Information theoretic considerations for cellular mobile radio
TL;DR: Some information-theoretic considerations used to determine upper bounds on the information rates that can be reliably transmitted over a two-ray propagation path mobile radio channel model, operating in a time division multiplex access (TDMA) regime, under given decoding delay constraints are presented.
Abstract: We present some information-theoretic considerations used to determine upper bounds on the information rates that can be reliably transmitted over a two-ray propagation path mobile radio channel model, operating in a time division multiplex access (TDMA) regime, under given decoding delay constraints. The sense in which reliability is measured is addressed, and in the interesting eases where the decoding delay constraint plays a significant role, the maximal achievable rate (capacity), is specified in terms of capacity versus outage. In this case, no coding capacity in the strict Shannon sense exists. Simple schemes for time and space diversity are examined, and their potential benefits are illuminated from an information-theoretic stand point. In our presentation, we chose to specialize to the TDMA protocol for the sake of clarity and convenience. Our main arguments and results extend directly to certain variants of other multiple access protocols such as code division multiple access (CDMA) and frequency division multiple access (FDMA), provided that no fast feedback from the receiver to the transmitter is available. >
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TL;DR: Using distributed antennas, this work develops and analyzes low-complexity cooperative diversity protocols that combat fading induced by multipath propagation in wireless networks and develops performance characterizations in terms of outage events and associated outage probabilities, which measure robustness of the transmissions to fading.
Abstract: We develop and analyze low-complexity cooperative diversity protocols that combat fading induced by multipath propagation in wireless networks. The underlying techniques exploit space diversity available through cooperating terminals' relaying signals for one another. We outline several strategies employed by the cooperating radios, including fixed relaying schemes such as amplify-and-forward and decode-and-forward, selection relaying schemes that adapt based upon channel measurements between the cooperating terminals, and incremental relaying schemes that adapt based upon limited feedback from the destination terminal. We develop performance characterizations in terms of outage events and associated outage probabilities, which measure robustness of the transmissions to fading, focusing on the high signal-to-noise ratio (SNR) regime. Except for fixed decode-and-forward, all of our cooperative diversity protocols are efficient in the sense that they achieve full diversity (i.e., second-order diversity in the case of two terminals), and, moreover, are close to optimum (within 1.5 dB) in certain regimes. Thus, using distributed antennas, we can provide the powerful benefits of space diversity without need for physical arrays, though at a loss of spectral efficiency due to half-duplex operation and possibly at the cost of additional receive hardware. Applicable to any wireless setting, including cellular or ad hoc networks-wherever space constraints preclude the use of physical arrays-the performance characterizations reveal that large power or energy savings result from the use of these protocols.
12,761 citations
Cites background from "Information theoretic consideration..."
...Finally, although previous work focuses primarily on ergodic settings and characterizes performance via Shanno n capacity or capacity regions, we focus on non-ergodic or delay-constrained scenarios and characterize performanc e by outage probability [11]....
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...In this section, we characterize performance of the protoco ls of Section III in terms of outage events and outage probabili ties [11]....
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...Throughout the rest of the paper, w assume that the reader is familiar with these latter areas, a nd refer the interested reader to [2]–[4], [9], [10], and refer nces therein, for an introduction to the relevant concepts from m ultiantenna systems and to [11] for an introduction to outage capacity for fading channels....
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...Consequently, we focus on delay-limited or non-ergodic sce narios, and evaluate performance of our protocols in terms of outage probability [11]....
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01 Nov 1999
TL;DR: In this paper, the authors investigate the use of multiple transmitting and/or receiving antennas for single user communications over the additive Gaussian channel with and without fading, and derive formulas for the capacities and error exponents of such channels, and describe computational procedures to evaluate such formulas.
Abstract: We investigate the use of multiple transmitting and/or receiving antennas for single user communications over the additive Gaussian channel with and without fading. We derive formulas for the capacities and error exponents of such channels, and describe computational procedures to evaluate such formulas. We show that the potential gains of such multi-antenna systems over single-antenna systems is rather large under independenceassumptions for the fades and noises at different receiving antennas.
12,542 citations
TL;DR: Results show that, even though the interuser channel is noisy, cooperation leads not only to an increase in capacity for both users but also to a more robust system, where users' achievable rates are less susceptible to channel variations.
Abstract: Mobile users' data rate and quality of service are limited by the fact that, within the duration of any given call, they experience severe variations in signal attenuation, thereby necessitating the use of some type of diversity. In this two-part paper, we propose a new form of spatial diversity, in which diversity gains are achieved via the cooperation of mobile users. Part I describes the user cooperation strategy, while Part II (see ibid., p.1939-48) focuses on implementation issues and performance analysis. Results show that, even though the interuser channel is noisy, cooperation leads not only to an increase in capacity for both users but also to a more robust system, where users' achievable rates are less susceptible to channel variations.
6,621 citations
TL;DR: A simple characterization of the optimal tradeoff curve is given and used to evaluate the performance of existing multiple antenna schemes for the richly scattered Rayleigh-fading channel.
Abstract: Multiple antennas can be used for increasing the amount of diversity or the number of degrees of freedom in wireless communication systems. We propose the point of view that both types of gains can be simultaneously obtained for a given multiple-antenna channel, but there is a fundamental tradeoff between how much of each any coding scheme can get. For the richly scattered Rayleigh-fading channel, we give a simple characterization of the optimal tradeoff curve and use it to evaluate the performance of existing multiple antenna schemes.
4,422 citations
Cites methods from "Information theoretic consideration..."
...As a step to prove Theorem 2, we will first discuss another commonly used concept for multiple-antenna channels: the outage capacity formulation, proposed in [11] for fading channels and applied to multiantenna channels in [1]....
