Unitary invariant and residual independent matrix distributions

The information that can be transmitted through a wireless channel, with multiple-antenna equipped transmitter and receiver, is crucially influenced by the channel behavior as well as by the structure of the input signal. We characterize in closed form the probability density function (pdf) of the output of MIMO block-fading channels, for an arbitrary SNR value. Our results provide compact expressions for such output statistics, paving the way to a more detailed analytical information-theoretic exploration of communications in presence of block fading. The analysis is carried out assuming two different structures for the input signal: the i.i.d. Gaussian distribution and a product form that has been proved to be optimal for noncoherent communication, i.e., in absence of any channel state information. When the channel is fed by an i.i.d. Gaussian input, we assume the Gramian of the channel matrix to be unitarily invariant and derive the output statistics in both the noise-limited and the interference-limited scenario, considering different fading distributions. When the product-form input is adopted, we provide the expressions of the output pdf as the relationship between the overall number of antennas and the fading coherence length varies. We also highlight the relation between our newly derived expressions and the results already available in the literature, and, for some cases, we numerically compute the mutual information, based on the proposed expression of the output statistics.

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“…, ψ m , we obtain (39). • For m > n, the distribution of the eigenvalues of H 0 H 0 H is given by (16):…”

Section: Appendix G Proof Of Propositionmentioning

confidence: 99%

“…[11]. When Θ 1 and Θ 2 are both scalar matrices, W is unitarily invariant and has a Beta type II distribution [16]. Specifically, when Θ 1 Θ −1 2 = ωI, the distribution of its ordered eigenvalues is given by…”

Section: B Matrix-variate Distributionsmentioning

confidence: 99%

Closed-Form Output Statistics of MIMO Block-Fading Channels

Alfano

Chiasserini

Nordio

et al. 2014

IEEE Trans. Inform. Theory

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“…It is known that the marginal distribution of this L × L upperleft block is itself inverse-Wishart distributed, with reduced degrees of freedom compared to the full matrix [23], i.e.,…”

Section: Appendix a Proof Of Theoremmentioning

confidence: 99%

Subspace Quantization Based Combining for Limited Feedback Block-Diagonalization

Schwarz¹,

Rupp²

2013

IEEE Trans. Wireless Commun.

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Spatial multiplexing of multiple users in a multiantenna broadcast system, i.e., multi-user MIMO, is a promising technique for improving the spectral efficiency of cellular networks. Still, practical implementations struggle with the difficulty of obtaining sufficiently accurate channel state information at the transmitter (CSIT), due to restrictions on the capacity of the CSI feedback links from the users. Without accurate CSIT, residual multi-user interference diminishes the potential performance gain of multi-user MIMO, challenging its value for practical realizations. In this work we show that the CSI feedback overhead can be significantly reduced if the number of spatially multiplexed data streams per user is less than the number of receive antennas, and the antenna outputs are appropriately combined. We propose an interference-unaware antenna combining algorithm that minimizes the CSI quantization error, which has the effect of minimizing multi-user interference at the price of reducing the received signal power. We mathematically analyze the performance of the proposed algorithm, substantiating its value for limited feedback systems. Numerical simulations confirm the potential of the proposed algorithm in comparison to a traditional technique that maximizes the received signal power.Index Terms-Limited feedback, quantized feedback, multiuser MIMO, block-diagonalization, antenna combining.

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“…It is easy to see that vec(ΔH T sr ) ∼ CN (0 MR×NS , Σ sr ⊗ Ψ T sr ) based on which ΔH sr is said to have a matrix-variate complex Gaussian distribution, which can be written as [7] ΔH sr ∼ CN MR,…”

Section: Problem Formulationmentioning

confidence: 99%

“…For the inner expectation, due to the fact that the distribution of ΔH sr is matrix-variate complex Gaussian with zero mean, the following equation holds [7] …”

Section: A Mse Averaged Over Channel Uncertaintiesmentioning

confidence: 99%

Bayesian Robust Linear Transceiver Design for Dual-Hop Amplify-and-Forward MIMO Relay Systems

Xing

2009

GLOBECOM 2009 - 2009 IEEE Global Telecommunications Conference

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In this paper, we address the robust linear transceiver design for dual-hop amplify-and-forward (AF) MIMO relay systems, where both transmitters and receivers have imperfect channel state information (CSI). With the statistics of channel estimation errors in the two hops being Gaussian, we formulate the robust linear-minimum-mean-square-error (LMMSE) transceiver design problem using the Bayesian framework, and derive a closed-form solution. Simulation results show that the proposed algorithm reduces the sensitivity of the relay system to channel estimation errors, and performs better than the algorithm using estimated channel only.

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Unitary invariant and residual independent matrix distributions

Abstract: Mathematical subject classification: Primary: 62E15; Secondary: 62H99.

Cited by 7 publications

References 12 publications

Closed-Form Output Statistics of MIMO Block-Fading Channels

Closed-Form Output Statistics of MIMO Block-Fading Channels

Subspace Quantization Based Combining for Limited Feedback Block-Diagonalization

Bayesian Robust Linear Transceiver Design for Dual-Hop Amplify-and-Forward MIMO Relay Systems

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