# A Generalized Framework for Joint Dynamic Optimal RF Interface Setting and
Next-Hop Selection in IoT networks with Similar Requests

Monireh Allah Gholi Ghasri, Ali Mohammad Afshin Hemmatyar A. M. A. Hemmatyar
was with the Department of Computer Engineering, Sharif University of
Technology, Azadi Ave., Tehran, Iran, e-mail:
(hemmatyar@sharif.edu).Manuscript received …. .., 2021; revised …. .., 2021.

###### Abstract

Many applications which run on the Internet-of-Things machines require similar
bandwidths. These machines are equipped with multiple Radio Frequency(RF)
interfaces for machine-to-machine or machine-to-Base Station(BS)
communications. Joint dynamic optimal RF interface setting and next-hop
selection in data transmission can maximize the network data rate. For this
purpose, we propose a generalized framework for simultaneous selection of
these components according to the required bandwidth of machines. This
framework is suitable for networks with multiple BSs and sources with similar
bandwidth requests. Simulation results show that using the proposed framework,
the average data rate of network sources increases up to 117%.

###### Index Terms:

RF interface setting, Next-hop selection, Multiple RF interfaces, Internet-of-
Things

##  I Introduction

Nowadays, Internet-of-Things (IoT) devices with various applications need
different requirements, such as BandWidth (BW) [1]. On the other hand, these
devices (machines and Base Stations (BS)) are equipped with multiple Radio
Frequency (RF) interfaces, such as Z-Wave, Bluetooth, and WiFi for Machine-to-
Machine communication (M2M) and NB-IoT, LTE-M, and LTE for Machine-to-BS (M2B)
communication. Therefore, they can use these RFs according to their needs.
Optimal RF selection according to the required BW of the network sources
maximizes their total data rate. Simultaneous use and dynamic optimal
selection of these RF interfaces along with next-hop (relay or BS) selection
helps to improve network data rate and reduce the interference of
communication signals in practice [2, 3, 4, 5]. Using the word dynamic in the
literature on RF interface setting means that instead of using only constant
RFs statically in communications, similar to an optimal relay selection by
static RF interfaces previously provided [3], RF should be dynamically
selected from the existing RFs according to the need.

Despite more attention to the proper selection of relays to improve network
coverage and data rate [6] where the direct channel with the BS is weak or
disconnected in previous works, the importance of RF interfaces setting
especially when choosing the next-hop in transmission has received less
attention. In this regard, while setting up the RF interface used in
smartphones is done manually or automatically by default, some studies provide
better methods by appropriate link and time determination or simultaneous
usage of multiple RF interfaces for handover[2, 7]. Some other works in this
area include maximizing the multi-cell unlicensed LTE and WiFi networks
throughput [8], and improving throughput and delay by concurrent transmission
with dual connectivity [9]. Unlike previous studies that focused more on dual-
connectivity in M2B communication, in a recent work, a dynamic optimal RF
interface setting for M2M communication with relay selection, called DORSA, in
a network cell with a BS has been considered [10].

To complete these approaches, a comprehensive framework is provided for
optimally selecting from M2M and M2B RF interfaces, along with the next-hop
of data transmission. Unlike mentioned works [2, 3, 6, 7, 8, 9, 10], in the
proposed framework, the dynamic optimal selection between both types of M2M
RFs and M2B RFs(for capillary and cellular part of a hybrid network,
respectively) is done simultaneously with each other and with relay selection.
In addition, unlike some previous work [3, 10], there is no limit to the
Number of (No.) BSs in the proposed problem-solving framework. Therefore, this
paper can be an extension of some previous works [3, 10].

Main Contributions: In this paper, the following contributions are provided:
\- A new generalized algorithmic framework for optimal selection of RF
interfaces and the next-hop (relay or BS) for data transmission according to
the requested BW of sources in an IoT network is proposed.
-Our framework can support IoT networks including multiple BSs and machines, each of which is equipped with multi-RF interfaces.
\- In our framework, all of the machines can use different multiple M2M and
M2B RF equipment (for capillary and cellular part of the network,
respectively) simultaneously to send data of sources with the same requested
BW.
\- Finally, using the presented framework can help to detect the upper bound
of the average total data rate of network sources to examine other algorithms
for next-hop selection and RF interface setting.

