## 2 Initial Cell Search Procedure
### Periodic Synchronization Signal Transmission  
Although the initial cell search problem requires both PSS and SSS signal transmissions, this paper only focuses on the transmission and detection of the PSS signals from the BS since this is the procedure to initially discover the BS that is significantly affected by the propagation loss characteristics of mmWave signals. In this work, a microcell system including a BS with multiple randomly distributed UEs inside the coverage area of interest is considered, as shown in Figure 1.  
Figure 1: Millimeter wave microcell considered in this paper.  
The height of the base station is assumed to be 50 m while each UE is placed at 2 m above the ground. The array antenna at the BS consists of multiple planar arrays to enable complete azimuthal coverage, as depicted by the six facets of the hexagon in Figure 1. The maximum coverage area is defined by a radius R = 600 m with BS at its center. Although it was shown in the real-world measurements in [4; 9; 27] that the receivers are usually in outage when they are deployed at more than 200 m, this is due to a number of factors such as cluster blockage, lognormal fading, fast fading that increase the total path loss of the channel. In this paper, we start our investigation with LOS channels with lognormal fading parameters to demonstrate the proof of concept for our proposed search algorithm. In this case, the choice of a coverage region with radius of R = 600 m is reasonable. Later, we will employ the empirical model given in (14) to investigate NLOS media. We demonstrate in the following sections that the searching procedure is dependent on the path loss characteristic of the channel, and the radius of the coverage is determined by the channel loss characteristics. To enable the use of adaptive array antennas at the BS, we assume that the maximum available array size at the BS is 144 elements on a square grid; i.e., \(12\times 12\) elements with half wavelength spacing. This allows us to exploit smaller portions of the array such as \(4\times 4\) or \(8\times 8\) as necessary for broader coverage where less power can be used. It will also be shown later that the use of adaptive array antennas offers many advantages in terms of flexibility and efficiency for cell search procedure. The antenna at each UE is assumed to be \(4\times 4\) with half wavelength spacing (total of 16 elements).  
The BS periodically transmits the PSS signals, one every \(T_{per}\) seconds as shown in Figure 2[21; 22]. The duration of the signal is denoted as \(T_{sig}\) seconds, which is the length of each time slot. Since the number of slots \(N_{slot}\) determines the total time required for the PSS signal detection, minimizing \(N_{slot}\) will significantly reduce the total time required for the initial cell search process, that is, the time for a UE in the cell to detect the PSS signal. As mentioned in the Introduction section, the use of directional antennas at BS plays an important role in determining the number of time slots required. Therefore, in this paper, given the microcell structure in Figure 1, our main objective is to determine the optimal search patterns using adaptive array at BS such that the entire area is covered by a minimum number of time slots.