Designing Power-Efficient Modulation Formats for Noncoherent Optical Systems

We optimize modulation formats for the additive white Gaussian noise channel with a nonnegative input constraint, also known as the intensity-modulated direct detection channel, with and without confining them to a lattice structure. Our optimization criteria are the average electrical and optical power. The nonnegativity input signal constraint is translated into a conical constraint in signal space, and modulation formats are designed by sphere packing inside this cone. Some remarkably dense packings are found, which yield more power-efficient modulation formats than previously known. For example, at a spectral efficiency of 1 bit/s/Hz, the obtained modulation format offers a 0.86 dB average electrical power gain and 0.43 dB average optical power gain over the previously best known modulation formats to achieve a symbol error rate of 10^-6. This modulation turns out to have a lattice-based structure. At a spectral efficiency of 3/2 bits/s/Hz and to achieve a symbol error rate of 10^-6, the modulation format obtained for optimizing the average electrical power offers a 0.58 dB average electrical power gain over the best lattice-based modulation and 2.55 dB gain over the best previously known format. However, the modulation format optimized for average optical power offers a 0.46 dB average optical power gain over the best lattice-based modulation and 1.35 dB gain over the best previously known format.Comment: Submitted to Globecom 201

Power efficient subcarrier modulation for intensity modulated channels

We compare formats for optical intensity modulation limited by thermal noise with the assumption of having ideal devices. At the same bitrate and bandwidth, a hitherto unknown format turns out to be more power efficient than known formats. This new modulation, which is a hybrid between on-off keying and phase-shift keying, belongs to the subcarrier modulation family. At asymptotically high signal-to-noise ratios, this hybrid scheme has a 1.2 dB average electrical power gain and 0.6 dB average optical power gain compared to OOK, while it has a 3.0 dB average electrical power gain and 2.1 dB average optical power gain compared to subcarrier QPSK

When to Use Optical Amplification in Noncoherent Transmission: An Information-Theoretic Approach

The standard solution for short-haul fiber-optic communications is to deploy noncoherent systems, i.e., to modulate and detect only the light intensity. In such systems, the signal is corrupted with optical noise from amplifiers and with thermal (electrical) noise. The capacity of noncoherent optical links has been studied extensively in the presence of either optical noise or thermal noise. In this paper, for the first time, we characterize the capacity under an average power constraint with both noise sources by establishing upper and lower bounds. In the two extreme cases of zero optical noise or zero thermal noise, we assess our bounds against some well-known results in the literature; improvements in both cases are observed. Next, for amplified fiber-optic systems, we study the trade-off between boosting signal energy (mitigating the effects of thermal noise) and adding optical noise. For a wide spectrum of system parameters and received power levels, we determine the optimal amplification gain. While mostly either no amplification or high-gain amplification is optimal, the best performance is for some parameter intervals achieved at finite gains

Calculation of Mutual Information for Partially Coherent Gaussian Channels with Applications to Fiber Optics

The mutual information between a complex-valued channel input and its complex-valued output is decomposed into four parts based on polar coordinates: an amplitude term, a phase term, and two mixed terms. Numerical results for the additive white Gaussian noise (AWGN) channel with various inputs show that, at high signal-to-noise ratio (SNR), the amplitude and phase terms dominate the mixed terms. For the AWGN channel with a Gaussian input, analytical expressions are derived for high SNR. The decomposition method is applied to partially coherent channels and a property of such channels called "spectral loss" is developed. Spectral loss occurs in nonlinear fiber-optic channels and it may be one effect that needs to be taken into account to explain the behavior of the capacity of nonlinear fiber-optic channels presented in recent studies.Comment: 30 pages, 9 figures, accepted for publication in IEEE Transactions on Information Theor

Optimizing Constellations for Single-Subcarrier Intensity-Modulated Optical Systems

We optimize modulation formats for the additive white Gaussian noise channel with nonnegative input, also known as the intensity-modulated direct-detection channel, with and without confining them to a lattice structure. Our optimization criteria are the average electrical, average optical, and peak power. The nonnegative constraint on the input to the channel is translated into a conical constraint in signal space, and modulation formats are designed by sphere packing inside this cone. Some dense packings are found, which yield more power-efficient modulation formats than previously known. For example, at a spectral efficiency of 1.5 bit/s/Hz, the modulation format optimized for average electrical power has a 2.55 dB average electrical power gain over the best known format to achieve a symbol error rate of 10^-6. The corresponding gains for formats optimized for average and peak optical power are 1.35 and 1.72 dB, respectively. Using modulation formats optimized for peak power in average-power limited systems results in a smaller power penalty than when using formats optimized for average power in peak-power limited systems. We also evaluate the modulation formats in terms of their mutual information to predict their performance in the presence of capacity-achieving error- correcting codes, and finally show numerically and analytically that the optimal modulation formats for reliable transmission in the wideband regime have only one nonzero point.Comment: submitted to IEEE Transactions on Information Theory, June 201

