Optimization of Heterogeneous Network Performances Based on the Signal Interferences Noise Ration ( SINR )

Integration of wireless and mobile networks to new generations constitutes a heterogeneous system, this is the case of LTE and WiFi networks. In this paper, we study and analyze the optimal performances of this system regarding the SINR(Signal Interference Noise Ration), the blocking probability and the user communication loss. The user mobility is represented by random wayPoint(RWP) model and users terminals equipped with multiple accesses interfaces. We have established a Markov chain to assess and analyze the performances obtained from the heterogeneous networks system. So we have proposed an average value of the signal power emitted in down-ling voice, the blocking probability of system connections.


Introduction
Considering the current tendency of high demand and the presence communication almost everywhere, the global mobility of services and users, the use and the deployment of wireless access and mobiles become a necessity.As they have different characteristics, these networks can support various services.So, the ideal is to build several networks in the same place to satisfy the diversity user's choices; it is the case of the complementarity Lte (4G) and Wi-Fi networks available presently.The heterogeneousness of these networks must be accompanied by an adequate user mobility such as Random waypoint which better represent the individual movements with stops, departures and other actions were related to an individual movement in the urban places.New methods of saving, transmission and sharing of the bandwidth are imperative.Among these methods we targeted the selection technique of better network based on the SINR whose selection parameters are the blocking probability and connections losses.
In the literature, we have noted the most used selection techniques of a network.The authors (Shen & Zeng, 2008) analyzed the signal power received (RSNS) then the available bandwidth(TBNS) of a heterogeneous networks system.They exploited this system parameters such as the blocking probability and connections losses, but they did not take into account the interference in their selection strategies that they displayed which made less successful the results obtained from the blocking probability and connections losses.Besides the works of (Yang & al., 2007), (Ayyappan & al., 2009), (Al-Ghadi & al., 2011) and (Yang & al., 2007) took into account the interference in the selection techniques that they adopted which is the one based on the SINR, which allowed them to improve the connections losses probability during a vertical handover.However, they did not approach through their analyses the connections blocking parameters.These are studied on the other hand by (Jabban & al., 2012) who obtained more satisfactory results than those of the authors who precede them by taking into account the system performances related to the blocking probability or better connections quality.Besides, (Vuong & al., 2007) took into account the user mobility(terminal-controlled mobility management) and other aspects such as the cost, the battery life cycle and the handover frequency.
But through all these studies, authors did not take into account the constraint based on the number of users occupying these bandwidth units to decrease an available congestion of the system.The peculiarity of our model of connections and disconnections of a user is that if he is connected, the system leaves a given state and moves to an other state before returning to this one in a well defined time interval.
The paper is organized as follows: section 2 introduces the model of studied heterogeneous system where all the parameters are established.The algorithm of the selection technique based on the SINR is studied at the level of the section 3. Through the section 4, we developed the users mobility model, which is Random Waypoint(RWP) which we consider more adequate to the individual users movement.The average access demand rate for a service is established in the section 5.The average demand rate of vertical and horizontal handover is calculated through section 6.In section 7, we established a Markov chain to analyze the numbers of units of busy bandwidth and those of the users having occupied these units.The performances system studied such as the SINR and the blocking probability and connections losses are estimated in section 8.The obtained results are simulated in section 9. We ended our study in section 10 by conclusion and future work.

Model of Heterogeneous Networks System
A prototype model of heterogeneous networks system is given by figure 1.Indeed, we have a circular service area Z 1 of radius R 1 covered entirely by the mobile network Lte (4 G).This service area is distributed in several homogeneous circular sub-zones (Z j ) 2≤ j≤m of radius r i among which each is covered by a wireless network (Wi-Fi).So Lte and Wi-Fi overlap in sub-zones Z i and the Wi-Fi networks are separated between them.We denote by Z 0 the part of the service area not covered by a Wi-Fi network.Where from we have: The users is equipped with devices to multiple accesses, have possibility of changing connections in the zones where networks overlap by choosing automatically the network having the highest SINR.In our study, we suppose that the LTE network supplies two types of services: those Multicasts or Unicasts whose numbers of units of bandwidth are respectively B mc 1 and B uc 1 .The number of users occupying these units of bandwidth is respectively N mc 1 and N uc 1 .Besides the numbers of units of bandwidth and users occupying these units at the level of every Wi-Fi network are respectively B i and N i .
In the service area Z 1 , we consider Q interferences sources distributed following a normal random distribution: Q = {I(q), q = 1...Q}.The selection method is based on the SINR then these interferences play a major role at the level of this strategy allowing to select a network.The various parameters of the heterogeneous networks system are assigned in the following table:

Selection Technique Based on the SINR
If a user is in a zone Z i where coexist both Lte and Wi-Fi then he has possibility of connecting recently or by handover to the network Lte or Wi-Fi.If the SINR is raised for the network Lte then the user connects there otherwise he is blocked to connect to the Wi-Fi network.The model RWP is the best adapted to the individual users movements.Indeed, it takes into account the individual users behavior such as their stops, departures and any action concerning the individual movement in a given zone.