##  II System Model

In this model, an IoT network with $N$ fixed machines and $N_{b}$ BSs is
considered. Each machine is equipped with $t^{M2M}$ M2M RF interfaces and
$t^{M2B}$ M2B RF interfaces and each BS is equipped with $t^{M2B}$ M2B RF
interfaces. Among the machines, there are $N_{s}$ sources and $N_{r}$ relays
that these $N$ machines, where $N=N_{s}+N_{r}$, are randomly placed around BSs
with a uniform distribution. An illustration of devices and communications in
the network model is shown in Fig. 1.

Figure 1: Illustration of devices and communications in the network model.

Assumptions: The assumptions for providing the desired framework are as
follows:

  1. 1.

The relation between sources with relays and base stations is N-to-One.

  2. 2.

The No. different channels of each M2M RF interface is equal to one.

  3. 3.

Different M2M and M2B RF interfaces do not overlap and do not interfere with
each other (such as WiFi with Bluetooth, LTE, and etc.).

  4. 4.

Requested BW of all sources are the same.

  5. 5.

The relaying protocol is Decode-and-Forward (DF).

Problem Formulation: Here are some of the relations used to formulate the
problem. The calculated data rate of the communication by DF relaying between
source $s$ and BS $b$ through relay $r$ is estimated by relation (1) in a time
slot [11].

$C_{{s,b}_{throughr}}=min\\{C^{t^{M2M}}_{s,r},C^{t^{M2B}}_{r,b}\\},$ (1)

. where $C^{t^{M2M}}_{s,r}$ is maximum data rate between $s$ and $r$ on
$t^{M2M}$th RF interface and $C^{t^{M2B}}_{r,b}$ is maximum data rate between
$r$ and $b$ on $t^{M2B}$th RF interface. To calculate the maximum data rate
between two devices (machine or BS) using $t$th RF
($C^{t^{M2M|B}}_{(n_{i},n_{j})}$), we consider the minimum value between the
data rate calculated for the channel (regardless of $t$th RF capacity) and the
maximum data rate capacity for $t$th RF ($C^{t^{M2M|B}}_{Max}$).

$C^{t^{M2M|B}}_{(n_{i},n_{j})}=min\\{C^{t^{M2M|B}}_{(n_{i},n_{j})-SH},C^{t^{M2M|B}}_{Max}\\},$
(2)

. where $C^{t^{M2M|B}}_{(n_{i},n_{j})-SH}$ is the maximum direct channel data
rate between $i$th and $j$th nodes on $t^{M2M|B}$th RF interface. It is
calculated using the Shannon-Hartley (SH) theorem from relation (3):

$C^{t^{M2M|B}}_{(n_{i},n_{j})-SH}=B^{t^{M2M|B}}_{(n_{i},n_{j})}log_{2}(1+\mathrm{SINR^{t^{M2M|B}}_{(n_{i},n_{j})}}),$
(3)

where $B^{t^{M2M|B}}_{(n_{i},n_{j})}$ is the BW of $t^{M2M|B}$th RF interface
channel between $i$th and $j$th nodes, and $SINR^{t^{M2M|B}}_{(n_{i},n_{j})}$
is Signal-to-Interference-plus-Noise-Ratio (SINR) of $t^{M2M|B}$th RF
interface channel between $i$th and $j$th nodes. Now, relation (II) formulates
the optimal next-hop selection and dynamic RF interface setting with the aim
of maximizing the total data rate of network sources.

$\displaystyle\operatorname*{Max}_{x,y,z}\begin{aligned}
&\sum_{i=0}^{(N_{s}-1)}{\sum_{j=0}^{(N_{q}-1)}\sum_{k=0}^{N{p}-1}}\\\
&x_{i,j}y_{j,k}c^{{}^{\prime\prime\prime}}_{i,k}+\sum_{i=0}^{(N_{s}-1)}\sum_{k=0}^{(N_{p}-1)}z_{i,k}c^{{}^{\prime}}_{i,k},\\\
\end{aligned}$ Subject to $\displaystyle x_{i,j},y_{j,k},z_{i,k}\in\\{0,1\\}:$
$\displaystyle\forall i,j,k:0\leq i<N_{s},0\leq j<N_{q},0\leq k<N_{p},$ (5)
$\displaystyle\sum_{i=0}^{(N_{s}-1)}x_{i,j}\leq
1,\sum_{k=0}^{(N_{p}-1)}y_{j,k}\leq 1,\forall j:0\leq j<N_{q},$
$\displaystyle\sum_{j=0}^{(N_{q}-1)}x_{i,j}\leq 1,$
$\displaystyle\sum_{k=0}^{(N_{p}-1)}z_{i,k}\leq 1,\forall i:0\leq i<N_{s}),$
(7)
$\displaystyle\sum_{i=0}^{(N_{s}-1)}{\sum_{j=0}^{(N_{q}-1)}\sum_{k=0}^{(N_{p}-1)}x_{i,j}y_{j,k}}$
$\displaystyle+\sum_{i=0}^{(N_{s}-1)}\sum_{k=0}^{(N_{p}-1)}z_{i,k}\leq
N_{b}Q_{BS}.$ (8)

