The performance of the proposed relay positioning algorithm is compared with that of the exist- ing algorithm [28] in networks with a single client and a single base station since no literature,
network. As the purpose of this subsection is the comparison of the search performance for relay positions of dierent algorithms in indoor environments, we will present the detailed evaluations of the channel prediction accuracy and the Gaussian process-based communication maps used in this comparison in the next section.
In [28], the optimal relay positions are obtained on the shortest RRT path between the base and client using the virtual force method. The RRT path from the base station to the client is generated, and the relays move on this 1-D RRT path. Consider n+ 2 agents consisting of Agent0 as the base, Agenti as the ith∈ {1,· · · , n}relay, and Agentn+1 as the client. The agents are congured as in Fig. 22 in which si denotes the RSSI between Agenti and Agenti+1 where i∈ {0,· · · , n} and fj(sj−1, sj) is the virtual force exerted to the Agentj where j ∈ {1,· · · , n}
as a function of the RSSIs between the node and its neighboring nodes. In each iteration, the virtual forces exerted to the relays are determined depending on the signal dierences between the adjacent nodes. For instance, Relayi moves towards Relayi+1(i.e. to the right side in Fig. 22) on the generated RRT path ifsi is worse thansi−1 (i.e.si−1> si). The higher the signal quality
Figure 22: Virtual force and network conguration.
dierence is, the stronger the virtual force is exerted to Relayi, the implication of which is the bigger shift of relay position towards the adverse signal along the path. The relays might be able to converge to a set of positions with better network performance as the movements towards the worse signal are expected to improve the signal quality in general. In this study, an RRT path is generated and segmented into 0.1m-long segments. Randomly initialized on the path, the position of Relayi is updated as:
xk+1i =xki +fik+1 (33)
fik+1=ski−1−ski, i∈ {1,· · ·, n}, (34) where xki, fik, ski, and n denote the position, virtual force, the next hop signal quality of the Agenti at kth iteration, and the number of the relays, respectively.
This relay positioning method might not be able to exactly pinpoint the optimal relay posi- tion due to the fact that the search area is restricted to a single path; better relay points not on the path can be found as a slight movement can induce the signicant change of signal quality in indoor environments.
For the comparison of the RRT-based approach with our algorithm, two environments are considered and the algorithms are implemented with one to three relays. The base and client is placed in the rst environment as depicted in Fig 23. The signal quality between the two nodes is signicantly attenuated due to the NLOS(non-line-of-sight) and the large internodal distance.
Table 4: The performance of the relay positioning methods in the rst environment (40 runs).
Optimized WCC cost, dBm Approach Number of relays
mean standard deviation
w/o relays - -77.90 -
1 -68.54 0.8676
2 -56.74 2.220
RRT-based [28]
3 -51.79 1.550
1 -65.41 0.0136
2 -54.18 0.3844
Proposed
3 -49.88 0.0229
Table 4 demonstrates the performance of the three approaches: without relays, the RRT- based algorithm, and the proposed algorithm, each of which was implemented 40 times. In all cases, the averages of the optimized WCC (OWCC) costs show that the network performance was signicantly improved compared to the case without relays. Note that although the mean values of OWCC for the RRT-based and proposed approaches are similar, the standard deviations of the RRT-based algorithm are considerably larger than those of the proposed algorithm. The deviations may be derived from the premature convergence of the gradient-based optimization and the variations of the generated RRT paths in each simulation. Considering these results the proposed algorithm outperformed the RRT-based algorithm in the environment. Figure 24 shows the sample relay positioning result of the two approaches in the rst environment when two relays are used. Even though the shortest path from the base to the client was found mostly in the right side corridor, the optimal relay positions found by the proposed algorithm were place in the left side corridor as shown in Fig. 24.
The second environment for the algorithm comparison is provided in Fig 25. In this case, a thin layered obstacle is placed on the shortest way from the base station to the client in the original map. Table 5 provides the average performance of 40 runs of the two approaches.
Table 5: The performance of the relay positioning methods in the second environment (40 runs).
Optimized WCC cost, dBm Approach Number of relays
mean standard deviation
w/o relays - -49.60 -
1 -51.95 8.787
2 -52.75 4.391
RRT-based [28]
3 -49.79 1.460
1 -39.24 0
2 -36.73 0.0130
Proposed
3 -36.27 0
Figure 25: Second environment for the algo- rithm comparison.
Figure 26: Relay positioning results in the sec- ond environment.
Figure 26 illustrates the sample result of the relay positioning with two relays in the second environment. Interestingly, notwithstanding the use of the relays, the average OWCC costs of the RRT-based algorithm was inferior to the WCC performance of the network even without relays. This is due to the restriction on search area to the geometrically feasible path between
nodes. The additional obstacle precludes the feasible shortest path through itself from being generated whereas wireless communication in the environment remains more or less intact. The placement of the obstacle results in the dramatic change in the RRT path but with the minor changes in communication quality between nodes. Consequently, the RRT-based algorithm ends up having longer physical distance between the base, relays and client as shown in Fig. 26; this clearly shows the limitation of the RRT-based algorithm in a certain environment. On the other hand, the proposed approach results in much better performance and substantially consistent results regardless of the number of the relays. In fact, the proposed algorithm returned almost the identical OWCC costs throughout the 40 runs.
5 Optimal Relay Positioning Experiments
Indoor relay positioning experiments are carried out to validate the proposed algorithm. Ex- periment setup including hardware and software and experiment results are described in this section.
5.1 Experiment Setup