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Compressed Channel Sensing: A New Approach to Estimating Sparse Multipath Channels
"... High-rate data communication over a multipath wireless channel often requires that the channel response be known at the receiver. Training-based methods, which probe the channel in time, frequency, and space with known signals and reconstruct the channel response from the output signals, are most co ..."
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Cited by 87 (9 self)
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High-rate data communication over a multipath wireless channel often requires that the channel response be known at the receiver. Training-based methods, which probe the channel in time, frequency, and space with known signals and reconstruct the channel response from the output signals, are most commonly used to accomplish this task. Traditional training-based channel estimation methods, typically comprising of linear reconstruction techniques, are known to be optimal for rich multipath channels. However, physical arguments and growing experimental evidence suggest that many wireless channels encountered in practice tend to exhibit a sparse multipath structure that gets pronounced as the signal space dimension gets large (e.g., due to large bandwidth or large number of antennas). In this paper, we formalize the notion of multipath sparsity and present a new approach to estimating sparse (or effectively sparse) multipath channels that is based on some of the recent advances in the theory of compressed sensing. In particular, it is shown in the paper that the proposed approach, which is termed as compressed channel sensing, can potentially achieve a target reconstruction error using far less energy and, in many instances, latency and bandwidth than that dictated by the traditional least-squares-based training methods.
Space-Time Wireless Systems: From Array Processing to MIMO Communications,
, 2006
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Learning sparse doublyselective channels
- in Proc. of Allerton Conf. on Communications, Control and Computing
, 2008
"... Abstract—Coherent data communication over doubly-selective channels requires that the channel response be known at the receiver. Training-based schemes, which involve probing of the channel with known signaling waveforms and processing of the corresponding channel output to estimate the channel para ..."
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Cited by 23 (8 self)
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Abstract—Coherent data communication over doubly-selective channels requires that the channel response be known at the receiver. Training-based schemes, which involve probing of the channel with known signaling waveforms and processing of the corresponding channel output to estimate the channel parameters, are commonly employed to learn the channel response in practice. Conventional training-based methods, often comprising of linear least squares channel estimators, are known to be optimal under the assumption of rich multipath channels. Numerous measurement campaigns have shown, however, that physical multipath channels tend to exhibit a sparse structure at high signal space dimension (time-bandwidth product), and can be characterized with significantly fewer parameters compared to the maximum number dictated by the delay-Doppler spread of the channel. In this paper, it is established that traditional training-based channel learning techniques are ill-suited to fully exploiting the inherent low-dimensionality of sparse channels. In contrast, key ideas from the emerging theory of compressed sensing are leveraged to propose sparse channel learning methods for both single-carrier and multicarrier probing waveforms that employ reconstruction algorithms based on convex/linear programming. In particular, it is shown that the performance of the proposed schemes come within a logarithmic factor of that of an ideal channel estimator, leading to significant reductions in the training energy and the loss in spectral efficiency associated with conventional training-based methods. I.
MSE-optimal training for linear timevarying channels
- in Proc. IEEE Internat. Conf. on Acoustics, Speech, and Signal Processing
, 2005
"... We consider pilot-aided transmission (PAT) for a general class of systems encompassing linear modulation and a linear time-varying channel. For these systems, and given a pilot energy constraint, we derive a tight lower bound on the mean squared error (MSE) of pilot-aided channel estimates as well a ..."
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Cited by 22 (6 self)
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We consider pilot-aided transmission (PAT) for a general class of systems encompassing linear modulation and a linear time-varying channel. For these systems, and given a pilot energy constraint, we derive a tight lower bound on the mean squared error (MSE) of pilot-aided channel estimates as well as necessary and sufficient conditions on PAT to attain this bound. We then apply these results to the design of single-antenna PAT for doubly selective channels and arrive at novel MSE-optimal PAT schemes. In this application, we assume a block-based cyclic-prefix PAT and a basis expansion model for the channel. 1.
Efficient Multicarrier Communication for Highly Spread Underwater Acoustic Channels
"... Abstract—In this paper we propose a novel method for communication over underwater acoustic channels that exhibit simultaneously large delay spread and Doppler spread, such as those found in the surf zone. In particular, we propose a coded pulse-shaped multicarrier scheme that converts the doubly di ..."
