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1

Cooperative Body Channel Communications

for Energy Efﬁcient Internet of Bodies

Abeer Alamoudi, Student Member, IEEE, Abdulkadir Celik, Senior Member, IEEE,

and Ahmed M. Eltawil, Senior Member, IEEE.

Abstract—The Internet of Bodies is a network formed by

wearable, implantable, ingestible, and injectable smart devices to

collect physiological, behavioral, and structural information from

the human body. Thus, the IoB technology can revolutionize the

quality of human life by using these context-rich data in myriad

smart-health applications. Radio frequency (RF) transceivers

have been typically preferred due to their availability and

maturity. However, for most RF standards (e.g. Bluetooth Low

Energy), the highly radiative omnidirectional RF propagation

(even at the lowest settings) reaches tens of meters of coverage,

thereby reducing energy efﬁciency, causing interference and co-

existence issues, and raising privacy and security concerns. On

the other hand, body channel communication (BCC) conﬁnes low-

power and low-frequency (10 kHz-100 MHz) signals to the human

body, leading to more secure and efﬁcient communications. Since

energy efﬁciency is one of the critical design parameters of IoB

networks, this paper focuses on energy-efﬁcient orthogonal body

channel access (OBA) and non-orthogonal body channel access

(NOBA) schemes with and without cooperation. To this aim,

three main BCC topologies are presented; point-to-point channel,

medium access channel, and broadcast channel. These topologies

are then used as building blocks to create IoB networks relying

on OBA and NOBA schemes for downlink (DL) and uplink (UL)

trafﬁc. For all schemes and trafﬁc directions, optimal transmit

power and phase time allocations are derived in closed-form,

which is essential to reduce energy consumption by eliminating

computational power. The closed-form expressions are further

leveraged to obtain maximum network size as a function of data

rate requirement, bandwidth, and hardware parameters.

Index Terms—Internet of bodies; capacitive coupling; galvanic

coupling; human body communications; body channel communi-

cations; multiple access; power control; energy efﬁcient; internet

of things, body area networks.

I. INTRODUCTION

SIMULTANEOUS technological advancements in micro-

electronics, signal processing, and wireless communi-

cations have paved the way for the advent of Internet of

Bodies (IoB). As a derivative of the vast Internet of Things

(IoT) paradigm, the IoB is deﬁned as a body-centric network

comprising wearable, ingestible, injectable, and implantable

smart devices located in, on, and around the human body

[1]. The IoB moves the focal point to the human body and

places intra-body and inter-body communication at the center

stage of connectivity. IoB enables a myriad of applications,

including but not limited to personalized medicine to offer

Authors are with the Computer, Electrical and Mathematical Sciences

and Engineering (CEMSE) Division, King Abdullah University of Science

and Technology (KAUST), Thuwal, KSA 23955-6900.

The authors gratefully acknowledge ﬁnancial support for this work from

the KAUST and the Smart Health Initiative (SHI) at KAUST

proactive and preventative care; remote patient monitoring and

rehabilitating patients; smart home assisted independent living

for seniors and people with disabilities; self-care and welfare

for a healthy and productive lifestyle; occupational health and

safety to protect critical personnel from workplace injuries and

work-related diseases; and sports and entertainment [2].

Since the IoB has its root in wireless body area networks,

the IEEE 802.15.6 standard provides foundational physical

(PHY) layer and medium access layer speciﬁcations for

short-range, ultra low power, and highly reliable wireless

communication within the body area [3]. To this aim, it

speciﬁes three PHY layer options: narrowband (NB) and

ultra-wideband (UWB) radio frequency (RF) communications

and body channel communications (BCC), a.k.a. the human

body communications. Although RF technology has gained a

widespread use thanks to its maturity and availability, they

are not always the best option to facilitate robust, secure and

scalable IoB networks due to the following major drawbacks

[1], [4]:

‚Highly radiative and omnidirectional propagation of RF

devices exposes sensitive data to the danger of eaves-

droppers, bio-hackers, and interceptors, thereby imposing

security and privacy threats. Even though the required

coverage is 5-10 centimeters around the human body, RF

systems such as BLE can reach tens of meters of wireless

coverage at the lowest transmit power setting [5], leading

to energy loss and potential security hazards.

‚Since most IoB devices operate on industrial, scientiﬁc,

and medical (ISM) bands to avoid licensing issues, inter-

ference and coexistence become major issues due to the

overpopulated IoT devices in the ISM bands.

‚Complex and power-hungry radio front ends limit the

node lifetime and necessitate larger area and battery sizes,

which contradicts with the objective of small form-factor

and energy self-sustainable IoB nodes.

Alternative to RF communications, the BCC exploits the

conductive properties of the human body by conﬁning the

transmitted signal to skin tissue at frequencies between 100

kHz to 100 MHz. Electrostatic ﬁelds are coupled to the

body using galvanic coupling (GC) or capacitive coupling

(CC). In the GC-BCC, both signal and ground electrodes

of the transmitter and receiver are in contact with the skin.

Transmission is initiated by passing small currents through

the body and detecting signals at the receiver end. Since

both the signal (forward) path and the return (backward)

are formed through the body, the GC-BCC is mainly char-

2

Fig. 1: Illustration of the capacitive body channel communi-

cations.

acterized by the dielectric properties of the body, granting

GC-BCC immunity to environmental effects. However, since

the operational frequency of GC-BCC is limited to below 1

MHz, it is incapable of supporting high-throughput and long-

range communications [6]. As shown in Fig. 1, the CC-BCC

requires only signal electrodes to be in contact with the body

tissues, leaving ground electrodes ﬂoating in the air. Since the

signal is subject to low attenuation in the forward path as a

result of high tissue conductivity, the overall channel loss is

inﬂuenced by over-the-air capacitive return (backward) paths

[1]. Even though the CC-BCC is affected by the variations

in the surrounding environment, it delivers a better channel

gain than the GC-BCC scheme and can meet the QoS demand

of IoB applications by exploiting higher frequencies. The

advantages offered by BCC communications over RF systems

can be summarized as follows [2], [4]: Coupling ultra low

power signals to the human body yields a negligible leakage,

thus providing improved physical layer security. Moreover, the

BCC channels experience a better channel gain than over-the-

air RF channels since the human body is more conductive

than air. Furthermore, the human body does not behave as an

antenna in the BCC frequency range (1 kHz-100 MHz), which

mitigates body shadowing effects and yields a more stable

wireless channel. The BCC frequency range also decouples

the transceiver size from the carrier wavelength and eliminates

the need for radio front-ends. As shown in Fig. 2, putting

all these virtues together paves the way for energy-efﬁcient

[7]

[8]

[9]

[10]

[11]

[12]

[13]

[14]

Fig. 2: Energy rfﬁciency comparison of BCC transceivers.

BCC transceivers in the order of pJ/bit levels, compared to

nJ/bit energy efﬁciency levels of commercial-off-the-shelf RF

transceivers.

A. Related Work

The development of BCC is owed to the research efforts

dedicated to modeling the channel characteristics and behavior

of human tissue in the presence of electromagnetic (EM)

ﬁelds. Hence, accurate channel models will facilitate efﬁcient

BCC transceivers [15] which are the key components of

the physical layer. To address the impact of environmental

effects, electrode placement on the body, intricate anatomy

of the human tissues, channel length, and varying electrode

speciﬁcations [16] [6], different models have been proposed.

In the context of CC-BCC, the channel modeling techniques

reported in the literature are analytical, circuit-based, numer-

ical, and empirical models. We refer interested readers to

[1] for a complete discussion on the different propagation

characterizations and models of body channels.

