Optimal DoF region of the two-user MISO-BC with general alternating CSIT

Abstract

In the setting of the time-selective two-user multiple-input single-output (MISO) broadcast channel (BC), recent work by Tandon et al. considered the case where — in the presence of error-free delayed channel state information at the transmitter (delayed CSIT) — the current CSIT for the channel of user 1 and of user 2, alternate between the two extreme states of perfect current CSIT and of no current CSIT. Motivated by the problem of having limited-capacity feedback links which may not allow for perfect CSIT, as well as by the need to utilize any available partial CSIT, we here deviate from this ‘all-or-nothing’ approach and proceed — again in the presence of error-free delayed CSIT — to consider the general setting where current CSIT now alternates between any two qualities. Specifically for I 1 and I 2 denoting the high-SNR asymptotic rates-of-decay of the mean-square error of the CSIT estimates for the channel of user 1 and of user 2 respectively, we consider the case where I 1 , I 2 ∊ {γ,α} for any two positive current-CSIT quality exponents γ, α as a result, the overall current CSIT — for both users' channels — alternates between any four states I 1 I 2 ∊ {γγ,γα, αγ, αα}. In a fast-fading setting where we consider communication over any number of coherence periods, and where each CSIT state I 1 I 2 is present for a fraction λ I1I2 ? of this total duration (naturally forcing λ αγ ; λ γα ; λ αα ; λ γγ = 1), we focus on the symmetric case of λ αγ = λ γα , and derive the optimal degrees-of-freedom (DoF) region to be the polygon with corner points {(0,0), (0,1), (λ, 1), (2;λ/3, 2;λ/3), (1, λ), (1,0)}, for some λ ≜ (λ γα ; λ γγ )γ ; (λ αγ ; λ αα )α, representing a measure of the average CSIT quality. The result, which is supported by novel communication protocols, naturally incorporates the aforementioned ‘Perfect current’ vs. ‘No current’ setting by limiting I 1 , I 2 ∊ {0,1}, as well as the Yang et al. and Gou and Jafar setting by forcing α = γ. Finally, motivated by recent interest in frequency correlated channels with unmatched CSIT, we also analyze the setting where there is no delayed CSIT.