There is, I think, something ethereal about i —the square root of minus one. I remember first hearing about it at school. It seemed an odd beast at that time—an intruder hovering on the edge of reality.

Usually familiarity dulls this sense of the bizarre, but in the case of i it was the reverse: over the years the sense of its surreal nature intensified. It seemed that it was impossible to write mathematics that described the real world in …

I and i

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Table Of Integrals Series And Products

The use of infrared radiation as a medium for high-speed short-range wireless digital communication is discussed. Available infrared links and local-area networks are described. Advantages and drawbacks of the infrared medium are compared to those of radio and microwave media. The physical characteristics of infrared channels using intensity modulation with direct detection (IM/DD) are presented including path losses and multipath responses. Natural and artificial ambient infrared noise sources are characterized. Strategies for designs of transmitter and receivers that maximize link signal-to-noise ratio (SNR) are described. Several modification formats are discussed in detail, including on-off keying (OOK) pulse-position modulation (PPM), and subcarrier modulation. The performance of these techniques in the presence of multipath distortion is quantified. Techniques for multiplexing the transmissions of different users are reviewed. The performance of an experimental 50-Mb/s on-off-keyed diffuse infrared link is described.

Wireless Infrared Communications

It is shown that, particularly for terrestrial cellular telephony, the interference-suppression feature of CDMA (code division multiple access) can result in a many-fold increase in capacity over analog and even over competing digital techniques. A single-cell system, such as a hubbed satellite network, is addressed, and the basic expression for capacity is developed. The corresponding expressions for a multiple-cell system are derived. and the distribution on the number of users supportable per cell is determined. It is concluded that properly augmented and power-controlled multiple-cell CDMA promises a quantum increase in current cellular capacity. >

On the capacity of a cellular CDMA system

We review the field of femtosecond pulse shaping, in which Fourier synthesis methods are used to generate nearly arbitrarily shaped ultrafast optical wave forms according to user specification. An emphasis is placed on programmable pulse shaping methods based on the use of spatial light modulators. After outlining the fundamental principles of pulse shaping, we then present a detailed discussion of pulse shaping using several different types of spatial light modulators. Finally, new research directions in pulse shaping, and applications of pulse shaping to optical communications, biomedical optical imaging, high power laser amplifiers, quantum control, and laser-electron beam interactions are reviewed.

Femtosecond pulse shaping using spatial light modulators

Free space optical (FSO) communications is a cost-effective and high bandwidth access technique, which has been receiving growing attention with recent commercialization successes. A major impairment in FSO links is the turbulence- induced fading which severely degrades the link performance. To mitigate turbulence-induced fading and, therefore, to improve the error rate performance, spatial diversity can be used over FSO links which involves the deployment of multiple laser transmitters/receivers. In this paper, we investigate the bit error rate (BER) performance of FSO links with spatial diversity over log- normal atmospheric turbulence fading channels, assuming both independent and correlated channels among transmitter/receiver apertures. Our analytical derivations build upon an approximation to the sum of correlated log-normal random variables. The derived BER expressions quantify the effect of spatial diversity and possible spatial correlations in a log-normal channel.

/pdf/ber-performance-of-free-space-optical-transmission-with-249sp2pvzf.pdf

BER Performance of Free-Space Optical Transmission with Spatial Diversity

Presents a new category of optical CDMA systems which work based on spectral encoding. In such systems, that the authors refer to as frequency-encoded CDMA (FE-CDMA) systems, the coding is done in the frequency domain while in the usual CDMA systems the code multiplies the modulation signal in the time domain. They present a new type of FE-CDMA system, based on encoding noncoherent broadband sources. They discuss the advantages of the system compared to other optical CDMA systems and present its performance. They show that very efficient, low-cost, CDMA systems can be obtained with an aggregate throughput of many gigabits per second. Also, for this system, the spreading gain of CDMA is independent of the modulation bandwidth. Hence, the system can accommodate variable bit rates, naturally. >

