## Samenvatting

We study the K-user, M-subchannel parallel multiple-input-single-output (MISO) broadcast channel (BC) under arbitrary levels of partial channel state information at the transmitter (CSIT). We show that the parallel subchannels constituting this setting are separable from a degrees-of-freedom (DoF) region perspective if and only if the partial CSIT pattern is totally ordered. This total order condition corresponds to users abiding by the same order, with respect to their CSIT quality levels, in each of the parallel subchannels. For instance, let α k [{l}]} and α j [{l]}$ be the CSIT quality parameters for users k and j over subchannel l. Under total order, having α k [{l}] ≥ α j [{l}] implies that α k [{m}] ≥ α j [{m}] holds for every subchannel m. In this case, the entire DoF region is achievable using simple separate coding, where a single-subchannel-type transmission scheme is employed in each subchannel. To show this separability result, we first derive an outer bound for the DoF region by extending the aligned image sets approach of Davoodi and Jafar to the considered setting. We then show that this outer bound coincides with the inner bound achieved through separate coding, given by the Minkowski sum of ${M}$ single-subchannel DoF regions, under the total order condition, hence settling the if part of the main theorem. To prove the only if part of the theorem, we identify a set of DoF tuples achievable through joint coding across subchannels, yet not achievable through separate coding whenever the total order condition is violated. Moreover, we also highlight the implications of our main result on the design of CSIT feedback schemes for multi-carrier multi-antenna wireless networks.

Originele taal-2 | Engels |
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Artikelnummer | 8943332 |

Pagina's (van-tot) | 4513-4529 |

Aantal pagina's | 17 |

Tijdschrift | IEEE Transactions on Information Theory |

Volume | 66 |

Nummer van het tijdschrift | 7 |

DOI's | |

Status | Gepubliceerd - jul. 2020 |

Extern gepubliceerd | Ja |

### Financiering

Manuscript received May 3, 2019; revised September 26, 2019; accepted December 19, 2019. Date of publication December 25, 2019; date of current version June 18, 2020. This work was supported in part by the U.K. Engineering and Physical Sciences Research Council (EPSRC) under Grant EP/N015312/1 and Grant EP/R511547/1. This work was presented in part at the 2017 IEEE Global Communications Conference and in part at the 2019 IEEE International Workshop on Signal Processing Advances in Wireless Communications.

Financiers | Financiernummer |
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Engineering and Physical Sciences Research Council | EP/N015312/1 |