Steve Hranilovic

Outage Capacity Optimization for Free-Space Optical Links With Pointing Errors

We investigate the performance and design of free-space optical (FSO) communication links over slow fading channels from an information theory perspective. A statistical model for the optical intensity fluctuation at the receiver due to the combined effects of atmospheric turbulence and pointing errors is derived. Unlike earlier work, our model considers the effect of beam width, detector size, and jitter variance explicitly. Expressions for the outage probability are derived for a variety of atmospheric conditions. For given weather and misalignment conditions, the beam width is optimized to maximize the channel capacity subject to outage. Large gains in achievable rate are realized versus using a nominal beam width. In light fog, by optimizing the beam width, the achievable rate is increased by 80% over the nominal beam width at an outage probability of 10-5. Well-known error control codes are then applied to the channel and shown to realize much of the achievable gains.

Capacity-achieving probability measure for conditionally Gaussian channels with bounded inputs

A conditionally Gaussian channel is a vector channel in which the channel output, given the channel input, has a Gaussian distribution with (well-behaved) input-dependent mean and covariance. We study the capacity-achieving probability measure for conditionally Gaussian channels subject to bounded-input constraints and average cost constraints. Many practical communication systems, including additive Gaussian noise channels, certain optical channels, fading channels, and interference channels fall within this framework. Subject to bounded-input constraint (and average cost constraints), we show that the channel capacity is achievable and we derive a necessary and sufficient condition for a probability measure to be capacity achieving. Under certain conditions, the capacity-achieving measure is proved to be discrete.

A review of communication-oriented optical wireless systems

This article presents an overview of optical wireless (OW) communication systems that operate both in the short- (personal and indoor systems) and the long-range (outdoor and hybrid) regimes. Each of these areas is discussed in terms of (a) key requirements, (b) their application framework, (c) major impairments and applicable mitigation techniques, and (d) current and/or future trends. Personal communication systems are discussed within the context of point-to-point ultra-high speed data transfer. The most relevant application framework and related standards are presented, including the next generation Giga-IR standard that extends personal communication speeds to over 1 Gb/s. As far as indoor systems are concerned, emphasis is given on modeling the dispersive nature of indoor OW channels, on the limitations that dispersion imposes on user mobility and dispersion mitigation techniques. Visible light communication systems, which provide both illumination and communication over visible or hybrid visible/infrared LEDs, are presented as the most important representative of future indoor OW systems. The discussion on outdoor systems focuses on the impact of atmospheric effects on the optical channel and associated mitigation techniques that extend the realizable link lengths and transfer rates. Currently, outdoor OW is commercially available at 10 Gb/s Ethernet speeds for Metro networks and Local-Area-Network interconnections and speeds are expected to increase as faster and more reliable optical components become available. This article concludes with hybrid optical wireless/radio-frequency (OW/RF) systems that employ an additional RF link to improve the overall system reliability. Emphasis is given on cooperation techniques between the reliable RF subsystem and the broadband OW system.

A pixelated MIMO wireless optical communication system

This paper introduces the pixelated wireless optical channel, which transmits data at high rates using a series of coded time-varying images. This multiple-input/multiple-output point-to-point wireless optical channel uses arrays of optical intensity transmitters and detectors to exploit the inherent spatial degrees of freedom and to realize significant gains in spectral efficiency over single-element systems. Spatial discrete multitone modulation is introduced as a means to combat low-pass spatial distortion and to alleviate spatial alignment problems of previous systems. The capacity of pixelated wireless optical channels is estimated by way of a water-pouring spectrum. A proof-of-concept experimental prototype is constructed using a 512times512 pixel liquid crystal display panel and 154times154 pixels of a charge-coupled device camera. A channel model is developed and the capacity estimated to be 22.4 kb/frame. An unoptimized multilevel code and multistage decoder is applied over the spatial frequency bins and shown to yield spectral efficiencies of approximately 1.7 kb/s/Hz over a range of 2 m

Capacity bounds for power- and band-limited optical intensity channels corrupted by Gaussian noise

