# 经济代写|博弈论代写Game Theory代考|Low Throughput

## 经济代写|博弈论代写Game Theory代考|SCN Coverage Optimization

As described above, coverage problems in small cell clusters mainly include coverage holes, loud neighbor overlap, cell overload and low throughput. The target of coverage optimization is to minimize these problems. It should be noted that to reduce coverage holes, loud neighbor overlap and cell overload, a control center could be deployed to make the small cells collaborate with each other. Frequent information exchange is needed between SBS and central controller which needs sufficient backhaul connection. If there is no control center in the system or the backhaul connection is limited, distributed coverage optimization should be employed which aims to maximize the throughput and only needs little information exchange between neighbors.

For centralized method, the target is to reduce coverage hole, avoid loud neighbor overlap and cell overload. Thus the objective function can be formulated as an area coverage ratio, given by
$$f=\frac{\sum S_{\text {cover }}}{\sum S_{\text {cover }}+\sum S_{\text {hole }}+\sum S_{\text {overlap }}}$$ where $\Sigma S_{\text {cover }}$ is the area properly covered without coverage holes and overlapping, $\Sigma S_{\text {hole }}$ and $\Sigma S_{\text {overlap }}$ are the area of coverage holes and overlapped area with loud neighbors, respectively, and $\Sigma S_{\text {cower }}+\Sigma S_{\text {havele }}+\Sigma S_{\text {overlap }}$ is the target area.

However, in real networks, it is difficult to measure the area of these spaces. Therefore, instead of the area coverage ratio shown in (9), a user coverage ratio (see (10) below) is employed to evaluate the coverage quality. The optimization problem is thus formulated as follows:
\begin{aligned} & \max \frac{N_{\text {serred }}}{N_{\text {scrued }}+N_{\text {hole }}+N_{\text {loud }}+N_{\text {ocerload }}} \ & \text { s.t. } \ & P_{\min } \leq P_{t x}(j) \leq P_{\max }, j \in J \ & |U(j)| \leq \Omega \end{aligned}
where $N_{\text {semede }} N_{\text {hole }}, N_{\text {loud }}$ and $N_{\text {overtaad }}$ are the number of normal users, users in holes, users in loud neighbor overlap area and users rejected by cell overload, respectively; $P_{\min }$ and $P_{\max }$ are the minimum and maximum transmission powers of the SBSs, respectively. As described before, $N_{\text {semede }}, N_{\text {balle }}, N_{\text {loumd }}$ and $N_{\text {onerlaad }}$ can be obtained from measurement reports of UEs. Obviously, when there are more users in normal state and less users in holes, loud neighbor overlap area and overload, the user coverage ratio (10) increases, demonstrating a better coverage quality.

## 经济代写|博弈论代写Game Theory代考|Overview of Particle Swarm Optimization

PSO is a population based stochastic optimization technique, inspired by social behavior of bird flocking or fish schooling (Kennedy \& Eberhart, 1995). It has been successfully applied in various research areas to solve multidimensional problems. In PSO, each single solution is a “bird” in the search space, which is called “particle”. The optimization objective is the fitness values of all the particles. A group of particles fly through the problem space by following the current optimum particles and finally the global optimum solution can be obtained (“Swarm Intelligence”).