Numerous design approaches were investigated in the liter-

ature to optimize BCC transceivers, including different cou-

pling methods, operational frequency ranges, and modulation

techniques to achieve enhanced performance with respect to

achievable throughputs and energy efﬁciency [16]. In addition,

the small form-factor and long battery lifetime requirements

of IoB nodes suggest that IoB transceivers are designed to

transmit at low power levels. Therefore, addressing the sensi-

tivity of the BCC receivers, which is the minimum received

power that guarantee the correct data retrieval, is crucial

for reliable communication networks. The authors in [17]

propose a CC-BCC transceiver implemented in 65 nm CMOS

process with dual operational modes, namely entertainment

and healthcare. In the former, a dual-band (40/160 MHz) full-

duplex transceiver that is binary phase-shift keying (BPSK)

based is considered to deliver -58 dBm sensitivity at 80

Mbps with 79 pJ{bit efﬁciency. While in the latter mode, the

super-regenerative transceiver adopting On-Off-Keying (OOK)

3

achieves -72 dBm sensitivity at 100 kbps for 42.5 µW power

consumption. Unlike most of the narrowband transceivers

operating at speciﬁc frequencies to alleviate interference at

the expense of energy efﬁciency, authors in [7] develop an

energy-efﬁcient broadband interference tolerant transceiver.

The transceiver utilizes time-domain interference rejection to

attain a 30 Mbps data rate and 6.3 pJ/b energy efﬁciency

with -63.3 dBm. Moreover, reference [18] demonstrates the

possibility of achieving -98.9 dBm sensitivity and energy efﬁ-

ciency of 3.8 nJ{bit for the operational range 164 kbps to 1.13

Mbps with the proposed standard mode operating transceiver.

This performance was obtained using a frequency selective

digital transmission (FSDT) modulation scheme. In Fig. 2

performance comparison of state-of-the-art BCC transceivers

and RF-based systems are illustrated. The aforementioned

efforts validated the enhanced performance of CC-BCC over

conventional RF systems, and the feasibility of efﬁcient, highly

sensitive BCC transceivers. This work tackles the networking

aspect of multiple communicating nodes in order to realize an

efﬁcient, reliable, connected BCC network.

The work in [4] was the ﬁrst to present a full-scale study

of capacitive body channel access scheme for a generic IoB

network. The purpose of the study was to evaluate regu-

lar and cooperative orthogonal and non-orthogonal access

schemes with regards to max-min rate, max-sum rate, and

QoS sufﬁcient regimes. To account for the wide range of IoB

applications, analytical expressions, numerical power control,

and phase time allocations for the three operational regimes

were provided. Albeit its valuable contributions, the work

presented in [4] does not shed light into the energy efﬁciency

and maximum achievable network size, which is one of the key

design goals of IoB networks. Thus, the work in [19] focused

on the energy efﬁciency of orthogonal and non-orthogonal

capacitive body access schemes and derived optimal power

allocations in closed-form for both uplink (UL) and downlink

(DL) trafﬁc. Moreover, the maximum network size is derived

for both directions under orthogonal and non-orthogonal sce-

narios. This paper extends [19] by introducing cooperative

body channel access schemes for higher energy efﬁciency;

deriving closed-form power allocations under successive inter-

ference cancellation (SIC) imperfections; optimizing the phase

time allocations between source nodes, relay, and hub; and

analyzing the network size under both perfect and imperfect

SIC conditions.

B. Main Contributions

The main contributions of this paper can be summarized as

follows:

‚Three primary BCC topologies are introduced: point-to-

point (P2P) topology, multiple access channel (MAC)

topology, and broadcast channel (BC) topology. These

topologies are then used as building blocks to facilitate

four main body channel access schemes: orthogonal body

channel access (OBA), non-orthogonal body channel

access (NOBA), and cooperative OBA (C-OBA), and

cooperative NOBA (C-NOBA).

‚After formulating the optimization problem for energy

efﬁcient networking problems for regular and cooperative

schemes, optimal power control levels are derived in

closed-form under perfect and imperfect SIC conditions.

Since phase times of sourceØrelay and relayØhub links

play a vital role in overall energy consumption, the

derived power allocations are leveraged to ﬁnd optimal

phase time allocation numerically.

‚Finally, the maximum achievable network size of each

topology is analyzed as a function of data rate require-

ment, SIC imperfections, and channel conditions. These

analyses are further extended by numerically ﬁnding the

optimal phase time allocation that gives the maximum

network size under cooperation.

Numerical results illustrate the circumstances under which

regular and cooperative schemes improve the performance of

the IoB network. Subject to different node deployment scenar-

ios, C-NOBA was shown to sustain the least sum of transmit

power among all other schemes, improving the overall energy

efﬁciency in UL and DL trafﬁc. Speciﬁcally, when moving the

grouped source nodes away from the hub, C-NOBA exhibits

up to 9%reduction in transmit power compared to NOBA

schemes. Moreover, the results also indicate the importance

of relay location regarding the hub and source nodes as an

optimal distance was noted, which provided 14%less power

consumption than regular schemes. C-NOBA schemes can

exhibit a 13%better effectiveness in total transmission power

than their regular counterparts at low QoS requirements as

the network size increases. Conversely, C-NOBA performance

is restrained to fewer nodes at higher QoS demands. It was

noted that adopting relayed links constitutes a bottleneck on

the maximum number of nodes Kmax compared to regular

schemes, since the total power of the relay node must be shared

by all. Compared to NOBA, the C-NOBA reduces the network

size by 31.7%and 69 %in UL and DL trafﬁc, respectively.

Numerical results also show that optimizing phase time alloca-

tion substantially improves the energy efﬁciency and network

size by mitigating the negative impacts of node deployment.

C. Paper Organization

The remainder of the article is organized as follows: Section

II presents body channel communication topologies followed

by regular and cooperative body channel access schemes

orthogonal and non-orthogonal for the capacitive channel.

This will provide insights on channel resource allocation,

maximum achievable throughput, and decoding processes.

Next, in Section III, problems are formulated and algorithms

for power control and phase time allocations are proposed,

respectively. Section IV derives the maximum feasible network

size for regular and cooperative orthogonal and non-orthogonal

schemes. For non-orthogonal, the closed-form expressions

were derived for both perfect and imperfect cancellations

scenarios. Simulation results are illustrated in Section V.

Finally, we conclude the paper in Section VI.

II. SY ST EM MO DE L

The system model considered in this paper consists of a

wearable hub device (e.g., smartwatch) communicating with

Kon-body IoB nodes in a time-slotted fashion in both uplink

4

(a) Regular and cooperative OBA schemes. (b) Regular and cooperative NOBA schemes.

Fig. 3: Illustration of the orthogonal and non-orthogonal capacitive body channel access schemes with and without cooperation.

(UL) and downlink (DL) directions. The hub acts as an access

point that coordinates transmissions in the network and with

off-body entities (e.g., smartphones, base stations, routers, etc.)

utilizing RF communication methods, e.g., cellular, Bluetooth,

Wi-Fi, etc. The node deployment in this work is not subject

to a speciﬁc arrangement as it is mainly determined by the

underlying application, which is out of this paper’s scope.

Throughout the paper, we symbolize the total available band-

width, time-slot duration, and thermal noise power spectral

density with B,T, and N0, respectively. Moreover, Prep-

resents the maximum power of the nodes and hub and is

selected to be within health and safety bounds. As illustrated

in Fig. 3, we will discuss three main BCC topologies: point-

to-point (P2P) channel, multiple access channels (MAC),

and Broadcast Channel (BC). These topologies constitute the

building blocks for regular and cooperative orthogonal and

non-orthogonal body access schemes OBA, NOBA, C-OBA,

and C-NOBA.

A. Body Channel Communication Topologies

In the rest of this subsection, we present BCC topologies

for two generic nodes, niand nh. In the rest of paper, we

assume channel reciprocity and denote UL and DL channel

gains by gh

iand gi

h,gh

i“gi

h, respectively.

1) Point-to-Point Channel: In the P2P topology, the infor-

mation of a pair of transmitter and receiver IoB nodes is sent

over a preassigned dedicated link. That is, the entire bandwidth

is split equally between Kavailable transmitters to form exclu-

sive connections with receivers in the network design phase.

