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Multiuser MIMO Achievable Rates with Downlink Training and Channel State Feedback
"... We consider a MIMO fading broadcast channel and compute achievable ergodic rates when channel state information is acquired at the receivers via downlink training and it is provided to the transmitter by channel state feedback. Unquantized (analog) and quantized (digital) channel state feedback sche ..."
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Cited by 111 (7 self)
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We consider a MIMO fading broadcast channel and compute achievable ergodic rates when channel state information is acquired at the receivers via downlink training and it is provided to the transmitter by channel state feedback. Unquantized (analog) and quantized (digital) channel state feedback schemes are analyzed and compared under various assumptions. Digital feedback is shown to be potentially superior when the feedback channel uses per channel state coefficient is larger than 1. Also, we show that by proper design of the digital feedback link, errors in the feedback have a minor effect even if simple uncoded modulation is used on the feedback channel. We discuss first the case of an unfaded AWGN feedback channel with orthogonal access and then the case of fading MIMO multiaccess (MIMOMAC). We show that by exploiting the MIMOMAC nature of the uplink channel, a much better scaling of the feedback channel resource with the number of base station antennas can be achieved. Finally, for the case of delayed feedback, we show that in the realistic case where the fading process has (normalized) maximum Doppler frequency shift 0 ≤ F < 1/2, a fraction 1 − 2F of the optimal multiplexing gain is achievable. The general conclusion of this work is that very significant downlink throughput is achievable with simple and efficient channel state feedback, provided that the feedback link is properly designed.
Training and Feedback Optimization for Multiuser MIMO Downlink
, 2009
"... We consider a MIMO fading broadcast channel where the fading channel coefficients are constant over timefrequency blocks that span a coherent time × a coherence bandwidth. In closedloop systems, channel state information at transmitter (CSIT) is acquired by the downlink training sent by the base s ..."
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Cited by 32 (2 self)
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We consider a MIMO fading broadcast channel where the fading channel coefficients are constant over timefrequency blocks that span a coherent time × a coherence bandwidth. In closedloop systems, channel state information at transmitter (CSIT) is acquired by the downlink training sent by the base station and an explicit feedback from each user terminal. In openloop systems, CSIT is obtained by exploiting uplink training and channel reciprocity. We use a tight closedform lower bound on the ergodic achievable rate in the presence of CSIT errors in order to optimize the overall system throughput, by taking explicitly into account the overhead due to channel estimation and channel state feedback. Based on three timefrequency block models inspired by actual systems, we provide some useful guidelines for the overall system optimization. In particular, digital (quantized) feedback is found to offer a substantial advantage over analog (unquantized) feedback.
Capacity per Unit Energy of Fading Channels with a Peak Constraint
 IEEE Trans. Inform. Theory
, 2004
"... A discretetime singleuser channel with correlated Rayleigh fading is analyzed. At low SNR, the capacity of such a channel is known to be achieved by input signals with large peak powers. Since such burstiness in the input signal may not be practically feasible, the possibility of such signals i ..."
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Cited by 31 (2 self)
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A discretetime singleuser channel with correlated Rayleigh fading is analyzed. At low SNR, the capacity of such a channel is known to be achieved by input signals with large peak powers. Since such burstiness in the input signal may not be practically feasible, the possibility of such signals is eliminated in the model by imposing a peak power constraint on every input symbol. A simple expression is given for the capacity per unit energy, in the presence of a peak constraint. The proof uses an adaptation of the simple formula of Verdu to a channel with memory. In addition to bounding the capacity of a channel with correlated fading, the result gives some insight into the relationship between the correlation in the fading process and the channel capacity.
Multiuser MIMO Downlink Made Practical: Achievable Rates with Simple Channel State Estimation and Feedback Schemes
"... We consider a MIMO fading broadcast channel and compute achievable ergodic rates when channel state information is acquired at the receivers via downlink training and explicit channel feedback is performed to provide transmitter channel state information (CSIT). Both “analog” and quantized (digital) ..."
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Cited by 22 (6 self)
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We consider a MIMO fading broadcast channel and compute achievable ergodic rates when channel state information is acquired at the receivers via downlink training and explicit channel feedback is performed to provide transmitter channel state information (CSIT). Both “analog” and quantized (digital) channel feedback are analyzed, and digital feedback is shown to be potentially superior when the feedback channel uses per channel coefficient is larger than 1. Also, we show that by proper design of the digital feedback link, errors in the feedback have a relatively minor effect even if simple uncoded modulation is used on the feedback channel. We extend our analysis to the case of fading MIMO Multiaccess Channel (MIMOMAC) in the feedback link, as well as to the case of a timevarying channel and feedback delay. We show that by exploiting the MIMOMAC nature of the uplink channel, a fully scalable system with both downlink multiplexing gain and feedback redundancy proportional to the number of base station antennas can be achieved. Furthermore, the feedback strategy is optimized by a nontrivial combination of timedivision and spacedivision multipleaccess. For the case of delayed feedback, we show that in the realistic case where the fading process has (normalized) maximum Doppler frequency shift 0 ≤ F < 1/2, a fraction 1 − 2F of the optimal multiplexing gain is achievable. The general conclusion of this work is that very significant downlink throughput is achievable with simple and efficient channel state feedback, provided that the feedback link is properly designed.
Noncoherent Capacity of Underspread Fading Channels
, 2008
"... We derive bounds on the noncoherent capacity of widesense stationary uncorrelated scattering (WSSUS) channels that are selective both in time and frequency, and are underspread, i.e., the product of the channel’s delay spread and Doppler spread is small. For input signals that are peak constrained ..."
