In this chapter, we examine basic modeling and characterization issues that arise from short-range communications over non-line-of-sight (NLOS) ultraviolet (UV) atmospheric scattering channels. We start by presenting the unique channel properties and history of NLOS UV communications, and introduce outdoor NLOS UV scattering link geometries. Both single and multiple scattering effects are considered, including channel impulse response and link path loss. Analysis and Monte Carlo simulation are employed to investigate the UV channel properties. We also report on experimental outdoor channel measurements, and compare with theoretical predictions.

Introduction

Why NLOS UV communications?

Within the ultraviolet (UV) spectrum 4∼400 nm, the UV-C band (sometimes called deep UV, or mid-UV) with wavelength range 200∼280 nm has unique atmospheric propagation characteristics that enable non-line-of-sight (NLOS) communications, as described in [33]. This band is essentially solar blind (e.g., see [17]), so that a ground-based photodetector can approach quantum-limited photon counting detection performance, and low-power sources can be used. At these wavelengths, scattering due to photon inter-action with atmospheric molecules and aerosols is very pronounced, and the relatively angle-independent scattering yields spatially diverse NLOS communications paths, e.g., see [21]. This rich scattering diversity enables unique NLOS optical communications, although the great majority of photons may be scattered away from the receiver and so the corresponding path loss is typically much higher than that occurring with a conventional optical LOS communication channel. The low solar background helps significantly in this regard, so that short-range links can be maintained with relatively low transmit power.

Motivation

The ability to guarantee security and privacy in communication are critical factors in encouraging people to accept and trust new tools and methods for today's information-based society (e.g. in eCommerce or eHealth) and for future services (e.g. eGovernment, eVoting). Cybercrime already hinders these new possibilities by creating widespread mistrust in these new services. Another problem is that a (perhaps unpublicized) break-through in mathematics or computer science could completely compromise current state-of-the-art encryption methods overnight, even those which are the basis of all existing internet banking transactions. This is because the security of cutting-edge public-key cryptography (conventional cryptography) relies on the computational difficulty of certain mathematical tasks, meaning that conventional cryptography alone can neither provide any evidence of eavesdropping nor guarantee strong security. The trend towards faster electronics provides the ability to handle longer keys, thus providing better security, but also increases the possibility to break keys. This also has another worrying effect: even using today's most advanced available security technology to protect data during communication with best practice and without making any mistakes, the ongoing improvements in technology (which hence require longer key lengths to ensure security) mean that today's transmitted data will not be secure for more than a few years. Thus, while encrypted data might be safe today, it can still be stored by the adversary now and then broken later on once the future technology has caught up with today's encryption.

Alternatively, modern quantum cryptography has created a new paradigm for cryptographic communication, which provides strong, long-term security and incontrovertible evidence of any attempted eavesdropping which is based on theoretically and experimentally proven laws of nature.

The popular adage, “a picture is worth a thousand words” suggests that it is often easier to convey a large amount of information in parallel by way of an image rather than by serial transmission of words. Indeed, this is the underlying inspiration for a new class of indoor optical wireless (OW) channels. In these channels data are conveyed by coordinating the transmission of a series of transmitters and receivers. So called, multiple-input multiple-output (MIMO) OW systems employ a number of optical sources as transmitters and a collection of photodiodes as receivers. The arrangement of emitters and detectors varies depending on application and implementation technology.

The use of MIMO techniques in radio channels is a long-standing topic of interest. It has been shown that by increasing the number of antennae in a radio system that a diversity gain can be achieved, i.e., an improvement in the reliability of the system can be had. Alternatively, it has been demonstrated that multiple transmitting and receiving antennae can be used to provide a boost in rate, i.e. a multiplexing gain. In fact, a formal trade-off between diversity and multiplexing gain in MIMO radio channels has been established [1].

The OW MIMO systems discussed in this chapter differ fundamentally from earlier work on radio channels. In particular, only indoor OW channels are considered here and are free of multipath fading. In addition, the signalling constraints imposed by intensity-modulated/direct-detection (IM/DD) systems limits the direct application of theory from radio channels. Nonetheless, MIMO techniques have been applied to OW channels to yield improvements in reliability and to improve data rates.