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Cited by 21 (3 self)
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Abstract—In this paper we propose a novel method for communication over underwater acoustic channels that exhibit simultaneously large delay spread and Doppler spread, such as those found in the surf zone. In particular, we propose a coded pulse-shaped multicarrier scheme that converts the doubly dispersive channel into an inter-carrier interference (ICI) channel with small ICI spread. The resulting ICI is mitigated using a soft noncoherent equalizer that leverages sparsity in the delay-power profile to generate near-optimal bit estimates with low complexity. The noncoherent equalizer uses a delay-power-profile estimate (rather than a channel estimate) which is obtained from pilots. Numerical simulations with surf-zone-like channels demonstrate performance close to genie-aided bounds. Index Terms—Underwater acoustic modems, underwater acoustic channels, multicarrier modulation, noncoherent decoding, turbo equalization, joint estimation and detection, sparse channels. I.
Improved Bayesian MIMO Channel Tracking for Wireless Communications: Incorporating Dynamical Channel Model, submitted for publication
"... Abstract — This paper investigates the improved decoder per-formance offered by incorporating dynamic linear modelling techniques when applied to particle filters for use in tracking the MIMO wireless channel. Conventional Bayesian-based receivers that perform channel tracking necessarily require a ..."
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Cited by 12 (2 self)
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Abstract — This paper investigates the improved decoder per-formance offered by incorporating dynamic linear modelling techniques when applied to particle filters for use in tracking the MIMO wireless channel. Conventional Bayesian-based receivers that perform channel tracking necessarily require a wireless channel model, typified by the use of a low order auto-regressive (AR) model. Normally, the model parameters are static in nature and are estimated a priori of any transmission; thus if the channel conditions change, a model mismatch occurs and system performance is degraded. Our method allows for time-varying channel statistics by modelling the channel fading rate as a Markov random walk. This new procedure allows the channel model to assume a time-varying behavior. As will be shown through simulations, the incorporation of dynamic modelling of time-dispersive channels not only offers superior performance, but at high SNR eliminates the error-rate floor commonly seen in systems using the static AR models. Index Terms — MIMO, wireless channel tracking, dynamic linear modelling, particle filtering.
On the Capacity and Energy Efficiency of Training-Based Transmissions over Fading Channels
"... 1 In this paper, the capacity and energy efficiency of training-based communication schemes employed for transmission over a-priori unknown Rayleigh block fading channels are studied. In these schemes, periodically transmitted training symbols are used at the receiver to obtain the minimum mean-squa ..."
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Cited by 11 (3 self)
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1 In this paper, the capacity and energy efficiency of training-based communication schemes employed for transmission over a-priori unknown Rayleigh block fading channels are studied. In these schemes, periodically transmitted training symbols are used at the receiver to obtain the minimum mean-square-error (MMSE) estimate of the channel fading coefficients. Initially, the case in which the product of the estimate error and transmitted signal is assumed to be Gaussian noise is considered. In this case, it is shown that bit energy requirements grow without bound as the signal-to-noise ratio (SNR) goes to zero, and the minimum bit energy is achieved at a nonzero SNR value below which one should not operate. The effect of the block length on both the minimum bit energy and the SNR value at which the minimum is achieved is investigated. Energy efficiency analysis is also carried out when peak power constraints are imposed on pilot signals. Flash training and transmission schemes are analyzed and shown to improve the energy efficiency in the low-SNR regime. In the second part of the paper, the capacity and energy efficiency of training-based schemes are investigated when the channel input is subject to peak power constraints. The capacity-achieving input structure is characterized and the magnitude distribution of the optimal input is shown to be discrete with a finite number of mass points. The capacity, bit energy requirements, and optimal resource allocation strategies are obtained through numerical analysis. The bit energy is again shown to grow without bound as SNR decreases to zero due to the presence of peakedness constraints. Capacity and energy-per-bit are also analyzed under the assumptions that the transmitter interleaves the data symbols before transmission over the channel, and per-symbol peak power constraints are imposed. The improvements in energy efficiency when on-off keying with fixed peak power and vanishing duty cycle is employed are studied. Comparisons of the performances of training-based and noncoherent transmission schemes are provided.
