Energy efficiency analysis of IEEE 802.15.6 based wireless body area networks in scheduled access mode

Abstract

This paper investigates the energy efficiency of IEEE 802.15.6 based wireless body area networks in the scheduled access mode. We assume that the hub operates in beacon mode with superframes and the nodes obtain scheduled allocation intervals consisting of finite number of allocation slots from the hub. In this paper, first of all, we present analytical models to compute the energy efficiency of the network for various scheduled allocation and acknowledgement policies assuming ideal channel conditions. The numerical and simulation results show that energy efficiency can be improved by (1) increasing the number of uploads in an active superframe, (2) increasing the payload size, (3) adopting block acknowledgement policy instead of immediate acknowledgement policy or (4) by decreasing the periodicity of allocations. We then present an analytical model to evaluate the energy efficiency in the presence of channel error. An approximate analytical solution for optimal frame size that maximize the energy efficiency of the network in error prone channel is obtained. For each node, we also provide analytical expression for the optimal allocation interval per superframe that maximize the energy efficiency of the network. Through extensive simulation studies, we establish that, in an error prone channel, the energy efficiency can be improved if the nodes make use of computed optimal frame size and optimal allocation interval for the uplink data transfer.

Appendix

Derivation of (54).

We consider (41) and try to get an optimal solution for $N^{*}_{Data}$ by setting $\dfrac{\partial {\eta ^{error}_{IAck}}}{\partial {N_{Data}}}$ =0. We make a few valid approximations to get the closed form solution for $N^{*}_{Data}$ . First of all, we assume that the energy consumption in the sleep and the idle states are negligible (since current consumption in these states are low as per Table 3). Further, we assume that Ack packets are transmitted by the hub for all the p uploads. In Eq. (5), we fix $M=2, S_{PLCPhdr}= 4$ and $S_{\textit{PSDU}}= 1$ [3]. Accordingly, the total header size is 286 bits consisting of PHY header $H_{p}$ of 214 bits and MAC header $H_{m}$ of 72 bits. Hence $N_{DataPSDU}$ of (1) can be approximated as equal to $N_{Data}+ H_{m}$. Removing the ceil function for simplification, Eq. (34) can be written as equal to $1-y^{(N_{Data}+H_{m})/k}$, where $\hbox {y}=1-P_{blk}$ and $N_{DataPPDU}$ of Eq. (5) can be approximated as equal to $H_{p} +(N_{Data}+ H_{m})n/k$. The numerator of (41) can be simplified as

$$\begin{aligned} u=y^{(N_{Data}+H_{m})/k}\;p\;((\psi _{TXData}P_{TX}+\psi _{RXData}P_{RX})T_{s})\;N_{Data}\;n/k \end{aligned}$$

(57)

We assume all p Ack frames are received by the node and accordingly the energy consumption of the node given by (39) can be approximated as:

$$\begin{aligned} \begin{aligned} v_{1}&\quad =E_{RXBeac}+E_{decBeac} +pT_{s}\;\psi _{TXData}P_{TX}(H_{p} +(N_{Data}+ H_{m})n/k)\\&\quad \quad +p(E_{RXIAck}+E_{decIAck})+2E_{Wup} \end{aligned} \end{aligned}$$

(58)

We further simplify the analysis by assuming that the energy for decoding the data frames to be negligible and hence the energy consumption of the hub given by (40) can be approximated as:

$$\begin{aligned} \begin{aligned} v_{2}&\quad =E_{TXBeac}+pT_{s}\;\psi _{RXData}P_{RX}(H_{p} +(N_{Data} + H_{m})n/k)\\&\quad \quad +pE_{TXIAck} \end{aligned} \end{aligned}$$

(59)

The energy efficiency given by (41) can be written as $\eta ^{error}_{IAck} \simeq u/(v_{1}+v_{2})$. The optimal frame size $N^{*}_{Data}$ is obtained by the solution of $\partial {(\eta ^{error}_{IAck})}/\partial {N_{Data}}$ =0 and is given by (54).