- Research
- Open Access

# A cooperator-assisted wireless body area network for real-time vital data collection

- Miyu Momoda
^{1}Email author and - Shinsuke Hara
^{2}

**2015**:238

https://doi.org/10.1186/s13638-015-0459-2

© Momoda and Hara. 2015

**Received:**25 December 2014**Accepted:**6 October 2015**Published:**29 October 2015

## Abstract

Wearable wireless body area network (WBAN) has attracted considerable attention as a means to collect vital data in sports training and urgent life-critical scenarios, which requires high reliability in links from sensor nodes to a central coordinator. Herein, cooperative relaying, which means retransmission not by sensor nodes themselves but through their cooperators, works effectively, since human postures do not suddenly change the states of the links in quite a short duration such as a retransmission interval.

In this paper, we propose a cooperator-assisted WBAN for real-time vital data collection. We show that the WBAN is realizable based on two kinds of medium access control (MAC) protocols such as a hybrid-time divison multiple access/carrier sense multiple access (TDMA/CSMA) and a TDMA, both of which are compliant with the IEEE 802.15.4.e standard, and evaluate the packet error rates and power consumptions for a hybrid-TDMA/CSMA-based WBAN and a TDMA-based WBAN. In the evaluation of packet error rates, we use the stored received signal strength indication (RSSI) data, which were obtained from experiments with three subjects in a realistic scenario composed of a series of different actions and postures in a mixed-indoor/outdoor environment.

## Keywords

- WBAN
- Cooperative transmission
- CSMA
- TDMA

## 1 Introduction

Wireless body area network (WBAN) is a short-range network for connecting nodes on a human body (wearable WBAN) or in a human body (implant WBAN). One key application includes vital data collection for patients and elderly people in medical and health care scenarios, where the energy consumption of sensor nodes is the most important factor for their long-term monitoring.

Another key application is vital data collection for workers such as firefighters, soldiers, and police officers in an urgent/life-critical scenario and for athletes in a sports-training scenario. For the former scenario, it is essential to monitor in real-time their physical and physiological states through collecting vital data from sensor nodes: body temperature meter, electro-cardio-graph (ECG), electro-myo-graph (EMG), tri-accelerometer, and SpO2 meter (for oxygen saturation) put on various positions of their bodies: left and right arms, left and right ankles, chest, finger and so on. On the other hand, for the latter scenario, it is also important to collect vital data in real-time, since trainers can train athletes with feedback information on their physical states. For the application, high reliability such as low packet error rate and low packet delay is the most important factor, in other words, because of their short operating times, the energy consumption of sensor nodes is not so critical. In this paper, we pay attention to how to guarantee high reliability in a WBAN.

Because of the short transmittable range, typically, less than 2 m, and the low transmission power, typically, less than 0.1 mW, a star topology has been mainly considered in WBANs, connecting a central WBAN coordinator (BANCO) to sensor nodes put on different positions of a human body [1]. For WBANs, candidates in unlicensed frequency bands are the 2.4 GHz industrial, scientific and medical (ISM) band and the 3.1–10.6 GHz ultra wide band (UWB) band, and their propagation channel characteristics have been well investigated [2–4]. In this paper, we assume the 2.4 GHz-ISM band, because in the frequency band, not only the IEEE 802.15.6 standard is now available but also a variety of inexpensive transceiver modules have been on the market, which are applicable for WBAN applications [5, 6].

Although the 2.4 GHz-ISM band has the advantages mentioned above, its major disadvantage is that it is not rich in diffraction. In a WBAN where there are BANCO and sensor nodes on different positions of a human body, in addition to the poorness of diffraction and the low transmission power, the directivity of antenna is much affected by the human body, so the direct link between them is easily and severely blocked, resulting in link disconnection.

