Pilot-assisted channel estimation based on second-order statistics

Training-based estimation of channel state information in multiantenna systems is analyzed herein. Closed-form expressions for the general Bayesian minimum mean square error (MMSE) estimators of the channel matrix and the squared channel norm are derived in a Rayleigh fading environment with known statistics at the receiver side. When the second-order channel statistics are available also at the transmitter, this information can be exploited in the training sequence design to improve the performance. Herein, mean square error (MSE) minimizing training sequences are considered. The structure of the general solution is developed, with explicit expressions at high and low SNRs and in the special case of uncorrelated receive antennas. The optimal length of the training sequence is equal or smaller than the number of transmit antennas.

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“…The survey in [6] compares the deterministic and Bayesian approach and, as expected, the latter is superior.…”

Section: Introductionmentioning

confidence: 52%

Training-based Bayesian MIMO channel and channel norm estimation

Björnson

Ottersten

2009

2009 IEEE International Conference on Acoustics, Speech and Signal Processing

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“…By nature, the channel is stochastic, which motivates Bayesian estimation-that is, modeling of the current channel state as a realization from a known multi-variate probability density function (PDF). There is also a large amount of literature on estimation of deterministic MIMO channels which are analytically tractable but in general provide less accurate channel estimates, as shown in [7], [8]. Herein, we concentrate on minimum mean square error (MMSE) estimation of the channel matrix and its squared Frobenius norm, given the first and second order system statistics.…”

mentioning

confidence: 99%

A Framework for Training-Based Estimation in Arbitrarily Correlated Rician MIMO Channels With Rician Disturbance

Björnson

Ottersten

2010

IEEE Trans. Signal Process.

233

288

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Abstract-In this paper, we create a framework for trainingbased channel estimation under different channel and interference statistics. The minimum mean square error (MMSE) estimator for channel matrix estimation in Rician fading multi-antenna systems is analyzed, and especially the design of mean square error (MSE) minimizing training sequences. By considering Kronecker-structured systems with a combination of noise and interference and arbitrary training sequence length, we collect and generalize several previous results in the framework. We clarify the conditions for achieving the optimal training sequence structure and show when the spatial training power allocation can be solved explicitly. We also prove that spatial correlation improves the estimation performance and establish how it determines the optimal training sequence length. The analytic results for Kronecker-structured systems are used to derive a heuristic training sequence under general unstructured statistics.The MMSE estimator of the squared Frobenius norm of the channel matrix is also derived and shown to provide far better gain estimates than other approaches. It is shown under which conditions training sequences that minimize the non-convex MSE can be derived explicitly or with low complexity. Numerical examples are used to evaluate the performance of the two estimators for different training sequences and system statistics. We also illustrate how the optimal length of the training sequence often can be shorter than the number of transmit antennas.

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“…Figure 3 also shows (dashed lines) that operating flashy scheme below the transition point can maintain the bit energy equal to its minimum. From Figure 3, we can also see that the dashdotted line plotted without spatial correlation (T c = 20) is above the real line of T c = 20 for about ¶ Generally, R t is not of low rank algebraically but with small eigenvalues decaying quickly [24]. Here for clarifying our results, we construct a rank-deficient R t algebraically by neglecting some small zero-approaching eigenvalues.…”

Section: Proofmentioning

confidence: 78%

“…In addition from (24) and for fixed N r , E r b /N 0 | →0 ∝ K 2 t /N t . It is not clear whether the value of K 2 t /N t will increase or decrease with N t , which depends on the concrete settings (such as spatial correlation and antenna aperture).…”

Section: Corollarymentioning

confidence: 92%

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Capacity lower bound and energy efficiency of training‐based MIMO systems over correlated channels

Pang¹,

Jin³

2009

Int J Communication

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SUMMARYThe behavior of training-based multiple-input multiple-output wireless communications over correlated channels is studied in the low signal-to-noise ratio (SNR) regime from an energy efficiency perspective. To start with, a relaxed but analytically more tractable capacity lower bound is derived where the impacts of channel spatial correlation are considered simply through the ranks of correlation matrices. It shows that, different from the independent and identically distributed case, the optimal training length no longer equals the number of transmit antennas but is just the same as the rank of transmit correlation matrix. Next, the bit energy requirements are analyzed based on the derived capacity lower bound. It shows that the minimum bit energy required for reliable communication is achieved at a nonzero SNR value below, which the bit energy grows to infinity with a zero-approaching wideband slope. Flash training and transmission scheme is also studied and shown to improve the energy efficiency. In addition, the impacts of spatial correlation, channel coherence interval and antenna number on the energy efficiency are analyzed. It shows that stronger spatial correlation leads to less bit energy, i.e. higher-energy efficiency. The minimum bit energy is achieved at lower SNR in a more correlated channel. Spatial correlation also helps to reduce the signal peakiness in the flash scheme. And larger coherence interval always improves energy efficiency at all SNR. Finally, the validity of the proposed results is verified by numerical simulations.

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Pilot-assisted channel estimation based on second-order statistics

Cited by 59 publications

References 36 publications

Training-based Bayesian MIMO channel and channel norm estimation

Training-based Bayesian MIMO channel and channel norm estimation

A Framework for Training-Based Estimation in Arbitrarily Correlated Rician MIMO Channels With Rician Disturbance

Capacity lower bound and energy efficiency of training‐based MIMO systems over correlated channels

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