As shown in Fig. 3a, the interference is inherently avoided by

such orthogonal network resource allocation. Accordingly, the

signal transmitted by niis received by nhas

9yh

i“bP gh

i9ωh

ixi`zh,@iPK(1)

where Kis the set of IoB nodes sorted in descending order

of the channel gains, 9ωh

iP r0,1sis the power weight assigned

to transmit the message of ni,xi,*, and zh„Np0, N0B{Kq

models the additive white Gaussian noise (AWGN) at receiver

nh. Consequently, the signal-to-noise ratio (SNR) of UL-P2P

is given by

9

γh

ipωq “ P gh

i9ωh

i

N0B{K,@iPK,(2)

where 9

ω“ r 9ωh

1,..., 9ωh

Ks. On the DL direction, nhcommuni-

cates with rest of the nodes utilizing its power budget equally

for transmission. When the total bandwidth and power are

equally distributed among Knodes, the SNR of DL-P2P can

be obtained as in (2) and given by

9

γi

hpωhq “ P gi

h9

ωi

h

N0B,@iPK,(3)

*We assume that all transmit messages satisfy Et|xi|2u “ 1,@i,

throughout the paper.

5

where 9

ωh“ r 9ω1

h,..., 9ωK

hs.

2) Multiple Access Channel: The MAC topology allows

multiple source nodes sharing the communication medium

to exploit the entire bandwidth Band transmit their data to

the same destination at the same time. This implies that the

received signal at the receiver node nhis a superposed version

of all transmit signals as follows

:

yh“ÿ

iPKbP gh

i:

ωh

ixi`zh,(4)

where :ωh

iP r0,1sis the power factor allocated to the message

of ni,xi, and zh„Np0, N0Bqis the AWGN at nh. Since yh

is a composition of all transmit signals, interference alleviation

techniques is necessary to decode each message. To this aim,

nhis equipped with a successive interference cancellation

(SIC) receiver that decodes messages in the descending order

of their reception power strength. To improve the spectral

efﬁciency of the MAC channel, a higher power weight must

be allocated to nodes with better channel conditions. In this

case, the node with ith strongest reception power will observe

interference from messages decoded later as follows

Cancelable Interference

hkkkkkkkikkkkkkkj

P gh

1:ωh

1ą... ą

loooooooomoooooooon

Upper Rank

P gh

i:ωh

i

Uncancellable Interference

hkkkkkkkkikkkkkkkkj

ą... ąP gh

K:ωh

K

loooooooooomoooooooooon

Lower Rank

,(5)

where gh

1ą. . . ągh

Kand :

ωh

1ą ¨ ¨ ¨ ą :ωh

K. Accordingly,

signal-to-interference-plus-noise ratio (SINR) of niis given

by

:γh

ip:

ωq “ P gh

i:ωh

i

ϵřnăi

nPKP gh

n:

ωh

n`řmąi

mPKP gh

m:

ωh

m`N0B,(6)

where :

ω“ r:ωh

1,...,:ωh

Ks, the ﬁrst term in the denominator

represent residual interference coming from lower rank nodes

due to the SIC imperfections, which is modeled by ϵP r0,1sto

capture channel estimation errors and hardware limitations. On

the other hand, the second term in the denominator represent

the uncancellable interference originated from the lower rank

nodes.

3) Broadcast Channel: Similar to the MAC topology, the

entire available bandwidth is exploited in the BC topology,

where nhbroadcasts superposition of messages intended for

rest of the nodes. In this case, the signal received by niis

given by

:

yi“ÿ

kPKbP gk

h:

ωk

hxk`zi,@iPK(7)

where power weights, :ωk

hP r0,1s, is subject to the total energy

constraint of nh, i.e., řkPK:ωk

hď1. Similar to the MAC

topology, the receiver node ni,@iPKperforms SIC procedure

to decode the message intended for itself. However, the power

allocation weights and decoding order must be in reverse order.

In this case, the weakest channel node is allocated with the

highest power weight and subject to interference from the rest

of nodes, which yields following relation

Uncancellable Interference

hkkkkkkkikkkkkkkj

P gh

1:

ωh

1ă... ă

loooooooooomoooooooooon

Lower Rank

P gh

i:

ωh

i

Cancellable Interference

hkkkkkkkkikkkkkkkkj

ă... ăP gh

K:

ωh

K

looooooooomooooooooon

Higher Rank

,(8)

where gh

1ą. . . ągh

Kand :

ωh

1ă ¨ ¨ ¨ ă :ωh

K. Accordingly, the

SINR of niis given by

:

γi

hp:

ωq “ P gi

h:

ωi

h

řnăi

nPKP gh

n:

ωh

n`ϵřmąi

mPKP gh

m:

ωh

m`N0B,(9)

where :

ω“ r:ω1

h,...,:ωK

hs, the ﬁrst and second terms in

the denominator represent the uncancellable and cancellable

interference originated from the lower and higher rank nodes,

respectively.

B. Regular Capacitive Body Channel Access

In this section, we explain how P2P, MAC, and BC

topologies can be leveraged to facilitate orthogonal and non-

orthogonal capacitive body channel access schemes.

1) Orthogonal Body Channel Access: In the OBA, multiple

access interference (MAI) is avoided by dedicating KP2P

links in both UL and DL over the entire time slot duration

T, as shown in Fig. 3a. By substituting the SNR of UL-P2P

given in (2) into Shannon-Hartley channel capacity formula,

the maximum achievable UL-OBA rate is expressed as

9

Rh

ip9

ωq “ B

Klog2`1`9γh

ip9

ωq˘,@iPK.(10)

Similarly, the maximum achievable DL rate, 9

Ri

hp9

ωhq,@iPK,

can be obtained by substituting DL-P2P given in (3) into (10).

2) Non-Orthogonal Body Channel Access: As shown in

Fig. 3b, the UL and DL trafﬁc is facilitated by MAC and BC

topologies, respectively. In this case, the maximum achievable

UL-NOBA rate can be obtained by using the SINR expression

of MAC topology given in (6) as follows

:

Rh

ip:

ωq “ Blog2`1`:γh

ip:

ωq˘,@iPK.(11)

Similarly, the maximum achievable DL-NOBA rate can be

obtained by using the SINR expression of BC topology given

in (9) as follows

:

Ri

hp:

ωq “ Blog2`1`:γi

hp:

ωq˘,@iPK.(12)

C. Cooperative Body Channel Access

In this section, we explain how P2P, MAC, and BC topolo-

gies can be leveraged to facilitate cooperative orthogonal and

non-orthogonal capacitive body channel access schemes. In the

UL/DL direction, the cooperation is performed in two phases

as shown in Fig. 3. In the former, the cooperating IoB node

(i.e., relay) remains idle to receive the transmitted signals from

hub/source nodes over λT duration, where λP r0,1sis the

phase time allocation factor. In the latter, the relay node nr

forward decoded messages sent by hub/source nodes along

with its own message to source/hub nodes over the remaining

time slot duration, p1´λqT.

1) Cooperative Orthogonal Body Channel Access: As

shown in Fig. 3a, the ﬁrst and second phases of C-OBA

schemes consists of K´1and KP2P links. Hence, received

signals from K´1source nodes, whose set is denoted by K´r,

follows the deﬁnition in (1) by replacing p¨qh,p¨qh

i, and Kwith

p¨qr,p¨qr

i, and K´r, respectively. Applying the same notational

6

changes to (2) and (10) yields the maximum achievable UL-

OBA rates during the ﬁrst phase as follows

9

Rr

ip9

ω1q “ B

K´1log2p1`9γr

ip9

ω1qq , i PK´r.(13)

where 9

ω1“ r 9ω1

1,..., 9ω1

r´1,9ω1

r`1,..., 9ω1

Ksis the power

allocation vector of nodes in the ﬁrst phase. In the second

phase, received signals by the hub node follows the deﬁnition

in (1) by replacing p¨qh

iwith p¨qh

r. Applying the same notational

changes to (2) and (10) yields the maximum achievable UL-

OBA rates during the second phase as follows

9

Rh

r,ip9

ω2q “ B

Klog2`1`9γh

rp9

ω2q˘, i PK.(14)

where 9

ω2“ r 9ω2

1,..., 9ω2

i,..., 9ω2

Ksis the power allocation

vector of nodes in the second phase. Accordingly, end-to-end

UL-OBA rate for niis given by

9

Rh

ip9

λ, 9

ω1,9

ω2q “ min ´9

λ9

Rr

ip9

ω1q,p1´9

λq9

Rh

r,ip9

ω2q¯,@iPK.

