## 1 Introduction
In general, the statistically optimum beamformer places nulls in the directions of interfering sources in an attempt to maximize the signal to noise ratio at the beamformer output. The weights in a data independent beamformer are designed so that the beamformer response approximate a desired response independent of the array data or data statistics. The design objective, approximating a desired response, is the same as that for classical finite impulse response (FIR) filter design. Using the classical FIR filter design techniques such as windowing, frequency response sampling, least squares, and minimax with Remez exchange algorithm, the beam weights are chosen to shape the main beam and sidelobe structure of the spatial response. In statistically optimum beamforming, the weights are chosen based on the statistics of the data received at the array. The goal is to optimize the beamformer response so that the output contains minimal contributions due to noise and signals arriving from directions other than the desired signal direction. Depending on the criteria for choosing statistically optimum beamformer weights, many different techniques are available: multiple sidelobe canceller (MSC), Maximum SNR, linearly constrained minimum variance beamforming (LCMV), generalized sidelobe canceller (GSC), and reference signal. In the'referencesignal' approach, the weights are chosen to minimize the mean square error between output and reference signal. The beam weight generation methods discussed so far require knowledge of second order statistics. Many adaptive algorithms for beamforming have been developed to track the beam weight when these statistics are unknown or change over time [16; 17]. However, the beam weight generation methods developed so far does not consider mmWave cellular systems where a large overhead is required for beam training. With the existing beamformers, the MS cannot identify the source (BS) of the received beam because there are many neighboring BSs transmitting their training signals. A large overhead is required to identify the source of the received beam and find an optimal beam in a mmWave cellular system with the existing beamformers. In this paper, we propose a new beam weight generation method that allows the MS to estimate the source of the received beam in mmWave cellular systems. In the proposed method, a Tx beamformer at the BS forms beams using the weights generated with its own CID so that the MS can estimate the source (CID) and AoD for each BS in multi-cell environments. Also, a subarray structure is proposed to facilitate a flexible length of training signal for the efficient transmission of training signal. In the proposed method, the beam weights are generated using a Zdoff-Chu (ZC) sequence. The BSs select ZC sequences with root indices corresponding to their CIDs for the construction of their beamformers and transmit their beams simultaneously in multi-cell environments. To the best of the authors' knowledge, there has been no attempt to generate the beam weight using the ZC sequence, although it (ZC) has been widely used for the design of synchronization signal and random access preamble. The method of CID and AoD estimation is also proposed for the MS using the signals received through beams generated by the proposed beam weight generation method. The performances of CID detection and AoD estimation for the proposed and conventional methods are compared by simulation with a simple mmWave cellular model in a LOS dominant condition. In Table 1, the notations commonly used in this paper are summarized.