# On the Optimisation of Practical Wireless Indoor and Outdoor Microcells Subject to QoS Constraints
## 1 Introduction  
Microcells along with macrocells have come a long way in mobile telecommunication industry to not only increase the capacity of the traditional cellular networks but also enlarge the coverage area of ultra-densed networks to support the distant area with low signal strength and high-mobility users [1; 2; 3; 4]. The mixture of cells of different sizes forms a generalised network model of multiple overlaying layers or tiers, namely heterogeneous wireless cellular networks [2; 5; 6; 7; 8; 9; 10; 11; 12], which have been shown to provide higher data rate and enhanced coverage for indoor and outdoor mobile users. Along with a number of advantages achieved with cell division approaches, the deployment of microcells raises a critical issue in cellular networks when the overlapping frequencies of different cells in the same area cause considerable interferences [13; 14]. The overlapping coverage also implies the wastage of resources, whereas a smaller number of cells could be used to maintain the same coverage area. Network planning and optimisation therefore need to be considered in the implementation of microcells in practical cellular networks. Recently, power control mechanism has been investigated with various power allocation and scheduling approaches to minimise the transmitted power at cells for mitigating interferences in cellular networks while still guaranteeing sufficiently received signal power at the mobile users [15; 16; 17; 18; 19]. However, considering the practical cellular networks, a number of buildings and mobile devices cause considerable fading, shadowing, noises and interferences. The signal-to-interference-plus-noise ratio is shown to be intractable for a heterogeneous network model and the conventional wireless cellular networks represented by hexagonal grids are too idealised to model the real networks [20; 21]. In order to model large-scale wireless networks, stochastic geometry has been exploited to develope tractable models that can not only realise the characteristics of the random network topology but also allow us to evaluate the performance of variant network models with tractable analytical results [20; 22; 23; 24; 25; 26; 27]. Although network planning and modelling have been studied in the literature with various approaches (e.g., [28; 29; 30; 31; 32; 33; 34; 35; 36; 37; 38; 39]), their deployment in the practical heterogeneous networks has still raised a number of concerns to cope with various building structures, antenna specifications, location, etc., which to the best of the authors' knowledge has not been well investigated and optimised, and thus costs mobile/telecommunications company high capital expenditures and operating expenses. In this paper, we investigate the optimisation of wireless indoor and outdoor microcells (WIOMs) in the practical networks subject to constraints of the coverage and quality-of-service (QoS) requirements. The main contributions of this paper can be summarised as follows:  
* An optimisation problem is firstly developed to minimise the number of cells subject to the constraints of the required coverage and QoS at a specific area within a WIOM network. Given the fact that the locations for deploying the cell sites are restricted, the locations of these optimal cells are also required to be determined. * A binary-search based cell positioning (BSCP) algorithm is proposed to not only find the optimal number of cells but also their optimal location given a preset candidate antenna positions. It is shown that the proposed BSCP allows us to determine the minimal number of cells with a low computational complexity compared to the conventional approach where exhaustive searches are utilised to iteratively validate all available locations for cell sites. * EDX SignalPro [40] is exploited as a simulation platform to verify the effectiveness of the proposed BSCP for the WIOMs.