(15)

Following similar steps above, end-to-end rate of niin the

DL-OBA scheme is given by

9

Ri

hp9

λ, 9

ω1,9

ω2q “ min ´9

λ9

Rr

h,ip9

ω2q,p1´9

λq9

Ri

rp9

ω1q¯,@iPK.

(16)

2) Cooperative Non-Orthogonal Body Channel Access: As

shown in Fig. 3b, the both phases of UL and DL C-NOBA

schemes consists of MAC and BC topologies, respectively. In

the UL direction, the signals received by nrfrom K´1source

nodes follows the deﬁnition in (4) by replacing p¨qh,p¨qh

i, and

Kwith p¨qr,p¨qr

i, and K´r, respectively. Applying the same

notational changes to (6) and (11) yields the achievable rates

during the ﬁrst phase as follows

:

Rr

ip9

ω1q “ Blog2p1`9γr

ip:

ω1qq , i PK´r.(17)

where :

ω1“ r:ωr

1,...,:ωr

r´1,:ωr

r`1,...,:ωr

Ks. In the second

phase, received signals by the hub node follows the deﬁnition

in (4) by replacing p¨qh

iwith p¨qh

r. Applying the same notational

changes to (6) and (11) yields the maximum achievable UL-

OBA rates during the second phase as follows

:

Rh

r,ip:

ω2q “ Blog2`1`:γh

rp:

ω2q˘, i PK.(18)

where :

ω2“ r:ωh

r,1,...,:ωh

r,K s. Accordingly, end-to-end UL-

NOBA rate for niis given by

:

Rh

ip:

λ, :

ω1,:

ω2q “ min ´:

λ9

Rr

ip:

ω1q,p1´:

λq:

Rh

r,ip:

ω2q¯,@iPK.

(19)

Following similar steps above, end-to-end rate of niin the

DL-NOBA scheme is given by

:

Ri

hp:

λ, :

ω1,:

ω2q “ min ´:

λ:

Rr

h,ip:

ω2q,p1´:

λq:

Ri

rp:

ω1q¯,@iPK.

(20)

III. PROB LE M FORMULATION

AN D SOLUTION METHODOLOGY

In this section, we ﬁrst formulate the total energy consump-

tion minimization problem then provide a solution methodol-

ogy to obtain optimal power weights and phase time allocation.

A. Problem Formulation

Our goal in this paper is to maximize the network longevity

while satisfying various QoS demands to meet the require-

ments of different applications. To this end, we formulate our

optimization problems to minimize total energy consumption

by optimizing power and phase time allocations. Throughout

this section, we omit p9

˝qand p:

˝qnotations to keep formula-

tions and solutions generic to both OBA and NOBA schemes.

1) OBA and NOBA: The optimization problem that op-

timizes the power allocation weights to minimize total UL

power consumption can be formulated as

PUL

REG : min

0ĺωĺ1Pÿ

iPK

ωh

i

C1: s.t. Rh

ipωq ě ¯

Ri,@i

,(21)

where C1is the QoS constraints that ensure that niis provided

with a data rate not less than its demand ¯

Riand ĺdenotes

the pairwise inequality. Similarly, the DL problem can be

formulated as

PDL

REG : min

0ĺωĺ1P

K

ÿ

i“1

ωi

h

C1: s.t. Ri

hpωq ě ¯

Ri,@i

C2:ÿ

k

ωk

hď1

,(22)

where C2is an additional constraint to ensure total DL

transmission power is less than the maximum transmission

power of nh.

2) C-OBA and C-NOBA: Apart from regular OBA and

NOBA schemes, we formulate the optimization problem to

jointly obtain power and phase time allocations which mini-

mize the total energy and maximize the network lifetime while

satisfying QoS demands as follows

PUL

COOP : min

0ďλď1

0ĺω1,ω2ĺ1

λT ÿ

iPK´r

ω1

i` p1´λqTÿ

iPK

ω2

i

C1: s.t. Rr

ipω1q ě ¯

Ri{λ, @iPK´r

C2:Rh

rpω2q ě ¯

Ri{ p1´λq,@iPK

,(23)

where C1and C2are the QoS constraints of the ﬁrst and

second phase satisfying the end-to-end data rate demands,

respectively. In (23), the phase time allocation plays a vital role

in overall energy consumption since λrequires QoS constraint

to be scaled by the phase time duration. Hence, λdetermines

the overall of energy consumed at both phases as shown in the

objective function. Likewise, the DL problem is formulated as

PDL

COOP : min

0ďλď1

0ĺω1,ω2ĺ1

λT ÿ

iPK

ω1

i` p1´λqTÿ

iPK´r

ω2

i

C1: s.t. Rr

hpω1q ě ¯

Ri{λ, @iPK

C2:Ri

rpω2q ě ¯

Ri{p1´λq,@iPK´r

C3:ÿ

i

ω1

iď1

C4:ÿ

i

ω2

iď1

(24)

where C3and C4are additional constraints to guarantee that

the total DL transmission power in both stages is within the

maximum transmission power limit.

7

B. Solution Methodology

Although above problems can be readily solved by convex

optimization solvers, the low-cost and ultra-low-power design

goals of IoB nodes necessitate the derivation of closed-form

optimal power allocations to reduce hardware cost and power

consumption related to the computational complexity.

1) OBA and NOBA: The optimal solution of both PUL

REG

and PDL

REG is attained by satisfying the QoS constraints at

equality since operating at data rate above threshold would

increase the overall power consumption. Therefore, the opti-

mal power weight allocations can be obtained by solving the

following system of equations

pI´ΓJqp“¯

Γσs.t. pą0,(25)

where the vectors are of size Kˆ1; matrices are of size

KˆK;pis the column vector of received powers; σis

the column vector of receiver noise with identical elements of

N0B;¯

Γ“diagp¯

Γ1,...,¯

Γi,...,¯

ΓKqis the diagonal matrix

of the SINR demands with respect to QoS demands; Iis the

identity matrix; and Jis the interference channel matrix whose

entries are given by

Jl

k“

$

’

’

’

’

’

’

’

’

’

’

’

’

’

’

’

&

’

’

’

’

’

’

’

’

’

’

’

’

’

’

’

%

P2P ,$

’

&

’

%

0, k ăl

0, k “l

0, k ąl

,

MAC ,$

’

&

’

%

ϵ, k ăl

0, k “l

1, k ąl

,

BC ,$

’

&

’

%

1, k ăl

0, k “l

ϵ, k ąl

,

(26)

where the cases 1, 0, and ϵrefer to no interference, cluster-

interference, and residual interference, respectively [20]. We

also draw attention that power levels in (25) are constrained to

piďP ωh

igh

ias a result of ωh

iď1in both UL-P2P and MAC.

Similarly, in DL-P2P and BC topologies, powers are subject

to řipiďPřiωi

hgi

hdue to řiωi

hď1along with piď

Přiωi

hgi

hdue to ωi

hď1. It is obvious from (26) that (25)

is generic to provides closed form power allocation to reach

minimum energy consumption objective. In what follows, we

provide closed-form power allocations for regular OBA and

NOBA schemes.

Lemma 1 (OBA closed-form optimal power allocation).De-

noting the SINR threshold of ni,@iPK,by ¯γiﬁ2

¯

RiK

B´1,

the optimal power allocations for regular OBA schemes (i.e.,

P2P topology) are given by

9ωh,‹

i“¯γiN0B

gh

iKP ,@iPK,and 9ωi,‹

h“¯γiN0B

gi

hP,@iPK,(27)

which is subject to 0ď9ωh,‹

iď1,@iPK,0ď9ωi,‹

hď1,@iP

K, and ři9

ωiPK,‹

hď1following from (21) and (22).

Proof. Please refer to Appendix A-A. ■

Lemma 2 (UL-NOBA closed-form optimal power allocation).

