**6.2. Energy results**

14 Will-be-set-by-IN-TECH

BS <sup>B</sup>

A

A

C

Case 10

B

distance to the BS increases. Cases 2-7 form a group of similar cases where the only variation is a permutation of the SNs involved in the connections. As expected, these cases have almost equal probability of being the optimal case for a given value of *d*LR. The same reasoning applies for Cases 8-13 and Cases 14-16. Interestingly, Cases 8-13 were never optimal in the

In fact, with Cases 2-7, and considering Case 2 as an example, SN A transmits *ST* bits on the LR, SN C transmits *ST* bits on the SR, and SN B transmits 2*ST* bits (its own data in addition to the data of SN C) on the LR. With Cases 14-16, and considering Case 14 as an example, SN B transmits *ST* bits on the SR, SN C transmits *ST* bits on the SR, and SN A transmits 3*ST* (its own data in addition to the data of SNs B and C) bits on the LR. In Cases 8-13, and considering Case 8 as an example, SN C transmits *ST* bits on the SR, SN B transmits 2*ST* bits (its own data in addition to the data of SN C) on the SR, and SN A transmits 3*ST* (its own data in addition to the data of SNs B and C) bits on the LR. Since the SNs are deployed in a confined area of interest, and since SR transmissions in this case can occur at high rates due to the relative proximity of SNs, Cases 14-16 would generally lead to lower energy consumption than Cases 8-13, since both groups have the same LR energy consumption (due to transmitting 3*ST* on the LR by one SN), but on the SR each of the other two SNs transmits *ST* with Cases 14-16. However, with

Case 15

BS

C

Case 4

BS <sup>B</sup>

BS <sup>B</sup>

C

C

A

Case 11

C

A

BS <sup>C</sup>

A

A

B

Case 12

C

Case 16

BS

BS <sup>C</sup>

B

A

Case 7

BS <sup>C</sup>

B

A

Case 13

B

A

B

Case 6

BS <sup>C</sup>

A

Case 5

BS <sup>B</sup>

BS <sup>A</sup>

B

B

C

Case 8

A

**Figure 3.** The 16 possible cases when *K* = 3.

Case 14

BS

BS <sup>A</sup>

C

C

B

Case 9

C

B

B

Case 3

BS <sup>A</sup>

C

Case 2

BS <sup>A</sup>

BS <sup>A</sup>

Case 1

obtained results.

B

C

This section presents the energy savings achieved by using the proposed multihop and clustering methods, compared to the non-cooperative scenario. In the non-cooperative approach, each SN sends the data on the LR to the BS without any collaboration with other SNs on the SR. Fig. 5 shows the normalized energy results for the various investigated scenarios. Significant energy savings are achieved compared to the non-cooperative scenario, regardless of the number of hops allowed. In fact, the clustering approach corresponding to *H* = 2 and the multihop approach with *H* = *K*, thus representing the two extreme cases, have a very comparable performance in terms of normalized energy. Fig. 5 shows that the gains are reduced as the distance to the BS decreases. This is due to a reduction in the energy needed on the LR without cooperation and not to an increase in energy consumption with the proposed approach, since the LR distance was reduced. This leads to an increase in the ratio *η*.

In fact, the results of Fig. 6, presenting the energy consumption results without normalization, show that the energy is reduced when the distance to the BS is reduced, as expected. The results of the energy consumption in the non-cooperative scenario are shown in Fig. 6 for reference. Values for *d*LR = 1000 m are not shown, since they are around an order of magnitude larger than the cooperative results, which makes all the plots of the various

**Figure 5.** Normalized energy consumption vs. the number of SNs for different values of *d*LR.

**Figure 6.** Energy consumption vs. the number of SNs for different values of *d*LR.

cooperative scenarios appear to overlap. Thus, the combination of Figs. 5 and 6 allows to display both the gains of cooperation compared to the non-cooperative scenario and to understand the variation of the energy gains with the distance to the BS.

