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313
Spectral Efficiency in the Wideband Regime
, 2002
"... The tradeoff of spectral efficiency (b/s/Hz) versus energy -per-information bit is the key measure of channel capacity in the wideband power-limited regime. This paper finds the fundamental bandwidth--power tradeoff of a general class of channels in the wideband regime characterized by low, but nonz ..."
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Cited by 393 (29 self)
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The tradeoff of spectral efficiency (b/s/Hz) versus energy -per-information bit is the key measure of channel capacity in the wideband power-limited regime. This paper finds the fundamental bandwidth--power tradeoff of a general class of channels in the wideband regime characterized by low, but nonzero, spectral efficiency and energy per bit close to the minimum value required for reliable communication. A new criterion for optimality of signaling in the wideband regime is proposed, which, in contrast to the traditional criterion, is meaningful for finite-bandwidth communication.
Mutual information and minimum mean-square error in Gaussian channels
- IEEE TRANS. INFORM. THEORY
, 2005
"... This paper deals with arbitrarily distributed finite-power input signals observed through an additive Gaussian noise channel. It shows a new formula that connects the input-output mutual information and the minimum mean-square error (MMSE) achievable by optimal estimation of the input given the out ..."
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Cited by 288 (34 self)
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This paper deals with arbitrarily distributed finite-power input signals observed through an additive Gaussian noise channel. It shows a new formula that connects the input-output mutual information and the minimum mean-square error (MMSE) achievable by optimal estimation of the input given the output. That is, the derivative of the mutual information (nats) with respect to the signal-to-noise ratio (SNR) is equal to half the MMSE, regardless of the input statistics. This relationship holds for both scalar and vector signals, as well as for discrete-time and continuous-time noncausal MMSE estimation. This fundamental information-theoretic result has an unexpected consequence in continuous-time nonlinear estimation: For any input signal with finite power, the causal filtering MMSE achieved at SNR is equal to the average value of the noncausal smoothing MMSE achieved with a channel whose signal-to-noise ratio is chosen uniformly distributed between 0 and SNR.
Sparse solution of underdetermined linear equations by stagewise orthogonal matching pursuit
, 2006
"... Finding the sparsest solution to underdetermined systems of linear equations y = Φx is NP-hard in general. We show here that for systems with ‘typical’/‘random ’ Φ, a good approximation to the sparsest solution is obtained by applying a fixed number of standard operations from linear algebra. Our pr ..."
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Cited by 274 (22 self)
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Finding the sparsest solution to underdetermined systems of linear equations y = Φx is NP-hard in general. We show here that for systems with ‘typical’/‘random ’ Φ, a good approximation to the sparsest solution is obtained by applying a fixed number of standard operations from linear algebra. Our proposal, Stagewise Orthogonal Matching Pursuit (StOMP), successively transforms the signal into a negligible residual. Starting with initial residual r0 = y, at the s-th stage it forms the ‘matched filter ’ Φ T rs−1, identifies all coordinates with amplitudes exceeding a specially-chosen threshold, solves a least-squares problem using the selected coordinates, and subtracts the leastsquares fit, producing a new residual. After a fixed number of stages (e.g. 10), it stops. In contrast to Orthogonal Matching Pursuit (OMP), many coefficients can enter the model at each stage in StOMP while only one enters per stage in OMP; and StOMP takes a fixed number of stages (e.g. 10), while OMP can take many (e.g. n). StOMP runs much faster than competing proposals for sparse solutions, such as ℓ1 minimization and OMP, and so is attractive for solving large-scale problems. We use phase diagrams to compare algorithm performance. The problem of recovering a k-sparse vector x0 from (y, Φ) where Φ is random n × N and y = Φx0 is represented by a point (n/N, k/n)
Capacity Scaling in MIMO Wireless Systems Under Correlated Fading
- IEEE TRANS. INFORM. THEORY
, 2002
"... Previous studies have shown that single-user systems employing-element antenna arrays at both the transmitter and the receiver can achieve a capacity proportional to , assuming independent Rayleigh fading between antenna pairs. In this paper, we explore the capacity of dual-antenna-array systems und ..."
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Cited by 262 (2 self)
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Previous studies have shown that single-user systems employing-element antenna arrays at both the transmitter and the receiver can achieve a capacity proportional to , assuming independent Rayleigh fading between antenna pairs. In this paper, we explore the capacity of dual-antenna-array systems under correlated fading via theoretical analysis and ray-tracing simulations. We derive and compare expressions for the asymptotic growth rate of capacity with antennas for both independent and correlated fading cases; the latter is derived under some assumptions about the scaling of the fading correlation structure. In both cases, the theoretic capacity growth is linear in but the growth rate is 10--20% smaller in the presence of correlated fading. We analyze our assumption of separable transmit/receive correlations via simulations based on a ray-tracing propagation model. Results show that empirical capacities converge to the limit capacity predicted from our asymptotic theory even at moderate n=16. We present results for both the cases when the transmitter does and does not know the channel realization.