Denoting the SINR threshold of ni,@iPK,by ¯γiﬁ2

¯

Ri

B´1,

the optimal power allocations for regular UL-NOBA scheme

(i.e., MAC topology) are given by

:ωh,‹

K“

¯γKN0B

P gh

K

1´´1`ϵ¯γK

1´ϵ¯„1´´1`ϵ¯γh

K

1`¯γK¯K´1ȷ,(28)

:

ωh,‹

i“:

ωh,‹

K

P gh

iˆ1`ϵ¯γh

i

1`¯γh

i˙K´i

,@iPK´K,(29)

which can be further reduced assuming perfect SIC (i.e., ϵÑ

0) as follows

:ωh,‹

i“N0B

P gh

i

¯γip1`¯γiqi´1,@iPK.(30)

As per (21) and (22),(28)-(30) are subject to 0ď9ωh,‹

iď

1,@iPK.

Proof. Please refer to Appendix A-A. ■

Lemma 3 (DL-NOBA closed-form optimal power allocation).

Denoting the SINR threshold of ni,@iPK,by ¯γiﬁ2

¯

Ri

B´1,

the optimal power allocations for regular UL-NOBA scheme

(i.e., BC topology) are given by

:ω1,‹

h“

¯γ1N0B

P g1

h

1´´1`ϵ¯γ1

1´ϵ¯„1´´1`ϵ¯γ1

1`¯γ1¯K´1ȷ,(31)

:

ωi,‹

h“:ω1,‹

h

P gi

hˆ1`ϵ¯γi

1`¯γi˙i´1

,@iPK´1,(32)

which can be further reduced assuming perfect SIC (i.e., ϵÑ

0) as follows

:ωi,‹

h“N0B

P gi

h

¯γip1`¯γiqK´i,@iPˆ

K.(33)

As per (21) and (22),(31)-(33) are subject to 0ď9ωi,‹

hď

1,@iPKand řiPK9

ωi,‹

hď1.

Proof. Please refer to Appendix A-A. ■

2) C-OBA and C-NOBA: As explained in the problem

formulation, the joint optimization of phase time allocation and

power weights is crucial as they determined the overall energy

consumption in a time slot duration. For a given λ, each phase

behaves as individual time slot and optimal power weights

that minimizes the overall consumption can be obtained by

Lemma 1, Lemma 2, and Lemma 3 for OBA, UL-NOBA, and

DL-NOBA schemes, respectively. Therefore, optimal λcan be

expeditiously obtained by Golden section search as explained

in Algorithm 1, which is explained as follows:

In Line 2, we initialize golden ratio τ, iteration index t,

lower bound parameter lb, and upper bound parameter ub.

Then, two initial points, λ1and λ1, are calculated based on

the golden ratio and evaluated by EVALUATE OBJECTIVE

FUNCTIONpλ, Ψqprocedure. This procedure sets parameters

for each phase (i.e., number of nodes, QoS constraint, etc.)

and obtain the minimum energy consumption for the given λ

by using corresponding Lemma as mentioned above. Based

on the evaluation of these initial probe points, the while loop

8

Algorithm 1 : Optimal Phase Time Allocation

1: Input: Ψ“ t ¯

Ri, P, g1,g2, N0, B, K, ϵ, D, µ, T u

2: τÐ?5´1

2, t Ð1,lb Ð0,ub Ð1

3: λ1Ðlb ` p1´τqpub-lbq, λ2Ðlb `τpub-lbq

4: fpλ1q Ð EVAL UATE OBJECTIVE FUNCTION(λ1,Ψ)

5: fpλ2q Ð EVAL UATE OBJECTIVE FUNCTION(λ2,Ψ)

6: while |ub - lb| ą µ&tďTdo

7: if fpλ1q<fpλ2qthen

8: ub Ðλ2,λ2Ðλ1,λ1Ðlb ` p1´τqpub-lbq

9: fpλ1q Ð EVAL UATE OBJECTIVE FUNCTION(λ1,Ψ)

10: fpλ2q Ð EVAL UATE OBJECTIVE FUNCTION(λ2,Ψ)

11: else

12: lb Ðλ1,λ1Ðλ2,λ2Ðlb `τpub-lbq

13: fpλ1q Ð EVAL UATE OBJECTIVE FUNCTION(λ1,Ψ)

14: fpλ2q Ð EVAL UATE OBJECTIVE FUNCTION(λ2,Ψ)

15: end if

16: tÐt`1

17: end while

18: if fpλ1q<fpλ2qthen

19: λ‹Ðλ1

20: fpλ‹q Ð fpλ1q

21: else

22: λ‹Ðλ2

23: fpλ‹q Ð fpλ2q

24: end if

25: return λ‹,fpλ‹q,

26: procedure EVAL UATE OBJECTIVE FUNCTION(λ, Ψ)

27: if D“1then // UL direction

28: K1ÐK´1// # nodes in the ﬁrst Phase

29: K2ÐK// # nodes in the second Phase

30: Ri

1Ð¯

Ri

λ// QoS demand in the ﬁrst Phase

31: Ri

2Ð¯

Ri

p1´λq// QoS demand in the second Phase

32: else // DL direction

33: K1ÐK// # nodes in the ﬁrst Phase

34: K2ÐK´1// # nodes in the second Phase

35: Ri

1Ð¯

Ri

λ// QoS demand in the ﬁrst Phase

36: Ri

2Ð¯

Ri

p1´λq// QoS demand in the second Phase

37: end if

38: ‹

ω1Ðsubstitute K1and Ri

1,@iPK,into (27) for OBA, (28)-(29)

for UL-NOBA, and (31)-(32) for DL-NOBA.

39: ‹

ω2Ðsubstitute K2and Ri

2,@iPK,into (27) for OBA, (28)-(29)

for UL-NOBA, and (31)-(32) for DL-NOBA.

40: return fpλq

41: end procedure

between Line 6 and Line 25 iteratively founds optimal λby

evaluating the objective for two intervals, discarding the one

with higher energy consumption, resetting bounds as per the

new interval, and calculating new probe points for the next

iterations. The loop terminates if the step tolerance (i.e., the

absolute value of difference between two selected λvalues) is

less than a accuracy of interest µor the maximum of number

of iterations is reached.

IV. MAX IM UM IOB N ET WO RK SI ZE ANALYS IS

The IoB applications may differ in required QoS and

number of nodes to provide a sufﬁcient service. Therefore,

this section analyzes the maximum feasible number of nodes

and derive closed-form network size, Kmax, as a function of

key parameters such as QoS demand, SIC error factor, channel

gain, and available bandwidth. Throughout this section, we

assume all nodes have a common data rate requirement, ¯

R,

for the sake of analytical tractability.

A. Maximum Network Size Analysis of OBA Schemes

Since OBA scheme consists of P2P links, the maximum

number of nodes can be directly obtained from SINR con-

straint of the node with the weakest channel gain, gmin. By

limiting the optimal power weights provided in Lemma 1 to

unity, Kmax can be obtained as in Lemma 4.

Lemma 4. Kmax for the UL-OBA scheme is given by

Kmaxp¯

R, gminq “ —

—

—

–´

W´1´´N0¯

R

gminPlogp2q¯B

logp2q¯

Rﬃ

ﬃ

ﬃ

ﬂ,(34)

where W´1p¨q is the ´1th branch of the Lambert-W function.

On the other hand, Kmax for the DL-OBA scheme is given by

Kmaxp¯

R, gminq “ ZB

¯

Rlog2ˆ1`P gmin

N0B˙^.(35)

Proof. Please see Appendix A-B. ■

B. Maximum Network Size Analysis of NOBA Schemes

In the UL-NOBA scheme, the IoB node with the strongest

channel is required to transmit with the highest power. There-

fore, as we add more users to the network, the strongest node

needs to increase its transmission power to satisfy QoS con-

straints, which may not be feasible after a certain network size.

Accordingly, Kmax can be obtained as in Lemma 5 by limiting

the optimal power weight of the strongest node given in (30)

Lemma 2 to unity, i.e., :ωh,‹

1ď1. Although the IoB node with

the weakest channel is required to transmit with the highest

power in the DL-NOBA, the overall network feasibility is

mainly determined by the total power consumption constraint,

i.e., řKmax

i“1:

ωh,‹

iď1, rather than the weakest channel node’s

individual feasibility. Accordingly, Kmax can be obtained as

in Lemma 5 by limiting the sum of optimal power weight of

the strongest node given in (33) Lemma 3 to unity.