Probability Density
The probability density of finding a user situated at a distance x of the convex service area center Z 1 and in a circular zone of radius r i placed at a distance d i of the cluster center is defined by (Hyytia & al., June 2006 ):

Probability P(Z i ) of Finding Users in a Sub-zone Z i
In function of the model RWP and based on results obtained by ()Hyytia & Virtamo, October 2007) , we proved that the average arrival rate of a user in a zone Z i of radius r i and situated at a distance d i of the service area center is established by the equation: 4.2 Probability P(Z i ) of finding users in a sub-zone Z i The probability to find users in a zone Z i of radius r i situated at a distance d i of the cluster center depends directly on the user mobility.So we are based on the RWP and the authors (Bettstetter & Wagner works, March 2002)to prove the probability as following equation: 5. Average New Access Demand Rate λ c(k) Z i for a Service We denote by λ c(k) Z 1 the average access demand rate for a service k in a zone Z 1 .So the average access demand rate for a service k, λ c(k) Z i , situated in a sub-cell Z i is defined by formula: (5) 6. Average Demand Rate of Handovers

Horizontal
Let n k Z 0 average user number accessing to the service k in the zone Z 0 .The average demand rate of horizontal handover τ c(k) Z 0 to the network W 1 for a service k is given by relation: Where η Z 1 Z 0 is the exit flow of users from the zone Z 0 outside of the cell Z 1 and is defined by: With ∆ c(k) the average residence time of users in a zone Z i .

Vertical
Let us denote by n k Z 0 the average number of users mobile accessing to the service k in the zone Z 0 .The average demand rate of vertical handover τ V(k) Z 0 to the network W i users accessing to the service k in the zone Z 0 and moving towards the zone Z i without having finished their connections is given by formula: Where η Z i Z 0 is the exit flow of users from the zone Z 0 towards the cell Z i and is defined by: With ∆ c(k) the average residence time of the users in a zone Z i .

Modeling Approach Based on a Markov Chain
We have established a Markov chain to model and define all the stages and the states of heterogeneous networks system in function of the number of units of busy bandwidth and users numbers occupying these units at real time.
By denoting M and S all the zones of the cluster and services which are available on it, so the size of our Markov chain is: s.(2m − 1) with | M |= m and | S |= s.

Various Stages and States of the System
When we consider the system at the given moment then we characterize it as being a stage of dynamic change.
Besides, the users connections and disconnections of the system define the states space which is given by: If a user n 0 connects to the network Lte in the zone: −1 If a user n 0 disconnects from the network Lte in the zone Z 0 State(E 1,2 ) • Stage 3: −1 If a user n 0 disconnects from the WiFi wireless of the zone • Stage 5: • Stage 6:

Figure 1 .
Figure 1.Model of service zone

ii
connected to the Lte network to the service k in the zone Z 0 n k 1,i Number of users connected to the Lte network to the service k in the zone Z i n k Number of users connected to the Wi-Fi wireless to the service k in the zone Z i b k 1,1 Number of units of busy bandwidth units of the Lte network of the service k in the zone Z 0 b k 1,i Number of units of busy bandwidth units of the Lte network of the service k in the zone Z i b k Number of units of busy bandwidth of the Wi-Fi wireless of the service k in the zone Z i N k PBR Number of resources blocks needed to supply a service k by the network Lte Table 3Number of users connected to the Wi-Fi wireless in the zone Z Number of units of busy bandwidth of the wireless Wi-Fi in the zone Z i • Stage 0:

Table 1 .
Parameters Lte and Wifi networks a user n 0 connects to the network Lte in the zone Z i State(E 2,4 ) −1 If a user n 0 disconnects from the network Lte of the zone Z i State(E 2,5 ) 1)If a user n 0 connects to the network Lte in the zone Z 0 by disconnecting from the network Lte of the zone Z i 1)If a user n 0 connects to the network Lte in the zone Z i by disconnecting from the WiFi wireless of the zone Z i