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

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<sub>1</sub> and I<sub>2</sub> 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<sub>1</sub>, I<sub>2</sub> ϵ {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<sub>1</sub>I<sub>2</sub> ϵ {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<sub>1</sub>I<sub>2</sub> is present for a fraction λ<sub>I1I2</sub> of this total duration (naturally forcing λ<sub>αγ</sub> ; λ<sub>γα</sub> ; λ<sub>αα</sub> ; λ<sub>γγ</sub> = 1), we focus on the symmetric case of λ<sub>αγ</sub> = λ<sub>γα</sub>, and derive the optimal degrees-of-freedom (DoF) region to be the polygon w- th corner points {(0,0), (0,1), (λ̅, 1), (2+λ/3, 2+λ/3), (1, λ̅), (1,0)}, for some λ̅ Δ (λ<sub>γα</sub> ; λ<sub>γγ</sub>)γ ; (λ<sub>αγ</sub> ; λ<sub>αα</sub>)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 I₁, I₂ ϵ {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.