In order to improve the reliability of wireless transmission, it is essential to use “the broadcast nature” inherent to wireless. In this sense, WBAN is advantageous, because there are many sensor nodes which cannot help receiving signals transmitted from other sensor nodes to a BANCO and can act as cooperators for them. It is well known that cooperative transmission, which means the use of cooperators or relays, improves the quality of wireless transmission by means of transmit diversity [7, 8]. In fact, for WBANs in the 2.4 GHz-ISM band, the performance of a cooperative transmission is discussed in an indoor walking scenario [9], an opportunistic relaying and a cooperative network coding are proposed [10, 11], and the effects of selection combining and maximum ratio combining with the help of relay are examined [12]. In addition, for WBANs assuming the IEEE 802.15.4 standard in the same frequency band [13], the advantage of relaying is suggested [14], and the performance is investigated [15, 16]. These works show the effectivity of cooperative transmission in WBANs, but their targets are all to improve the energy efficiency for prolonging the lifetime of the networks, which are common to those in general wireless sensor networks. Furthermore, for a sensor node in a WBAN, other sensor nodes can be candidates for its cooperator, so a BANCO needs to select the best one out of them, but these works use a pre-determined sensor node as a cooperator for each sensor node, without discussing how to select it out of them. There are some works addressing cooperator selection schemes, but a single human motion is assumed for a prediction-based relay selection in the 2.4 GHz-ISM band [17], and the UWB band is targeted [18], whose radio propagation characteristic is totally different from that of the 2.4 GHz-ISM band.

This paper proposes a cooperator-assisted WBAN for ensuring real-time vital data collection [19, 20]. In a WBAN, the radio channel characteristic around the wearer dynamically changes according to not only his/her action and posture but also the environment surrounding him/her such as indoors and outdoors. This implies that a cooperator suited for each sensor node also dynamically changes according to the physical situation around the wearer, so adaptive cooperator selection recognizing the temporal radio channel characteristic seems interesting and promising. It must be difficult, however, since the physical situations are infinite, so the proposed WBAN selects a single sensor node out of other sensor nodes for each sensor node, which can act as a *moderately* good cooperator commonly in different physical situations. Furthermore, the proposed cooperator selection is distributed, and in addition to it, the proposed WBAN selects an adequate sensor node as a BANCO. In the performance evaluation of the proposed WBAN, on the other hand, we use the stored received signal strength indication (RSSI) data obtained from experiments with three subjects in a realistic scenario composed of a series of different actions and postures in a mixed-indoor/outdoor environment.

It is better to realize a cooperator-assisted WBAN using a current wireless communication standard, and in this sense, one way is the use of a decode-and-forward transmission in which cooperators retransmit their once-stored packets after their parent sensor nodes transmit packets to a BANCO. Regarding medium access control (MAC) protocol, this is realizable in time division multiple access (TDMA) or carrier sense multiple access (CSMA). TDMA seems suitable for highly reliable cooperator-assisted WBAN, since it can avoid packet collisions. However, TDMA have some problems. One is the lack of frames, namely, selecting one coordinator per sensor node doubles the number of required frames. For instance, in the IEEE 802.15.4-2011 standard, the number of frames per superframe is limited up to 16 including a beacon frame, so this means that the maximum number of sensor nodes is limited up to 7 in a WBAN, which is too small. Another is the delay of retransmission. For successful reception of each frame in a superframe, a BANCO can broadcast its acknowledgement (ACK) packet only in the beacon frame of the next superframe. Therefore, if cooperators retransmit their packets after recognizing their ACKs, the retransmission is delayed by the time period of one superframe.

In this paper, we propose the use of low latency deterministic network (LLDN) in the IEEE 802.15.4e standard [21] for realizing a cooperator-assisted WBAN [22], where we show two superframe designs using a TDMA and a hybrid-TDMA/CSMA. Furthermore, these two designs introduce different power consumptions, so using the values of power consumptions for a typical transceiver module, we compare the power consumptions between them.

The remainder of this paper is organized as follows. Section 2 presents the system model and assumptions. Section 3 describes the superframe design criteria. Section 4 discusses the principle of the cooperator selection and explains the selection algorithms for cooperator and BANCO in detail. Section 5 outlines the experiment on the RSSI measurement, and Section 6 shows the performance of the proposed cooperator/BANCO selections using the measured RSSI data. Finally, Section 7 concludes the paper.