Lemma 5. Kmax for the UL-NOBA scheme under perfect SIC

case (ϵÑ0) is given by

Kmaxp¯

R, gmaxq “ —

—

—

–1`

log ´P gmax

¯γN0B¯

logp1`¯γqﬃ

ﬃ

ﬃ

ﬂ,(36)

where gmax is the maximum channel gain in the network. On

the other hand, Kmax for the DL-NOBA scheme under perfect

SIC case (ϵÑ0) is given by

Kmaxp¯

R, gminq “ [logpρ`1

ρq

logp1`¯γq_.(37)

where ρ“N0B

P¯gand all nodes are assumed to have a channel

gain of ¯g“gmin {2, which represent a hypothetical node

located in the middle between the hub node and the source

node with the weakest channel gain.

Proof. Please see Appendix A-C. ■

The maximum network size analysis can be further extended

to NOBA schemes under imperfect SIC conditions as follows

9

Lemma 6. Kmax for the UL-NOBA scheme under imperfect

SIC conditions (ϵą0) is given by

Kmaxp¯

R, gmax, ϵq “

—

—

—

–1`

log ´N0B

P gmax ´ϵp1`¯γq

1´ϵ¯´log ´1`ϵ¯γ

1´ϵ¯

log ´1`ϵgmax

1´ϵ¯ﬃ

ﬃ

ﬃ

ﬂ.(38)

On the other hand, Kmax for the DL-NOBA scheme under

perfect SIC case (ϵą0) is given by

Kmaxp¯

R, gmin, ϵq “ —

—

—

–

log pφ`ϵ¯γq ´ log pφ`¯γq

log ´1`ϵ¯γ

1`¯γ¯ﬃ

ﬃ

ﬃ

ﬂ,(39)

where φ“N0B¯γ

P¯gand all nodes are assumed to have a

channel gain of ¯g“gmin{2, which represent a hypothetical

node located in the middle between the hub node and the

source node with the weakest channel gain.

Proof. Please see Appendix A-D. ■

C. Maximum Network Size Analysis of Cooperative Schemes

The analyses presented clearly show that QoS demand and

channel gains play a vital role in maximum network size of

regular OBA and NOBA schemes. In the case of cooperation,

the maximum network size is determined by the minimum of

network size of both phases, each of which heavily depends on

channel gains to/from the relay node and phase time allocation,

which determines the QoS demand to be met at each phase,

i.e., ¯

R{λand ¯

R{p1´λq. In light of above discussions,

the maximum network size of cooperative schemes can be

obtained as shown in the following corollary.

Corollary 1. Denote g1

max and g1

min as the maximum and

minimum channel gain between source nodes and relay node,

respectively. Likewise, denote gh

ras the channel gain between

the relay and the hub nodes. Following from Lemma 4, Kmax

for OBA schemes are given by

Kmaxp¯

R, λ, gmin, g h

rq “

min ˆKmax ˆ¯

R

λ, gmin˙, Kmax ˆ¯

R

1´λ, gh

r˙˙,(40)

where the inner terms of minp¨,¨q function is obtained from

(34) and (35) for UL-OBA and DL-OBA schemes, respectively.

The Kmax for NOBA schemes similarly follows from Lemma

6 as

Kmaxp¯

R, λ, gmin, g h

r, ϵq “

min ˆKmax ˆ¯

R

λ, gmin, ϵ˙, Kmax ˆ¯

R

1´λ, gh

r, ϵ˙˙,

(41)

where the inner terms of minp¨,¨q function is obtained from

(38) and (39) for UL-NOBA and DL-NOBA schemes, re-

spectively. The optimal cooperative network size K‹

max can

be numerically obtained by substituting optimal phase time

allocation, λ‹, into (40) and (41) for C-OBA and C-NOBA

schemes, respectively.

Algorithm 2 : Optimal Phase Time Allocation for Kmax

1: Input: Ψ“ t ¯

Ri, P, g1,g2, N0, B, ϵ, D, µ, T u

2: τÐ?5´1

2, t Ð1,lb Ð0,ub Ð1

3: λ1Ðlb `τpub-lbq, λ2Ðub ´τpub-lbq

4: Kmaxpλ1q Ð EVAL UATE Kmax (λ1,Ψ)

5: Kmaxpλ2q Ð EVAL UATE Kmax (λ2,Ψ)

6: while |ub - lb| ą µ&tďTdo

7: if Kmaxpλ1q<Kmax pλ2qthen

8: lb Ðλ2,λ2Ðλ1,λ1Ðlb `τpub-lbq

9: Kmaxpλ1q Ð EVAL UATE Kmax (λ1,Ψ)

10: Kmaxpλ2q Ð EVAL UATE Kmax (λ2,Ψ)

11: else

12: ub Ðλ1,λ1Ðλ2,λ2Ðub `τpub-lbq

13: Kmaxpλ1q Ð EVAL UATE Kmax (λ1,Ψ)

14: Kmaxpλ2q Ð EVAL UATE Kmax (λ2,Ψ)

15: end if

16: tÐt`1

17: end while

18: if Kmaxpλ1q<Kmax pλ2qthen

19: λ‹Ðλ1

20: Kmaxpλ‹q Ð Kmax pλ1q

21: else

22: λ‹Ðλ2

23: Kmaxpλ‹q Ð Kmax pλ2q

24: end if

25: return λ‹,Kmaxpλ‹q,

26: procedure EVAL UATE Kmax(λ, Ψ)

27: Ri

1Ð¯

Ri

λ// QoS demand in the ﬁrst Phase

28: Ri

2Ð¯

Ri

p1´λq// QoS demand in the second Phase

29: K1Ðsubstitute Ri

1and gmin, into (34) and (35) for UL-OBA and

DL-OBA respectively, into (38) and (39) for UL-NOBA and

DL-NOBA, respectively.

30: K2Ðsubstitute Ri

2and gh

r, into (34) and (35) for UL-OBA and

DL-OBA respectively, into (38) and (39) for UL-NOBA and

DL-NOBA, respectively.

31: Kmax Ðmin pK1, K2q

32: return Kmax

33: end procedure

Proof. The corollary directly follows from Lemma 4-Lemma

6 by considering the bottleneck of two phases. The λ‹can

obtained as shown in Algorithm 2, following Algorithm 1. ■

TABLE I: Simulation Parameters

Par. Val. Par. Val.

B 1 MHz N0-174 dBm/Hz

K3 T 1 sec.

P0 dBm R 1 Mbps

ϵ0

V. SIMULATION RESU LTS

This section evaluates the performance of the proposed

energy-efﬁcient body channel access topologies and schemes

in terms of transmit power and network size for different

node deployment scenarios, QoS requirements, and SIC im-

perfections. The simulation parameters summarized in Table I

will be utilized throughout this section unless explicitly stated

otherwise. Moreover, throughout simulations we exploit the

proposed frequency dependent parametric path loss model in

[4] to calculate P Lh

ithe path loss between niand nh. The

linear channel gain between niand nhis then obtained by

gh

i“10´P Lh

i{10.

10

Fig. 4: Illustration for the node deployment simulations for

OBA schemes.

A. The Impact of Node Deployment on Energy Efﬁciency

The impact of the source node and relay deployment on

the transmit power is investigated in Fig. 5 and 6. In both

simulations, the network comprises three BCC-enabled IoB

nodes that exploit regular OBA, NOBA, C-OBA, and C-NOBA

schemes. To further elucidate the difference between the two

cases, both node deployment scenarios are illustrated in Fig.

4 for OBA schemes which also apply to NOBA schemes.

Fig. 5a plots the sum of transmit power for UL (left y-axis)

and DL (right y-axis) trafﬁc in OBA and NOBA schemes

with and without cooperation against the change in group

distance. The group distance denotes the cumulative change

in distance for source nodes n2and n3due to sweeping n1.

