The Jacobi MIMO channel

Dar, Ronen; Feder, Meir; Shtaif, Mark

doi:10.1109/isit.2012.6284000

Cited by 16 publications

(63 citation statements)

References 7 publications

Supporting

Mentioning

Contrasting

Unclassified

Order By: Relevance

“…The idea of the proposed approach stems from our observations that moment expressions of high-SNR mutual information can be efficiently obtained by means of integrals over matrix-valued channel densities. This is contrary to the existing approach [ 1 , 2 , 3 , 4 , 5 , 6 , 8 , 9 , 10 , 11 ], where the starting point is the seemingly simpler integrals over the eigenvalue densities of channel matrices.…”

Section: Introductionmentioning

confidence: 81%

“…Efforts have been made to understand the statistical properties of MIMO mutual information for different channel models. However, knowledge in the literature is essentially limited to either the exact mean values [ 1 , 2 , 3 , 4 , 5 , 6 ] or the limiting means and variances [ 7 , 8 , 9 , 10 , 11 ]. The first moment is relevant to the ergodic mutual information, whereas the higher order moments describe the outage probability essential to study to slow or block fading channels.…”

Section: Introductionmentioning

confidence: 99%

See 1 more Smart Citation

Matrix Integral Approach to MIMO Mutual Information Statistics in High-SNR Regime

Wei

Liu

Liang

et al. 2019

Entropy

View full text Add to dashboard Cite

In this work, an analytical framework for deriving the exact moments of multiple-input- multiple-output (MIMO) mutual information in the high-signal-to-noise ratio (SNR) regime is proposed. The idea is to make efficient use of the matrix-variate densities of channel matrices instead of the eigenvalue densities as in the literature. The framework is applied to the study of the emerging models of MIMO Rayleigh product channels and Jacobi MIMO channels, which include several well-known channels models as special cases. The corresponding exact moments of any order for the high-SNR mutual information are derived. The explicit moment expressions are utilized to construct simple yet accurate approximations to the outage probability. Despite the high-SNR nature, simulation shows usefulness of the approximations with finite SNR values in the scenario of low outage probability relevant to MIMO communications.

show abstract

Section: Introductionmentioning

confidence: 81%

Section: Introductionmentioning

confidence: 99%

Matrix Integral Approach to MIMO Mutual Information Statistics in High-SNR Regime

Wei

Liu

Liang

et al. 2019

Entropy

View full text Add to dashboard Cite

show abstract

“…[10] that, for m t , m r satisfying the condition m t m r ≤ m, the squared nonzero singular values of H 11 have the same distribution as the eigenvalues of the Jacobi ensemble J m max ; m − m max ; m min , where m min minfm t ; m r g and m max maxfm t ; m r g. For m t m r > m, it can be shown[11] that m t m r − m singular values of H 11 are equal to unity with probability 1, whereas the remaining m − m max nonzero singular values of H 11 are equal to the nonzero singular values of H 22 and hence follow the distribution of the Jacobi ensemble J m − m min ; m min ; m − m max . The latter property can be seen by noting that the unitarity of H implies that H † 11 H 11 H † 21 H 21 I m t and H 21 H † 21 H 22 H † 22 I m−m r .Since the noise is additive circularly symmetric Gaussian, the capacity for a given channel realization is known[7] and given by logdetI m t ρ 2 H † 11 H 11 .…”

mentioning

confidence: 99%

“…In the case m t m r ≤ m, using the joint PDF of λ j , one finds that the ergodic capacity satisfies [11] Cm t ;m r ;m;ρ…”

mentioning

confidence: 99%

See 1 more Smart Citation

The underaddressed optical multiple-input, multiple-output channel: capacity and outage

2012

Self Cite

View full text Add to dashboard Cite

We study an optical space-division multiplexed system where the number of modes that are addressed by the transmitter and receiver is allowed to be smaller than the total number of optical modes supported by the fiber. This situation will be of relevance if, for instance, fibers supporting more modes than can be processed with current multiple-input, multiple-output technology are deployed with the purpose of future-proof installation. We calculate the ergodic capacity and the outage probability of the link and study their dependence on the number of addressed modes at the transmitter and receiver.

show abstract

On the ergodic secrecy capacity and secrecy outage probability of the MIMOME Rayleigh wiretap channel

Guerreiro

Fraidenraich

Souza

2015

Trans. Emerging Tel. Tech.

View full text Add to dashboard Cite

In this paper, we study the multiple-input multiple-output multiple-eavesdropper wiretap channel in the nonergodic and ergodic scenarios, both with stationary Rayleigh distributed fading channels. For the ergodic scenario, we derive a new closed-form expression for the ergodic secrecy capacity with full channel state information at the transmitter (CSIT) of the main and the eavesdropper channels, allowing the covariance matrix to be time-varying. A lower bound for the ergodic capacity with full CSIT, in which the covariance matrix is fixed for the entire transmission period is also derived. The first expression is restricted to the high signal-to-nose ratio (SNR) limit, with n t transmit antennas, n r receive antennas .n r > n t / and n e D n t eavesdropper antennas (n t n r n t setup). The second expression is restricted to the n t n t n t antenna setup. For the nonergodic scenario, we derive a new closed-form expression for the secrecy outage probability in the high SNR limit, in a 2 n r 2 setup with n r > 2. We are also able to calculate an upper bound for the secrecy outage probability in other antenna setups.

show abstract

The Jacobi MIMO channel

Cited by 16 publications

References 7 publications

Matrix Integral Approach to MIMO Mutual Information Statistics in High-SNR Regime

Matrix Integral Approach to MIMO Mutual Information Statistics in High-SNR Regime

The underaddressed optical multiple-input, multiple-output channel: capacity and outage

On the ergodic secrecy capacity and secrecy outage probability of the MIMOME Rayleigh wiretap channel

Contact Info

Product

Resources

About