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169
Spectral Efficiency in the Wideband Regime
, 2002
"... The tradeoff of spectral efficiency (b/s/Hz) versus energy perinformation bit is the key measure of channel capacity in the wideband powerlimited regime. This paper finds the fundamental bandwidthpower tradeoff of a general class of channels in the wideband regime characterized by low, but nonz ..."
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Cited by 285 (29 self)
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The tradeoff of spectral efficiency (b/s/Hz) versus energy perinformation bit is the key measure of channel capacity in the wideband powerlimited regime. This paper finds the fundamental bandwidthpower 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 finitebandwidth communication.
Capacity Scaling in MIMO Wireless Systems Under Correlated Fading
 IEEE TRANS. INFORM. THEORY
, 2002
"... Previous studies have shown that singleuser systems employingelement 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 dualantennaarray systems und ..."
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Cited by 183 (2 self)
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Previous studies have shown that singleuser systems employingelement 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 dualantennaarray systems under correlated fading via theoretical analysis and raytracing 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 1020% smaller in the presence of correlated fading. We analyze our assumption of separable transmit/receive correlations via simulations based on a raytracing 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.
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 NPhard 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 172 (20 self)
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Finding the sparsest solution to underdetermined systems of linear equations y = Φx is NPhard 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 sth stage it forms the ‘matched filter ’ Φ T rs−1, identifies all coordinates with amplitudes exceeding a speciallychosen threshold, solves a leastsquares 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 largescale problems. We use phase diagrams to compare algorithm performance. The problem of recovering a ksparse vector x0 from (y, Φ) where Φ is random n × N and y = Φx0 is represented by a point (n/N, k/n)
Mutual information and minimum meansquare error in Gaussian channels
 IEEE Trans. Inform. Theory
, 2005
"... Abstract — This paper deals with arbitrarily distributed finitepower input signals observed through an additive Gaussian noise channel. It shows a new formula that connects the inputoutput mutual information and the minimum meansquare error (MMSE) achievable by optimal estimation of the input given ..."
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Cited by 138 (23 self)
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Abstract — This paper deals with arbitrarily distributed finitepower input signals observed through an additive Gaussian noise channel. It shows a new formula that connects the inputoutput mutual information and the minimum meansquare 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 signaltonoise 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 discretetime and continuoustime noncausal MMSE estimation. This fundamental informationtheoretic result has an unexpected consequence in continuoustime 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 signaltonoise ratio is chosen uniformly distributed between 0 and SNR. Index Terms — Mutual information, Gaussian channel, minimum meansquare error (MMSE), Wiener process, optimal
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 106 (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 multipleinput multipleoutput (MIMO) channels can then be used in conjunction with scheduling and ratefeedback 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 “channelhardening ” 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
Iterative construction of optimum signature sequence sets in synchronous CDMA systems
 IEEE Trans. Inform. Theory
, 1989
"... Abstract—Recently, optimum signature sequence sets that maximize the capacity of singlecell synchronous code division multiple access (CDMA) systems have been identified. Optimum signature sequences minimize the total squared correlation (TSC); they form a set of orthogonal sequences, if the number ..."
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Cited by 69 (9 self)
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Abstract—Recently, optimum signature sequence sets that maximize the capacity of singlecell synchronous code division multiple access (CDMA) systems have been identified. Optimum signature sequences minimize the total squared correlation (TSC); they form a set of orthogonal sequences, if the number of users is less than or equal to the processing gain, and a set of Welch bound equality (WBE) sequences, otherwise. We present an algorithm where users update their transmitter signature sequences sequentially, in a distributed fashion, by using available receiver measurements. We show that each update decreases the TSC of the set, and produces better signature sequence sets progressively. We prove that the algorithm converges to a set of orthogonal signature sequences when the number of users is less than or equal to the processing gain. We observe and conjecture that the algorithm converges to a WBE set when the number of users is greater than the processing gain. At each step, the algorithm replaces one signature sequence from the set with the normalized minimum mean squared error (MMSE) receiver corresponding to that signature sequence. Since the MMSE filter can be obtained by a distributed algorithm for each user, the proposed algorithm is amenable to distributed implementation. Index Terms—Code division multiple access (CDMA), distributed interference avoidance, minimum mean squared error (MMSE), optimum signature sequence sets, Welch bound equality (WBE) sequences. I.
