**4.1. Collecting Information stage**

In this block the MS with BS assistance try to collect the information about some criteria that will help the cell selection decision. As highlighted earlier, this paper proposes three criteria decision, viz; CINR, BW and Congestion delay.

For the CINR criteria, the SBS regularly broadcast information about the nBSs through the neighbour advertisement messages (MOB\_NBR-ADV). Additionally, the MS and the SBS can retrieve more information about the nBSs after the MS finished scanning, such as CINR and RSSI. The CINR is defined as the power ratio between a carrier and the interference and noise power [5].

$$\text{CINR} = 10 \log\_{10} \frac{\text{C}\_r}{P\_I + P\_N} \tag{15}$$

Where, *Cr* is the received carrier power, *PI* is the interference power and *PN* is the noise power. The available BW in WiMAX cell metric can be estimated based on [11]; after scanning process, the MS can exploit the information element (IE) in the DL-MAP/UL-MAP messages and aggregate the number of the allocated downlink and uplink physical slots (PSs). The available

**Alternatives ranking using TOPSIS** 

**Collecting Info**

CINR

Weighted CINR

**Criteria weighting using AHP**

Weighted BW

BW

Congestion delay

Hybrid AHP and TOPSIS Methods Based Cell Selection (HATCS) Scheme for Mobile WiMAX

Weighted Congestion delay

t

Where *τ* is the period of time that we can get number of frame, *SDL* <sup>−</sup> *free* is the number of unused PSs within *τ* while the *CDL* <sup>−</sup>*slot* is the number of bits that can be transmitted in one downlink

Every nBS will inform the SBS its congestion delay through the backbone, and the SBS will

AHP is used to determine the weights for the three criteria -- CINR, BW and delay. It was reported that classical MADM methods cannot efficiently handle a decision problem with


**Cell Selection**

http://dx.doi.org/10.5772/55894

93

<sup>1</sup> ( ) ( ,) () *DL DL free DL slot BW t S t t C t*

send these values to the MS by the advertisement messages (MOB\_NBR-ADV).

t

downlink BW can be estimated as follows;

**Figure 3.** The proposed cell selection scheme

**Application QoS requirements**

**4.2. Weighting criteria using AHP**

imprecise data that decision criteria could contain [14].

PS.

Hybrid AHP and TOPSIS Methods Based Cell Selection (HATCS) Scheme for Mobile WiMAX http://dx.doi.org/10.5772/55894 93

**Figure 3.** The proposed cell selection scheme

**Figure 2.** AHP calculation processes

92 Selected Topics in WiMAX

TOPSIS method.

power [5].

**4.1. Collecting Information stage**

decision, viz; CINR, BW and Congestion delay.

**4. Hybrid AHP and TOPSIS based cell selection**

The conventional cell selection scheme in Mobile WiMAX is only based on the received signal strength. However, it is not sufficient to meet the different user application requirements that WiMAX promises to meet. The proposed scheme considers multiple criteria; CINR, BW and congestion delay for cell selection using some MCDM methods, AHP and TOPSIS. As shown in Figure 3, the proposed cell selection scheme can be divided into three main functions: "collecting info" which collects the decision criteria and network conditions, "criteria weight‐ ing" which processes criteria weighting using AHP methods based on application QoS requirements, and "alternatives ranking" which finalizes the process of cell selection using

In this block the MS with BS assistance try to collect the information about some criteria that will help the cell selection decision. As highlighted earlier, this paper proposes three criteria

For the CINR criteria, the SBS regularly broadcast information about the nBSs through the neighbour advertisement messages (MOB\_NBR-ADV). Additionally, the MS and the SBS can retrieve more information about the nBSs after the MS finished scanning, such as CINR and RSSI. The CINR is defined as the power ratio between a carrier and the interference and noise

<sup>10</sup> 10log *<sup>r</sup>*

*<sup>C</sup> CINR*

*I N*

*P P* <sup>=</sup> <sup>+</sup> (15)

Where, *Cr* is the received carrier power, *PI* is the interference power and *PN* is the noise power.