We determine upper and lower bounds on the channel capacity of power- and bandwidth-constrained optical intensity channels corrupted by white Gaussian noise. These bounds are shown to converge asymptotically at high optical signal-to-noise ratios (SNRs). Unlike previous investigations on low-intensity Poisson photon counting channels, such as some fiber optic links, this channel model is realistic for indoor free space optical channels corrupted by intense ambient light. An upper bound on the capacity is found through a sphere-packing argument while a lower bound is computed through the maxentropic source distribution. The role of bandwidth is expressed by way of the effective dimension of the set of signals and, together with an average optical power constraint, is used to determine bounds on the spectral efficiency of time-disjoint optical intensity signaling schemes. The bounds show that, at high optical SNRs, pulse sets based on raised-quadrature amplitude modulation (QAM) and prolate spheroidal wave functions have larger achievable maximum spectral efficiencies than traditional rectangular pulse basis sets. This result can be considered as an extension of previous work on photon counting channels which closely model low optical intensity channels with rectangular pulse shapes.

Design and Implementation of Color-Shift Keying for Visible Light Communications

Color-shift keying (CSK) is a visible light communication intensity modulation scheme, outlined in IEEE 802.15.7, that transmits data imperceptibly through the variation of the color emitted by red, green, and blue light emitting diodes. An advantage of CSK is that the power envelope of the transmitted signal is fixed; therefore, CSK reduces the potential for human health complications related to fluctuations in light intensity. In this work, a rigorous design framework for high order CSK constellations is presented. A key benefit of the frame work is that it optimizes constellations while accounting for crosstalk between the color communication channels. In addition, and unlike previous approaches, the method is capable of optimizing 3-D constellations. Furthermore, a prototype CSK communication system is presented to validate the performance of the optimized constellations, which provide gains of 1-3 dB over standard 805.15.7 constellations.

Optical intensity-modulated direct detection channels: signal space and lattice codes

Traditional approaches to constructing constellations for electrical channels cannot be applied directly to the optical intensity channel. This work presents a structured signal space model for optical intensity channels where the nonnegativity and average amplitude constraints are represented geometrically. Lattice codes satisfying channel constraints are defined and coding and shaping gain relative to a baseline are computed. An effective signal space dimension is defined to represent the precise impact of coding and shaping on bandwidth. Average optical power minimizing shaping regions are derived in some special cases. Example lattice codes are constructed and their performance on an idealized point-to-point wireless optical link is computed. Bandwidth-efficient schemes are shown to have promise for high data-rate applications, but require greater average optical power.

Performance of PPM on terrestrial FSO links with turbulence and pointing errors

In recent work, the error performance of on-off keying has been investigated for free-space optical (FSO) links impaired by both turbulence and pointing loss. In the current letter, the analytical framework is extended to M-ary pulse-position modulation (PPM), providing exact results for M = 2. Since the approach is not directly applicable to PPM signals with M > 2, a closed-form approximation of the average symbol error probability is derived for this case, which is shown via simulation to be tight over a wide SNR range of interest.

All-Optical Multihop Free-Space Optical Communication Systems

All-optical relaying techniques are proposed to improve the error performance and overall distance coverage of free-space optical (FSO) communication systems. An all-optical amplify-and-forward (OAF) relaying technique is presented where the received optical field is amplified at each relay. A novel channel model is developed including field distributions and weak turbulence. Simulation results indicate that OAF significantly enhances the BER performance, but is severely degraded by background light. In order to remove the impact of background noise, an optical regenerate-and-forward (ORF) relaying technique is also presented. At a bit rate of 10 Gbps, using two equally-spaced OAF relays under a turbulence-free atmospheric condition increases the total communicating distance by 0.9 km over direct transmission at a BER of 10-5, while using two ORF relays provides an additional gain in range of 1.9 km. In general, replacing OAF relays by ORF relays extends the total communicating distance at a cost of implementation complexity.

Diversity Gain and Outage Probability for MIMO Free-Space Optical Links with Misalignment

A novel statistical channel model for multiple-input multiple-output (MIMO) free-space optical (FSO) communication systems impaired by atmospheric and misalignment fading is developed. A slow-fading channel model is considered and the outage probability is derived as a performance measure. The diversity gain defined as the signal-to-noise ratio (SNR) exponent at high SNR is analyzed. Interestingly in the presence of misalignment fading the diversity gain depends only on the misalignment variance and is independent of the number of transmitters M and receivers N. Increasing the number of transmitters and receivers only results in a lower probability of outage for a given SNR, however, the rate of change is unaffected. Contrary to this case, the diversity gain of MIMO FSO systems in the presence of atmospheric fading and no misalignment is shown to be proportional to the number of transmitters and receivers, in particular the product MN.