## 2 System Model and Assumptions

We assume a WBAN system model that consists of total *N*
_{no
d
e
} nodes including vital sensor nodes and one BANCO on a human body. Putting different ID numbers of 1,2,⋯,*N*
_{no
d
e
} to the nodes, we define a set of node ID numbers as V_{no
d
e
}. We also assume that any node can measure the RSSI for its received packet. Each node periodically senses vital signs and transmits its data packets to a BANCO, and then, the BANCO transmits collected data to an off-body node for monitoring his/her physical and physiological state. The purpose of this paper is to improve the reliability of the wireless network among the sensor nodes and the BANCO. Thus, the network between the BANCO and the off-body node is out of the scope of the paper. For example, we can use 3G/LTE as the network [23].

### 2.1 Cooperative transmission

*i*(

*i*=1,2,⋯,

*N*

_{no d e }),

*j*(

*j*=1,2,⋯,

*N*

_{no d e },

*j*≠

*i*,

*j*≠

*k*), and

*k*(

*k*=1,2,⋯,

*N*

_{no d e },

*k*≠

*i*), respectively.

### 2.2 Sensor node model

*N*

_{se n s o r }kinds of sensors all operating with analog to digital (A/D) resolution of

*q*bits/sample and sampling rate of

*F*Hz, and it aggregates

*M*

_{s}successively sensed data into a single data burst with additional information of

*d*bits such as timestamp. Therefore, the payload size is given by

*L*

_{o}bits to the payload. Defining the data transmission rate as

*R*bits/s, the data packet duration becomes

### 2.3 Packet success rate model

*n*th packet (

*n*=1,2,⋯,

*N*

_{pa c k e t }) from the

*l*th node to the

*m*th node (

*l*,

*m*=1,2,⋯,

*N*

_{no d e },

*l*≠

*m*) is given by

*L*

_{pa c k e t }and

*B*

*E*

*R*

_{ l,m }(

*n*) are the packet length in bits and the bit error rate in the

*n*th packet from the

*l*th node to the

*m*th node, respectively. We refer to the IEEE 802.15.4 standard [13] as the bit error rate:

*S*

*N*

*R*

_{ l,m }(

*n*) is the signal to noise power ratio (SNR) for the

*n*th packet from the

*l*th node to the

*m*th node:

*R*

*S*

*S*

*I*

_{ l,m }(

*n*) is the measured RSSI for the

*n*th packet from the

*l*th node to the

*m*th node, and

*P*

_{no i s e }is the noise power given by

where *NF*, *N*
_{no
i
s
e
} and *B*
_{ch
} are the noise figure, thermal noise density, and channel bandwidth, respectively.

## 3 Superframe design criteria

The IEEE 802.15.4e standard defines the LLDN that is described as follows: a superframe is divided into a beacon slot and timeslots of equal length which are assigned to specific nodes. A coordinator periodically transmits beacons for synchronization with the superframe structure. Each timeslot is able to be assigned to exactly one node, called a slot owner, which has access privilege in the timeslot, namely, it transmits without using CSMA. Provided that more than one node wishes to transmit in a timeslot, which is referred to as a shared group timeslot, any nodes except a coordinator transmit using CSMA. In a shared group time slot, a coordinator broadcasts a clear to send (CTS) shared group frame to indicate that the timeslot is not used by the slot owner. Then, a node sends a request to send (RTS) frame and waits for a CTS frame from the coordinator in a response to it. After data transmission of other nodes, the coordinator can fully or partly occupy a timeslot for data transmission as well.

In the following two subsections, we show how to apply the LLDN to the cooperator-assisted BAN system.

### 3.1 LLDN-based hybrid TDMA/CSMA

*N*

_{no d e }− 1 shared group timeslots. The slot owner of the

*i*th timeslot is exactly the

*i*th node, and it selects its cooperator as a member of its shared group. In the

*i*th timeslot, the

*i*th node is able to send its packet to a BANCO without packet collision, namely, in a TDMA manner. Only if the BANCO does not successfully receive the packet, it transmits a CTS shared group frame back to the

*i*th node, so the

*i*th cooperator attempts to transmit its stored packet. Here, the key is that

*the CTS shared group frame acts as a negative acknowledgement (NACK) packet for the ith node as well as its cooperator*.

