Performance analysis of an advanced heterogeneous mobile network architecture with multiple small cell layers

Abstract

The integration of small cell technologies into the current mobile network operators is a necessity for providing capacity and coverage improvement in the future mobile networks (5G). This integration paves the way for heterogeneous networking. In this paper, a novel heterogeneous architecture for the efficient integration of small cell technology into the current mobile networks is developed, namely advanced heterogeneous mobile network (AHMN). AHMN architecture consists of a stack of multiple cell layers wherein the upper layer is the macrocell layer while under this layer, a number of lower small cell layers are formed. Focusing on femtocells and metrocells, as the most typical paradigms of small cells, a femtocell layer which serves the indoor traffic activity of femtocell users is considered, while the metrocell serves the outdoor traffic activities as well as the overflow traffic from femtocells. The overall heterogeneous network (HetNet) is completed with the macrocell overlay layer, which serves only the macrocell users and the overflowed traffic from the underlay metrocell layer. In the proposed AHMN architecture, the metrocell layer is deployed as a complementary layer between the macrocell and femtocell layers and facilitates the handover traffic interaction between the edge layers. Meanwhile, the mobility management in this architecture is critical and hence, the interaction between successive network layers, due to the handover (HO) traffic, is analyzed. Furthermore, for each network layer, a guard channel scheme is proposed in order to minimize the HO dropping rate of the mobile users. We show both analytically and by simulation the capability of AHMN in offloading traffic and reducing the blocking/dropping probability compared with the traditional macrocellular network.

Appendices

Appendix 1

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 metrocell and the time duration from the instant the session starts to the instant the FUE 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/η _m . Meanwhile, due to the femtocell users (FUEs) and femtocell are randomly distributed within the metrocell, the time duration Y is uniformly distributed in X. Then for t > 0, the probability density function (pdf) of Y is given by

$$f_{Y} (t) = \int_{x = t}^{\infty} {\frac{1}{x}(\eta_{m} e^{{- \eta_{m} x}})} dx = \eta_{m} \int_{{\eta_{m} t}}^{\infty} {\frac{{e^{- x}}}{x}} dx$$

(43)

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

$$f_{Y} (t) = \eta_{m} \varGamma (0,\eta_{m} t),$$

(44)

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

$$\varGamma (a,x) = \int\limits_{x}^{\infty} {\gamma^{a - 1} e^{- \gamma}} d\gamma$$

(45)

Taking Laplace transform of (44), we have

$$f_{Y}^{*} (s) = \left\{{\frac{{\ln (1 + s/\eta_{m})}}{{s/\eta_{m}}}} \right\}$$

(46)

Then the probability P _nc can be expressed as

$$P_{nc} = \Pr \{Y < T_{C} \} = f_{Y}^{*} (\mu_{C})$$

(47)

Then

$$P_{nc} = \left\{{\frac{{\ln (1 + \mu_{C}/\eta_{m})}}{{\mu_{C}/\eta_{m}}}} \right\}$$

(48)

Appendix 2

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

$$\begin{aligned} F_{Z} (t) & = 1 - [1 - F_{Y} (t)][1 - F_{{T_{C}}} (t)] \\ & = 1 - e^{{- \mu_{C} t}} + F_{Y} (t)e^{{- \mu_{C} t}} \\ \end{aligned}$$

(49)

The Laplace transform of the CDF $F_{Z} (t)$ is given by

$$F_{Z}^{*} (s) = \frac{{\mu_{C}}}{{s \cdot (\mu_{C} + s)}} + F_{Y}^{*} (s + \mu_{C})$$

(50)

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

$$f_{Z}^{*} (s) = s \cdot F_{Z}^{*} (s) = \frac{{\mu_{C}}}{{(\mu_{C} + s)}} + s \cdot F_{Y}^{*} (s + \mu_{C})$$

(51)

Then the mean value of Z is given by

$$\begin{aligned} E\{Z\} & = - \frac{{df_{Z}^{*} (s)}}{ds}|_{s = 0} \\ & = \frac{1}{{\mu_{C}}} - F_{Y}^{*} (\mu_{C}) = \frac{1}{{\mu_{C}}} - \frac{1}{{\mu_{C}}}f_{Y}^{*} (\mu_{C}) \\ & = \frac{1}{{\mu_{C}}} - \frac{1}{{\mu_{C}}}\left[{\frac{{\ln (1 + \mu_{C}/\eta_{m})}}{{\mu_{C}/\eta_{m}}}} \right] \\ \end{aligned}$$

(52)