The available BW in WiMAX cell metric can be estimated based on [11]; after scanning process, the MS can exploit the information element (IE) in the DL-MAP/UL-MAP messages and aggregate the number of the allocated downlink and uplink physical slots (PSs). The available downlink BW can be estimated as follows;

$$BW\_{DL}(t) = \frac{1}{\tau} \quad S\_{DL-free}(t-\tau, t) \quad C\_{DL-slot}(t) \tag{16}$$

Where *τ* is the period of time that we can get number of frame, *SDL* <sup>−</sup> *free* is the number of unused PSs within *τ* while the *CDL* <sup>−</sup>*slot* is the number of bits that can be transmitted in one downlink PS.

Every nBS will inform the SBS its congestion delay through the backbone, and the SBS will send these values to the MS by the advertisement messages (MOB\_NBR-ADV).

#### **4.2. Weighting criteria using AHP**

AHP is used to determine the weights for the three criteria -- CINR, BW and delay. It was reported that classical MADM methods cannot efficiently handle a decision problem with imprecise data that decision criteria could contain [14].

For that, the use of fuzzy logic can be used to deal with imprecise information and combine and evaluate multiple criteria simultaneously. Hence, fuzzy logic concept provides a robust mathematical framework in which handover decision can be formulated as a Fuzzy MADM.

alterative score is chosen for the TBS. As mentioned earlier, TOPSIS concept is that the chosen alternative should have the shortest distance from the positive ideal solution (PIS) and the farthest from the negative. More explanation about this will be discussed in details in the

Hybrid AHP and TOPSIS Methods Based Cell Selection (HATCS) Scheme for Mobile WiMAX

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95

In this section a numerical analysis of the proposed scheme is performed, and then compared with the Weighted Sum Method (WSM) and conventional signal strength based cell selection. The criteria weighting based on user application requirements have been calculated previ‐ ously, as shown in equation (17) and (18) for real-time and non real-time applications respec‐

Suppose that we have three candidate TBSs as shown in Figure 1. After the information collection stage, the MS will maintain the criteria values in a decision matrix, *Dm*(*A*). The decision matrix consists of three criteria, viz CINR in dB, BW in Kbps and congestion delay in

1 23 2048 300

*CINR BW Cong Delay*

é ù ê ú <sup>=</sup> ê ú

(19)

(20)

(21)

3 24 148 110

Using the TOPSIS method, *Dm*(*A*) first has to be normalized first using equation (7), because

1 0.5770 0.9807 0.8960

é ù ê ú <sup>=</sup>

3 0.6021 0.0709 0.3285

1 0.3569 0.0649 0.2822

é ù ê ú <sup>=</sup>

3 0.3724 0.0047 0.1035

ë û

After getting the normalized decision matrix, it is weighted using by multiplying it with the weighting factor. Two types of application have been considered, therefore, we have two

ë û

( ') 2 0.5519 0.1820 0.2987

For the real-time application, the weighted decision matrix is as shown in equation (21).

( ') 2 0.3414 0.0120 0.0941

ê ú ë û

( ) 2 22 380 100

*BS*

*BS*

the criteria use different units. The normalized matrix is shown in (20).

*BS*

*BS*

weighting factors, which will produce two weighted decision matrices.

*BS*

*BS*

*Dm A BS*

*r*

*Dm A BS*

*Dm A BS*

numerical analysis section.

**5. Numerical analysis**

ms for three candidate BSs as shown in (19).

tively.

The scale used is represented by the intensities between each other according to the funda‐ mental scale. The fundamental scale is validated according to effectiveness and theoretical justifications according to [18]. The scale consists of nine levels. To make it even easier to judge, one can use a more restricted scale with five levels: 1 is equal importance, 3 is moderate importance, 5 is strong importance, 7 is very strong or demonstrated importance and 9 is extreme importance. Because different application have different requirements, in this paper, we consider two types of application -- VoIP as a real-time application example and Media Content Downloads as a non-real-time application example. Tables 2 and 3 show the pair-wise relative importance of the decision criteria for the real-time and non real-time applications respectively.


**Table 2.** Pair-wise Matrix for real-time application


**Table 3.** Pair-wise Matrix for non real-time application

Based on the AHP procedure explained earlier the weighting vector for the real time applica‐ tion and non real-time applications are as shown in equations (17), and (18).

$$w\_r = \begin{bmatrix} 0.6186 & 0.0662 & 0.3149 \end{bmatrix} \tag{17}$$

$$w\_{nr} = \begin{bmatrix} 0.6186 & 0.3149 & 0.0662 \end{bmatrix} \tag{18}$$