*T*

_{be a c o n },

*T*

_{CC A },

*T*

_{SI F S },

*T*

_{to },

*T*

_{LI F S },

*T*

_{bo },

*T*

_{CT S S G },

*T*

_{CT S }, and

*T*

_{RT S }, respectively, in order to accommodate (

*N*

_{no d e }−1) timeslots within a single superframe with duration of

*T*

_{SF }, the time slot duration

*T*

_{ts }needs to satisfy the following two criteria:

### 3.2 LLDN-based TDMA

Figure 2
b shows the other way to apply the LLDN to the cooperator-assisted WBAN. A superframe is divided into 2(*N*
_{no
d
e
}−1) timeslots, where the (2*i*−1)th and 2*i*th timeslots are assigned by the BANCO to the *i*th node and its cooperator, respectively. Whenever a cooperator successfully receives the packet of its parent node, it attempts to transmit its stored packet. Unlike the hybrid TDMA/CSMA, cooperative transmissions are always conducted whether the direct transmission fails or not.

*T*

_{ts }needs to satisfy the following two criteria:

## 4 Cooperator and BANCO selections

We assume that the *k*th node has been selected as a temporal BANCO.

### 4.1 Optimal cooperator selection

*i*th source node, a node giving the highest packet success rate should be selected as its cooperator. Therefore, the optimal cooperator selection algorithm is summarized as Algorithm 1, where the metric in the maximization problem is the packet success rate for the two-hop link from the

*i*th source node to the BANCO via the

*j*th cooperator candidate, which is given by

In Algorithm 1, for each source node, its cooperator can be selected independently packet by packet. The calculation of packet success rate may be the most computationally intensive, but focusing only on the cost of solving the maximization problem, the computational complexity of Algorithm 1 becomes \(O(N_{\mathrm node}^{2} N_{\mathrm packet})\) (see the Appendix 1). Note that the optimal cooperator selection is unrealistic in the sense that the BANCO needs to measure the packet success rates for the *i*th source node via all the *j*th nodes (*j*∈V_{no
d
e
},*j*≠*k*, *j*≠*i*) simultaneously packet by packet.

### 4.2 Proposed cooperator selection

In the proposed cooperator selection, the packet transmission is composed of two processes: a flooding process and a data transmission process. During the flooding process, the WBAN wearer takes different actions and postures, and the RSSIs of all links are measured at the same time by repeating a process where all nodes broadcast and re-broadcast their packets. After the flooding process, an adequate cooperator for each source node and a BANCO are selected based on the collected RSSIs information. Selected cooperators are considered to be moderately effective for the different actions and postures.

Hereby, we explain the flooding process in detail. Assume that each node broadcasts hello packets *N*
_{he
l
l
o
} times (*n*=1,⋯,*N*
_{he
l
l
o
}). When a node directly receives a hello packet from another node, the node measures the RSSI of the packet and re-broadcasts *only once* the packet *adding the measured RSSI in it*. When a node receives a re-broadcast hello packet, the node no longer re-broadcasts it. In this case, defining two sets of the indices of the hello packets which are transmitted from the *i*th source node and received at the BANCO *directly* and *via the jth cooperator candidate* as \({\mathrm Z}_{\textit {ik}}^{1}\) and \({\mathrm Z}_{\textit {ijk}}^{2}\) with their elements \(n_{\textit {ik}}^{1}\, \big (n_{\textit {ik}}^{1} \in {\mathrm Z}_{\textit {ik}}^{1}\big)\) and \(n_{\textit {ijk}}^{2}\, \big (n_{\textit {ijk}}^{2} \in {\mathrm Z}_{\textit {ijk}}^{2}\big)\), respectively, the *k*th node can know the RSSI of the first link as \({RSSI}_{\textit {ij}}\big (n_{\textit {ijk}}^{2}\big)\) and that of the second link as \({RSSI}_{\textit {jk}}\big (n_{\textit {ijk}}^{2}\big)\).

