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LTE heterogeneous networks (HetNets) is becoming a popular topic since it was first developed in 3GPP Release 10. HetNets has the advantage to assemble various cell networks and enhance users’ Quality of Service (QoS) within the system. However, its development is still constrained by two main issues: 1) Load imbalance caused by different transmission powers for various tiers, and 2) The unbalanced transmission power may also increase unnecessary handover rate. In order to solve the first issue, Cell range expansion (CRE) can be applied in the system, which will benefit lower-tier cell during user association phase; CRE, Hysteresis Margin (HM) and Time-to-Trigger (TTT) will be utilized to bound UE within lower tier network of HetNets and therefore solve the second issue. On the other hand, the relationship of these parameters may be complicated and even reduce QoS if they are chosen incorrectly. This paper will evaluate the advantage and disadvantage of all three parameters and propose a Markov Chain Process (MCP) based method to find optimal HM, CRE and TTT values. And then, the simulation is taken and the optimal combination for our scenario is obtained to be 1 dB, 6 dB and 60 ms respectively. First contribution of this paper is to map the HetNets handover process into MCP and all the phases of handover can be calculated and analysed in probability way, so that further prediction and simulation can be realised. Second contribution is to establish a mathematical method to model the relationship of HM, CRE and TTT in HetNets, therefore the coordination of these three important parameters is achieved to obtain system optimization.

In 3GPP Release 10 [

First issue is load imbalance caused by different transmission powers for various tiers. Due to structure of HetNets, UEs within the network may receive signals not only from same tier but also higher tiers. Since UEs prefer to choose signal with higher receiving power to obtain a better user quality of service (QoS), they may stick to higher tier cells and refuse to offload to lower tier cell. As a result, HetNets cannot operate efficiently higher tier cell that is overloaded while lower tier cell is of no use [

In order to solve the first issue, the 3GPP first introduced the Cell Range Expansion (CRE) in release 10, this parameter can be considered as a virtual bias that added to the actual UE received power part to help UE with the association decision, the CRE is a practical power control technique in 3GPP standardization [

The second issues can be solved by reasonable selecting different HM values to control the Handover Rate (HOR). As introduced in the previous part, the utilization of CRE will cause great impact in handover procedures. The deterministic of CRE is normally based on the cell load and network system performance, HOR is not considered when the CRE is chosen. It is introduced another virtual bias which is called handover Hysteresis Margin (HM) [

This paper is organized as follows, in section two, a brief introduction of HetNets system model is included [

With the set up of the aforementioned three parameters, the mobility model of the UE can be determined. We consider that each UE has its initial location information, moving speed and moving direction associating to the current

serving cell from time 1, which is represented by TTI 1. The current serving cell at TTI 1 is decided by the Receive Signal Strength (RSS) from different cells RSSm and RSSs. After TTI 1, the UEs will start to move as its assigned mobility model until TTI reaches 100. Due to the change of locations, UE’s distance to macro cell (D_{m}) and small cell (D_{s}) will change accordingly. When the UE move to the small cell boundary and the RSS of the serving and target cell represented by RSS_{S} and RSS_{T} satisfy Equation (1) for TTT time a handover will happen.

R S S T ≥ R S S S + H M (1)

Due to HetNets scenario applied in this paper, two different pathloss model is adopted for different tier UEs. The pathloss model for macro cell UE can be expressed as Equation (1). The distance d is in kilometres.

δ M , t , k = 128.1 + 37.6 log 10 ( d M , t , k ) (2)

The distance d is in kilometres, the δ_{M,t,k} can be understanding as the pathloss of k UE at time slot t with macro cell M. In a HetNet scenario [

δ S , t , k = 140.7 + 36.7 log 10 ( d S , t , k ) (3)

where the S inside the subscript represent the cell type is small cell. Then, we define the included angle θ as the angle of UE and small cell, the distance between macro cell and small cell is expressed as D which is shown in _{m} and D_{s} can be calculated as:

D m = D 2 − 2 D D s cos 2 ( θ ) + D s 2 (4)

Based on Equation (2) and Equation (3) the RSS_{i,t,k} of a certain UE allocated to a certain cell at each time slot can be calculated.

R S S i , t , k = P t i , t , k ξ i , t , k δ i , t , k (5)

The Signal to Interference and Noise Ratio (SINR) can be derived from Equation (5), which is shown as follows.

S I N R i , t , k = P t i , t , k ξ i , t , k δ i , t , k ∑ j = 1 , j ≠ i n P t j , t , k ξ j , t , k δ j , t , k + σ 2 (6)

In Equation (6), the numerator represents the receiving signal strength which is affected by variables i, t and k. Similarly, the interference is the summation of surrounding cells signal strength and expressed by the first part of denominator. While, the second part σ^{2} is the thermal noise.

We applied the same Markov model from our previous work [

In order to achieve the optimization values for HetNets, probability formula should be obtained from this MCP. Consider a UE’s initial state is M1, which represents that it is link to a macro cell right now. Its probability of moving to next state M2 is P_{M(x)}, meanwhile, its probability of moving back to itself is 1- P_{M(x)}. The same rule applies for all M states until Mn transfer to I1, which means that handover process is initiated. Within I states, it has 100% chance to move to next I state till handover process is finished and UE has been reallocated to small cell, which is in S1 state. The rules for S and I’ are the same for M and I states, so that the whole MCP loop is established. One important property for I and I’ states is that traffic signals play the dominant part to guarantee the handover process during these phases. Consequently, UE can barely receive information signal during handover states and too many handover phases will dramatically reduce the UE’s QoS.