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Cited by 20 (2 self)
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We derive bounds on the noncoherent capacity of widesense stationary uncorrelated scattering (WSSUS) channels that are selective both in time and frequency, and are underspread, i.e., the product of the channel’s delay spread and Doppler spread is small. For input signals that are peak constrained in time and frequency, we obtain upper and lower bounds on capacity that are explicit in the channel’s scattering function, are accurate for a large range of bandwidth and allow to coarsely identify the capacityoptimal bandwidth as a function of the peak power and the channel’s scattering function. We also obtain a closedform expression for the firstorder Taylor series expansion of capacity in the limit of large bandwidth, and show that our bounds are tight in the wideband regime. For input signals that are peak constrained in time only (and, hence, allowed to be peaky in frequency), we provide upper and lower bounds on the infinitebandwidth capacity and find cases when the bounds coincide and the infinitebandwidth capacity is characterized exactly. Our lower bound is closely related to a result by Viterbi (1967). The analysis in this paper is based on a discretetime discretefrequency approximation of WSSUS time and frequencyselective channels. This discretization explicitly takes into account the underspread
Interplay of spectral efficiency, power and Doppler spectrum for referencesignalassisted wireless communication
 IEEE Trans. Commun
, 2008
"... Abstract—Expressions relating spectral efficiency, power, and Doppler spectrum, are derived for Rayleighfaded wireless channels with Gaussian signal transmission. No side information on the state of the channel is assumed at the receiver. Rather, periodic reference signals are postulated in accorda ..."
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Cited by 16 (9 self)
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Abstract—Expressions relating spectral efficiency, power, and Doppler spectrum, are derived for Rayleighfaded wireless channels with Gaussian signal transmission. No side information on the state of the channel is assumed at the receiver. Rather, periodic reference signals are postulated in accordance with the functioning of most wireless systems. The analysis relies on a wellestablished lower bound, generally tight and asymptotically exact at low SNR. In contrast with most previous studies, which relied on blockfading channel models, a continuousfading model is adopted. This embeds the Doppler spectrum directly in the derived expressions, imbuing them with practical significance. Closedform relationships are obtained for the popular ClarkeJakes spectrum and informative expansions, valid for arbitrary spectra, are found for the low and highpower regimes. While the paper focuses on scalar channels, the extension to multiantenna settings is also discussed. Index Terms—Rayleigh fading, spectral efficiency, mutual information, channel estimation, Doppler spectrum. I.
Degrees of freedom in noncoherent stationary MIMO fading channels
 in Proc. Winterschool on Coding and Inform. Theory
, 2005
"... Abstract — New nonasymptotic upper bounds on the capacity of noncoherent multipleinput multipleoutput (MIMO) Gaussian fading channels with memory are proposed. These bounds are used to derive upper bounds on the fading number of regular Gaussian fading channels and on the prelog of nonregular ..."
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Cited by 15 (7 self)
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Abstract — New nonasymptotic upper bounds on the capacity of noncoherent multipleinput multipleoutput (MIMO) Gaussian fading channels with memory are proposed. These bounds are used to derive upper bounds on the fading number of regular Gaussian fading channels and on the prelog of nonregular ones. The resulting bounds are tight in the multipleinput singleoutput (MISO) spatially IID Gaussian case whence they yield the exact fading number and prelog. A new approach is proposed for the derivation of lower bounds on the fading number of MIMO channels. This approach is applied to derive a lower bound on the fading number of spatially IID zeromean Gaussian fading channels with memory. The new upper and lower bounds on the fading number demonstrate that when the number of receive antennas does not exceed the number of transmit antennas, the fading number of zeromean spatially IID slowly varying Gaussian MIMO channels is proportional to the number of degrees of freedom, i.e., to the minimum of the number of transmit and receive antennas. We conjecture that the same is true also when the number of receive antennas exceeds the number of transmit antennas. The singleinput multipleoutput case that was recently solved by Lapidoth & Moser supports this conjecture. I.
A channel that heats up
 in Proceedings of the 2007 IEEE Symposium on Information Theory
, 2007
"... Abstract — Motivated by onchip communication, a channel model is proposed where the variance of the additive noise depends on the weighted sum of the past channel input powers. For this channel, an expression for the capacity per unit cost is derived, and it is shown that the expression holds also ..."
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Cited by 15 (5 self)
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Abstract — Motivated by onchip communication, a channel model is proposed where the variance of the additive noise depends on the weighted sum of the past channel input powers. For this channel, an expression for the capacity per unit cost is derived, and it is shown that the expression holds also in the presence of feedback. I.
The fading number of multipleinput multipleoutput fading channels with memory
 in Proc. IEEE Int. Symposium on Inf. Theory
, 2007
"... Abstract—The fading number of a general (not necessarily Gaussian) regular multipleinput multipleoutput (MIMO) fading channel with arbitrary temporal and spatial memory is derived. The channel is assumed to be noncoherent, i.e., neither receiver nor transmitter have knowledge about the channel st ..."
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Cited by 13 (3 self)
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Abstract—The fading number of a general (not necessarily Gaussian) regular multipleinput multipleoutput (MIMO) fading channel with arbitrary temporal and spatial memory is derived. The channel is assumed to be noncoherent, i.e., neither receiver nor transmitter have knowledge about the channel state, but they only know the probability law of the fading process. The fading number is the second term in the asymptotic expansion of channel capacity when the signaltonoise ratio (SNR) tends to infinity. It is shown that the fading number can be achieved by an input that is the product of two independent processes: a stationary and circularly symmetric direction (or unit) vector process whose distribution needs to be chosen such that it maximizes the fading number, and a nonnegative magnitude process that is independent and identically distributed (IID) and that escapes to infinity. Additionally, in the more general context of an arbitrary stationary channel model satisfying some weak conditions on the channel law, it is shown that the optimal input distribution is stationary apart from some edge effects. I.