*4.2. Energy Consumption of Wireless Nodes*

Typically, in the task-offloading paradigm, computing tasks are created by end devices (e.g., wireless sensor nodes, central devices). Therefore, the energy requirement at the level of the wireless node, as well as the network, are emphasized. Therefore, characterizing the energy consumption of the end device is crucial to create a balance between the energy requirement, demands and consumption. Essentially, the wireless sensor node is composed of four main units: energy management unit, communication unit, data processing unit and sensing unit. The energy management unit is responsible for converting the energy retrieved from either the battery or the energy-harvesting circuit into a suitable energy level, which can be used to supply the electronics of the node. Using energy harvesting helps to reduce the dependency on the battery power by extending the lifetime of the node itself [78]. The communication unit contains the radio transceiver module used for wireless communication. The processing unit is the core of the node, where all data processing and node activity is carried out. The last unit contains the embedded sensors, which can be either passive or active and are responsible for the sensing and actuating tasks. Basically, the effective lifetime of the node is dependent on the available, residual energy and the required amount of energy to successfully carry out the assigned task. Consequently, the total energy consumption is deducted in relation to the energy supply and energy consumption during data processing and communication. Considering the

energy provided by the harvesting module and the module consumption, the effective residual energy at a time instance *t* is estimated in accordance with the consumed, harvested and residual energy amounts of the previous time instance.

$$E\_{\rm Res}(t) = E\_{\rm Res}(t-1) - E\_{\rm Cons} + E\_{\rm Hartree} \tag{4}$$

*ERes*(*t*), *ERes*(*t* − 1), *ECons* and *EHarv* are the residual energy of the node at a time instance *t*, the residual energy at a time instance (*t* − 1), energy consumption and the energy of the harvesting module, respectively (see Appendix A).

The general definition of the energy consumption within a sensor node is presented in Equation (5).

$$E\_{\rm Cons} = E\_{\rm transceiver} + E\_{\rm System} + E\_{\rm Sening} \tag{5}$$

where *ETransceiver*, *ESystem* and *ESensing* are the energy consumed during the reception and transmission of data packet, energy consumed within the coding and decoding activities and the energy consumed during sensing activities, respectively.

With respect to the standard energy consumption model, the *ETransceiver* is presented based on the transmitter and receiver electronic definition as presented in Equations (7) and (9). The total energy consumption, within the radio module during data transmission, becomes:

$$E\_{\rm Cons} = E\_{\rm R\_x} + E\_{T\_x} + E\_{\rm System} + E\_{\rm Sening} \tag{6}$$

The energy of transmission and reception are dependent on the number of transmitted data bits over a distance *d*, where *Eelec* is the electrical energy of the circuitry needed to transmit or to receive a *l* bit data packet. *d* is the distance between the receiver and transmitter.

$$E\_{T\_x} = \begin{cases} E\_{elec} \times l + E\_{fs} \times l \times d^2 \,, \quad d \le d\_T\\ E\_{elec} \times l + E\_{amp} \times l \times d^4 \,, \quad d > d\_T \end{cases} \tag{7}$$

The distance between both transmitter and receiver is dependent on the medium access and therefore, it is defined based on *ǫ<sup>f</sup>* and *ǫamp*, which present the energy consumption factor for free space and for the multipath radio models, respectively. The threshold distance *d<sup>T</sup>* is defined as:

$$d\_T = \sqrt{\frac{\mathfrak{e}\_{fs}}{\mathfrak{e}\_{amp}}}\tag{8}$$

The energy consumption during the reception is defined based on the number of communicated bits *l*, which is defined in Equation (9). The list of the used parameters with their typical values is illustrated in Appendix A.

$$E\_{R\_x}(l) = E\_{\text{elec}} \times l \tag{9}$$

Eventually, the effective energy consumption of a wireless node depends strongly on how often it sends and receives data packets, and processes sensor information.

Task offloading offers a promising solution to reduce the workload on the installed devices, by adopting specific algorithms where the task realization is offloaded to devices with efficient energy sources and computation capabilities. In the context of WBANs and wearable solutions, intensive computing is mitigated from the wireless sensor to the edge and from the cloud to the fog. It presents an efficient solution to manage the intensive communication and computation in a limited energy source environment. Moreover, by adopting an energy-harvesting solution, the energy of the system can be kept available to carry out the assigned tasks in real time and continuously, which remains challenging for different applications, such as in the case of real-time and continuous pulse monitoring [79], motion tracking [80], exoskeleton manipulation [81] and the maintenance and monitoring of implantable devices [82]. To this end, providing continuous and efficient power supply to wearable and implantable devices presents a highly addressed challenge in recent

research [83–85]. As part of this, integrating energy-harvesting technologies with taskoffloading approaches allows end devices to endure for a long time to support long-term task processing [86–88].
