km multi-mode fiber and optical couplers at both ends, are measured for the operating wavelength of 1576 nm.

Optical fiber sensors have reached a high state of maturity. Besides the high number of sensor groups, multi-mode fiber evanescent field sensors can be found in a lot of applications. Here, the signal source commonly excites many optical modes under steady-state conditions. Perturbations of the fiber then produce leaky modes. Thus, a simple intensity detector measures the degree of perturbation. In some cases also restricted mode launching conditions have been applied. They resulted in higher sensitivity but showed a narrower measurement range. Considering the individual modes as carriers of information we adapted multiple-input multiple-output (MIMO) signal processing which is well studied in the telecommunications community, for improvements on both the sensor sensitivity and its measurement range. In this paper MIMO signal processing is investigated for fiber optic sensor applications. A (2x2) MIMO implementation is realized by using lower-order and higher-order mode groups of a gradient-index multi-mode fiber as separate transmission channels. A micro-bending pressure sensor changes these separate transmission characteristics and introduces additional crosstalk. By observing the layer specific weight-factors of the MIMO system the amount of load applied was determined. Experiments verified a good correlation between the change of the MIMO weight coefficients and the load applied to the sensor and thus verified that MIMO signal processing can beneficially be used for fiber optic sensor applications. The experimental results also verified the superior sensitivity and measurement range when MIMO signal processing is utilized.

A (2×2) multiple-input multiple-output (MIMO) implementation for signal processing is realized by using lower-order and higher-order fibre mode groups and experimentally explored for fibre optical force sensor applications. We describe the experimental setup utilized for the measurements and confirm a high correlation between an optical fibre sensor measurand and MIMO processed data, for the first time.

Polynomial matrix singular value decomposition (PSVD) plays a very important role in broadband multiple-input multiple-output (MIMO) systems. It can be used to decompose a broadband MIMO channel matrix in order to recover the transmitted signals corrupted by the channel interference (CI) at the receiver. In this paper, a novel algorithm, known as multiple shift second order sequential best rotation (MS-SBR2), is proposed to compute the approximate PSVD. Simulations are implemented under a (2 × 2) optical MIMO channel model. Bit error rate (BER) performances are evaluated among different transmission schemes. In addition, power allocation (PA) scheme is investigated to further optimize the BER performance.