TY - JOUR

T1 - On the Separability of Parallel MISO Broadcast Channels under Partial CSIT

T2 - A Degrees of Freedom Region Perspective

AU - Joudeh, Hamdi

AU - Clerckx, Bruno

PY - 2020/7

Y1 - 2020/7

N2 - 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.

AB - 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.

KW - Broadcast channel

KW - channel state information at transmitter

KW - degrees-of-freedom

KW - parallel channels

UR - http://www.scopus.com/inward/record.url?scp=85077283622&partnerID=8YFLogxK

U2 - 10.1109/TIT.2019.2962136

DO - 10.1109/TIT.2019.2962136

M3 - Article

AN - SCOPUS:85077283622

VL - 66

SP - 4513

EP - 4529

JO - IEEE Transactions on Information Theory

JF - IEEE Transactions on Information Theory

SN - 0018-9448

IS - 7

ER -