Motivated by wireless communications at high carrier frequencies in 5G and 6G systems (mmWaves, sub-THz), we consider a state-dependent channel model with in-block memory referred to as the Gaussian beam-pointing (GBP) channel. A transmitter equipped with a large antenna array wishes to communicate with a receiver located at an unknown angle of departure (AoD). The AoD defines discrete channel states, taking values in a discrete set of M possible values (quantized beam “directions”), constant within a coherence block and changing independently across blocks. Each block spans Q time slots of length q channel uses (also referred to as signal dimension). At the end of each slot, the transmitter receives a (strictly causal) feedback signal which may represent either the detection result of some radar sensor, or an explicit feedback signal from the receiver. The GBP model, a realistic extension of a binary beam-pointing channel studied in the authors’ previous paper, offers a sufficiently simple yet insightful model for understanding channel capacity in beamforming-based communication systems. We establish both an upper bound and an approximate inner bound on capacity that can be calculated by solving carefully designed optimization problems. Numerical examples demonstrate that our proposed transmission strategy achieves a near-optimal achievable rate when the signal dimension q is large enough.