*μ*(

*j*) and

*N*

_{cm a x }as the multiplicity of the

*j*th cooperator candidate and its allowable largest value, respectively. The proposed strict cooperator selection algorithm is summarized as Algorithm 2, where the metric in the maximization problem is modified as

Algorithm 2 is mathematically not tractable, since there are too many candidates to be evaluated for finding the optimal solution for each *j* and furthermore selectable cooperator candidates for one source node is affected by those for other source nodes. In fact, the computational complexity of the algorithm is lower-bounded as *O*((*N*
_{no
d
e
}−1)!) (see the Appendix 2). Therefore, we need to simplify Algorithm 2.

#### 4.2.1 Without multiplicity constraint

*N*

_{cm a x }=

*N*

_{no d e }−2, we can select a cooperator independently for each source node, in other words, we can simply remove the constraint from Algorithm 2. Here, we introduce one more simplifications, that is, replacement of the packet success rate calculation by an RSSI calculation, taking into consideration the fact that the packet success rate is a monotonous increasing function on the RSSI and the packet success rate through a two-hop link is more affected by the one in a worse link:

In this case, the simplified cooperator selection algorithm without multiplicity constraint is summarized as Algorithm 3. Its computational complexity is \(O\left (N_{\mathrm node}^{2}\right)\) (see the Appendix 3).

#### 4.2.2 With multiplicity constraint

*i*th source node as

*q*th maximum out of (·). In (15),

*c*

_{ ikq }is the

*q*th element of C

_{ ik }which has the essentiality metric as

*c*

_{ ikq }with larger

*ε*

_{ ikq }is more essential for the

*i*th source node. In addition, let us define the number of packets lost in the direct link from the

*i*th source node to the BANCO as the unreliability metric:

where the direct link of the *i*th source node with larger *υ*
_{
ik
} is less reliable.

*j*th cooperator candidate as

where \(~\mathop {u{\mathrm th}\min }\{(\cdot) \}\) denotes the function picking up the *u*th minimum out of (·), and the source node *s*
_{
jku
} with smaller *u* is more removable from *S*
_{
jk
}.

*j*

^{′}the cooperator candidate has \(N^{\prime }_{\mathrm cmax}>N_{\mathrm cmax}\) parent source nodes:

The element \(s_{j'ku}\phantom {\dot {i}\!}\) with smaller *u* has the smaller essentiality metric on *j*
^{′}the cooperator candidate, so in this sense, it is quite natural to examine the removability from \(s_{j'k1}\phantom {\dot {i}\!}\). However, when comparing the unreliability metrics of \(s_{j'k1}\phantom {\dot {i}\!}\) and \(s_{j'k2}\phantom {\dot {i}\!}\), namely, \(\upsilon _{s_{j'k1}k}\) and \(\upsilon _{s_{j'k2}k}\), if \(\upsilon _{s_{j'k1}k} > \upsilon _{s_{j'k2}k}\), then it may be better not to remove \(s_{j'k1}\phantom {\dot {i}\!}\), because it implies that \(s_{j'k1}\phantom {\dot {i}\!}\) requires more help from a cooperator. Therefore, in the proposed algorithm, every examination the elements of S_{
jk
}, either of *s*
_{
j
k1} or *s*
_{
j
k2} is always removed from S_{
jk
}, which satisfies a certain condition. The simplified cooperator selection algorithm with multiplicity constraint is summarized as Algorithm 4, where the “remove” operation contains renumbering the remaining elements after the removal, and *ρ* is a scaling factor for the unreliability comparison. Its computational complexity is \(O\big (N_{\mathrm node}^{3}\big)\) (see the Appendix 4).

#### 4.2.3 Proposed BANCO selection

*k*th node as a BANCO (

*k*=1,2,⋯,

*N*

_{no d e }), the BANCO is finally selected. Here, it is reasonable that the adequate BANCO should receive as many packets with larger RSSIs as possible from

*all other*nodes directly or indirectly. Therefore, based on the

*minmax*criterion which can ensure that all nodes’ packet error rates are not extremely high, the metric of the BANCO selection can be given by

The BANCO selection algorithm is summarized as Algorithm 5. For each temporally selected BANCO (*k*=1,2,⋯,*N*
_{no
d
e
}), the BANCO selection metric is calculated, so its computational complexity is \(O\left (N_{\mathrm node}^{2}\right)\) (see the Appendix 5).

