Contiguous Beams refers to a set of adjacent or neighboring directional beams that are formed to cover a specific angular range or spatial sector in networks. Beamforming is a technique used to shape the direction of transmitted or received signals in order to enhance communication performance. Contiguous beams are created by focusing energy in a particular direction, and when these beams are adjacent to each other, they form a contiguous set. This approach enhances the efficiency of wireless communication by providing focused coverage, reducing interference, and optimizing the use of available spectrum resources.

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Optimal Single-User Interactive Beam Alignment with Feedback Delay

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Communication in Millimeter wave (mmWave) band relies on narrow beams due to directionality, high path loss, and shadowing. One can use beam alignment (BA) techniques to find and adjust the direction of these narrow beams. In this paper, BA at the base station (BS) is considered, where the BS sends a set of BA packets to scan different angular regions while the user listens to the channel and sends feedback to the BS for each received packet. It is assumed that the packets and feedback received at the user and BS, respectively, can be correctly decoded. Motivated by practical constraints such as propagation delay, a feedback delay for each BA packet is considered. At the end of the BA, the BS allocates a narrow beam to the user including its angle of departure for data transmission and the objective is to maximize the resulting expected beamforming gain. A general framework for studying this problem is proposed based on which a lower bound on the optimal performance as well as an optimality achieving scheme are obtained. Simulation results reveal significant performance improvements over the state-of-the-art BA methods in the presence of feedback delay.

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On Single-User Interactive Beam Alignment in Millimeter Wave Systems: Impact of Feedback Delay

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Narrow beams are key to wireless communications in millimeter wave frequency bands. Beam alignment (BA) allows the base station (BS) to adjust the direction and width of the beam used for communication. During BA, the BS transmits a number of scanning beams covering different angular regions. The goal is to minimize the expected width of the uncertainty region (UR) that includes the angle of departure of the user. Conventionally, in interactive BA, it is assumed that the feedback corresponding to each scanning packet is received prior to transmission of the next one. However, in practice, the feedback delay could be larger because of propagation or system constraints. This paper investigates BA strategies that operate under arbitrary fixed feedback delays. This problem is analyzed through a source coding perspective where the feedback sequences are viewed as source codewords. It is shown that these codewords form a codebook with a particular characteristic which is used to define a new class of codes called d—unimodal codes. By analyzing the properties of these codes, a lower bound on the minimum achievable expected beamwidth is provided. The results reveal potential performance improvements in terms of the BA duration it takes to achieve a fixed expected width of the UR over the state-of-the-art BA methods which do not consider the effect of delay.

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