  Sensing capabilities as an integral part of the network have been identified
as a novel feature of sixth-generation (6G) wireless networks. As a key driver,
millimeterwave (mmWave) communication largely boosts speed, capacities, and
connectivity. In order to maximize the potential of mmWave communication,
precise and fast beam acquisition (BA) is crucial, since it compensates for a
high pathloss and provides a large beamforming gain. Practically, the
angle-of-departure (AoD) remains almost constant over numerous consecutive time
slots, the backscatter signal experiences some delay, and the hardware is
restricted under the peak power constraint. This work captures these main
features by a simple binary beam-pointing (BBP) channel model with in-block
memory (iBM) [1], peak cost constraint, and one unit-delayed feedback. In
particular, we focus on the sensing capabilities of such a model and
characterize the performance of the BA process in terms of the Hamming
distortion of the estimated channel state. We encode the position of the AoD
and derive the minimum distortion of the BBP channel under the peak cost
constraint with no communication constraint. Our previous work [2] proposed a
joint communication and sensing (JCAS) algorithm, which achieves the capacity
of the same channel model. Herein, we show that by employing this JCAS
transmission strategy, optimal data communication and channel estimation can be
accomplished simultaneously. This yields the complete characterization of the
capacity-distortion tradeoff for this model.
