On the Capacity of "Beam-Pointing'' Channels with Block Memory and Feedback: The Binary Case

Millimeter-wave (mmWave) communication is one of the key enablers for 5G systems as it provides larger system bandwidth and the possibility of packing numerous antennas in a small form factor for highly directional communication. In order to materialize the potentially very high beamforming gain, the transmitter and receiver beams need to be aligned. Practically, the Angle-of-Departure (AoD) remains almost constant over numerous consecutive time slots, which presents a state-dependent channel with memory. In addition, the backscatter signal can be modeled as a (causal) generalized feedback. The capacity of such channels with memory is generally an open problem in information theory. Towards solving this difficult problem, we consider a ``toy model'', consisting of a binary state-dependent (BSD) channel with in-block memory (iBM) [1] and one unit-delayed feedback. The capacity of this model under the peak transmission cost constraint is characterized by an iterative closed-form expression. We propose a capacity-achieving scheme where the transmitted signal carries information and meanwhile uniformly and randomly probes the beams with the help of feedback.