### Abstract

This paper studies communication outages in multiple-input multiple-output (MIMO) block-fading channels with imperfect channel state information at the receiver (CSIR). Using mismatched decoding error exponents, we prove the achievability of the generalized outage probability, the probability that the generalized mutual information (GMI) is less than the data rate, and show that this probability is the fundamental limit for independent and identically distributed (i.i.d.) codebooks. Then, using nearest neighbor decoding, we study the generalized outage probability in the high signal-to-noise ratio (SNR) regime for random codes with Gaussian and discrete signal constellations. In particular, we study the SNR exponent, which is defined as the high-SNR slope of the error probability curve on a logarithmic-logarithmic scale. We show that the maximum achievable SNR exponent of the imperfect CSIR case is given by the SNR exponent of the perfect CSIR case times the minimum of one and the channel estimation error diversity. Random codes with Gaussian constellations achieve the optimal SNR exponent with finite block length as long as the block length is larger than a threshold. On the other hand, random codes with discrete constellations achieve the optimal SNR exponent with block length growing with the logarithm of the SNR. The results hold for many fading distributions, including Rayleigh, Rician, Nakagami-m, Nakagami-q and Weibull as well as for optical wireless scintillation distributions such as lognormal-Rice and gamma-gamma.

Original language | English |
---|---|

Article number | 6157055 |

Pages (from-to) | 1483-1517 |

Number of pages | 35 |

Journal | IEEE Transactions on Information Theory |

Volume | 58 |

Issue number | 3 |

DOIs | |

Publication status | Published - 27 Feb 2012 |

Externally published | Yes |

### Fingerprint

### Keywords

- Block-fading channels
- channel state information
- diversity
- error exponent
- generalized mutual information (GMI)
- imperfect channel state information
- MIMO
- multiple antenna
- nearest neighbor decoding
- outage probability
- SNR exponent

### ASJC Scopus subject areas

- Information Systems
- Computer Science Applications
- Library and Information Sciences

### Cite this

*IEEE Transactions on Information Theory*,

*58*(3), 1483-1517. [6157055]. https://doi.org/10.1109/TIT.2011.2173719

**Nearest neighbor decoding in MIMO block-fading channels with imperfect CSIR.** / Asyhari, A. Taufiq; Guillén I Fàbregas, Albert.

Research output: Contribution to journal › Article

*IEEE Transactions on Information Theory*, vol. 58, no. 3, 6157055, pp. 1483-1517. https://doi.org/10.1109/TIT.2011.2173719

}

TY - JOUR

T1 - Nearest neighbor decoding in MIMO block-fading channels with imperfect CSIR

AU - Asyhari, A. Taufiq

AU - Guillén I Fàbregas, Albert

PY - 2012/2/27

Y1 - 2012/2/27

N2 - This paper studies communication outages in multiple-input multiple-output (MIMO) block-fading channels with imperfect channel state information at the receiver (CSIR). Using mismatched decoding error exponents, we prove the achievability of the generalized outage probability, the probability that the generalized mutual information (GMI) is less than the data rate, and show that this probability is the fundamental limit for independent and identically distributed (i.i.d.) codebooks. Then, using nearest neighbor decoding, we study the generalized outage probability in the high signal-to-noise ratio (SNR) regime for random codes with Gaussian and discrete signal constellations. In particular, we study the SNR exponent, which is defined as the high-SNR slope of the error probability curve on a logarithmic-logarithmic scale. We show that the maximum achievable SNR exponent of the imperfect CSIR case is given by the SNR exponent of the perfect CSIR case times the minimum of one and the channel estimation error diversity. Random codes with Gaussian constellations achieve the optimal SNR exponent with finite block length as long as the block length is larger than a threshold. On the other hand, random codes with discrete constellations achieve the optimal SNR exponent with block length growing with the logarithm of the SNR. The results hold for many fading distributions, including Rayleigh, Rician, Nakagami-m, Nakagami-q and Weibull as well as for optical wireless scintillation distributions such as lognormal-Rice and gamma-gamma.

AB - This paper studies communication outages in multiple-input multiple-output (MIMO) block-fading channels with imperfect channel state information at the receiver (CSIR). Using mismatched decoding error exponents, we prove the achievability of the generalized outage probability, the probability that the generalized mutual information (GMI) is less than the data rate, and show that this probability is the fundamental limit for independent and identically distributed (i.i.d.) codebooks. Then, using nearest neighbor decoding, we study the generalized outage probability in the high signal-to-noise ratio (SNR) regime for random codes with Gaussian and discrete signal constellations. In particular, we study the SNR exponent, which is defined as the high-SNR slope of the error probability curve on a logarithmic-logarithmic scale. We show that the maximum achievable SNR exponent of the imperfect CSIR case is given by the SNR exponent of the perfect CSIR case times the minimum of one and the channel estimation error diversity. Random codes with Gaussian constellations achieve the optimal SNR exponent with finite block length as long as the block length is larger than a threshold. On the other hand, random codes with discrete constellations achieve the optimal SNR exponent with block length growing with the logarithm of the SNR. The results hold for many fading distributions, including Rayleigh, Rician, Nakagami-m, Nakagami-q and Weibull as well as for optical wireless scintillation distributions such as lognormal-Rice and gamma-gamma.

KW - Block-fading channels

KW - channel state information

KW - diversity

KW - error exponent

KW - generalized mutual information (GMI)

KW - imperfect channel state information

KW - MIMO

KW - multiple antenna

KW - nearest neighbor decoding

KW - outage probability

KW - SNR exponent

UR - http://www.scopus.com/inward/record.url?scp=84857728027&partnerID=8YFLogxK

U2 - 10.1109/TIT.2011.2173719

DO - 10.1109/TIT.2011.2173719

M3 - Article

VL - 58

SP - 1483

EP - 1517

JO - IEEE Transactions on Information Theory

JF - IEEE Transactions on Information Theory

SN - 0018-9448

IS - 3

M1 - 6157055

ER -