### **6.3. Delay results**

16 Will-be-set-by-IN-TECH

Multihop: dLR=300m Clustering: dLR=300m Multihop: dLR=500m Clustering: dLR=500m Multihop: dLR=1000m Clustering: dLR=1000m

Multihop: BS at center of 1x1km cell Clustering: BS at center of 1x1km cell

0 5 10 15 20 25 30 35 40 45 50

Number of sensor nodes

0 10 20 30 40 50

Number of sensor nodes

**Figure 5.** Normalized energy consumption vs. the number of SNs for different values of *d*LR.

Multihop: dLR=300m Clustering: dLR=300m No cooperation: dLR=300m Multihop: dLR=500m Clustering: dLR=500m No cooperation: dLR=500m

**Figure 6.** Energy consumption vs. the number of SNs for different values of *d*LR.

0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1

Energy (Joules)

Normalized energy (η)

**Figure 7.** Average delay per SN vs. the number of SNs for different values of *d*LR.

In this section, the impact of multihop-based energy minimization on delay performance is investigated. The transmitter at each hop is considered to wait until it receives all the data from the previous hop before starting transmission. In addition, at each hop, it is considered that transmission is done in parallel using orthogonal channels within the same cluster or within clusters at close proximity. The channels can be reused at clusters located further away. This corresponds, in practice, to the use of OFDMA with different subchannels allocated to each transmitter-receiver link, or to the use of CDMA with different orthogonal codes allocated to each transmitter-receiver link.

Fig. 7 shows the delay results averaged over the SNs. However, in delay sensitive applications, the interest is in the delay incurred by each SN. Therefore, Fig. 8 shows the maximum delay, i.e., the delay incurred by the last SN to send its data to the BS. In other words, this corresponds to the total delay needed to transmit the measurements of all SNs in the network, thus corresponding to the worst case result. Figs. 7 and 8 show that the delay increases with the distance to the BS, since a longer distance leads to lower achievable rates on the LR,

**Figure 8.** Total delay to distribute the content to all SN vs. the number of SNs for different values of *d*LR.

which leads to an increase in data transmission time. In addition, the clustering approach outperforms the multihop approach by leading to shorter delays in all the investigated scenarios. Fig. 7 shows that when SNs are deployed in a confined area at a distance *d*LR from the BS, the multihop approach leads to average delays comparable to the non-cooperative scenario when *d*LR = 300m, and to better average delay performance when *d*LR increase to 500m. The trend continues with larger distances. When the BS is placed at the cell center, with the SNs deployed throughout the cell area, the non-cooperative scenario leads to better average delay than the multihop approach, but not than the clustering approach.

Fig. 8 shows that the proposed cooperative methods significantly outperform the non cooperative case by leading to shorter maximum delay. Particularly, the clustering method leads to considerably shorter maximum delay compared to both the multihop approach and the non-collaborative scenario.

Thus, the suboptimal clustering approach leads to significant energy savings that are comparable to the multihop approach as shown in Figs. 5 and 6, and it leads to much shorter delays in transmitting the measurement data as shown in Figs. 7 and 8, and thus constitutes a suitable approach leading to both energy and delay efficiency in WSNs.

### **6.4. Bandwidth savings**


**Table 4.** Number of Collaborative Clusters for *K* = 50

In this section, traffic offloading from the BS due to using the proposed approach is investigated. Table. 4 shows the number of SNs transmitting the data directly to the BS on the LR, in the case where a network of *K* = 50 SNs is deployed. This corresponds to the number of wireless channels needed on the LR. It should be noted that in the example of Table. 4, the multihop and clustering approach lead to the same number of clusters, although the transmission occurs on different routes inside each cluster. From Table 4 it can be seen that a significant portion of the LR bandwidth can be freed due to implementing the proposed approach. In fact, around 46%, 68%, and 84% of the bandwidth can be saved when *d*LR = 300, 500, and 1000 meters, respectively. In addition, when the WSN is deployed throughout the cell area with the BS at the cell center, 30% of the LR bandwidth can be saved. When the proposed approach is implemented network wide, the significantly reduced loads of some BSs might be accommodated by other more loaded BSs. The initial BSs would be switched-off in this case. Hence, the proposed approach would contribute to green communications at the BS level, although its initial purpose was to save battery energy of SNs.