Introduction

Free-space optical communication (FSO) offers many potential advantages. These include: high bandwidth, security, non-interference, and a large amount of available spectrum. Many of these advantages are related to optics' short wavelength relative to radio-frequency (RF) or microwave systems. At optical wavelengths even a small transmit aperture can produce highly directional beams, and optical receivers can focus light down to very small spots. To make use of this high optical antenna gain very good pointing is required. Even a small telescope, with a 1 cm diameter, has a diffraction-limited beam divergence of less than 250 micro-radians in the near-infrared. Pointing with this accuracy is challenging, particularly if one or both ends of the link are in motion. Active FSO systems with high pointing accuracy are often large, heavy, and have high power consumption [1]. Such systems are also complex, which can lead to reliability issues.

Despite these challenges, direct FSO links – those with active terminals on both ends – have many good applications. There are, however, other applications in which the two ends of the link have different payload and power capabilities. Some examples include: unattended sensors, small unmanned aerial vehicles (UAVs), and small, tele-operated robots. For these applications a modulating retro-reflector (MRR) may be an appropriate solution.

Optical MRRs couple passive retro-reflectors with electro-optic modulators to allow long-range, free-space optical communication with a laser, and pointing/acquisition/tracking system, required on only one end of the link. As shown in Figure 13.1, a conventional free-space optical communications terminal, the interrogator, is used on one end of the link to illuminate the MRR on the other end of the link with a continuous-wave beam.

The transport capabilities of optical communication systems have increased tremendously in the past two decades, primarily due to advances in optical devices and technologies, and have enabled the Internet as we know it today with all its impacts on the modern society. Future internet technologies should be able to support a wide range of services containing a large amount of multimedia over different network types at high transmission speeds. The future optical networks should allow the interoperability of radio frequency (RF), fiber-optic and free-space optical (FSO) technologies. However, the incompatibility of RF/microwave and fiber-optics technologies is an important limiting factor in efforts to further increase future transport capabilities of such hybrid networks. Because of its flexibility, FSO communication is a technology that can potentially solve the incompatibility problems between RF and optical technologies. Moreover, FSO technologies can address any type of connectivity needs in optical networks. To elaborate, in metropolitan area networks (MANs), FSO communications can be used to extend the existing MAN rings; in enterprise networks, FSO can be used to enable local area network (LAN)-to-LAN connectivity and intercampus connectivity; and, last but not the least, FSO is an excellent candidate for the last-mile connectivity.

Introduction

Infrared (IR) indoor optical wireless (OW) potentially combines the high bandwidth availability of optical communications with the mobility found in radio frequency (RF) wireless communication systems. So although IR is currently overshadowed by a multitude of home and office RF wireless networking schemes, it has significant potential when bandwidth demand is high. Compared to an RF system, OW offers the advantageous opportunity for high-speed medium- to short-range communications operating within a virtually unlimited and unregulated bandwidth spectrum using lower-cost components. Furthermore, OW systems may be securely deployed with immunity to adjacent communication cell interference because the signal radiation cannot penetrate opaque barriers such as walls. Low transceiver costs, coupled with rapid deployment and compatibility with the existing optical fiber communication systems mean that OW is an attractive alternative when fiber deployment is difficult [1], [2]. Moreover, band-width congestion in the RF domain has led to the installation of optical hotspots in public buildings and application-specific OW hotspots can be integrated into future office designs [3]. Optical wireless communication has attracted considerable attention from the academic community. From its short-distance, low-speed origins [4], OW has become a viable addition to communication systems with promising prospects, having passed the 155 Mbps indoor landmark during the 1990s [5]. In recent years, techniques such as multispot diffusion (MSD) [6], angular diversity [7], and rate adaptive modulation [8] have been adopted as will be discussed later in this chapter.

