## 1 Introduction  
In millimeter-wave (mmWave) cellular systems, directional beamforming antennas are necessary at both the base station (BS) and mobile station (MS) to compensate for high attenuation in the mmWave frequency band and to extend the transmission range. A small misalignment between the transmitting (Tx) and receiving (Rx) beams in mmWave communication systems may cause a significant loss in the received power, particularly for systems with narrow beams. Therefore, beam training in mmWave communication systems is necessary to find an angle of departure (AoD) and an angle of arrival (AoA) to achieve maximum beamforming efficiency. Many different AoD/AoA estimation techniques and beam training protocols have been investigated because it requires a large amount of training time and network resources [1; 2; 3]. Unlike mmWave systems, multiple antenna systems at lower carrier frequencies have a relatively small number of elements, each with its own radio frequency (RF) chain. This provides control of individual baseband signals associated with each element, enabling sophisticated channel estimation including frequency-selective spatio-temporal processing. However, in mmWave communication systems, the digital baseband cannot directly access all antennas due to the small number of RF chains, so it is difficult to accurately estimate the high-dimensional MIMO channel. Several channel estimation schemes have been recently proposed for mmWave systems. Specifically, [4; 5] proposed the adaptive codebook-based channel sounding scheme, where the transmitter and receiver search for the best beam pair by adjusting the predefined precoding and combining codebook. However, the channel estimation resolution is limited by the codebook size. [6; 7] was able to achieve better angle (AoA and AoD) estimation by performing an amplitude comparison with respect to the auxiliary beam pair. On the other hand, [8; 9] could estimate the channel (AoA and AoD) with reduced training overhead by exploiting the angular channel sparsity in mmWave communication systems. Compressive sensing techniques (orthogonal matching pursuit: OMP) leveraging mmWave channel spatial sparsity can overcome the limitations of codebook beam training [10; 11]. In mmWave systems, a beamforming initiator transmits training signals so that beamforming responders can estimate the Tx beam direction of the initiator during the preparation stage for data communication. The responder estimates the Tx beam direction of the initiator using the signals received from different directions of beams in the beam training period [12]. However, in mmWave cellular systems, the MS needs to know the source (BS) as well as the beam direction because many neighboring BSs transmit their training signals at the same time. Thus, in mmWave cellular systems, the beam training signal containing the cell ID (CID) of the BS needs to be transmitted so that the MS can identify both the source (BS) and direction of the beam. However, the overhead required for transmission of the beam training signal with CID information increases in proportion to the number of CIDs included in the beam training signal, because neighboring BSs need to transmit their own beam training signals in different time slots corresponding to their CIDs, or transmit their own preamble signals mapped to their CIDs, to reduce inter-beam interferences among BSs [13; 14]. In this paper, we propose a new beam weight generation method that can reduce the overhead of beam training in mmWave cellular systems. A lot of research on the beam weight generation has been done in the past. The beam weight generation methods can be classified as either data independent or statistically optimum, depending on how the weight are chosen [15; 16; 17]. The weight in a data independent beamformer do not depend on the array data and are chosen to present a specified response for all signal/interference scenarios. The weights in a statistically optimum beamformer are chosen based on the statistics of the array data to optimize the array response.