The used variables and problem constraints are defined as follows:
-The No. $Rel-RF^{M2M}-BS-RF^{M2B}$ quadruple and $BS-RF^{M2B}$ pair are represented by $N_{q}=(N^{M2M}_{t}N^{M2B}_{t}N_{r}N_{b})$ and $N_{p}=N^{M2B}_{t}N_{b}$, respectively.
\- $x_{i,j}$: is 1 if $i$th source has selected the $j$th $Rel-RF^{M2M}-BS-
RF^{M2B}$ quadruple and 0 otherwise,
\- $y_{j,k}$: is 1 if $j$th $Rel-RF^{M2M}-BS-RF^{M2B}$ quadruple has selected
the $k$th $BS-RF^{M2B}$ pair and 0 otherwise,
\- $z_{i,k}$ : is 1 if $i$th source has selected the $k$th $BS-RF^{M2B}$ pair
and 0 otherwise,
\- $c_{i,j}$: the data rate between $i$th source and $j$th $Rel-RF^{M2M}-BS-
RF^{M2B}$ quadruple,
\- $c^{{}^{\prime}}_{i,k}$: the data rate between $i$th source and $k$th $BS-
RF^{M2B}$ pair,
\- $c^{{}^{\prime\prime}}_{j,k}$: the data rate between $j$th $Rel-
RF^{M2M}-BS-RF^{M2B}$ quadruple and $k$th $BS-RF^{M2B}$ pair,
\- $c^{{}^{\prime\prime\prime}}_{i,k}=min\lceil
c_{i,j},c^{{}^{\prime\prime}}_{j,k}\\}$ (according to relation (1)),
\- $N_{s}$: the No. sources.
\- $N_{r}$: the No. relays,
\- $N^{M2M}_{t}$: the No. M2M RF interfaces,
\- $N^{M2B}_{t}$: the No. M2B RF interfaces,
\- $Q_{BS}$: quota or total connection capacity of each BS which is obtained
by $Q_{BS}=\sum_{t^{M2B}=0}^{(N_{t}^{M2B}-1)}Q^{t^{M2B}}_{BS}$, where
$Q^{t^{M2B}}_{BS}=min\\{{\lfloor\frac{BW^{t^{M2B}}_{BS}}{BW_{s}}\rfloor},{Cap^{t^{M2B}}_{BS}}\\}$,
$BW^{t^{M2B}}_{BS}$ is the BW of the M2B RF interface, $BW_{s}$ equals to
requested BW of sources, and $Cap^{t^{M2B}}_{BS}$ is the capacity of the No.
user connections to $t^{M2B}$’th RF.
\- The first summation of inequality (LABEL:eq:optEq_firstnEq) represents each
$Rel-RF^{M2M}-BS-RF^{M2B}$ quadruple can only be assigned to a single source.
\- The constraint of the second summation in inequality
(LABEL:eq:optEq_firstnEq) is that each $Rel-RF^{M2M}-BS-RF^{M2B}$ quadruple
can only be connected to a single BS is represented.
\- The constraint of the first summation in inequality (7) is that each source
can only be connected to a single $Rel-RF^{M2M}-BS-RF^{M2B}$ quadruple.
\- The constraint of the second summation in inequality (7) is that each
source can only be connected to a single $BS-RF^{M2B}$ pair.
\- The constraint of the summation in inequality (8) represents the total No.
two-hop (the first summation) and direct (the second summation) connections to
BSs is less than or equal to the total connection capacity of BSs
($N_{b}Q_{B}S$).

##  III The Proposed Framework for Dynamic Optimal Next-Hop Selection and RF
Interface Setting Algorithm (DONSA)

To generalize DORSA [10], we provide a generalized framework for the RF
interface and next-hop selection algorithm in an IoT network, with no
restrictions on RF interface type (M2M or M2B), No. RF interfaces, No.
machines, and No. BSs. The following set of steps will be implemented under
the mentioned generalized framework. The No. network components (machines,
BSs, and RF interfaces) and the data rate between devices are inputs of the
desired framework. A schematic of the proposed framework for DONSA is shown in
Fig. 2. In the following, we explain the steps of solving the problem using a
$k$-AP solver [3] in this framework with a brief explanation. The optimality
of the $k$-AP solver used in our proposed algorithm has already been proven
[3].