Optimized eight-dimensional lattice modulation format for IM-DD 56 Gb/s optical interconnections using 850 nm VCSELs

In this paper a novel eight-dimensional lattice optimized modulation format, Block Based 8-dimensional/8-level (BB8), is proposed, taking into account the tradeoff between high performance and modulation simplicity. We provide an experimental performance comparison with its n-level pulse amplitude modulation counterparts in a 28 GBd 850-nm vertical-cavity surface-emitting laser based intensity-modulation direct-detection system. Successful data transmission over 100 m multimode fiber links of OM3 and OM4 types is demonstrated, with a power margin close to 2 dB at 100GBASE-SR4 forward error correction threshold. A simplified bit-to-symbol mapping and corresponding symbol-to-bit demapping algorithms, together with a hyperspace hard-decision, are designed specifically for applications of short-reach data links. These algorithms are expected to use affordable computational resources with relatively low latency

Mapping multiplexing technique (MMT): a novel intensity modulated transmission format for high-speed optical communication systems

There is a huge rapid growth in the deployment of data centers, mainly driven from the increasing demand of internet services as video streaming, e-commerce, Internet Of Things (IOT), social media, and cloud computing. This led data centers to experience an expeditious increase in the amount of network traffic that they have to sustain due to requirement of scaling with the processing speed of Complementary metal–oxide–semiconductor (CMOS) technology. On the other side, as more and more data centers and processing cores are on demand, as the power consumption is becoming a challenging issue. Unless novel power efficient methodologies are innovated, the information technology industry will be more liable to a future power crunch. As such, low complex novel transmission formats featuring both power efficiency and low cost are considered the major characteristics enabling large-scale, high performance data transmission environment for short-haul optical interconnects and metropolitan range data networks. In this thesis, a novel high-speed Intensity-Modulated Direct-Detection (IM/DD) transmission format named “Mapping Multiplexing Technique (MMT)” for high-speed optical fiber networks, is proposed and presented. Conceptually, MMT design challenges the high power consumption issue that exists in high-speed short and medium range networks. The proposed novel scheme provides low complex means for increasing the power efficiency of optical transceivers at an impactful tradeoff between power efficiency, spectral efficiency, and cost. The novel scheme has been registered as a patent (Malaysia PI2012700631) that can be employed for applications related but not limited to, short-haul optical interconnects in data centers and Metropolitan Area networks (MAN). A comprehensive mathematical model for N-channel MMT modulation format has been developed. In addition, a signal space model for the N-channel MMT has been presented to serve as a platform for comparison with other transmission formats under optical channel constraints. Especially, comparison with M-PAM, as meanwhile are of practical interest to expand the capacity for optical interconnects deployment which has been recently standardized for Ethernet IEEE 802.3bs 100Gb/s and in today ongoing investigation activities by IEEE 802.3 400Gb/s Ethernet Task Force. Performance metrics have been considered by the derivation of the average electrical and optical power for N-channel MMT symbols in comparison with Pulse Amplitude Modulation (M-PAM) format with respect to the information capacity. Asymptotic power efficiency evaluation in multi-dimensional signal space has been considered. For information capacity of 2, 3 and 4 bits/symbol, 2-channel, 3-channel and 4-channel MMT modulation formats can reduce the power penalty by 1.76 dB, 2.2 dB and 4 dB compared with 4-PAM, 8-PAM and 16-PAM, respectively. This enhancement is equivalent to 53%, 60% and 71% energy per bit reduction to the transmission of 2, 3 and 4 bits per symbol employing 2-, 3- and 4-channel MMT compared with 4-, 8- and 16-PAM format, respectively. One of the major dependable parameters that affect the immunity of a modulation format to fiber non-linearities, is the system baud rate. The propagation of pulses in fiber with bitrates in the order > 10G, is not only limited by the linear fiber impairments, however, it has strong proportionality with fiber intra-channel non-linearities (Self Phase Modulation (SPM), Intra-channel Cross-Phase Modulation (IXPM) and Intra-channel Four-Wave Mixing (IFWM)). Hence, in addition to the potential application of MMT in short-haul networks, the thesis validates the practicality of implementing N-channel MMT system accompanied by dispersion compensation methodologies to extend the reach of error free transmission (BER ≤ 10-12) for Metro-networks. N-Channel MMT has been validated by real environment simulation results to outperform the performance of M-PAM in tolerating fiber non-linearities. By the employment of pre-post compensation to tolerate both residual chromatic dispersion and non-linearity, performance above the error free transmission limit at 40Gb/s bit rate have been attained for 2-, 3- and 4-channel MMT over spans lengths of up to 1200Km, 320 Km and 320 Km, respectively. While, at an aggregated bit rate of 100 Gb/s, error free transmission can be achieved for 2-, 3- and 4-channel MMT over spans lengths of up to 480 Km, 80 Km and 160 Km, respectively. At the same spectral efficiency, 4-channel MMT has realized a single channel maximum error free transmission over span lengths up to 320 Km and 160 Km at 40Gb/s and 100Gb/s, respectively, in contrast with 4-PAM attaining 240 Km and 80 Km at 40Gb/s and 100Gb/s, respectively

