Abstract
The degrees of freedom (DoF) region is characterized for the 2-user multiple input multiple output (MIMO) broadcast channel (BC), where the transmitter is equipped with M antennas, the two receivers are equipped with N 1 and N 2 antennas, and the levels of channel state information at the transmitter (CSIT) for the two users are parameterized by β 1 , β 2 , respectively. The achievability of the DoF region was established by Hao, Rassouli and Clerckx, but no proof of optimality was heretofore available. The proof of optimality is provided in this work with the aid of sum-set inequalities based on the aligned image sets (AIS) approach.
Highlights
The availability of channel state information at the transmitter(s) (CSIT) greatly affects the capacity of wireless networks, so much so that even the coarse degrees of freedom (DoF) metric is significantly impacted
The setting of interest is a 2-user multiple input multiple output (MIMO) broadcast channel (BC) where the transmitter is equipped with M antennas, the two receivers are equipped with N1 and N2 antennas, and the levels of CSIT for the two users are parameterized by β1, β2 ∈ [0, 1], respectively, such that βi = 0 represents no CSIT, βi = 1 represents perfect CSIT, and the intermediate values represent corresponding levels of partial CSIT
From the achievability side, note that the DoF innerbound shown in [6] remains unaffected if the number of transmit antennas is reduced to N1 + N2
Summary
The availability of channel state information at the transmitter(s) (CSIT) greatly affects the capacity of wireless networks, so much so that even the coarse degrees of freedom (DoF) metric is significantly impacted. The setting of interest is a 2-user MIMO BC where the transmitter is equipped with M antennas, the two receivers are equipped with N1 and N2 antennas, and the levels of CSIT for the two users are parameterized by β1, β2 ∈ [0, 1], respectively, such that βi = 0 represents no CSIT, βi = 1 represents perfect CSIT, and the intermediate values represent corresponding levels of partial CSIT Existing results for this channel focus primarily on the two extremes of perfect CSIT and no CSIT. For arbitrary antenna configurations and arbitrary levels of partial CSIT, an achievable DoF region is established by Hao, Rassouli and Clerckx in [6] The optimality of this achievable region has been shown in [6] for certain parameter regimes (mainly N1 ≤ N2, M ≤ N2), based on existing bounds, as well as AIS arguments. The proof makes use of the sumset inequalities recently developed in [5]
Sign-in/Register to view highlights & summary 
Submitted Version (
Free)
Published Version
Talk to us
Join us for a 30 min session where you can share your feedback and ask us any queries you have
Schedule a call