### Abstract

We consider a K-user multiple-input single-output (MISO) broadcast channel (BC) where the channel state information (CSI) of user i(i=1,2, K) may be instantaneously perfect (P), delayed (D), or not known (N) at the transmitter with probabilities λP^{i} ^{P}, λ_{D} ^{i}, and λ_{N} ^{i}, respectively. In this setting, according to the three possible CSI at the transmitter (CSIT) for each user, knowledge of the joint CSIT of the K users could have at most 3^{K} states. In this paper, given the marginal probabilities of CSIT (i.e., λ_{P} ^{i}, λ_{D} ^{i}, and λ_{N} ^{i}), we derive an outer bound for the degrees of freedom (DoF) region of the K-user MISO BC. Subsequently, we tighten this outer bound by considering a set of inequalities that capture some of the 3^{K} states of the joint CSIT. One of the consequences of this set of inequalities is that for K≥3, it is shown that the DoF region is not completely characterized by the marginal probabilities in contrast to the two-user case. Afterwards, the tightness of these bounds is investigated through the discussion on the achievability. Finally, a two user multiple-input multiple-output BC having CSIT among P and N is considered in which an outer bound for the DoF region is provided, and it is shown that in some scenarios, it is tight.

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

Article number | 7378965 |

Pages (from-to) | 1312-1325 |

Number of pages | 14 |

Journal | IEEE Transactions on Information Theory |

Volume | 62 |

Issue number | 3 |

DOIs | |

Publication status | Published - 2016 Mar 1 |

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### Keywords

- alternating/hybrid channel state information at the transmitter (CSIT)
- Degrees of freedom (DoF)
- multiple-input multiple-output (MIMO) broadcast channel (BC)

### ASJC Scopus subject areas

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

### Cite this

*IEEE Transactions on Information Theory*,

*62*(3), 1312-1325. [7378965]. https://doi.org/10.1109/TIT.2016.2517060

**DoF analysis of the MIMO broadcast channel with alternating/hybrid CSIT.** / Rassouli, Borzoo; Hao, Chenxi; Clercks, Bruno.

Research output: Contribution to journal › Article

*IEEE Transactions on Information Theory*, vol. 62, no. 3, 7378965, pp. 1312-1325. https://doi.org/10.1109/TIT.2016.2517060

}

TY - JOUR

T1 - DoF analysis of the MIMO broadcast channel with alternating/hybrid CSIT

AU - Rassouli, Borzoo

AU - Hao, Chenxi

AU - Clercks, Bruno

PY - 2016/3/1

Y1 - 2016/3/1

N2 - We consider a K-user multiple-input single-output (MISO) broadcast channel (BC) where the channel state information (CSI) of user i(i=1,2, K) may be instantaneously perfect (P), delayed (D), or not known (N) at the transmitter with probabilities λPi P, λD i, and λN i, respectively. In this setting, according to the three possible CSI at the transmitter (CSIT) for each user, knowledge of the joint CSIT of the K users could have at most 3K states. In this paper, given the marginal probabilities of CSIT (i.e., λP i, λD i, and λN i), we derive an outer bound for the degrees of freedom (DoF) region of the K-user MISO BC. Subsequently, we tighten this outer bound by considering a set of inequalities that capture some of the 3K states of the joint CSIT. One of the consequences of this set of inequalities is that for K≥3, it is shown that the DoF region is not completely characterized by the marginal probabilities in contrast to the two-user case. Afterwards, the tightness of these bounds is investigated through the discussion on the achievability. Finally, a two user multiple-input multiple-output BC having CSIT among P and N is considered in which an outer bound for the DoF region is provided, and it is shown that in some scenarios, it is tight.

AB - We consider a K-user multiple-input single-output (MISO) broadcast channel (BC) where the channel state information (CSI) of user i(i=1,2, K) may be instantaneously perfect (P), delayed (D), or not known (N) at the transmitter with probabilities λPi P, λD i, and λN i, respectively. In this setting, according to the three possible CSI at the transmitter (CSIT) for each user, knowledge of the joint CSIT of the K users could have at most 3K states. In this paper, given the marginal probabilities of CSIT (i.e., λP i, λD i, and λN i), we derive an outer bound for the degrees of freedom (DoF) region of the K-user MISO BC. Subsequently, we tighten this outer bound by considering a set of inequalities that capture some of the 3K states of the joint CSIT. One of the consequences of this set of inequalities is that for K≥3, it is shown that the DoF region is not completely characterized by the marginal probabilities in contrast to the two-user case. Afterwards, the tightness of these bounds is investigated through the discussion on the achievability. Finally, a two user multiple-input multiple-output BC having CSIT among P and N is considered in which an outer bound for the DoF region is provided, and it is shown that in some scenarios, it is tight.

KW - alternating/hybrid channel state information at the transmitter (CSIT)

KW - Degrees of freedom (DoF)

KW - multiple-input multiple-output (MIMO) broadcast channel (BC)

UR - http://www.scopus.com/inward/record.url?scp=84961987978&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=84961987978&partnerID=8YFLogxK

U2 - 10.1109/TIT.2016.2517060

DO - 10.1109/TIT.2016.2517060

M3 - Article

AN - SCOPUS:84961987978

VL - 62

SP - 1312

EP - 1325

JO - IEEE Transactions on Information Theory

JF - IEEE Transactions on Information Theory

SN - 0018-9448

IS - 3

M1 - 7378965

ER -