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...Thus, instead of using the machinery of the error exponent theory, we exploit the special properties of fading channels and develop a simple approach, based on the outage capacity formulation [11], to analyze the diversity–multiplexing tradeoff in the high-SNR regime....
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TL;DR: This work develops and analyzes space-time coded cooperative diversity protocols for combating multipath fading across multiple protocol layers in a wireless network and demonstrates that these protocols achieve full spatial diversity in the number of cooperating terminals, not just theNumber of decoding relays, and can be used effectively for higher spectral efficiencies than repetition-based schemes.
Abstract: We develop and analyze space-time coded cooperative diversity protocols for combating multipath fading across multiple protocol layers in a wireless network. The protocols exploit spatial diversity available among a collection of distributed terminals that relay messages for one another in such a manner that the destination terminal can average the fading, even though it is unknown a priori which terminals will be involved. In particular, a source initiates transmission to its destination, and many relays potentially receive the transmission. Those terminals that can fully decode the transmission utilize a space-time code to cooperatively relay to the destination. We demonstrate that these protocols achieve full spatial diversity in the number of cooperating terminals, not just the number of decoding relays, and can be used effectively for higher spectral efficiencies than repetition-based schemes. We discuss issues related to space-time code design for these protocols, emphasizing codes that readily allow for appealing distributed versions.
4,385 citations
Cites background from "Information theoretic consideration..."
...below some fixed spectral efficiencyis referred to as an outage event, and the probability of an outage event, , is referred to as the outage probability of the channel [8]....
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References
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Book•
01 Jan 1943TL;DR: Combinations involving trigonometric and hyperbolic functions and power 5 Indefinite Integrals of Special Functions 6 Definite Integral Integral Functions 7.Associated Legendre Functions 8 Special Functions 9 Hypergeometric Functions 10 Vector Field Theory 11 Algebraic Inequalities 12 Integral Inequality 13 Matrices and related results 14 Determinants 15 Norms 16 Ordinary differential equations 17 Fourier, Laplace, and Mellin Transforms 18 The z-transform
Abstract: 0 Introduction 1 Elementary Functions 2 Indefinite Integrals of Elementary Functions 3 Definite Integrals of Elementary Functions 4.Combinations involving trigonometric and hyperbolic functions and power 5 Indefinite Integrals of Special Functions 6 Definite Integrals of Special Functions 7.Associated Legendre Functions 8 Special Functions 9 Hypergeometric Functions 10 Vector Field Theory 11 Algebraic Inequalities 12 Integral Inequalities 13 Matrices and related results 14 Determinants 15 Norms 16 Ordinary differential equations 17 Fourier, Laplace, and Mellin Transforms 18 The z-transform
27,354 citations
01 Jan 1960
TL;DR: In this article, the authors summarized the principal results of a series of statistical studies in the last seven years on the intensity distributions due to rapid fading, and presented an extremely simplified method for estimating the improvement available from various systems of diversity reception.
Abstract: This paper summarizes the principal results of a series of statistical studies in the last seven years on the intensity distributions due to rapid fading The method of derivation and the principal characteristics of the m-distribution, originally found in our hf experiments and described by the author, are outlined Its applicability to both ionospheric and tropospheric modes of propagation is fairly well confirmed by some observations Its theoretical background is also discussed in detail A theoretical interpretation of the log-normal distribution is given on the basis of this formula An extremely simplified method is presented for estimating the improvement available from various systems of diversity reception The mutual dependences between the m-formula and other basic distributions are fully discussed Some generalized forms of the basic distributions are also investigated in relation to the m-formula Two methods of approximating a given function with the m-distribution are shown The joint distribution of two variables, each of which follows the m-distribution, is derived in two different ways Based on this, some useful associated distributions are also discussed
2,441 citations
TL;DR: In this article, Toeplitz forms are used for the trigonometric moment problem and other problems in probability theory, analysis, and statistics, including analytic functions and integral equations.
Abstract: Part I: Toeplitz Forms: Preliminaries Orthogonal polynomials. Algebraic properties Orthogonal polynomials. Limit properties The trigonometric moment problem Eigenvalues of Toeplitz forms Generalizations and analogs of Toeplitz forms Further generalizations Certain matrices and integral equations of the Toeplitz type Part II: Applications of Toeplitz Forms: Applications to analytic functions Applications to probability theory Applications to statistics Appendix: Notes and references Bibliography Index.
2,279 citations
Book•
01 Jan 1984
TL;DR: In this paper, Toeplitz forms are used for the trigonometric moment problem and other problems in probability theory, analysis, and statistics, including analytic functions and integral equations.
Abstract: Part I: Toeplitz Forms: Preliminaries Orthogonal polynomials. Algebraic properties Orthogonal polynomials. Limit properties The trigonometric moment problem Eigenvalues of Toeplitz forms Generalizations and analogs of Toeplitz forms Further generalizations Certain matrices and integral equations of the Toeplitz type Part II: Applications of Toeplitz Forms: Applications to analytic functions Applications to probability theory Applications to statistics Appendix: Notes and references Bibliography Index.
1,643 citations
"Information theoretic consideration..." refers background or methods in this paper
...where the asymptotic properties of the eigenvalues [42], [ 43 ] along with the strict bandlimitness assumption, that is: Ss(f) = O,V(fl > W, have been incorporated....
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...against the Poisson kernel [ 43 ] giving 1/r [(l - r2)/(1 + r2 - 27 cos O)] exp-2q(1--7 ‘Os @) do. Substituting q = P/( 1 r2) and assembling all the relevant sums in (D8) gives the expression for the probability distribution function...
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