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

TL;DR

This paper investigates the capacity of a simplified binary beam-pointing channel with memory and feedback, providing a closed-form capacity expression and a novel probing scheme for mmWave systems.

Contribution

It introduces a binary channel model with memory and feedback, deriving its capacity and proposing a scheme that combines information transmission with beam probing.

Findings

Capacity characterized by an iterative closed-form expression.

Proposed scheme achieves capacity by combining information transmission and beam probing.

Provides insights into beam alignment and feedback utilization in mmWave channels.

Abstract

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.