This is implemented by setting the channel lengths l1

2and

l1

3at 20 and 40 cm, respectively. Then the channel length

between n1and nhis increased from 20 cm up to 160 cm.

As a result the grouped source nodes with n1are also swept

and the end-to-end channel lengths for n2and n3in regular

schemes are obtained by lh

2“lh

1`l1

2and lh

3“lh

1`l1

3,

respectively. For cooperative links, n1is selected to act as

a relay since it is the closest node to the hub. This means

that source nodes n2and n3will maintain the same distance

in reference to the relay throughout the simulations. As can

be observed, cooperative schemes improved energy efﬁciency,

i.e., provided a reduction in transmission power compared

to regular schemes. The reduction in transmit power ranges

between 1%to 9%in both directions. Indeed, the improvement

is more notable with pushing the nodes further away from the

hub. This is because by increasing the channel length between

source nodes and the hub, more power will be allocated

in regular schemes to mitigate the channel conditions and

communicate directly with the hub. Further, the performance

of C-NOBA in both UL and DL directions, which is matched

with C-OBA in UL when operating at low QoS, has the

least power consumption over the entire channel length range.

Whereas in DL transmission, OBA schemes perform worse

than their non-orthogonal counterparts at all times. Because

20 40 60 80 100 120 140 160

-75

-70

-65

-60

-55

-50

-45

-75

-70

-65

-60

-55

-50

-45

(a)

20 40 60 80 100 120 140 160

0

0.2

0.4

0.6

0.8

1

0

0.2

0.4

0.6

0.8

1

(b)

Fig. 5: Changing the Distance of the Group.

the maximum transmission power of nhin the ﬁrst phase and

nrin the second phase is equally split between source nodes.

Fig. 5b demonstrates the change in optimal phase time allo-

cation λ‹that is adjusted to minimize the end-to-end transmit

power in UL and DL against change in group distance. In UL

trafﬁc, when lh

1ălr

ithe duration of the ﬁrst phase is longer

compared to the second phase, and conversely, when the relay

is placed very far-away from nh, the second phase occurs

over a longer time slot. While in DL, the more signiﬁcant the

difference between nhand nris, the longer the duration of

the ﬁrst phase is.

Fig. 6a demonstrates the effect of changing relay

distance,n1, on the sum of transmit power for a network

consisting of three IoB nodes. In this case, the channel lengths

lh

2and lh

3are set to 120 cm and 160 cm, respectively.To

investigate the effect of the relay, we increase the channel

length from the ﬁrst node to the hub node ‘ lh

1up to 100

cm. Accordingly, the channel lengths in the ﬁrst phase of

cooperation will change depending on the relay location.

Thus, in cooperative schemes, the channel lengths of the ﬁrst

phase are obtained by lr

i“lh

i´lh

r. As shown in Fig. 6a,

the cooperative schemes improve the sum of transmit power

11

20 40 60 80 100

-75

-70

-65

-60

-55

-50

-75

-70

-65

-60

-55

-50

(a)

20 40 60 80 100

0

0.1

0.2

0.3

0.4

0.5

0.6

0.7

0.8

0

0.1

0.2

0.3

0.4

0.5

0.6

0.7

0.8

(b)

Fig. 6: Changing the Relay distance.

by an 11 %average reduction compared to their regular

counterparts. Yet the most important observation is that when

the relay is somewhat between the hub and source nodes,

transmit power reaches a minimum in cooperative schemes.

Which corresponds to achieving a 14 %power reduction

in cooperative schemes. However, pushing the relay closer

to source nodes, the transmit power will increase with a

further increase in the hub and relay separation. On the other

hand, regular schemes maintain their performance over the

entire distance vector since lh

2and lh

3are ﬁxed throughout the

simulation.

Likewise, Fig. 6b demonstrate the change in optimal phase

time allocation λ˚that is adjusted to minimize the End-To-

End transmission power in UL and DL with respect to group

localization. In UL trafﬁc, when lh

1ălr

itime allocated for

the ﬁrst phase is longer compared to the second phase and

conversely when the relay is placed very faraway from nhthe

second phase occurs over a longer time slot. The opposite is

true in DL as larger distance between nhand nris translated

into longer phase. Both Fig. 5b and Fig. 6b clearly show how

λis optimized by Algorithm 1 to minimize overall energy

consumption by manipulating λto mitigate the adverse effects

(a)

(b)

Fig. 7: Sum of Tx. Power w.r.t QoS and K

10-8 10-6 10-4 10 -2

-50

-45

-40

-35

-30

Fig. 8: Effect of SIC

of node deployment.

12

B. The Impact of QoS, K, and ϵon Energy Efﬁciency

The impact of network size and QoS requirements on the

transmit power consumption is investigated in Fig. 7a and Fig.

7b for orthogonal and non-orthogonal schemes, respectively.

A network supporting up to 9 IoB nodes with all nodes

demanding the same QoS levels is simulated. We ﬁx the

channel length lh

1at 60 cm and place additional nodes to

the network at 5ˆicm from n1. At low QoS demands,

particularly below 0.5 Mbps, the effectiveness of cooperation

is realized at a larger network size. For instance, at 100 kbps,

C-NOBA improved the total transmit power performance from

9%when K=1 to 13.7 %when K=9 compared to NOBA.

However, at high QoS, as we add more nodes to the network,

the performance of cooperative schemes deteriorate, depending

on λ‹nodes are required to satisfy ě¯

R, which suggests that

higher powers will be allocated to meet the rate requirements.

Fig. 8 addresses the effect of SIC imperfections by plotting

the transmission power against cancellation error. The results

are generated for an IoB network with nodes deployed at

lh

1“40 cm, l1

2“120 cm and l1

3“160 cm with investigating

two QoS requirements: 500 kbps and 1 Mbps. Note that the

orthogonal schemes are independent of ϵ, unlike their non-

orthogonal counterparts. Accordingly, they sustain the same

sum of transmit power at all times. First, we note that in

regular schemes, NOBA has a better performance compared

to OBA as long as the SIC error is kept below 0.03. Which is

anticipated since power weights in NOBA are dependent on ϵ.

Second, at QoS 500 kbps and 1 Mbps, C-NOBA is found to

outperform NOBA in terms of the total transmit power by 8.6

%and 12.6 %, respectively. However, at ϵ“0.02 the situation

is reversed and NOBA schemes will be more effective. It is

worth noting that, beyond ϵ“0.03, it becomes infeasible

for C-NOBA to operate, which is mainly since, in C-NOBA,

SIC mitigation is performed in two phases. Hence, low SIC

efﬁciency will increase the power weights until it approaches

infeasibility as ϵinhibits achieving the SINR thresholds.

C. The Impact of QoS and ϵon Kmax

Fig. 9a and Fig. 9b compare the maximum number of

nodes to be supported in an IoB network exploiting regular

and cooperative OBA, and NOBA schemes with respect to

QoS demands. The results are plotted for analytically derived

Kmax expressions and the maximum feasible number of nodes

determined by simulations. The ﬁgures exhibit that as a result

of NOBA’s throughput efﬁciency, it can support more nodes

when compared to other schemes. It was determined that OBA

and C-NOBA, on average, can support 55.6 %and 31.7%,

less nodes, respectively, compared to the NOBA scheme. The

reason for such performance in cooperation is that during the

second phase, all nodes share the relay’s power to achieve

their SINR requirements, which constitutes a bottleneck on

the overall network size. Similarly, in DL, both OBA and

C-NOBA, on average, support 69 %less nodes than NOBA

scheme.

Fig. 10 plot Kmax obtained by CF and simulation for a

network adopting NOBA schemes with respect to cancellation

error ϵfor three different QoS requirements 0.5 Mbps, 1 Mbps,

106107

0

5

10

15

20

25

30

(a)

106107

0

5

10

15

20

25

30

(b)

Fig. 9: Kmax vs. QoS for NOBA,C-NOBA,OBA,and C-OBA

in UL and DL

and 10 Mbps. In generating this results lh

1was ﬁxed at 50 cm

and the additional source nodes where uniformly distributed

as lh

K“lh

1`4pK“1q. It is obvious that in both directions

NOBA scheme can tolerate up to ϵ“1e´5to deliver the

maximum network size at both 0.5 Mbps and 1 Mbps. Which

again demonstrates NOBA’s SINR efﬁciency. One can note

the plus-minus one deviation between CF and simulation for

DL Kmax. This is because we assumed that all nodes have

the same channel gain to approximate the sum of weights and

come up with the CF Kmax expression.

