Abstract-Analog beamforming with phased arrays is a promising technique for 5G wireless communication at millimeter wave frequencies. Using a discrete codebook consisting of multiple analog beams, each beam focuses on a certain range of angles of arrival or departure and corresponds to a set of fixed phase shifts across frequency due to practical hardware considerations. However, for sufficiently large bandwidth, the gain provided by the phased array is actually frequency dependent, which is an effect called beam squint, and this effect occurs even if the radiation pattern of the antenna elements is frequency independent. This paper examines the nature of beam squint for a uniform linear array (ULA) and analyzes its impact on codebook design as a function of the number of antennas and system bandwidth normalized by the carrier frequency. The criterion for codebook design is to guarantee that each beam's minimum gain for a range of angles and for all frequencies in the wideband system exceeds a target threshold, for example 3 dB below the array's maximum gain. Analysis and numerical examples suggest that a denser codebook is required to compensate for beam squint. For example, 54% more beams are needed compared to a codebook design that ignores beam squint for a ULA with 32 antennas operating at a carrier frequency of 73 GHz and bandwidth of 2.5 GHz. Furthermore, beam squint with this design criterion limits the bandwidth or the number of antennas of the array if the other one is fixed.

A series of quantum voting protocols of continuous variables is proposed. Three methods are employed to ensure that the quantum voting obeys some desirable rules. Entanglement is used to keep voters away from the voting results. We enable voters to operate identically to represent the same vote to prevent the tallyman from gaining information about individual voters. We also propose an effective scheme to prevent voters from voting more than once. In both two-valued and multivalued ballot protocols, several specific constraints are set to meet the rules.

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We present a tracking algorithm to maintain the communication link between a base station (BS) and a mobile station (MS) in a millimeter wave (mmWave) communication system, where antenna arrays are used for beamforming in both the BS and MS. Downlink transmission is considered, and the tracking is performed at the MS as it moves relative to the BS. Specifically, we consider the case that the MS rotates quickly due to hand movement. The algorithm estimates the angle of arrival (AoA) by using variations in the radiation pattern of the beam as a function of this angle. Numerical results show that the algorithm achieves accurate beam alignment when the MS rotates in a wide range of angular speeds. For example, the algorithm can support angular speeds up to 800 degrees per second when tracking updates are available every 10 ms.

The Bode-Fano bounds on the integral over all frequency of the logarithm of the reflection coefficient between a source and a load, connected to each other through a passive matching network, are well-known measures of the bandwidth of the matching network and load. When there are multiple coupled loads being driven by multiple independent sources, the notion of a single reflection coefficient is not obvious since energy delivered to one load port may reflect, in part, out another port. Establishing the maximum possible bandwidth of the matching network and loads requires the development of a broadband matching theory that applies to coupled systems. We define a bandwidth measure for coupled loads based on the integral logarithm of their collective power reflection, and develop upper bounds on this measure. These upper bounds can be used to examine the effects of coupling on bandwidth, and to evaluate the broadband performance of matching networks for an arbitrary number of coupled loads.