Sensors_**2013**, _13_, 6448-6476; doi:10.3390/s130506448  
_Sensors_**ISSN 1424-8220**  
www.mdpi.com/journal/sensors  
_Article_  
A Novel Power Efficient Location-Based Cooperative Routing with Transmission Power-Upper-Limit for Wireless Sensor Networks  
**[PERSON] 1, [PERSON] 2,3,*, [PERSON] 4 and [PERSON] 1**  
1 School of Electronics and Information Engineering, Beihang University, Beijing 100191, China; E-Mails: [EMAIL_ADDRESS] (J.S. ); [EMAIL_ADDRESS] (K.L.) 2 Wireless Network Group (WNG), Universitat Polit\(\,\)cnica de Catalunya, c./JordiGirona 1-3 M\(\,\)dul C3, Barcelona 08034, Spain  
3 i2 CAT Foundation, Gran Capit\(\,\)a\(\,\)2-4 (Nexus Building), Barcelona 08034, Spain  
4 Research Center for Eco-environment Sciences, Department of Atmospheric Chemistry, Chinese Academy of Sciences, Beijing 100085, China; E-Mail: [EMAIL_ADDRESS]  
* Author to whom correspondence should be addressed; E-Mail: [EMAIL_ADDRESS]; Tel. : +34-93-401-6013; Fax: +34-93-401-5981. _Received: 22 March 2013; in revised form: 3 May 2013 / Accepted: 9 May 2013 / Published: 15 May 2013_  
==ERROR: No output for this page==
Figure 13 shows the impact of different node density on transmission success rate of the three algorithms. There is an obvious inflection point both in PELCR-TP with and without BAS when the node density is around 0.003/m\({}^{2}\). When the density is larger than this point, the transmission success rate of PELCR-TP algorithm shows a stable and level trend, while a sharp drop when the density is smaller than that point. In addition the inflection point of PLRR appears around 0.008/m\({}^{2}\). The sharp drop of transmission success rate occurs when the average maximum transmission distance nodes can provide in this condition is shorter than the average distance between the nodes, so the value of the inflection point can indirectly reflect the ability of an algorithm that the maximum transmission distance nodes can provide, which can be calculated from Equation (7). This indicates that compared with PLRR algorithm, PELCR-TP algorithm can transmit farther under the same conditions. The inflection points like in Figure 13 also appear in Figure 14, which is likewise caused by insufficient transmission distance according to Equation (7) when the sending power upper limit is very low. However, the difference is that for PELCR-TP algorithm without BAS there is a slope when power upper limit is larger than the inflection point. As this slope does not occur in PELCR-TP algorithm with BAS, it may be caused by the bad nodes' influence. In addition, there is no obvious inflection point for PLRR algorithm. Figure 15 shows the impact of different path loss index on transmission success rate of the three algorithms. Only in the PELCR-TP algorithm with BAS an obvious inflection point appears where \(k\) is around 3.5. The reason for this point can be also attributed to the insufficient transmission distance according to Equation (7) when path loss index is high. The difference between PELCR-TP algorithm with and without BAS, that there is an obvious slope for the latter when \(k\) is smaller than 3.5, may indicate that when the power upper limit is low (0.0001 w) and path loss index is high, according to Equation (8), the outage probability for each hop will increase and create some \"bad nodes\". Here we need to mention that when the path loss index is near 2.0, the transmission success rates of PELCR-TP algorithm with and without BAS, are almost equal and approaching 1.0. This phenomenon can be explained as follows: when the value of path loss index is near 2.0, the transmission environment is close to the ideal environment and the hop number in a whole link will be few, according to Equations (8) and (10); as the destination node cannot be set up as a bad node, it will reduce the ratio  
Figure 16: Transmission success rate _vs_. Bad node rate. +++  
of bad nodes in the entire link. This can also be used to explain the drop of transmission success rate of PLCR algorithm where \(k\) goes from 2.0 to 2.3.