VI. CONCLUSION

Toward accelerating the adoption of IoB in multiple sectors

while embracing the technological advancements in BCC, we

model and evaluate the performance of orthogonal and non-

orthogonal schemes with and without cooperation to establish

highly secure and efﬁcient networks. Hence, P2P, MAC, and

BCC topologies are presented along with optimal closed-form

power control techniques to permit multipoint communication

and meet the different QoS requirements. Further, line search

algorithms are presented for joint optimal power and phase

13

10-5 100

0

5

10

15

20

25

30

0

5

10

15

20

25

30

Fig. 10: Kmax vs. SIC error ϵfor NOBA

time allocations to facilitate cooperative communications.

Lastly, to address the full capacity in each scheme, the maxi-

mum number of supportable nodes was analytically obtained.

Namely, closed-form Kmax expressions were extended to con-

sider SIC imperfections and cooperative schemes. Thoroughly

performed simulations identiﬁed the network settings under

which cooperation is more beneﬁcial than regular schemes in

terms of the sum of transmit power. Conversely, regular NOBA

schemes illustrated better capabilities to improve the network

size.

VII. ACKNOWLEDGEMENT

We would like to thank Qi Huang from CCSL group for

his help in preparing Fig. 2.

APPENDIX A

A. Derivation of Optimal Power Weights

It is worth noting that interference matrix Jin (25) can

be assumed to be irreducible since it has non-negative ele-

ments and ϵ“0is unattainable in practice due to the SIC

imperfections [20], [21]. Following from Perron-Frobenius

theorem [22], maximum modulus eigenvalue of Jis real

and positive, while the corresponding eigenvector is positive

componentwise. Thereby, a feasible solution to (25) exists

if and only if the magnitude of the maximum eigenvalue

of Hﬁ¯

ΓJ is less than unity, i.e., ρHă1[21], [20].

Accordingly, optimal power weights ‹

ωcan be obtained from

p‹“ pI´Jq´1¯

Γσ“P‹

ωg, where gis the vector of channel

gains sorted in descending order. By using the eigenvalue

equation Hν“λHν, the optimal power allocations can be

obtained as described in [23].

B. Kmax for OBA

For UL-OBA scheme, Kmax can be obtained by constrain-

ing optimal power weight in (27) as shown in Lemma 1, i.e.,

¯γiN0B

¯gK P ď1where ¯γ“2¯

RK

B´1. For the sake of analytical

tractability, assuming ¯γ"1yields ¯γ«2¯

RK

Band allows us to

obtain Kmax by leveraging Lambert-W function as shown in

(34). For the DL-OBA, above approximation is not necessary

and Kmax can be directly derived from ¯γN0B

¯gP ď1as shown

in (35).

C. Kmax for NOBA under Perfect SIC Conditions

Following from (30) and discussions before Lemma 5,

Kmax for UL perfect NOBA case can be obtained by solving

N0B

P gmax ¯γp1`¯γqKmax´1ď1for Kmax. To obtain Kmax in

the DL perfect NOBA case, we ﬁrst obtain the sum of power

weights as follows

K

ÿ

i“1

ωi“

K

ÿ

i“1

ρ¯γp¯γ`1qK1

p¯γ`1qi“

K

ÿ

i“1

aϱi,(42)

where ρ“N0B

P¯g,¯g“gmin {2, and ϱﬁ1

p¯γ`1q, and a“ρ¯γ ϱ´K.

The last term in (42) corresponds to well-known geometric

progression formula, i.e.,

n

ÿ

i“m

aϱkﬁapϱm´ϱn`1q

1´ϱ.(43)

By setting m“1and n“Kin (43), (42) can be rewritten

as

K

ÿ

i“1

ωi“ρ¯γϱ´Kpϱ´ϱK`1q

1´ϱ“ρ¯γ

1´ϱpϱ1´K´ϱq.(44)

By substituting ϱﬁ1

p¯γ`1qinto (44), we can rewrite the total

power constraint as

K

ÿ

k“1

ωk“ρ“p1`¯γqK´1‰ď1.(45)

Solving (45) for Kyields the Kmax as follows

Kmax “[logpρ`1

ρq

logp1`¯γq_.(46)

D. Maximum Number of Nodes for Imperfect SIC DL-NOBA

Following similar approach to Appendix A-C, deﬁne

řK

i“1ω1

hp1`¯γϵ

1`¯γqi´1ď1where in this case ω1

his found as

ω1

h“φ

1´´1`ϵγ1

h

1´ϵ¯„1´´1`ϵγ1

h

1`γ1

h¯K´1ȷ(47)

which represents the ﬁrst term of the geometric series and the

common ratio in this case is ϱ“ p1`¯γ ϵ

1`¯γq. Based on the sum

of ﬁnite geometric series řK

i“1ω1

hp1`¯γϵ

1`¯γqi´1can be written as

K

ÿ

i“1

ωi“

K

ÿ

i“1

aϱi´1“1´ϱK

1´ϱ(48)

By substituting ϱﬁp1`¯γϵ

1`¯γqinto (48), and solve for řK

i“1ωkď

1, which yields

Kmax “—

—

—

–

log pφ`ϵ¯γq ´ log pφ`¯γq

log ´1`ϵ¯γ

1`¯γ¯ﬃ

ﬃ

ﬃ

ﬂ.(49)

14

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PLACE

PHOTO

HERE

Abeer Alamoudi (Student Member, IEEE) Abeer

AlAmoudi received the B.Sc. degree in electrical

and computer engineering from Effat University,

Saudi Arabia, Jeddah, in 2019, and the M.Sc. degree

in electrical engineering and computer engineering

from King Abdullah University of Science and

Technology (KAUST), Saudi Arabia, Thuwal, in

2021. She is currently a Ph.D. student working in

the communications and computing systems lab at

KAUST. Her research sensors and wireless sensor

network.

Abdulkadir Celik (Senior Member, IEEE) received

the M.S. degree in electrical engineering in 2013,

the M.S. degree in computer engineering in 2015,

and the Ph.D. degree in co-majors of electrical

engineering and computer engineering in 2016 from

Iowa State University, Ames, IA, USA. He was a

post-doctoral fellow at King Abdullah University of

Science and Technology (KAUST) from 2016 to

2020. Since 2020, he has been a research scientist

at the communications and computing systems lab

at KAUST. His research interests are in the areas of

wireless communication systems and networks.

Ahmed M. Eltawil (Senior Member, IEEE) is a

Professor of Electrical and Computer Engineering at

King Abdullah University of Science and Technol-

ogy (KAUST) where he joined the Computer, Elec-

trical and Mathematical Science and Engineering

Division (CEMSE) in 2019. Prior to that he was with

the Electrical Engineering and Computer Science

Department at the University of California, Irvine

(UCI) since 2005. At KAUST, he is the founder

and director of the Communication and Computing

Systems Laboratory (CCSL). His current research

interests are in the general area of smart and connected systems with an

emphasis on mobile systems. He received the Doctorate degree from the

University of California, Los Angeles, in 2003 and the M.Sc. and B.Sc.

degrees (with honors) from Cairo University, Giza, Egypt, in 1999 and 1997,

respectively. Dr. Eltawil has been on the technical program committees and

steering committees for numerous workshops, symposia, and conferences

in the areas of low power computing and wireless communication system

design. He received several awards, including the NSF CAREER grant

supporting his research in low power computing and communication systems.

He is a senior member of the IEEE and a senior member of the National

Academy of Inventors, USA. He received two United States Congressional

certiﬁcates recognizing his contributions to research and innovation. In 2021,

he was selected as “Innovator of the Year” by the Henry Samueli School of

Engineering at the University of California, Irvine.