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320
Towards an Information Theory of Large Networks: An Achievable Rate Region
 IEEE Trans. Inform. Theory
, 2003
"... Abstract — We study communication networks of arbitrary size and topology and communicating over a general vector discrete memoryless channel. We propose an informationtheoretic constructive scheme for obtaining an achievable rate region in such networks. Many wellknown capacitydefining achievabl ..."
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Cited by 161 (9 self)
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Abstract — We study communication networks of arbitrary size and topology and communicating over a general vector discrete memoryless channel. We propose an informationtheoretic constructive scheme for obtaining an achievable rate region in such networks. Many wellknown capacitydefining achievable rate regions can be derived as special cases of the proposed scheme. A few such examples are the physically degraded and reverselydegraded relay channels, the Gaussian multipleaccess channel, and the Gaussian broadcast channel. The proposed scheme also leads to inner bounds for the multicast and allcast capacities. Applying the proposed scheme to a specific wireless network of nodes located in a region of unit area, we show that a transport capacity of ¡£ ¢ bitmeters/sec is feasible in a certain family of networks, as compared to the best possible transport capacity ¡£¢§ ¦ ¨ ¤ of bitmeters/sec in [16] where the receiver capabilities were limited. Even though the improvement is shown for a specific class of networks, a clear implication is that designing and employing more sophisticated multiuser coding schemes can provide sizable gains in at least some large wireless networks. Index Terms — Discrete memoryless channels, Gaussian channels, multiuser communications, network information theory,
Space–time transmit precoding with imperfect channel feedback
 IEEE Trans. Inform. Theory
, 2001
"... Abstract—The use of channel feedback from receiver to transmitter is standard in wireline communications. While knowledge of the channel at the transmitter would produce similar benefits for wireless communications as well, the generation of reliable channel feedback is complicated by the rapid time ..."
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Cited by 144 (6 self)
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Abstract—The use of channel feedback from receiver to transmitter is standard in wireline communications. While knowledge of the channel at the transmitter would produce similar benefits for wireless communications as well, the generation of reliable channel feedback is complicated by the rapid time variations of the channel for mobile applications. The purpose of this correspondence is to provide an information–theoretic perspective on optimum transmitter strategies, and the gains obtained by employing them, for systems with transmit antenna arrays and imperfect channel feedback. The spatial channel, given the feedback, is modeled as a complex Gaussian random vector. Two extreme cases are considered: mean feedback, in which the channel side information resides in the mean of the distribution, with the covariance modeled as white, and covariance feedback, in which the channel is assumed to be varying too rapidly to track its mean, so that the mean is set to zero, and the information regarding the relative geometry of the propagation paths is captured by a nonwhite covariance matrix. In both cases, the optimum transmission strategies, maximizing the information transfer rate, are determined as a solution to simple numerical optimization problems. For both feedback models, our numerical results indicate that, when there is a moderate disparity between the strengths of different paths from the transmitter to the receiver, it is nearly optimal to employ the simple beamforming strategy of transmitting all available power in the direction which the feedback indicates is the strongest. Index Terms—Antenna arrays, fading channels, feedback communication, space–time codes, spatial diversity, transmit beamforming, wireless communication. I.
Capacity and Optimal Resource Allocation for Fading Broadcast Channels: Part I: Ergodic Capacity
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Adaptive Coded Modulation for Fading Channels
 IEEE TRANS. COMMUN
, 1998
"... We apply coset codes to adaptive modulation in fading channels. Adaptive modulation is a powerful technique to improve the energy efficiency and increase the data rate over a fading channel. Coset codes are a natural choice to use with adaptive modulation since the channel coding and modulation desi ..."
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Cited by 130 (10 self)
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We apply coset codes to adaptive modulation in fading channels. Adaptive modulation is a powerful technique to improve the energy efficiency and increase the data rate over a fading channel. Coset codes are a natural choice to use with adaptive modulation since the channel coding and modulation designs are separable. Therefore, trellis and lattice codes designed for additive white Gaussian noise (AWGN) channels can be superimposed on adaptive modulation for fading channels, with the same approximate coding gains. We first describe the methodology for combining coset codes with a general class of adaptive modulation techniques. We then apply this methodology to a spectrally efficient adaptive Mary quadrature amplitude modulation (MQAM) to obtain trelliscoded adaptive MQAM. We present analytical and simulation results for this design which show an effective coding gain of 3 dB relative to uncoded adaptive MQAM for a simple fourstate trellis code, and an effective 3.6dB coding gain for an eightstate trellis code. More complex trellis codes are shown to achieve higher gains. We also compare the performance of trelliscoded adaptive MQAM to that of coded modulation with builtin time diversity and fixedrate modulation. The adaptive method exhibits a power savings of up to 20 dB.
Degrees of freedom in adaptive modulation: a unified view
 IEEE Trans. Commun
, 2001
"... Abstract—We examine adaptive modulation schemes for flatfading channels where the data rate, transmit power, and instantaneous BER are varied to maximize spectral efficiency, subject to an average power and BER constraint. Both continuousrate and discreterate adaptation are considered, as well as ..."
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Cited by 124 (4 self)
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Abstract—We examine adaptive modulation schemes for flatfading channels where the data rate, transmit power, and instantaneous BER are varied to maximize spectral efficiency, subject to an average power and BER constraint. Both continuousrate and discreterate adaptation are considered, as well as average and instantaneous BER constraints. We find the general form of power, BER, and data rate adaptation that maximizes spectral efficiency for a large class of modulation techniques and fading distributions. The optimal adaptation of these parameters is to increase the power and data rate and decrease the BER as the channel quality improves. Surprisingly, little spectral efficiency is lost when the power or rate is constrained to be constant. Hence, the spectral efficiency of adaptive modulation is relatively insensitive to which degrees of freedom are adapted. Index Terms—Adaptive modulation, communication systems, fading channels, spectral efficiency. I.