## 5 Experiment on RSSI measurement

Specifications of the chip antenna

Description | Value |
---|---|

Length | 8 mm |

Width | 3 mm |

Height | 1 mm |

Gain | 2 dBi max |

e VSWR | 2 max |

## 6 Performance evaluation and discussions

System parameters

Description | Parameter | Value |
---|---|---|

Data transmission rate |
| 250 kbits/s |

Number of nodes |
| 10 nodes |

Sampling rate |
| 100 Hz |

Number of sensors |
| 3 sensors/node |

A/D resolution |
| 8 bits |

Additional information |
| 16 bits |

Packet overhead length |
| 72 bits |

Number of aggregated date per packet |
| 10 data |

Noise figure |
| 10 dB |

Thermal noise density |
| −174 dBm/Hz |

Channel bandwidth |
| 2 MHz |

### 6.1 Superframe design

Designed superframe parameters

Description | Parameter | Value |
---|---|---|

Data packet duration |
| 1.89 ms |

Clear channel assessment |
| 0.128 ms |

Beacon |
| 0.416 ms |

CTS shared group frame |
| 0.384 ms |

RTS frame |
| 0.416 ms |

CTS frame |
| 0.416 ms |

Long interframe space |
| 0.64 ms |

| 3.16 ms | |

Short interframe space |
| 0.192 ms |

Timeout time |
| 4.5 ms |

Backoff time |
| 2.24 ms |

Timeslot duration |
| 11.0 ms |

### 6.2 Computer simulation and results on the packet error rate

We conducted computer simulations to evaluate the packet error rate of the cooperator-assisted WBAN with the designed superframe parameters using the stored RSSI data obtained in the experiment. One simulation session is repeated until each node broadcasts 3000 hello packets in the flooding process and transmits 10,000 data packets in the data transmission process for each case of all BANCO’s positions. We confirmed that there was little difference in the packet error rate between the hybrid-TDMA/CSMA and TDMA, so in the following figures, the packet error rate is common to the two MACs.

*lower*packet error rate but cannot always select the node giving the

*lowest*packet error rate. To select a BANCO, the proposed algorithm uses the sum of RSSIs through the direct and indirect links to each source node, in other words, only the average (first moment) of the RSSI temporal variation (see (21)). In reality, the packet error rate depends on not simply the average but complicatedly the distribution of the RSSI, so to improve the BANCO selection performance, we need to take into consideration its higher-order moments in the algorithm. On the other hand, in some applications, it is required to select the BANCO position in advance. The results indicate that “left waist” is an adequate position as the BANCO for all subjects.

*ρ*) for the unreliability comparison in the cooperator selection with multiplicity constraint (see line 18 in Algorithm 4). From the result, we set

*ρ*= 1.5 in the following, but there is no large dependency on

*ρ*observed in the figure, so we may simply compare \(\upsilon _{s_{jk1}k}\) with \(\upsilon _{s_{jk2}k}\) just setting

*ρ*= 1.0.

*N*

_{cm a x }=1,2,4, and

*ρ*=1.5 for the cooperator selection with multiplicity constraint. The packet error rate with

*N*

_{cm a x }=1 is likely to be worse than the packet error rates with

*N*

_{cm a x }=2 and 4 for almost all BANCO positions, but between with

*N*

_{cm a x }=2, 4, and without multiplicity constraint, there is no large difference in the packet error rates. This implies that, in the WBAN with ten nodes on different positions of a human body, any node has multiple better cooperator candidates. From the result, we can see that

*N*

_{cm a x }=2 must be fair in terms of both the packet error rate and energy saving for cooperators.

Consumption current values for a typical RF module

State | Consumption current |
---|---|

Transmission | 24 mA |

Reception | 20 mA |

Standby | 1.3 |

Power consumption comparison

MAC | Power consumption |
---|---|

TDMA | 1.0 |

TDMA/CSMA | 0.76 |

## 7 Conclusion

In this paper, we have shown that, to enable a cooperator-assisted WBAN, a hybrid-TDMA/CSMA is realizable by making effective use of CTS shared group frame, and a TDMA is also realizable in the IEEE 802.15.4e LLDN. In addition, we have evaluated the packet error rate of a cooperator/BANCO selection based on both the hybrid-TDMA/CSMA and TDMA by computer simulations, where we have used the stored RSSI data obtained from a mixed indoor/outdoor environment with three subjects.

