Directional Cell Search Delay Analysis for Cellular Networks With Static Users

Cell search is the process for a user to detect its neighboring base stations (BSs) and make a cell selection decision. Due to the importance of beamforming in 5G cellular networks including both the millimeter wave and sub-6 GHz networks, there is a need for a better understanding of the directional cell search delay performance. A cellular network with fixed BS and user locations is considered, so as to take into account the strong temporal correlations that exist for the SINR experienced by each BS and user in this context. For Poisson cellular networks with Rayleigh fading channels, a closed-form expression for the spatially averaged mean cell search delay of all users is derived. This mean cell search delay for a noise-limited network is proved to be infinite whenever the non-line-of-sight path loss exponent is larger than two. For interference-limited networks, a phase transition for the mean cell search delay is shown to exist in terms of the number of BS beams <inline-formula> <tex-math notation="LaTeX">$M$ </tex-math></inline-formula>: the mean cell search delay is infinite when <inline-formula> <tex-math notation="LaTeX">$M$ </tex-math></inline-formula> is smaller than a threshold and finite otherwise. Beam-sweeping is also demonstrated to be effective in decreasing the cell search delay, especially for cell edge users.