This paper is motivated by the need for fundamental understanding of ultimate limits of bandwidth efficient delivery of higher bit-rates in digital wireless communications and to also begin to look into how these limits might be approached. We examine exploitation of multi-element array (MEA) technology, that is processing the spatial dimension (not just the time dimension) to improve wireless capacities in certain applications. Specifically, we present some basic information theory results that promise great advantages of using MEAs in wireless LANs and building to building wireless communication links. We explore the important case when the channel characteristic is not available at the transmitter but the receiver knows (tracks) the characteristic which is subject to Rayleigh fading. Fixing the overall transmitted power, we express the capacity offered by MEA technology and we see how the capacity scales with increasing SNR for a large but practical number, n, of antenna elements at both transmitter and receiver.

We investigate the case of independent Rayleigh faded paths between antenna elements and find that with high probability extraordinary capacity is available. Compared to the baseline n = 1 case, which by Shannon‘s classical formula scales as one more bit/cycle for every 3 dB of signal-to-noise ratio (SNR) increase, remarkably with MEAs, the scaling is almost like n more bits/cycle for each 3 dB increase in SNR. To illustrate how great this capacity is, even for small n, take the cases n = 2, 4 and 16 at an average received SNR of 21 dB. For over 99% of the channels the capacity is about 7, 19 and 88 bits/cycle respectively, while if n = 1 there is only about 1.2 bit/cycle at the 99% level. For say a symbol rate equal to the channel bandwith, since it is the bits/symbol/dimension that is relevant for signal constellations, these higher capacities are not unreasonable. The 19 bits/cycle for n = 4 amounts to 4.75 bits/symbol/dimension while 88 bits/cycle for n = 16 amounts to 5.5 bits/symbol/dimension. Standard approaches such as selection and optimum combining are seen to be deficient when compared to what will ultimately be possible. New codecs need to be invented to realize a hefty portion of the great capacity promised.

/pdf/on-limits-of-wireless-communications-in-a-fading-environment-2nxyevgur3.pdf

On Limits of Wireless Communications in a Fading Environment when UsingMultiple Antennas

Wireless 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

Ad hoc networks are a new wireless networking paradigm for mobile hosts. Unlike traditional mobile wireless networks, ad hoc networks do not rely on any fixed infrastructure. Instead, hosts rely on each other to keep the network connected. Military tactical and other security-sensitive operations are still the main applications of ad hoc networks, although there is a trend to adopt ad hoc networks for commercial uses due to their unique properties. One main challenge in the design of these networks is their vulnerability to security attacks. In this article, we study the threats on ad hoc network faces and the security goals to be achieved. We identify the new challenges and opportunities posed by this new networking environment and explore new approaches to secure its communication. In particular, we take advantage of the inherent redundancy in ad hoc networks-multiple routes between nodes-to defend routing against denial-of-service attacks. We also use replication and new cryptographic schemes, such as threshold cryptography, to build a highly secure and highly available key management service, which terms the core of our security framework.

/pdf/securing-ad-hoc-networks-3hudjv4io2.pdf

Securing ad hoc networks

This comprehensive treatment of network information theory and its applications provides the first unified coverage of both classical and recent results. With an approach that balances the introduction of new models and new coding techniques, readers are guided through Shannon's point-to-point information theory, single-hop networks, multihop networks, and extensions to distributed computing, secrecy, wireless communication, and networking. Elementary mathematical tools and techniques are used throughout, requiring only basic knowledge of probability, whilst unified proofs of coding theorems are based on a few simple lemmas, making the text accessible to newcomers. Key topics covered include successive cancellation and superposition coding, MIMO wireless communication, network coding, and cooperative relaying. Also covered are feedback and interactive communication, capacity approximations and scaling laws, and asynchronous and random access channels. This book is ideal for use in the classroom, for self-study, and as a reference for researchers and engineers in industry and academia.

Network Information Theory

An analysis of an asynchronous phase-coded spread-spectrum multiple-access communication system is presented. The results of this analysis reveal which code parameters have the greatest impact on communication performance and provide analytical tools for use in preliminary system design. Emphasis is placed on average performance rather than worst-case performance and on code parameters which can be computed easily.

Performance Evaluation for Phase-Coded Spread-Spectrum Multiple-Access Communication--Part I: System Analysis

Binary maximal-length linear feedback shift register sequences (m-sequences) have been successfully employed in communications, navigation, and related systems over the past several years. For the early applications, m-sequences were used primarily because of their excellent periodic autocorrelation properties. For many of the recent systems applications, however, the crosscorrelation properties of such sequences are at least as important as the autocorrelation properties, and the system performance depends upon the aperiodic correlation in addition to the periodic correlation. This paper presents a survey of recent results and provides several new results on the periodic and aperiodic crosscorrelation functions for pairs of m-sequences and for pairs of related (but not maximal-length) binary shift register sequences. Also included are several recent results on correlation for complex-valued sequences as well as identities relating the crosscorrelation functions to autocorrelation functions. Examples of problems in spread-spectrum communications are employed to motivate the choice of correlation parameters that are considered in the paper.

Crosscorrelation properties of pseudorandom and related sequences

Binary direct-sequence spread-spectrum multiple-access communications, an additive white Gaussian noise channel, and a coherent correlation receiver are considered. An expression for the output of the receiver is obtained for the case of random signature sequences, and the corresponding characteristic function is determined. The expression is used to study the density function of the multiple-access interference and to determine arbitrarily tight upper and lower bounds on the average probability of error. The bounds, which are obtained without making a Gaussian approximation, are compared to results obtained using a Gaussian approximation. The effects of transmitter power, the length of the signature sequences, and the number of interfering transmitters are illustrated. Each transmitter is assumed to have the same power, although the general approach can accommodate the case of transmitters with unequal powers.

Error Probabilities for Binary Direct-Sequence Spread-Spectrum Communications with Random Signature Sequences

An analysis of the code sequence parameters that are most important to the communication performance of an asynchronous phase-coded spread-spectrum multiple-access communication system is presented. Previously known bounds and computational techniques for such parameters are surveyed. Some new results on mean-square correlation are included.

Performance Evaluation for Phase-Coded Spread-Spectrum Multiple-Access Communication--Part II: Code Sequence Analysis

Approximations are obtained for the average probability of error in an asynchronous direct-sequence spread-spectrum multiple-access communications system. Both binary and quaternary systems are considered, and the chip waveforms are allowed to be arbitrary time-limited waveforms with time duration equal to the inverse of the chip rate. The approximation is based on the integration of the characteristic function of the multiple-access interference. The amount of computation required to evaluate this approximation grows only linearly with the product of the number of simultaneous transmitters and the number of chips per bit. The accuracy of the approximation is extremely good in most cases, but it can be improved, if necessary, by an application of a series expansion. Numerical results are presented for specific chip waveforms and signature sequences.

Michael B. Pursley

Papers

Performance Evaluation for Phase-Coded Spread-Spectrum Multiple-Access Communication--Part I: System Analysis

Crosscorrelation properties of pseudorandom and related sequences

Error Probabilities for Binary Direct-Sequence Spread-Spectrum Communications with Random Signature Sequences

Performance Evaluation for Phase-Coded Spread-Spectrum Multiple-Access Communication--Part II: Code Sequence Analysis

Error Probability for Direct-Sequence Spread-Spectrum Multiple-Access Communications--Part II: Approximations