Scaling up MIMO: Opportunities and challenges with very large arrays
, 2011
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Multipleantenna channel hardening and its implications for rate feedback and scheduling
- IEEE Transactions on Information Theory
, 2004
"... Wireless data traffic is expected to grow over the next few years and the technologies that will provide data services are still being debated. One possibility is to use multiple antennas at basestations and terminals to get very high spectral efficiencies in rich scattering environments. Such multi ..."
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Cited by 159 (2 self)
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Wireless data traffic is expected to grow over the next few years and the technologies that will provide data services are still being debated. One possibility is to use multiple antennas at basestations and terminals to get very high spectral efficiencies in rich scattering environments. Such multiple-input multiple-output (MIMO) channels can then be used in conjunction with scheduling and rate-feedback algorithms to further increase channel throughput. This paper provides an analysis of the expected gains due to scheduling and bits needed for rate feedback. Our analysis requires an accurate approximation of the distribution of the MIMO channel mutual information. Because the exact distribution of the mutual information in a Rayleigh fading environment is difficult to analyze, we prove a central limit theorem for MIMO channels with a large number of antennas. While the growth in average mutual information (capacity) of a MIMO channel with the number of antennas is well understood, it turns out that the variance of the mutual information can grow very slowly or even shrink as the number of antennas grows. We discuss implications of this “channel-hardening ” result for data and voice services, scheduling and rate feedback. We also briefly discuss the implications when shadow fading effects are included. Index Terms—Wireless communications, transmit diversity, receive diversity, fading channels 1
Zigzag decoding: Combating hidden terminals in wireless networks
, 2008
"... This paper presents ZigZag, an 802.11 receiver design that combats hidden terminals. ZigZag’s core contribution is a new form of interference cancellation that exploits asynchrony across successive collisions. Specifically, 802.11 retransmissions, in the case of hidden terminals, cause successive co ..."
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Cited by 158 (10 self)
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This paper presents ZigZag, an 802.11 receiver design that combats hidden terminals. ZigZag’s core contribution is a new form of interference cancellation that exploits asynchrony across successive collisions. Specifically, 802.11 retransmissions, in the case of hidden terminals, cause successive collisions. These collisions have different interference-free stretches at their start, which ZigZag exploits to bootstrap its decoding. ZigZag makes no changes to the 802.11 MAC and introduces no overhead when there are no collisions. But, when senders collide, ZigZag attains the same throughput as if the colliding packets were a priori scheduled in separate time slots. We build a prototype of ZigZag in GNU Radio. In a testbed of 14 USRP nodes, ZigZag reduces the average packet loss rate at hidden terminals from 72.6% to about 0.7%.
Generalized Approximate Message Passing for Estimation with Random Linear Mixing
, 2012
"... We consider the estimation of an i.i.d. random vector observed through a linear transform followed by a component-wise, probabilistic (possibly nonlinear) measurement channel. A novel algorithm, called generalized approximate message passing (GAMP), is presented that provides computationally effici ..."
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Cited by 123 (18 self)
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We consider the estimation of an i.i.d. random vector observed through a linear transform followed by a component-wise, probabilistic (possibly nonlinear) measurement channel. A novel algorithm, called generalized approximate message passing (GAMP), is presented that provides computationally efficient ap-proximate implementations of max-sum and sum-problem loopy belief propagation for such problems. The algorithm extends earlier approximate message passing methods to incorporate arbitrary distributions on both the input and output of the transform and can be applied to a wide range of problems in nonlinear compressed sensing and learning. Extending an analysis by Bayati and Montanari, we argue that the asymptotic componentwise behavior of the GAMP method under large, i.i.d. Gaussian transforms is described by a simple set of state evolution (SE) equations. From the SE equations, one can exactly predict the asymptotic value of virtually any componentwise performance metric including mean-squared error or detection accuracy. Moreover, the analysis is valid for arbitrary input and output distributions, even when the corresponding optimization problems are non-convex. The results match predictions by Guo and Wang for relaxed belief propagation on large sparse matrices and, in certain instances, also agree with the optimal performance predicted by the replica method. The GAMP methodology thus provides a computationally efficient methodology, applicable to a large class of non-Gaussian estimation problems with precise asymptotic performance guarantees.
