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

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

Underwater sensor nodes will find applications in oceanographic data collection, pollution monitoring, offshore exploration, disaster prevention, assisted navigation and tactical surveillance applications. Moreover, unmanned or autonomous underwater vehicles (UUVs, AUVs), equipped with sensors, will enable the exploration of natural undersea resources and gathering of scientific data in collaborative monitoring missions. Underwater acoustic networking is the enabling technology for these applications. Underwater networks consist of a variable number of sensors and vehicles that are deployed to perform collaborative monitoring tasks over a given area. In this paper, several fundamental key aspects of underwater acoustic communications are investigated. Different architectures for two-dimensional and three-dimensional underwater sensor networks are discussed, and the characteristics of the underwater channel are detailed. The main challenges for the development of efficient networking solutions posed by the underwater environment are detailed and a cross-layer approach to the integration of all communication functionalities is suggested. Furthermore, open research issues are discussed and possible solution approaches are outlined. � 2005 Published by Elsevier B.V.

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Underwater acoustic sensor networks: research challenges

Information Theory and Reliable Communication

In this paper we review the most peculiar and interesting information-theoretic and communications features of fading channels. We first describe the statistical models of fading channels which are frequently used in the analysis and design of communication systems. Next, we focus on the information theory of fading channels, by emphasizing capacity as the most important performance measure. Both single-user and multiuser transmission are examined. Further, we describe how the structure of fading channels impacts code design, and finally overview equalization of fading multipath channels.

/pdf/fading-channels-information-theoretic-and-communications-2ipqbail97.pdf

Fading channels: information-theoretic and communications aspects

For networks that are deployed for long-term monitoring of environmental phenomena, it is of crucial importance to design an efficient data gathering scheme that prolongs the lifetime of the network. To this end, we exploit the sparse nature of the monitored field and consider a Random Access Compressed Sensing (RACS) scheme in which the sensors transmit at random to a fusion center which reconstructs the field. We provide an analytical framework for system design that captures packet collisions due to random access as well as packet errors due to communication noise. Through analysis and examples, we demonstrate that recovery of the field can be attained using only a fraction of the resources used by a conventional TDMA network, while employing a scheme which is simple to implement and requires no synchronization.

/pdf/design-of-a-random-access-network-for-compressed-sensing-35898o12g0.pdf

Design of a random access network for compressed sensing

We propose a spatial combining technique for detection of multicarrier underwater acoustic communication signals using a vertical array of receivers. Instead of estimating the channel for each receiver independently and ignoring the angles of arrival of each of the channel paths, the suggested technique is based on spatially filtering each of the channel paths by steering a multi-frequency beamformer to their angles of arrival. As the number of channel paths is usually smaller than the number of the receivers, this process reduces the dimensionality of the model and involves a lower computational load. The signals at the output of the beamformer are then decoded in a coherent or differentially-coherent form. Simulation results show that angle-of-arrival-based detection outperforms the traditional angle-of-arrival-ignorant spatial combining methods for low signal to noise ratio and moderate range.

Angle-of-arrival-based detection of underwater acoustic OFDM signals

Capacity scaling laws are analyzed in an underwater acoustic network with n regularly located nodes. A narrow-band model is assumed where the carrier frequency is allowed to scale as a function of n. In the network, we characterize an attenuation parameter that depends on the frequency scaling as well as the transmission distance. A cut-set upper bound on the throughput scaling is then derived in extended networks. Our result indicates that the upper bound is inversely proportional to the attenuation parameter, thus resulting in a highly power-limited network. Furthermore, we describe an achievable scheme based on the simple nearest-neighbor multi-hop (MH) transmission. It is shown under extended networks that the MH scheme is order-optimal as the attenuation parameter scales exponentially with √n (or faster). Finally, these scaling results are extended to a random network realization.

/pdf/multi-hop-routing-is-order-optimal-in-underwater-extended-4o2f24q06n.pdf

Multi-hop routing is order-optimal in underwater extended networks

In the papers of I.K. Zhuk, then more completely of E. Molnar, I. Prok, J.
 Szirmai all simplicial 3-tilings have been classified, where a symmetry
 group acts transitively on the simplex tiles. The involved spaces depends on
 some rotational order parameters. When a vertex of a such simplex lies out
 of the absolute, e.g. in hyperbolic space H3, then truncation with its polar
 plane gives a truncated simplex or simply, trunc-simplex. Looking for
 symmetries of these tilings by simplex or trunc-simplex domains, with their
 side face pairings, it is possible to find all their group extensions,
 especially Coxeter’s reflection groups, if they exist. So here, connections
 between isometry groups and their supergroups is given by expressing the
 generators and the corresponding parameters. There are investigated
 simplices in families F3, F4, F6 and appropriate series of trunc-simplices.
 In all cases the Coxeter groups are the maximal ones.

/pdf/coxeter-groups-as-automorphism-groups-of-solid-transitive-3-7ysiugbltm.pdf

Coxeter Groups as Automorphism Groups of Solid Transitive 3-simplex Tilings

Motivated by recent experimental observations, where differentially coherent detection outperforms coherent detection on certain underwater acoustic channels, we revisit the performance of these two methods with respect to the achievable rate in orthogonal frequency-division multiplexing systems. Our comparison is based on a class of time-varying channels, where coherent quadrature phase shift keying (QPSK) detection requires channel estimation through a set of designated pilot symbols, while differentially coherent QPSK (DQPSK) enjoys an almost pilot-free detection. We show that given the cost of pilot overhead and channel estimation errors, the average rate achievable with DQPSK can be higher than that of QPSK. We use analytical results to identify channels for which this is the case, and expand the results to larger constellation sizes such as 8PSK, 16PSK, and 16QAM. In addition to acoustic channels, wireless radio channels with unusually long delay spread or high Doppler spread, such as those found in unmanned aerial systems and high-speed trains, may also benefit from using differentially coherent detection. In general, differentially coherent detection is favored in rapidly time-varying channels which require large pilot overhead and/or whose bit error rate performance is dominated by channel estimation errors. Our analysis includes the results for array receivers and soft detectors, showing that the favorable parameter range for differentially coherent detection expands significantly in both cases.

https://par.nsf.gov/servlets/purl/10084225

Milica Stojanovic

Papers

Design of a random access network for compressed sensing

Angle-of-arrival-based detection of underwater acoustic OFDM signals

Multi-hop routing is order-optimal in underwater extended networks

Coxeter Groups as Automorphism Groups of Solid Transitive 3-simplex Tilings

On the Average Achievable Rate of QPSK and DQPSK OFDM Over Rapidly Fading Channels