# Optimal Base Station Density of Dense Network:
## 1 Introduction
### Motivation and Related Work  
Although network densification can offer greater capacity and offload more data traffic from existing congested networks, the growth of interference among SmBSs accelerates, particularly since the interferers are nearer and larger in number. Interference will then become the biggest constraint to network capacity improvement. Initially, when SmBSs are sparse, increasing the density can provide more available channels and enhance the network capacity. Nevertheless, as the density grows, the interference will heavily degrade the signal-to-interference-plus-noise ratio (SINR) and limits the capacity. It brings an interesting question: is there an optimal SmBS density that maximizes the network capacity?  
However, a further issue that needs to be considered is that high SINR (or link capacity) does not necessarily mean high throughput. If the base station is congested, its performance can also be poor. This is why we often lose mobile connection even though it displays full signal strength on our phones. Thus, contrary to intuition, aggressively offloading users to SmBSs is not always right and can lead to severe performance degradation. This is particularly significant for those SmBSs working in unlicensed bands where BSs are operating in listen before talk (LBT) mode and back off if collision happens. In such a situation, load fulfills the same important role as SINR does, for unreasonable load assignment eventually exhausts channel resources and aggravates the throughput. Therefore, how can the offloading be load-aware?  
Exploring these two interesting questions is the subject of this work. There is a significant amount of research focusing on the issue of network densification. For example, [PERSON] et al. [6] and [PERSON] et al. [7] explored the energy efficiency from perspectives of the joint scheduling method and deployment strategies. [PERSON] et al. [8] and [PERSON] et al. [9] investigated the backhaul through both theoretical and practical solutions. Other questions in dense network, such as spectrum sharing [10,11], small cell discovery [12], resource management [13,14], mobile caching [15], small cell boundary [16] and the economic issues [17] of densification were also researched in the references. However, these works did not solve the problem of interference, which is one of the biggest problems in dense networks.  
Some research has noted the problem of interference. Interference management was considered in [18,19] using cooperative bargaining game and mean-field game, respectively. [PERSON] et al. [20] and [PERSON] et al. [21] proposed time-frequency domain algorithm and power allocation algorithm to coordinate the inter-cell interference. In addition, the same question was considered by [PERSON] et al. [22] using a power control scheme. Nevertheless, these works have not examined the relation between interference and densification, namely how the base station density influences the interference and what the limit of densification is. They are the fundamental questions of interference in ultra-dense networks. To answer the above questions, the calculation of the interference in dense HetNets is necessary. However, it is tricky since the location of base stations in HetNets is random and irregular. A tractable model to describe the location of irregularly deployed BSs is proposed in [23], called Poisson point process (PPP). Based on this model, several key metrics of HetNets performance were studied, such as coverage probability and SINR distribution [24, 25, 26, 27]. Nevertheless, these works have still not given the answer to the optimal base station density for maximizing the capacity of dense network. In addition, all existing research lacks consideration about the load of small cell base stations, especially when these BSs work in contention-based channels. Thus, none can answer the two questions asked above.