Introduction

In free-space optical (FSO) communication an optical carrier is employed to convey information wirelessly. FSO systems have the potential to provide fiber-like data rates with the advantages of quick deployment times, high security, and no frequency regulations. Unfortunately such links are highly susceptible to atmospheric effects. Scintillation induced by atmospheric turbulence causes random fluctuations in the received irradiance of the optical laser beam [1]. Numerous studies have shown that performance degradation caused by scintillation can be significantly reduced through the use of multiple-lasers and multiple-apertures, creating the well-known multiple-input multiple-output (MIMO) channel (see e.g. [2], [3], [4], [5], [6], [7], [8], [9], [10]). However, it is the large attenuating effects of cloud and fog that pose the most formidable challenge. Extreme low-visibility fog can cause signal attenuation on the order of hundreds of decibels per kilometer [11]. One method to improve the reliability in these circumstances is to introduce a radio frequency (RF) link to create a hybrid FSO/RF communication system [12], [13], [14], [15], [16], [11]. When the FSO link is blocked by cloud or fog, the RF link maintains reliable communications, albeit at a reduced data rate. Typically a millimeter wavelength carrier is selected for the RF link to achieve data rates comparable to that of the FSO link. At these wavelengths, the RF link is also subject to atmospheric effects, including rain and scintillation [17], [18], [19], [20], [21], but less affected by fog.

Introduction and channel models

Optical communications take place at high frequencies at which it is sometimes difficult to modulate the phase and frequency of the transmitted signal. Instead, some optical systems modulate the intensity of the signal. Such systems are consequently fundamentally different from standard (e.g., mobile) wireless systems. For example, the channel input cannot be negative because it corresponds to the instantaneous light intensity. Also, since the light intensity, and thus the input, is proportional to the instantaneous optical power, the average-power constraints apply linearly to the input and not, as is usual in standard radio communications, to its square.

In this chapter we focus on communication systems that employ pulse amplitude modulation (PAM), which in the case of optical communication is called pulse intensity modulation. In such systems the transmitter modulates the information bits onto continuous-time pulses of duration T, and the receiver preprocesses the incoming continuous-time signal by integrating it over nonoverlapping intervals of length T. Such continuous-time systems can be modeled as discrete-time channels where the (discrete) time k input and output correspond to the integrals of the continuous-time transmitted and received signals (i.e., optical intensities) from kT to (k + 1)T. Note that for such discrete-time systems, the achieved data rate is not measured in bits (or nats) per second, but in bits (or nats) per channel use.

We discuss three different discrete-time, pulse intensity modulated, optical channel models: the discrete-time Poisson channel, the free-space optical intensity channel, and the optical intensity channel with input-dependent Gaussian noise.

Introduction

Amidst revolutionary communication technologies of recent decades such as optical fiber and wireless systems other forms of communication technologies are popping up in order to complete or complement the ever-increasing and insatiable need for communications links in today's society. Among many such niche technologies optical wireless communication technology, in particular, is begining to enjoy a wide range of applications and attention from many industries for short-range interchip applications to interplanetary space applications. Furthermore, optical wireless systems have attracted even further considerable growth in research and development since they can be appropriate alternatives for wireless or fiber-optic communication systems in some specific applications. Indoor wireless LANs, atmospheric optical links, and submarine optical wireless systems have grown in importance where lightwave communications is preferred to radio communications. This preference in various applications can be originated from security requirements, radio interference avoidance, no need for reserving frequency bands and cost of development [1]–[9].

In this chapter we study and analyze a particular and advanced form of optical wireless communication systems namely optical code-division multiple-access (OCDMA) in the context of wireless optical systems. As wireless optical communication systems get more mature and become viable for multi-user communication systems, advanced multiple-access techniques become more important and attractive in such systems. Among all multiple-access techniques in optical domain, OCDMA is of utmost interest because of its flexibility, ease of implementation, no need for synchronization among many users, and soft traffic handling capability.

Intensity modulation/direct detection (IM/DD) schemes are widely used in wireless optical applications. The interest in using IM/DD schemes stems from the fact that they can be easily implemented in transmitter and receiver sides.