The proposed cooperator/BANCO selection works well in the realistic environment with typical transmission power of −10 dBm, and the proposed cooperator selection is superior to the random selection by about 8 dB. It is also shown by our computer simulations that it is important to select adequate cooperators for each subject. The TDMA was slightly disadvantageous over hybrid-TDMA/CSMA in terms of power consumption. However, the TDMA is simple; it requires no CCA, CTS frame and RTS frame, so it can shorten the timeslot duration thus accommodate more nodes for the same data packet duration. This must be the advantage of the TDMA.

The proposed BANCO selection was not able to always select the best node as the BANCO for the three subjects. To investigate a more efficient BANCO selection using higher-order moments of RSSI variation at the sacrifice of computational complexity must be one of our future works.

## 8 Appendix 1

*i*(

*i*=1,2,⋯,

*N*

_{no d e },

*i*≠

*k*), and each

*n*(

*n*=1,2,⋯,

*N*

_{pa c k e t }), we need to find the maximum out of a set of \(M_{i,j,k;n}^{opt}\) with the number of elements =

*N*

_{no d e }−2. Since finding the maximum out of a set of

*N*values requires

*N*comparisons, the computational complexity of Algorithm is given by

## 9 Appendix 2

*N*

_{cm a x }=1, the computational complexity of Algorithm 2 is minimized, since the number of combinations of cooperator candidates is minimized. Although each source node cannot select itself as its cooperator, but its number is approximated as (

*N*

_{no d e }−2)!. Therefore, the computational complexity of Algorithm is lower-bounded as

## 10 Appendix 3

*i*(

*i*=1,2,⋯,

*N*

_{no d e },

*i*≠

*k*), we need to find the minimum out of a set of \(M_{i,j,k}^{smp}\) with the number of elements =

*N*

_{no d e }−2, so the computational complexity of Algorithm 3 is given by

## 11 Appendix 4

*N*values is given by

*O*(

*N*

^{2}) for the worst case [25], the computational complexities of constructing

*C*

_{ ik }for

*i*=1,2,⋯,

*N*

_{no d e },

*i*≠

*k*(line 2–8) and

*S*

_{ jk }for

*j*=1,2,⋯,

*N*

_{no d e },

*j*≠

*k*(line 9–26) are respectively given by

*N*

_{no d e }− 2) are the same. In this case, the cooperator candidate needs to compare the unreliability metrics of its parent source nodes

*N*

_{no d e }−2−

*N*

_{cm a x }times. Then, in the second round of parent node removal, it happens when the best cooperator candidates of remaining source nodes (

*N*

_{no d e }−2−

*N*

_{cm a x }) are the same. In this case, the cooperator candidate needs to compare the unreliability metrics of its parent source nodes

*N*

_{no d e }−2−2

*N*

_{cm a x }times. In this way, the worst case happens when comparisons decreases from

*N*

_{no d e }−2−

*N*

_{cm a x }at the rate of

*N*

_{cm a x }a round until it becomes less than

*N*

_{cm a x }. Therefore, its computational complexity is calculated as

where ⌈(·)⌉ is ceiling of (·), namely, the smallest integer not less than (·). Note this cost is still less than \(O\left (N_{\mathrm node}^{3}\right)\).

## 12 Appendix 5

*k*(

*k*=1,2,⋯,

*N*

_{no d e }), we need to find the minimum out of a set of \(M_{k,i}^{BANCO}\) with the number of elements =

*N*

_{no d e }−1, so the computational complexity of the proposed BANCO selection is given by

## Declarations

### Acknowledgements

This work was also supported in part by the Research Grant of Support Center for Advanced Telecommunications Technology Research (SCAT) of Japan.

**Open Access** This article is distributed under the terms of the Creative Commons Attribution 4.0 International License (http://creativecommons.org/licenses/by/4.0/), which permits unrestricted use, distribution, and reproduction in any medium, provided you give appropriate credit to the original author(s) and the source, provide a link to the Creative Commons license, and indicate if changes were made.

## Authors’ Affiliations

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