# Game Algorithm for Resource Allocation Based on Intelligent Gradient in HetNet
## 2 System Model  
The paper adopts a downlink bilayer HetNet model consisting of a macro base station and femtocells. Figure 1 schematically shows a downlink communication system. Downlink transmission links in the HetNet model consist of five parts. The solid line represents the useful signal, while the dash line represents the interference signal. The community contains one macro base station \(m\) and several femtocells \(F_{j},j\in\{1,2,\ldots,N\}\). Base stations of the same type are in the same layer and enjoy the same transmitting power. In previous system models, femtocells are normally randomly and evenly distributed. However, in actual environment, different regions have different requirements for capacity. Thus, the actual network deployment will display a certain feature of randomness. Hence, we build a commonly applicable HetNet model with consideration of random and independent distribution of base stations. Femtocell is assumed to be subject to an independent Poisson point process with a density of \(\lambda_{j}\), and this process is only related with the parameter of density. Macro users and femtocell users are assumed to be randomly distributed, with a number of \(S_{m}\) and \(S_{Fj}\), respectively [22; 23]. Then \(m_{i}\) refers to the \(i\)th macrocell user, and \(F_{j,i}\) refers to the \(i\)th user of \(S_{Fj}\). Considering spectrum scarcity and increasing capacity demand, full frequency multiplex has become a main feature of a multilayer HetNet [24], but it will lead to severe cross-layer interference, especially when macro users are close to a femtocell. The channel transmission model is a mixed one consisting of path loss and shadow fading with logarithmic normal distribution. The overlapping of the two can reflect the decrease of signal strength with distance and random decline of path loss caused by obstacles (indoor walls) in communication link, hence restoring the actual communication link to the largest degree [25]. Based on base station and location information of users, modeling is conducted of SINR of different users for analysis. For macro users, they undergo interference of all femtocells in the community. It is assumed that the macro base station has a transmitting power of \(P_{m}\) located at (0, 0) and, for each \(j\) in \(\{1,2,\ldots,N\}\), a femtocell \(F_{j}\) located at \(\left(x_{j},y_{j}\right)\) and with a transmitting power of \(P_{F_{j}}\), namely \(FBS_{j}\). When macro base station user \(m_{i}\) is located at \(\left(x,y\right)\), urban space transmission formula \(128+37.6\times\log_{10}(dist)\)[26] is adopted, where \(dist\) means the distance between the user and base station. The SINR of the user can be calculated as follows:  
\[SINR_{m_{i}}=\frac{P_{m,m_{i}}}{\sum_{j=1}^{N}P_{F_{j},m_{i}}+N_{0}} \tag{1}\]  
where \(P_{m,m_{i}}\) and \(P_{F_{j},m_{i}}\) are the received signal power from \(m\) and \(F_{j}\) to the user \(m_{i}\) respectively, which are calculated as \(P_{m,m_{i}}=P_{m}\cdot 10^{-\frac{128+37.6\times\log_{10}\left(x^{2}+y^{2} \right)^{1/2}}{10}}\) and \(P_{F_{j},m_{i}}=P_{F_{j}}\cdot 10^{-\frac{128+37.6\times\log_{10}\left(x-x_{j} \right)^{2}+\left(y-y_{j}\right)^{2}}{10}}\). \(N_{0}\) is the noise power. For femtocell user \(F_{ij}\), they will undergo interference from macro base station and other femtocells. Each \(k\) in \(\{1,2,\ldots,N\}\), a femtocell \(F_{k}\) located at \(\left(x_{k},y_{k}\right)\) and with transmitting power of \(P_{F_{k}}\), namely \(FBS_{k}\). When the femtocell user \(F_{i,j}\) is located at\(\left(x_{f},y_{f}\right)\), the received signal power mentioned in the Equation (2) will adopt indoor space transmission formula \(127+30\times\log_{10}(dist)\)[27].