This is a tutorial on some basic non-asymptotic methods and concepts in random matrix theory. The reader will learn several tools for the analysis of the extreme singular values of random matrices with independent rows or columns. Many of these methods sprung off from the development of geometric functional analysis since the 1970s. They have applications in several fields, most notably in theoretical computer science, statistics and signal processing. A few basic applications are covered in this text, particularly for the problem of estimating covariance matrices in statistics and for validating probabilistic constructions of measurement matrices in compressed sensing. This tutorial is written particularly for graduate students and beginning researchers in different areas, including functional analysts, probabilists, theoretical statisticians, electrical engineers, and theoretical computer scientists.

Introduction

Asymptotic and non-asymptotic regimes

Random matrix theory studies properties of N × n matrices A chosen from some distribution on the set of all matrices. As dimensions N and n grow to infinity, one observes that the spectrum of A tends to stabilize. This is manifested in several limit laws, which may be regarded as random matrix versions of the central limit theorem. Among them is Wigner's semicircle law for the eigenvalues of symmetric Gaussian matrices, the circular law for Gaussian matrices, the Marchenko–Pastur law for Wishart matrices W = A* A where A is a Gaussian matrix, the Bai–Yin and Tracy–Widom laws for the extreme eigenvalues of Wishart matrices W.

This chapter generalizes compressed sensing (CS) to reduced-rate sampling of analog signals. It introduces Xampling, a unified framework for low-rate sampling and processing of signals lying in a union of subspaces. Xampling consists of two main blocks: analog compression that narrows down the input bandwidth prior to sampling with commercial devices followed by a nonlinear algorithm that detects the input subspace prior to conventional signal processing. A variety of analog CS applications are reviewed within the unified Xampling framework including a general filter-bank scheme for sparse shift-invariant spaces, periodic nonuniform sampling and modulated wideband conversion for multiband communications with unknown carrier frequencies, acquisition techniques for finite rate of innovation signals with applications to medical and radar imaging, and random demodulation of sparse harmonic tones. A hardware-oriented viewpoint is advocated throughout, addressing practical constraints and exemplifying hardware realizations where relevant.

Introduction

Analog-to-digital conversion (ADC) technology constantly advances along the route that was delineated in the last century by the celebrated Shannon–Nyquist [1, 2] theorem, essentially requiring the sampling rate to be at least twice the highest frequency in the signal. This basic principle underlies almost all digital signal processing (DSP) applications such as audio, video, radio receivers, wireless communications, radar applications, medical devices, optical systems and more. The ever growing demand for data, as well as advances in radio frequency (RF) technology, have promoted the use of high-bandwidth signals, for which the rates dictated by the Shannon–Nyquist theorem impose demanding challenges on the acquisition hardware and on the subsequent storage and DSP processors.

In recent years, tremendous progress has been made in high-dimensional inference problems by exploiting intrinsic low-dimensional structure. Sparsity is perhaps the simplest model for low-dimensional structure. It is based on the assumption that the object of interest can be represented as a linear combination of a small number of elementary functions, which are assumed to belong to a larger collection, or dictionary, of possible functions. Sparse recovery is the problem of determining which components are needed in the representation based on measurements of the object. Most theory and methods for sparse recovery are based on an assumption of non-adaptive measurements. This chapter investigates the advantages of sequential measurement schemes that adaptively focus sensing using information gathered throughout the measurement process. In particular, it is shown that adaptive sensing can be significantly more powerful when the measurements are contaminated with additive noise.

Introduction

High-dimensional inference problems cannot be accurately solved without enormous amounts of data or prior assumptions about the nature of the object to be inferred. Great progress has been made in recent years by exploiting intrinsic low-dimensional structure in high-dimensional objects. Sparsity is perhaps the simplest model for taking advantage of reduced dimensionality. It is based on the assumption that the object of interest can be represented as a linear combination of a small number of elementary functions. The specific functions needed in the representation are assumed to belong to a larger collection or dictionary of functions, but are otherwise unknown.