## Degrees of freedom in some underspread MIMO fading channels (2006)

Venue: | IEEE Trans. Inform. Theory |

Citations: | 14 - 2 self |

### BibTeX

@ARTICLE{Etkin06degreesof,

author = {Raúl H. Etkin and Student Member and David N. C. Tse},

title = {Degrees of freedom in some underspread MIMO fading channels},

journal = {IEEE Trans. Inform. Theory},

year = {2006},

pages = {1576--1608}

}

### Years of Citing Articles

### OpenURL

### Abstract

fading channel in which the fading process varies slowly over time. Assuming that neither the transmitter nor the receiver have knowledge of the fading process, do multiple transmit and receive antennas provide significant capacity improvements at high signal-to-noise ratio (SNR)? For regular fading processes, recent results show that capacity ultimately grows doubly logarithmically with the SNR independently of the number of transmit and receive antennas used. We show that for the Gauss–Markov fading process in all regimes of practical interest the use of multiple antennas provides large capacity improvements. Nonregular fading processes show completely different high-SNR behaviors due to the perfect predictability of the process from noiseless observations. We analyze the capacity of MIMO channels with nonregular fading by presenting a lower bound, which we specialize to the case of band-limited slowly varying fading processes to show that the use of multiple antennas is still highly beneficial. In both cases, regular and nonregular fading, this capacity improvement can be seen as the benefit of having multiple spatial degrees of freedom. For the Gauss–Markov fading model and all regimes of practical interest, we present a communication scheme that achieves the full number of degrees of freedom of the channel with tractable complexity. Our results for underspread Gauss–Markov and band-limited nonregular fading channels suggest that multiple antennas are useful at high SNR. Index Terms—Channel capacity, decision-oriented training, fading number, high signal-to-noise ratio (SNR), multiple antennas, noncoherent communication. I.

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Citation Context ...ronments, systems with multiple transmit and multiple receive antennas (multiple-input multiple-output (MIMO) systems) can have very large capacities. In particular, Foschini and Gans [1] and Telatar =-=[2]-=- considered a channel with transmit and receive antennas, with Rayleigh flat-faded channel gains independent and identically distributed (i.i.d.) across antenna pairs, and showed that at high signal-t... |

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Citation Context ...om is a useful measure of that performance gain, even without the assumption of perfect CSI. B. Related Works The first-order Gauss–Markov fading model was analyzed in the context of a SISO system in =-=[11]-=-, where it is shown that as the SNR increases to infinity, Gaussian inputs result in bounded mutual information. It is also shown that for this kind of inputs, the mutual information only increases su... |

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Citation Context ...fading process is nonregular, it can be perfectly predicted from noiseless observations of its infinite past, and one should expect different high SNR capacity asymptotics. In fact, Lapidoth shows in =-=[8]-=-, [9] that in the case of nonregular fading the capacity can grow as , , or , , in a single-input single-output (SISO) channel. Therefore, regular and nonregular fading processes can result in complet... |

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Citation Context ...ocessing [21] (PSP) to obtain reliable decisions for channel estimation before the reception of the complete codewords. A practical example of noncoherent sequence detection using PSP can be found in =-=[22]-=-. V. PROOFS OF THE UPPER BOUNDS In this section, we will present the proofs of Theorems 3 and 4. We first prove Theorem 3 in Section V-A introducing many results that are also useful in the proof of T... |

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Citation Context ... upper bound for the fading number for the case where remains open. C. Nonregular Fading Processes The high SNR capacity of SISO channels with nonregular fading processes was recently studied in [8], =-=[9]-=-. It is shown that depending on how the noisy prediction error of the fading process varies with , 11 the capacity can show very different high SNR behaviors. In particular, it is shown that if , 12 t... |

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Citation Context ...regardless of the SNR. The effect of channel measurement errors in a SISO channel was studied in [13], where bounds on mutual information were applied to a Gauss–Markov fading model. Weingarten et al.=-=[14]-=- analyze the MIMO case with Gaussian inputs and scaled nearest neighbor decoding with some side information at the receiver. Our characterization of the first regime is consistent with these results, ... |

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Citation Context ...erence time of the channel represents the time over which the fading coefficients are highly correlated. If we define as the time over which the autocorrelation function is above of its value at then =-=[16]-=- where is the maximum Doppler shift given by , where is the mobile speed and is the wavelength. We can compute the autocorrelation of the process defined by (2), set it equal to and solve for the corr... |