Backhaul metro cell-based guard channel in femto/macro cellular heterogeneous networks

Abstract

The heterogeneous network (HetNet) deployed small cells technology in order to overcome the problems of holes “blind spots” coverage in 3G and 4G mobile networks. In this work, we propose a hierarchical HetNet layout comprises of three layers, macro, metro and femto cells. The metro cell is deployed as a backhaul layer in-between macro cell and femto cell layers and operates in a complementary fashion to fulfill handover (HO) traffic interplay between successive layers. Accordingly, the femto cell serves indoor traffic activity of femto users, while metro cell serves the outdoor traffic activities as well as the overflow traffic from femto cells. In addition, in order to reduce the failure probability of femto users handed over to metro cell, a guard channel scheme is employed to prioritize the HO call over new call requests. The highest layer in HetNet, macro cell only serves macro users and the overflowed traffic from the lower layer. Then, we develop a realistic teletraffic model in order to measure the QoS metrics of the proposed HetNet. The numerical results show the capability of HetNet with coexisting small cells to offload traffic from traditional macro cellular network in terms of reducing the blocking probability.

Appendices

Appendix A

In this Appendix, we derive the probability $P_{nc}$, let $X$ and $Y$ denote the time duration from an intermediate instant to the border of the metro cell and the time duration from the instant the session starts to the instant the femto user comes to the border of its femto cell. Due to the memoryless property, the random variable $X$ follows the same exponential distribution with mean $1/\eta _{m}$. However, due to the FUEs and femto cell are randomly distributed within the metro cell, the time duration $Y$ is uniformly distributed in $X$. Then for $t >0$, the probability density function (pdf) of $Y$ is given by

$$\begin{aligned} f_Y (t)=\int _{x=t}^\infty {\frac{1}{x}(\eta _m e^{-\eta _m x})} dx=\eta _m \int _{\eta _m t}^\infty {\frac{e^{-x}}{x}} dx \end{aligned}$$

(38)

By using Mathematica package, the pdf of $Y$ can be expressed as

$$\begin{aligned} f_Y (t)=\eta _m \Gamma (0,\eta _m t), \end{aligned}$$

(39)

where $\Gamma (a,x)$ is an upper incomplete Gamma function which given by.

$$\begin{aligned} \Gamma (a,x)=\int _x^\infty {\gamma ^{a-1}e^{-\gamma }} d\gamma \end{aligned}$$

(40)

Taking Laplace transform of (39), we have

$$\begin{aligned} f_Y^*(s)=\left\{ {\frac{\ln (1+s/\eta _m )}{s/\eta _m }} \right\} \end{aligned}$$

(41)

Then the probability $P_{nc}$ can be expressed as

$$\begin{aligned} P_{nc} {=}\Pr \{ Y<T_C \}{=}f_Y^*(\mu _C )\, \hbox {then}\, P_{nc} {=}\left\{ {\frac{\ln (1{+}\mu _C /\eta _m )}{\mu _C /\eta _m }} \right\} \nonumber \\ \end{aligned}$$

(42)

Appendix B

In this Appendix, we derive the mean value of $Z,\, E\{Z\}$. The cumulative distribution function of the random variable $Z$ is given by

$$\begin{aligned} F_Z (t)= & {} 1-[1-F_Y (t)][1-F_{T_C } (t)]\nonumber \\= & {} 1-e^{-\mu _C t}+F_Y (t)e^{-\mu _C t} \end{aligned}$$

(43)

The Laplace transform of the CDF $F_Z (t)$ is given by

$$\begin{aligned} F_Z^{*} (s)=\frac{\mu _C }{s\cdot (\mu _C +s)}+F_Y^{*} (s+\mu _C) \end{aligned}$$

(44)

The Laplace transform of the pdf of the random variable $Z$ is given by

$$\begin{aligned} f_Z^*(s)=s\cdot F_Z^{*} (s)=\frac{\mu _C }{(\mu _C +s)}+s\cdot F_Y^{*} (s+\mu _C ) \end{aligned}$$

(45)

Then the mean value of $Z$ is given by

$$\begin{aligned} E\{Z\}= & {} -\frac{df_Z^{*} (s)}{ds}|_{s=0}\nonumber \\= & {} \frac{1}{\mu _C }-F_Y^{*} (\mu _C )=\frac{1}{\mu _C }-\frac{1}{\mu _C }f_Y^{*} (\mu _C )\nonumber \\= & {} \frac{1}{\mu _C }-\frac{1}{\mu _C }\left[ {\frac{\ln (1+\mu _C /\eta _m )}{\mu _C /\eta _m }} \right] \end{aligned}$$

(46)