On the Asymptotic Capacity of Stationary Gaussian Fading Channels

Lapidoth, Amos

doi:10.1109/tit.2004.840889

Cited by 141 publications

(231 citation statements)

References 11 publications

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“…Here we shall present results for the multiple-input single-output (MISO) (n R = 1) case when the fading is spatially independent and Gaussian. For non-regular fading capacity can grow with the SNR in various ways [3], [4]. When it grows logarithmically in the SNR we define the pre-log under a peak power constraint by…”

Section: Introductionmentioning

confidence: 99%

The fading number and degrees of freedom in non-coherent MIMO fading channels: a peace pipe

Koch¹,

Lapidoth²

2005

Proceedings. International Symposium on Information Theory, 2005. ISIT 2005.

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Abstract-New non-asymptotic upper bounds on the capacity of non-coherent multiple-input multiple-output (MIMO) Gaussian fading channels with memory are proposed. These upper bounds are used to derive upper bounds on the fading number of regular Gaussian fading channels and on the pre-log of nonregular ones. The resulting bounds are tight in the multiple-input single-output (MISO) spatially independent Gaussian case when the entries in the fading vector are either zero-mean or possess the same spectral distribution function.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 zero-mean Gaussian fading channels.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 zero-mean 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 multiple-output case that was recently solved by Lapidoth & Moser supports this conjecture.

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Section: Introductionmentioning

confidence: 99%

The fading number and degrees of freedom in non-coherent MIMO fading channels: a peace pipe

Koch¹,

Lapidoth²

2005

Proceedings. International Symposium on Information Theory, 2005. ISIT 2005.

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“…There have been already several attempts to approximate the capacity of noncoherent fading channels by bounds, see, e.g., [1], [2]. For the case of i.i.d.…”

Section: Motivation and Setupmentioning

confidence: 99%

“…As this scenario corresponds to the basic model of nearly all realistic mobile communication systems it is particularly important. Nevertheless, determining the capacity of this channel turns out to be notoriously difficult and the problem is still open in general.There have been already several attempts to approximate the capacity of noncoherent fading channels by bounds, see, e.g., [1], [2]. For the case of i.i.d.…”

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confidence: 99%

Convergence of the conditional per symbol entropy for stationary Gaussian fading channels for almost all input sequences

Dörpinghaus

Gaffke

Imhof

et al. 2013

2013 Information Theory and Applications Workshop (ITA)

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Abstract-In the present work, a discrete-time stationary Rayleigh flat-fading channel with unknown channel state information at the transmitter and the receiver is considered. The law of the channel is assumed to be known at the receiver and the fading process is supposed to be a stationary Gaussian process with an absolutely summable autocorrelation function. The conditional per symbol entropy of the output given the input is shown to converge to a constant for almost every realization of i.i.d. input variables. This implies the existence of the corresponding conditional entropy rate. Moreover, a novel inequality yielding a lower bound for the rate is derived. I. MOTIVATION AND SETUPWe consider a stationary Rayleigh flat-fading channel where the channel state information is unknown at the transmitter and the receiver. Moreover, the law of the channel is assumed to be known at the receiver. Often, this channel is referred to as noncoherent fading channel. As this scenario corresponds to the basic model of nearly all realistic mobile communication systems it is particularly important. Nevertheless, determining the capacity of this channel turns out to be notoriously difficult and the problem is still open in general.There have been already several attempts to approximate the capacity of noncoherent fading channels by bounds, see, e.g., [1], [2]. For the case of i.i.d. zero-mean proper Gaussian input symbols, which are capacity-achieving in the coherent setup, in [3] bounds on the achievable rate have been derived. One of the hardest problems when studying the capacity or achievable rate of stationary Rayleigh fading channels is the evaluation of the conditional entropy rate of the channel fading process. This is the main topic of the present paper. The proofs and extended material are contained in technical report [4]. A. Channel ModelWe consider an ergodic discrete-time jointly proper Gaussian [5] flat-fading channel, whose output at time k is given by

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“…Note that otherwise the capacity can increase with the SNR in various ways. For instance, in [6] fading channels are studied that result in a capacity which increases double-logarithmically with the SNR, and in [1] spectral distribution functions are presented for which capacity grows as a fractional power of the logarithm of the SNR.…”

Section: Channel Capacity and The Pre-logmentioning

confidence: 99%

Gaussian Fading is the Worst Fading

Koch

Lapidoth

2006

2006 IEEE International Symposium on Information Theory

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The capacity of peak-power limited, single-antenna, noncoherent, flat-fading channels with memory is considered. The emphasis is on the capacity pre-log, i.e., on the limiting ratio of channel capacity to the logarithm of the signal-to-noise ratio (SNR), as the SNR tends to infinity. It is shown that, among all stationary & ergodic fading processes of a given spectral distribution function and whose law has no mass point at zero, the Gaussian process gives rise to the smallest pre-log. The assumption that the law of the fading process has no mass point at zero is essential in the sense that there exist stationary & ergodic fading processes whose law has a mass point at zero and that give rise to a smaller prelog than the Gaussian process of equal spectral distribution function. An extension of our results to multiple-input single-output fading channels with memory is also presented.

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On the Asymptotic Capacity of Stationary Gaussian Fading Channels

Cited by 141 publications

References 11 publications

The fading number and degrees of freedom in non-coherent MIMO fading channels: a peace pipe

The fading number and degrees of freedom in non-coherent MIMO fading channels: a peace pipe

Convergence of the conditional per symbol entropy for stationary Gaussian fading channels for almost all input sequences

Gaussian Fading is the Worst Fading

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