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.

Cooperative diversity in wireless networks: Efficient protocols and outage behavior

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.

/pdf/capacity-of-multi-antenna-gaussian-channels-3axdfdd5ns.pdf

Capacity of Multi‐antenna Gaussian Channels

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.

http://dns2.asia.edu.tw/~ysho/YSHO-English/2000%20Engineering/PDF/IEE%20Tra%20Com51,%201927.pdf

User cooperation diversity. Part I. System description

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.

/pdf/diversity-and-multiplexing-a-fundamental-tradeoff-in-4fmf0wuqet.pdf

Diversity and multiplexing: a fundamental tradeoff in multiple-antenna channels

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.

/pdf/distributed-space-time-coded-protocols-for-exploiting-45tscq31v3.pdf

Distributed space-time-coded protocols for exploiting cooperative diversity in wireless networks

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. >

Information theoretic considerations for cellular mobile radio

This paper treats the problem of communicating a memoryless unit-variance Gaussian source to three receivers. Two channels are available, each with a separate receiver. A third receiver has the outputs of both channels available. We obtain an expression for the simultaneously achievable distortions (mean-squared error). This problem applies to the following situation: Assume that high-quality reproduction of a source is desired at a single receiver which is connected to the source over a pair of links operating in parallel. Further assume that the links are unreliable in that either may fail, and that the source encoder is unaware of the failures. One can then ask how “robust” a system designed for this situation can be. That is, what are the limits on the fidelity achievable when both links are functioning if graceful degradation is required during the failure of either link? An inverse relation between performance in the two modes is obtained in the sense that, as performance in the presence of both links approaches its theoretical optimum, average distortion during failures becomes large. Conversely, if near-ideal performance during link failures is desired, then the distortion achieved when both links operate is far from its optimum value.

On a source-coding problem with two channels and three receivers

Consider the following situation. K data bits are to be encoded into N> K bits and transmitted over a noiseless channel. An intruder can observe a subset of his choice of size μ < N. The encoder is to be designed to maximize the intruder's uncertainty about the data given his μ intercepted channel bits, subject to the condition that the intended receiver can recover the K data bits perfectly from the N channel bits. The optimal trade-offs among the parameters K, N, and μ and the intruder's uncertainty H (H is the "conditional entropy" of the data given the μ intercepted channel bits) were found. In particular, it was shown that for μ = N − K, a system exists with H ≈ K − l. Thus, for example, when N = 2K and μ = K, it is possible to encode the K data bits into 2K channel bits, so that by looking at any K channel bits, the intruder obtains no more than one bit of the data.

Wire-tap channel II

Since the appearance of [10] by Gaarder and Wolf, it has been well known that feedback can enlarge the capacity region of the multiple access channel. In this paper a deterministic feedback code is presented for the two-user Gaussian multiple access channel, which is shown to allow reliable communication at all points inside a region larger than any previously obtained. An outer bound is given which is shown to coincide with the achievable region, thus yielding the capacity region of this channel exactly.

The capacity of the white Gaussian multiple access channel with feedback

Consider the following situation. K data hits are to be encoded into N > K bits and transmitted over a noiseless channel. An intruder can observe a subset of his choice of size µ < N. The encoder is to be designed to maximize the intruder's uncertainty about the data given his N intercepted channel bits, subject to the condition that the intended receiver can recover the K data bits perfectly from the N channel bits. The optimal tradoffs between the parameters K, N, µ. and the intruder's uncertainty H (H is the "conditional entropy" of the data given the µ. intercepted channel bits) were found. In particular, it was shown that for µ = N - K, a system exists with H ? K - 1. Thus, for example, when N = 2K and µ = K, it is possible to encode the K data bits into 2K channel bits, so that by looking at any K channel bits, the intruder obtains essentially no information about the data.

Lawrence Howard Ozarow

Papers

Information theoretic considerations for cellular mobile radio

On a source-coding problem with two channels and three receivers

Wire-tap channel II

The capacity of the white Gaussian multiple access channel with feedback

Wire-tap channel II