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Cooperative Body Channel Communications for Energy Efficient Internet of Bodies

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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 coexistence 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.
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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
igi
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
ibP 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 zhNp0, 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
:
yhÿ
iPKbP gh
i:
ωh
ixi`zh,(4)
where :ωh
iP r0,1sis the power factor allocated to the message
of ni,xi, and zhNp0, 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
:
yiÿ
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
i1
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;¯
Γdiagp¯
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 ¯γi2
¯
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 ¯γi2
¯
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,
iN0B
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 ¯γi2
¯
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,
hN0B
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: λÐλ1
20: fpλq Ð fpλ1q
21: else
22: λÐλ2
23: fpλq Ð fpλ2q
24: end if
25: return λ,fpλq,
26: procedure EVAL UATE OBJECTIVE FUNCTION(λ, Ψ)
27: if D1then // UL direction
28: K1ÐK´1// # nodes in the first Phase
29: K2ÐK// # nodes in the second Phase
30: Ri
1Я
Ri
λ// QoS demand in the first Phase
31: Ri
2Я
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
1Я
Ri
λ// QoS demand in the first Phase
36: Ri
2Я
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¯
R
,(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
i1:
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`¯γq
,(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 ρN0B
P¯gand all nodes are assumed to have a channel
gain of ¯ggmin {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¯
.(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¯
,(39)
where φN0B¯γ
P¯gand all nodes are assumed to have a
channel gain of ¯ggmin{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 min,¨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 min,¨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: λÐλ1
20: Kmaxpλq Ð Kmax pλ1q
21: else
22: λÐλ2
23: Kmaxpλq Ð Kmax pλ2q
24: end if
25: return λ,Kmaxpλq,
26: procedure EVAL UATE Kmax(λ, Ψ)
27: Ri
1Я
Ri
λ// QoS demand in the first Phase
28: Ri
2Я
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 λcan
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
i10´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
2lh
1`l1
2and lh
3lh
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 λthat 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
ilh
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 λnodes 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
140 cm, l1
2120 cm and l1
3160 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 ϵ0.02 the situation
is reversed and NOBA schemes will be more effective. It is
worth noting that, beyond ϵ0.03, 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 NOBAs 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
Klh
1`4pK1q. It is obvious that in both directions
NOBA scheme can tolerate up to ϵ1e´5to deliver the
maximum network size at both 0.5 Mbps and 1 Mbps. Which
again demonstrates NOBAs 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 ϵ0is 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 H¯
ΓJ is less than unity, i.e., ρHă1[21], [20].
Accordingly, optimal power weights
ωcan be obtained from
p“ pI´Jq´1¯
ΓσP
ωg, where gis the vector of channel
gains sorted in descending order. By using the eigenvalue
equation HνλHν, 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 ¯γ2¯
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
i1
ωi
K
ÿ
i1
ρ¯γp¯γ`1qK1
p¯γ`1qi
K
ÿ
i1
i,(42)
where ρN0B
P¯g,¯ggmin {2, and ϱ1
p¯γ`1q, and aρ¯γ ϱ´K.
The last term in (42) corresponds to well-known geometric
progression formula, i.e.,
n
ÿ
im
kapϱm´ϱn`1q
1´ϱ.(43)
By setting m1and nKin (43), (42) can be rewritten
as
K
ÿ
i1
ωiρ¯γϱ´Kpϱ´ϱK`1q
1´ϱρ¯γ
1´ϱpϱ1´K´ϱq.(44)
By substituting ϱ1
p¯γ`1qinto (44), we can rewrite the total
power constraint as
K
ÿ
k1
ωkρp1`¯γqK´1ď1.(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
i1ω1
hp1`¯γϵ
1`¯γqi´1ď1where in this case ω1
his found as
ω1
hφ
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
i1ω1
hp1`¯γϵ
1`¯γqi´1can be written as
K
ÿ
i1
ωi
K
ÿ
i1
i´11´ϱK
1´ϱ(48)
By substituting ϱp1`¯γϵ
1`¯γqinto (48), and solve for řK
i1ωkď
1, which yields
Kmax
log pφ`ϵ¯γq ´ log pφ`¯γq
log ´1`ϵ¯γ
1`¯γ¯
.(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.
ResearchGate has not been able to resolve any citations for this publication.
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