On the capacity of large Gaussian relay networks
 IEEE Trans. Inf. Theory
, 2005
"... Abstract—The capacity of a particular large Gaussian relay network is determined in the limit as the number of relays tends to infinity. Upper bounds are derived from cutset arguments, and lower bounds follow from an argument involving uncoded transmission. It is shown that in cases of interest, up ..."
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Cited by 108 (6 self)
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Abstract—The capacity of a particular large Gaussian relay network is determined in the limit as the number of relays tends to infinity. Upper bounds are derived from cutset arguments, and lower bounds follow from an argument involving uncoded transmission. It is shown that in cases of interest, upper and lower bounds coincide in the limit as the number of relays tends to infinity. Hence, this paper provides a new example where a simple cutset upper bound is achievable, and one more example where uncoded transmission achieves optimal performance. The findings are illustrated by geometric interpretations. The techniques developed in this paper are then applied to a sensor network situation. This is a network joint source–channel coding problem, and it is well known that the source–channel separation theorem does not extend to this case. The present paper extends this insight by providing an example where separating source from channel coding does not only lead to suboptimal performance—it leads to an exponential penalty in performance scaling behavior (as a function of the number of nodes). Finally, the techniques developed in this paper are extended to include certain models of ad hoc wireless networks, where a capacity scaling law can be established: When all nodes act purely as relays for a single source–destination pair, capacity grows with the logarithm of the number of nodes. Index Terms—Capacity, CEO problem, joint source–channel coding, network, relay, sensor network, separation theorem, uncoded transmission. I.
Capacity of Rayleigh Fading Channels under Different Adaptive Transmission and . . .
 IEEE TRANSACTIONS ON VEHICULAR TECHNOLOGY
, 1999
"... We study the Shannon capacity of adaptive transmission techniques in conjunction with diversity combining. This capacity provides an upper bound on spectral efficiency using these techniques. We obtain closedform solutions for the Rayleigh fading channel capacity under three adaptive policies: opti ..."
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Cited by 86 (7 self)
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We study the Shannon capacity of adaptive transmission techniques in conjunction with diversity combining. This capacity provides an upper bound on spectral efficiency using these techniques. We obtain closedform solutions for the Rayleigh fading channel capacity under three adaptive policies: optimal power and rate adaptation, constant power with optimal rate adaptation, and channel inversion with fixed rate. Optimal power and rate adaptation yields a small increase in capacity over just rate adaptation, and this increase diminishes as the average received carriertonoise ratio (CNR) or the number of diversity branches increases. Channel inversion suffers the largest capacity penalty relative to the optimal technique, however, the penalty diminishes with increased diversity. Although diversity yields large capacity gains for all the techniques, the gain is most pronounced with channel inversion. For example, the capacity using channel inversion with twobranch diversity exceeds that of a singlebranch system using optimal rate and power adaptation. Since channel inversion is the least complex scheme to implement, there is a tradeoff between complexity and capacity for the various adaptation methods and diversitycombining techniques.
Transmitter Optimization and Optimality of Beamforming for Multiple Antenna Systems with Imperfect Feedback
"... We solve the transmitter optimization problem and determine a necessary and sucient condition under which beamforming achieves Shannon capacity in a narrowband point to point communication system employing multiple transmit and receive antennas. We assume perfect channel state information at the rec ..."
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Cited by 80 (5 self)
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We solve the transmitter optimization problem and determine a necessary and sucient condition under which beamforming achieves Shannon capacity in a narrowband point to point communication system employing multiple transmit and receive antennas. We assume perfect channel state information at the receiver (CSIR) and imperfect channel state feedback from the receiver to the transmitter. We consider the cases of mean and covariance feedback. The channel is modeled at the transmitter as a matrix of complex jointly Gaussian random variables with either a zero mean and a known covariance matrix (covariance feedback), or a nonzero mean and a white covariance matrix (mean feedback). For both cases we develop a necessary and sucient condition for when the Shannon capacity is achieved through beamforming, i.e. the channel can be treated like a scalar channel and onedimensional codes can be used to achieve capacity. We also provide a waterpouring interpretation of our results and nd that less channel uncertainty not only increases the system capacity but may also allow this higher capacity to be achieved with scalar codes which involves signi cantly less complexity in practice than vector coding.
Adaptive Modulation over Nakagami Fading Channels
, 1998
"... We first study the capacity of Nakagami multipath fading (NMF) channels with an average power constraint for three power and rate adaptation policies. We obtain closedform solutions for NMF channel capacity for each power and rate adaptation strategy. Results show that rate adaptation is the key to ..."
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Cited by 75 (5 self)
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We first study the capacity of Nakagami multipath fading (NMF) channels with an average power constraint for three power and rate adaptation policies. We obtain closedform solutions for NMF channel capacity for each power and rate adaptation strategy. Results show that rate adaptation is the key to increasing link spectral efficiency. We analyze therefore the performance of constantpower variablerate MQAM schemes over NMF channels. We obtain closedform expressions for the outage probability, spectral efficiency and average biterrorrate (BER) assuming perfect channel estimation and negligible time delay. We also analyze the impact of time delay on the BER of adaptive MQAM. Keywords Link Spectral Efficiency, Adaptive Modulation Techniques, and Nakagami Fading. I. Introduction The radio spectrum available for wireless services is extremely scarce, while demand for these services is growing at a rapid pace [1]. Hence spectral efficiency is of primary concern in the design of fut...