Large System Performance of Linear Multiuser Receivers in Multipath Fading Channels
 IEEE Trans. Inform. Theory
, 2000
"... A linear multiuser receiver for a particular user in a codedivision multipleaccess (CDMA) network gains potential benefits from knowledge of the channels of all users in the system. In fast multipath fading environments we cannot assume that the channel estimates are perfect and the inevitable cha ..."
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Cited by 68 (3 self)
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A linear multiuser receiver for a particular user in a codedivision multipleaccess (CDMA) network gains potential benefits from knowledge of the channels of all users in the system. In fast multipath fading environments we cannot assume that the channel estimates are perfect and the inevitable channel estimation errors will limit this potential gain. In this paper, we study the impact of channel estimation errors on the performance of linear multiuser receivers, as well as the channel estimation problem itself. Of particular interest are the scalability properties of the channel and data estimation algorithms: what happens to the performance as the system bandwidth and the number of users (and hence channels to estimate) grows? Our main results involve asymptotic expressions for the signaltointerference ratio of linear multiuser receivers in the limit of large processing gain, with the number of users divided by the processing gain held constant. We employ a random model for the spreading sequences and the limiting signaltointerference ratio expressions are independent of the actual signature sequences, depending only on the system loading and the channel statistics: background noise power, energy profile of resolvable multipaths, and channel coherence time. The effect of channel uncertainty on the performance of multiuser receivers is succinctly captured by the notion of effective interference.
HighSNR power offset in multiantenna communication
 IEEE Transactions on Information Theory
, 2005
"... Abstract—The analysis of the multipleantenna capacity in the high regime has hitherto focused on the high slope (or maximum multiplexing gain), which quantifies the multiplicative increase as a function of the number of antennas. This traditional characterization is unable to assess the impact of ..."
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Cited by 59 (13 self)
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Abstract—The analysis of the multipleantenna capacity in the high regime has hitherto focused on the high slope (or maximum multiplexing gain), which quantifies the multiplicative increase as a function of the number of antennas. This traditional characterization is unable to assess the impact of prominent channel features since, for a majority of channels, the slope equals the minimum of the number of transmit and receive antennas. Furthermore, a characterization based solely on the slope captures only the scaling but it has no notion of the power required for a certain capacity. This paper advocates a more refined characterization whereby, as a function of �f, the high capacity is expanded as an affine function where the impact of channel features such as antenna correlation, unfaded components, etc., resides in the zeroorder term or power offset. The power offset, for which we find insightful closedform expressions, is shown to play a chief role for levels of practical interest. Index Terms—Antenna correlation, channel capacity, coherent communication, fading channels, high analysis, multiantenna arrays, Ricean channels.
Linear Multiuser Receivers in Random Environments
 IEEE Trans. Inform. Theory
, 2000
"... We study the signaltointerference (SIR) performance of linear multiuser receivers in random environments, where signals from the users arrive in "random directions." Such random environment may arise in a DSCDMA system with random signature sequences, or in a system with antenna diversity where t ..."
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Cited by 55 (2 self)
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We study the signaltointerference (SIR) performance of linear multiuser receivers in random environments, where signals from the users arrive in "random directions." Such random environment may arise in a DSCDMA system with random signature sequences, or in a system with antenna diversity where the randomness is due to channel fading. Assuming that such random directions can be tracked by the receiver, the resulting SIR performance is a function of the directions and therefore also random. We study the asymptotic distribution of this random performance in the regime where both the number of users and the number of degrees of freedom in the system are large, but keeping their ratio fixed. Our results show that for both the decorrelator and the minimum meansquare error (MMSE) receiver, the variance of the SIR distribution decreases like 1 , and the SIR distribution is asymptotically Gaussian. We compute closedform expressions for the asymptotic means and variances for both receivers. Simulation results are presented to verify the accuracy of the asymptotic results for finitesized systems.