Mapping multiplexing technique (MMT): a novel intensity modulated transmission format for high-speed optical communication systems

There is a huge rapid growth in the deployment of data centers, mainly driven from the increasing demand of internet services as video streaming, e-commerce, Internet Of Things (IOT), social media, and cloud computing. This led data centers to experience an expeditious increase in the amount of network traffic that they have to sustain due to requirement of scaling with the processing speed of Complementary metal–oxide–semiconductor (CMOS) technology. On the other side, as more and more data centers and processing cores are on demand, as the power consumption is becoming a challenging issue. Unless novel power efficient methodologies are innovated, the information technology industry will be more liable to a future power crunch. As such, low complex novel transmission formats featuring both power efficiency and low cost are considered the major characteristics enabling large-scale, high performance data transmission environment for short-haul optical interconnects and metropolitan range data networks. In this thesis, a novel high-speed Intensity-Modulated Direct-Detection (IM/DD) transmission format named “Mapping Multiplexing Technique (MMT)” for high-speed optical fiber networks, is proposed and presented. Conceptually, MMT design challenges the high power consumption issue that exists in high-speed short and medium range networks. The proposed novel scheme provides low complex means for increasing the power efficiency of optical transceivers at an impactful tradeoff between power efficiency, spectral efficiency, and cost. The novel scheme has been registered as a patent (Malaysia PI2012700631) that can be employed for applications related but not limited to, short-haul optical interconnects in data centers and Metropolitan Area networks (MAN). A comprehensive mathematical model for N-channel MMT modulation format has been developed. In addition, a signal space model for the N-channel MMT has been presented to serve as a platform for comparison with other transmission formats under optical channel constraints. Especially, comparison with M-PAM, as meanwhile are of practical interest to expand the capacity for optical interconnects deployment which has been recently standardized for Ethernet IEEE 802.3bs 100Gb/s and in today ongoing investigation activities by IEEE 802.3 400Gb/s Ethernet Task Force. Performance metrics have been considered by the derivation of the average electrical and optical power for N-channel MMT symbols in comparison with Pulse Amplitude Modulation (M-PAM) format with respect to the information capacity. Asymptotic power efficiency evaluation in multi-dimensional signal space has been considered. For information capacity of 2, 3 and 4 bits/symbol, 2-channel, 3-channel and 4-channel MMT modulation formats can reduce the power penalty by 1.76 dB, 2.2 dB and 4 dB compared with 4-PAM, 8-PAM and 16-PAM, respectively. This enhancement is equivalent to 53%, 60% and 71% energy per bit reduction to the transmission of 2, 3 and 4 bits per symbol employing 2-, 3- and 4-channel MMT compared with 4-, 8- and 16-PAM format, respectively. One of the major dependable parameters that affect the immunity of a modulation format to fiber non-linearities, is the system baud rate. The propagation of pulses in fiber with bitrates in the order > 10G, is not only limited by the linear fiber impairments, however, it has strong proportionality with fiber intra-channel non-linearities (Self Phase Modulation (SPM), Intra-channel Cross-Phase Modulation (IXPM) and Intra-channel Four-Wave Mixing (IFWM)). Hence, in addition to the potential application of MMT in short-haul networks, the thesis validates the practicality of implementing N-channel MMT system accompanied by dispersion compensation methodologies to extend the reach of error free transmission (BER ≤ 10-12) for Metro-networks. N-Channel MMT has been validated by real environment simulation results to outperform the performance of M-PAM in tolerating fiber non-linearities. By the employment of pre-post compensation to tolerate both residual chromatic dispersion and non-linearity, performance above the error free transmission limit at 40Gb/s bit rate have been attained for 2-, 3- and 4-channel MMT over spans lengths of up to 1200Km, 320 Km and 320 Km, respectively. While, at an aggregated bit rate of 100 Gb/s, error free transmission can be achieved for 2-, 3- and 4-channel MMT over spans lengths of up to 480 Km, 80 Km and 160 Km, respectively. At the same spectral efficiency, 4-channel MMT has realized a single channel maximum error free transmission over span lengths up to 320 Km and 160 Km at 40Gb/s and 100Gb/s, respectively, in contrast with 4-PAM attaining 240 Km and 80 Km at 40Gb/s and 100Gb/s, respectively