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:
& \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
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 ).


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

如上所述,小小区集群中的覆盖问题主要包括覆盖空洞、大邻居重叠、小区过载和低吞 吐量。覆盖优化的目标是尽量减少这些问题。需要注意的是,为了减少覆盖空洞、嘈杂 的邻居重疍和小区过载,可以部署一个控制中心来使小型小区相互协作。SBS 和中央控 制器之间需要频繁的信息交换,需要足够的回程连接。如果系统中没有控制中心或回程 连接受限,则应采用分布式覆盖优化,旨在最大化吞吐量并且只需要邻居之间的少量信 息交换。
对于集中式方法,目标是减少覆盖空洞,避免响亮的邻居重㫜和小区过载。因此,目标 函数可以表示为面积覆盖率,由下式给出
f=\frac{\sum S_{\text {cover }}}{\sum S_{\text {cover }}+\sum S_{\text {hole }}+\sum S_{\text {overlap }}}
在哪里 $\Sigma S_{\text {cover }}$ 区域是否正确覆盖,没有覆盖孔和重疍, $\Sigma S_{\text {hole }}$ 和 $\Sigma S_{\text {overlap }}$ 分别是覆 盖空洞的面积和与响亮的邻居重叠的面积,以及 $\Sigma S_{\text {cower }}+\Sigma S_{\text {havele }}+\Sigma S_{\text {overlap }}$ 是 目标区域。
然而,在真实网络中,很难测量这些空间的面积。因此,代替(9)中所示的区域覆盖 率,采用用户覆盖率(参见下面的(10))来评估覆盖质量。优化问题因此表述如下:
\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
在哪里 $N_{\text {semede }} N_{\text {hole }}, N_{\text {loud }}$ 和 $N_{\text {overtaad }}$ 分别是正常用户数、空洞用户数、大声邻居 重疍区用户数和被小区过载拒绝的用户数; $P_{\min }$ 和 $P_{\max }$ 分别是 SBS 的最小和最大传输 功率。如前所述, $N_{\text {semede }}, N_{\text {balle }}, N_{\text {loumd }}$ 和 $N_{\text {onerlaad }}$ 可以从UE的测量报告中获 得。显然,当正常状态用户较多,空洞、大声邻居重疍区和过载用户较少时,用户覆盖 率(10)增加,覆盖质量较好。

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”)。
在small cell集群中, small cell的行为很像蜂群: 它们不能太近也不能太远;一个实体 (小型小区) 的变化可能会影响相邻实体;相邻实体需要共同协作以获得全球最佳解决 方案。因此,粒子群算法可以用来解决小、区集群的覆盖优化问题。首先,在小蜂窝簇 与群体中的粒子之间建立关联,导频小蜂窝发射功率和粒子位置,以及功率调整和粒子 速度。此外,(10) 可以作为 PSO 中的适应度函数。在标准 PSO
(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]
在哪里 $\bar{P}i(t+1)$ 和 $\bar{P}_i(t)$ 是更新的、当前的和导频的 $\mathrm{SCN}$ 发射功率 $i$ ,分别和 $\bar{\delta}_i(t+1)$ 和 $\bar{\delta}_i(t)$ 分别是更新的和当前的功率调整。而且, $\omega$ 是惯性权重,通常设置为 正值,从 1.4 减少到 0.5 以提高 PSO 的性能(Shi \& Eberhart,1998)。Pshest ${ }^i(t)$ 是粒子找到的最优解 $i$ 在之前的迭代中,即导频发射功率矢量SCN可以达到最好的覆盖 率。 $\vec{P}$ ghest $(t)$ 是所有发现的最佳导频发射功率矢量 $N$ 以前的粒子 $t$ 迭代。 $r_1$ 和 $r_2$ 是均 匀分布的随机值 $[0,1]$. . (15)中的第二项 $c_1 r_1\left[\vec{P} s b e s t^i(t)-\vec{P} i(t)\right]$ 代表个人影响力和 第三任期 $c_2 r_2\left[\vec{P}{\text {gbest }}(t)-\vec{P}_i(t)\right]$ 称为社会影响力。 $c_1$ 和 $c_2$ 分别是个人和社会术语 的权重,两者都可以设置为 2 (Kennedy \&\& Eberhart, 1995)。

经济代写|博弈论代写Game Theory代考







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