Optical code-division-multiplexed systems based on spectral encoding of noncoherent sources

Direct-sequence spread spectrum with differential phase shift-keying (DPSK) modulation and code-division multiple-access is a promising approach for wireless communications in an indoor environment, which is characterized in this paper by a Rayleigh-fading multipath channel. In this study, we consider two specific channel models having different path-delay distributions and average path power profiles. A star configuration, in which each user exercises average power control in transmitting to a central station, is the basic communication unit, which could be one cell in a cellular hierarchy. We obtain the performance of a single link between a user and its receiver in the central station, and consider two types of diversity, selection diversity and predetection combining to exploit the multipath. A similar system with coherent PSK (CPSK) modulation has been studied previously for one of the channel models considered here. For the same channel model, we show that the irreducible error probability with selection diversity is about half an order of magnitude higher when DPSK is used instead of CPSK. With predetection combining, the performance improves significantly in comparison with selection diversity as the diversity order increases. DPSK modulation with predetection combining is akin to coherent PSK with optimal maximal-ratio combining, but is simpler to implement. The performance with selection diversity for a second channel model, which is based on measurements in an office building, is not significantly different. This indicates that the spreadspectrum approach is rather robust to the path-delay distribution and average path-power profile.

Direct-Sequence Spread Spectrum with DPSK Modulation and Diversity for Indoor Wireless Communications

This paper deals with the problem of interconnection of many high-speed bursty traffic users via an optical passive star coupler. Each user can tune its laser over a range of wavelengths, thus resulting in a wavelength division multiplexed communication. The total number of wavelengths over which user tunability exists could be much smaller than the number of users. Therefore, some form of random access sharing and packet switching may be necessary. We propose several protocols that require each user to have a tunable receiver. The information on "where" and "when" to tune the laser is confined to a control (setup) channel that users tune to when in idle mode. An interconnection between two users lasting for the length of a data packet is set up on the control channel by the transmitting user who informs the receiving user where to tune in order to receive the data packet. No centralized control or coordination is required among the users. After analyzing each protocol, we present the throughput/ delay versus the offered traffic and the delay versus throughput in a sequence of plots. We show that in typical applications an average throughput of up to 0.95 can be achieved at a reasonable average delay using one of these protocols. In our benchmark examples we present an optical local area network (LAN) with a total throughput of 100- Gbit/s in which every user has access to a 1-Gbit/s data rate and the network can support over 1000 users. The protocols can be used in a) large LAN's that do not require a large capacity, b) small LAN's (1 kin) that require a large capacity and c) large LAN's (tens of kilometers) that require a rather large capacity.

Protocols for very high-speed optical fiber local area networks using a passive star topology

The present invention relates to a wireless PBX network wherein direct sequence spread spectrum multiple access is used for voice and data communications to support a plurality of local-local and local-external calls. The present wireless PBX arrangement comprises a plurality of local user transceivers using a first separate unique chip sequence patterns for information communication and a second common chip sequence pattern for call-set up; and a central PBX comprising (a) a plurality of PBX transceivers, each of which uses a separate first chip sequence pattern which is matched to a corresponding local user transceiver; (b) a switching means for interconnecting local users to each other or to an external network via the associated PBX transceivers; and (c) a call set-up receiver responsive solely to initial call set-up information sent by any user using the second common chip sequence pattern. Optional selection diversity or equal gain combining diversity and/or error correction encoding may also be included in the transceivers.

Mohsen Kavehrad

Papers

BER Performance of Free-Space Optical Transmission with Spatial Diversity

Optical code-division-multiplexed systems based on spectral encoding of noncoherent sources

Direct-Sequence Spread Spectrum with DPSK Modulation and Diversity for Indoor Wireless Communications

Protocols for very high-speed optical fiber local area networks using a passive star topology

Spread spectrum wireless PBX