Since we have understood all the states’ physical meanings, we may be able to establish transfer probability formula, which is P_{M(x)} and P_{S(x)} shown in _{M,x,k}) but also from small cell (RSS_{S,x,k}). These two signal powers will compete to transfer UE from S states to I’ states. When RSS_{M,x,k} is the greater one, it will lead to the situation that UE has the intention to initiate handover process and reluctant to stay in small cell network. The situation will be opposite if RSS_{S,x,k} is the larger one. At this time, HM bias, α, and CRE bias, β, will increase the weight of RSS_{S,x,k} and constrain UE from moving back to the macro cell, which is shown in Equation (8). In Equation (7), however, they may play the opposite roles because CRE has another function to offload UEs from macro cell to small one.

The transfer probability formulas are expressed as below:

P M ( x ) = β R S S S , x , k α R S S M , x , k + β R S S S , x , k (7)

P S ( x ) = R S S M , x , k R S S M , x , k + α β R S S S , x , k (8)

Transfer Matrix T can be obtained after the MC process and its transit probability is defined, then, the model of UEs’ handover process affecting by HM and CRE is established.

M1 | M2 | M3 | M4 | I1 | I2 | I3 | I4 | S1 | S2 | S3 | S4 | I1' | I2' | I3' | I4' | |
---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|

M1 | 1-_{PM(x)} | _{PM(x)} | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 |

M2 | 1-_{PM(x)} | 0 | _{PM(x)} | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 |

M3 | 1-_{PM(x)} | 0 | 0 | _{PM(x)} | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 |

M4 | 1-_{PM(x)} | 0 | 0 | 0 | _{PM(x)} | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 |

I1 | 0 | 0 | 0 | 0 | 0 | 1 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 |

I2 | 0 | 0 | 0 | 0 | 0 | 0 | 1 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 |

I3 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 1 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 |

I4 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 1 | 0 | 0 | 0 | 0 | 0 | 0 | 0 |

S1 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 1-_{PS(x)} | _{PS(x)} | 0 | 0 | 0 | 0 | 0 | 0 |

S2 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 1-_{PS(x)} | 0 | _{PS(x)} | 0 | 0 | 0 | 0 | 0 |

S3 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 1-_{PS(x)} | 0 | 0 | _{PS(x)} | 0 | 0 | 0 | 0 |

S4 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 1-_{PS(x)} | 0 | 0 | 0 | _{PS(x)} | 0 | 0 | 0 |

I1' | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 1 | 0 | 0 |

I2' | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 1 | 0 |

I3' | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 1 |

I4' | 1 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 |

V x = V 1 ∏ i = 1 x T i (9)

In Equation (9), the V_{1} is the probability of UE’s initial state, which is expressed as 1 in the vector. For example, if a macro cell UE is in the state M1 in time 1, then its initial probability vector will be expressed as [1, 0, 0, ..., 0]. With the TTI increases, the UE is moving, which will cause the probability Pmx and Psx changing in the Markov Transfer Matrix (T), according to Equation (9), the vector V will also change. As a result, the vector for any UE at any step x can be calculated, so that the HOR in each state will be obtained.

In this section, simulation is taken to analyse the CRE, HM and TTT under different combination, the simulated parameters are summarized in

Parameters | Value |
---|---|

Carrier frequency | 1800 MHz |

Bandwidth | 1 MHz |

Cell layout | Single macro to small cell |

Transmit power of macro cell | 40 W/46 dBm |

Transmit power of small cell | 0.25 W/24 dBm |

Noise power | −174 dBm |

Number of TTI | 100 |

CRE | 1 - 10 dB |

HM | 1 - 10 dB |

TTT | 40, 60, 80, 100 ms |

network efficiency can be maintained. As a result, CRE and HM may take opposite effects on handover control when UEs try to handover from macro cell to small cell. It also explains why handover rate will still remain 3% no matter what CRE value the network takes. However, HM’s effect on increasing total throughput is limited due to its lack of offloading effect in HetNets network. Its rapid effect of handover control also restricts that HM bias may not reach a large value. Therefore, an optimal combination of CRE and HM value is required for HetNets network.

Equation (7), CRE will help to offload UEs from macro cell to small cell. As TTT’s effect on handover drops, CRE may lead a small growth of handover rate for I states in

By analysing the relationship among CRE, HM and TTT, TTT is set to be 60 ms, which meets our predefined mobility model. Then, the combination of CRE and HM is simulated by optimizing system total throughput and

This paper proposes a Markov Chain Based Process to model HetNets system and analyses three main parameters during HetNets UEs offloading and handover―HM, CRE and TTT. This paper also establishes a mathematical method to model the relationship of HM, CRE and TTT in HetNets, therefore the coordination of these three important parameters is achieved to obtain system optimization. Finally, the optimal combination of HM and CRE for system performance is generated by our proposed MCP model, which is 1 dB and 6 dB respectively. However, the mobility model in our current work is not practical yet because we assume all the UEs’ velocity remains still during the whole TTT. In our future work, we will focus on establishing a more realistic mobility model and also take further study on how the velocity changing affects HetNets Handover.

This work was partly funded by the European Union’s Horizon 2020 research and innovation programme under grant agreement No. 734798.

Zhang, B.L., Qi, W.J. and Zhang, J. (2017) A Markov Based Performance Analysis of Handover and Load Balancing in HetNets. Int. J. Communications, Network and System Sciences, 10, 223-233. https://doi.org/10.4236/ijcns.2017.1010013