On the spectral efficiency of noncoherent doubly selective channels
- In Proc. Allerton Conf. Commun., Control, and Computing
, 2006
"... In this paper, we consider noncoherent single-antenna communication over doubly selective block-fading channels that obey a complex-exponential basis expansion model. In our noncoherent setup, neither the transmitter nor the receiver know the channel fading coefficients, though both know the channel ..."
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Cited by 11 (6 self)
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In this paper, we consider noncoherent single-antenna communication over doubly selective block-fading channels that obey a complex-exponential basis expansion model. In our noncoherent setup, neither the transmitter nor the receiver know the channel fading coefficients, though both know the channel statistics. First, we show that, when the inputs are chosen from continuous distributions, the achievable spectral efficiency (i.e., the pre-log factor in the channel capacity expression) equals max(0, 1− NdelayNDopp/N), where N, Ndelay, and NDopp denote the channel’s discrete block-fading interval, discrete delay spread, and discrete Doppler spread, respectively. Next, we study pilot-aided transmission (PAT) over this channel. In the case of strictly doubly selective fading (i.e., NDopp> 1 and Ndelay> 1), we establish that affine minimum mean-squared error (MMSE) PAT schemes are spectrally inefficient, but we provide guidelines for the design of spectrally efficient affine PAT schemes and give an example of one such scheme. Index Terms — Noncoherent channels, doubly selective channels, doubly dispersive channels, non-coherent communication, spectral efficiency, channel capacity, achievable rates, pilot symbols, training symbols, channel estimation. I.
Efficient communication over highly spread underwater acoustic channels
- in Proc. ACM International Workshop on Underwater Networks (WUWNet
, 2007
"... In this paper we propose a novel method for communication over underwater acoustic channels for which the product of delay-spread and Doppler-spread is large, such as those pertaining to the surf zone. In particular, we propose the use of pulse-shaped multicarrier modulation to convert the doubly di ..."
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Cited by 10 (3 self)
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In this paper we propose a novel method for communication over underwater acoustic channels for which the product of delay-spread and Doppler-spread is large, such as those pertaining to the surf zone. In particular, we propose the use of pulse-shaped multicarrier modulation to convert the doubly dispersive channel into an inter-carrier interference (ICI) channel with small ICI spread. We then propose a novel joint ICI-estimation/data-detection strategy which performs near optimally yet at low complexity, due to the use of an efficient tree search algorithm and the ability to leverage sparseness in the delay-power profile. The delay-power profile, which itself varies in time, can be readily tracked via pilots. Numerical simulations show that our technique gives performance close to genie-aided bounds over highly spread channels.
An energy efficiency perspective on training for fading channels
- In Proceedings of IEEE International Symposium on Information Theory (ISIT
, 2007
"... In this paper, the bit energy requirements of training-based transmission over block Rayleigh fading channels are studied. Pilot signals are employed to obtain the minimum mean-square-error (MMSE) estimate of the channel fading coefficients. Energy efficiency is analyzed in the worst case scenario w ..."
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Cited by 9 (3 self)
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In this paper, the bit energy requirements of training-based transmission over block Rayleigh fading channels are studied. Pilot signals are employed to obtain the minimum mean-square-error (MMSE) estimate of the channel fading coefficients. Energy efficiency is analyzed in the worst case scenario where the channel estimate is assumed to be perfect and the error in the estimate is considered as another source of additive Gaussian noise. It is shown that bit energy requirement grows without bound as the SNR goes to zero, and the minimum bit energy is achieved at a nonzero SNR value below which one should not operate. The effect of the block length on both the minimum bit energy and the SNR value at which the minimum is achieved is investigated. Flash training schemes are analyzed and shown to improve the energy efficiency in the low-SNR regime. Energy efficiency analysis is also carried out when peak power constraints are imposed on pilot signals. Abstract — 1 I.