In small cell clusters, the behavior of small cells is quite swarm like: they cannot be too close or too far away; change of one entity (small cell) may affect neighboring entities; neighboring entities need to collaborate together to get a global best solution. Therefore, PSO can be employed to solve the coverage optimization problem of small cell clusters. First of all, associations are set up between the small cell cluster and the particles in the swarm, pilot transmit power of small cells and particle position, and power adjustment and the velocity of the particle. Moreover, (10) can be taken as the fitness function in PSO. In standard PSO (Kennedy \& Eberhart, 1995; Shi \& Eberhart, 1998), each particle position $P_i$ represents a possible solution, where $i \in[1, N]$ is the index of the particle and $N$ is the population of the particle group. Accordingly, in coverage optimization for $\mathrm{SCN}$, the pilot transmit power of the $\mathrm{SCN} i$ can be associated to the particle position, i.e., $\vec{P}i=\left[P t x_1^i, P t x_2^i, \ldots, P t x_n^i\right]$, where $n$ is the total number of SAPs in the cluster. Assuming that there are $N$ SCNs, the pilot transmit power of SCN $i$ is updated according to $\mathrm{PSO}$ algorithm as follows \begin{aligned} & \bar{P}_i(t+1)=\bar{P}_i(t)+\vec{\delta}_i(t+1) \ & \vec{\delta}_i(t+1)=\omega \vec{\delta}_i(t)+c_1 r_1\left[\vec{P}{\text {stest }}^i(t)-\vec{P}i(t)\right]+c_2 r_2\left[\vec{P}{\text {gbest }}(t)-\vec{P}i(t)\right] \end{aligned} where $\bar{P}_i(t+1)$ and $\bar{P}_i(t)$ are the updated and current and pilot transmit powers of SCN $i$, respectively, and $\bar{\delta}_i(t+1)$ and $\bar{\delta}_i(t)$ are the updated and current power adjustment, respectively. Moreover, $\omega$ is the inertia weight which is usually set to a positive value decreasing from 1.4 to 0.5 to improve the performance of PSO (Shi \& Eberhart, 1998). $\bar{P}{s h e s t}^i(t)$ is the best solution found by particle $i$ in the previous iterations, i.e., the pilot transmit power vector for the $\mathrm{SCN}$ that can achieve the best coverage. $\vec{P}{\text {ghest }}(t)$ is the best pilot transmit power vector found by all $N$ particles in the previous $t$ iterations. $r_1$ and $r_2$ are random values uniformly distributed in $[0,1]$. The second term in (15) $c_1 r_1\left[\vec{P}{s b e s t}^i(t)-\vec{P}i(t)\right]$ stands for personal influence and the third term $c_2 r_2\left[\vec{P}{\text {gbest }}(t)-\vec{P}_i(t)\right]$ is called social influence. $c_1$ and $c_2$ are weights for personal and social terms, respectively, and both can be set to 2 (Kennedy \& Eberhart, 1995 ).

# 博弈论代考

## 经济代写|博弈论代写Game Theory代考|SCN Coverage Optimization

$$f=\frac{\sum S_{\text {cover }}}{\sum S_{\text {cover }}+\sum S_{\text {hole }}+\sum S_{\text {overlap }}}$$

$$\max \frac{N_{\text {serred }}}{N_{\text {scrued }}+N_{\text {hole }}+N_{\text {loud }}+N_{\text {ocerload }}} \quad \text { s.t. } P_{\min } \leq P_{t x}(j) \leq P_{\max }, j \in J$$

## 经济代写|博弈论代写Game Theory代考|Overview of Particle Swarm Optimization

PSO 是一种基于种群的随机优化技术，其灵感来自鸟群或鱼群的社会行为 (Kennedy $\backslash \&$ Eberhart, 1995)。它已成功应用于各个研究领域，以解决多维问题。在 PSO 中，每一 个单解都是搜索空间中的一只“鸟”，称为”粒子”。优化目标是所有粒子的适应度值。一 群粒子跟随当前最优粒子在问题空间中飞行，最终得到全局最优解（”群体智能”）。

(Kennedy\&Eberhart, 1995; Shi\&Eberhart, 1998) 中，每个粒子位置 $P_i$ 代表一个可能的 解决方案，其中 $i \in[1, N]$ 是粒子的指数和 $N$ 是粒子群的种群。因此，在覆盖优化中 $\mathrm{SCN}$ ，导频发射功率 $S C N i$ 可以与粒子位置相关联，即 $\vec{P} i=\left[P t x_1^i, P t x_2^i, \ldots, P t x_n^i\right]$ ， 在哪里 $n$ 是集群中 SAP 的总数。假设有 $N \mathrm{SCNs}$ ， SCN的导频发射功率泿据更新PSO算法如下
$$\bar{P}i(t+1)=\bar{P}_i(t)+\vec{\delta}_i(t+1) \quad \vec{\delta}_i(t+1)=\omega \vec{\delta}_i(t)+c_1 r_1\left[\vec{P}{\text {stest }^i}(t)-\vec{P} i(t)\right]$$

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