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Table 2 Averaged optimal set \(\left \{\mathrm {E}\{{x^{o}_{r}}\}, \mathrm {E}\{{y^{o}_{r}}\}, \mathrm {E}\{{P^{o}_{1}}\}, \mathrm {E}\{{P^{o}_{2}}\}\right \}\) for on-body transmissions

From: Joint optimal relay location and power allocation for ultra-wideband-based wireless body area networks

Along-torso scenario ( d r =0)

d SD

0.5 m

0.6 m

0.7 m

0.8 m

\(\text {E}\{{x^{o}_{r}}\}\)

−0.30

−0.36

−0.42

−0.48

\(\text {E}\{{y^{o}_{r}}\}\)

0

0

0

0

\(\text {E}\{{P^{o}_{1}}\}\)

0.70 P s

0.70 P s

0.70 P s

0.70 P s

\(\text {E}\{{P^{o}_{2}}\}\)

0.30 P s

0.30 P s

0.30 P s

0.30 P s

Around-torso scenario when d r =0 . 2 m

d SD

0.5 m

0.6 m

0.7 m

0.8 m

\(\text {E}\{{x^{o}_{r}}\}\)

−0.41

−0.51

−0.61

−0.70

\(\text {E}\{{y^{o}_{r}}\}\)

0

0

0

0

\(\text {E}\{{P^{o}_{1}}\}\)

0.40 P s

0.48 P s

0.54 P s

0.59 P s

\(\text {E}\{{P^{o}_{2}}\}\)

0.60 P s

0.52 P s

0.46 P s

0.41 P s

Around-torso scenario without body motion when d r =0 . 2 m

d SD

0.5 m

0.6 m

0.7 m

0.8 m

\(\text {E}\{{x^{o}_{r}}\}\)

−0.42

−0.52

−0.62

−0.72

\(\text {E}\{{y^{o}_{r}}\}\)

0

0

0

0

\(\text {E}\{{P^{o}_{1}}\}\)

0.42 P s

0.50 P s

0.56 P s

0.61 P s

\(\text {E}\{{P^{o}_{2}}\}\)

0.58 P s

0.50 P s

0.44 P s

0.39 P s