Step 1- Transforming dynamic optimal RF interface setting and next-hop
selection problem to a $k$-AP: To solve the desired problem, firstly we must
model the problem into a $k$-AP. To achieve this model, a weighted bipartite
graph equivalent to the principal problem is defined. In this graph, we seek
to maximize the total weight of the selected edges.

Now, we define the vertices of the graph. One part of the graph (e.g. the left
side) contains vertices equivalent to the sources (as in previous works [3,
10]), but the other part dedicated to this problem must be defined in such a
way that the definition of the desired problem does not change and there
should be one-to-one connections between the two parts.

For this purpose, after studies, we define $Rel-RF^{M2M}-BS-RF^{M2B}$
quadruple and $BS-RF^{M2B}$ pair as vertices representing the elements of the
second part (e.g. the right side). The maximum No. possible edges of the
bipartite graph is equal to $k=min(N_{s},N_{b}Q_{b})$, where the connection
capacity of each BS is equal to
$Q_{b}=\sum^{N_{t^{M2B}}-1}_{l=0}N_{ch_{{t^{M2B}}_{l}}}$, and
$N_{ch_{{t^{M2B}}_{l}}}$ is the No. channels of each M2B RF interface. Thus,
the main problem transforms to a $K$-AP.

Figure 2: Schematic of the proposed framework for DONSA.

Step 2- Transforming the obtained $k$-AP to an standard assignment problem
(s-AP): Now to remove the $k$ edge selection constraint in the graph of
$k$-AP, the obtained $k$-AP is transformed to an s-AP. For this purpose, we
must transform the graph in such a way that there is no constraint to the
selection of the No. edges [3, 10]. Therefore, without losing the generality
of the problem, we add a No. vertices and related edges to one or both parts
of the graph. Now, in this way, we can reach the equivalent answer to the main
problem in the new s-AP, with the aim of maximizing the total weight of the
selected edges in the new graph. The schematic of the obtained s-AP graph in
step 2 of DONSA is shown in Fig. 3.

Figure 3: Schematic of the obtained s-AP graph in step 2 of DONSA.

Without losing generality, the weight of edges with at least one new
additional vertex is defined as follows:
\- The weight of edge with the second vertex from new vertices on the other
part is equal to zero which has no effect on the selection of edges, and
\- The weight of edge with the second vertex from the previous vertices on the
other part is equal to infinite (or in practice large enough $A_{value}$, for
example $A_{value}=1+\sum_{edges}wight^{AnyEdge}$).

Also, in general, the No. additional vertices are as follows:

  1. 1.

if $N_{s}\geq N_{b}Q_{BS}$: $N_{s}-k$ vertices are added to the right side and
$N^{M2M}_{t}N^{M2B}_{t}N_{r}N_{b}$ vertices are added to the left side to
cover unmatched sources.

  2. 2.

else if $N_{s}<N_{b}Q_{BS}$: Due to the fact that the connection capacity of
BSs is more than the No. sources and all sources can be matched, there is no
need to add a new vertex to the right side of the graph. Just to make the two
sides of the graph symmetrical, equivalent to the No. differences between the
No. vertices on the right side and the left side (e.g.
$N^{M2M}_{t}N^{M2B}_{t}N_{r}+N_{b}Q_{BS}-N_{s}$), add the vertex to the left
side.

Note: if No. channels per each M2B RF interface ($N^{M2B}_{{ch}_{t}}$) was
more than $N_{s}$, initially, the maximum $N^{M2B}_{{ch}_{t}}$ can be
considered equal to $N_{s}$ to reduce the time complexity of the problem
solution.

Step 3- Solving the obtained s-AP: In some studies, to solve the optimal relay
selection problem, it can be transformed to an s-AP, then the available tools
such as the Hungarian algorithm can be used to solve it [3, 10]. Since the
Hungarian algorithm is a common solver with a polynomial-time complexity, that
is able to find the optimal solution of an s-AP as a maximum weighted matching
problem [12], in the proposed framework, it is used to solve the obtained
s-AP.

Now, in this step, the equivalent matrix to the obtained s-AP graph in step 2
of DONSA is given as the input of the Hungarian algorithm. In the other words,
the elements of this matrix represent the connection between network devices
and the data rate of one-hop and two-hop connections between sources and other
network devices (relays and BSs) on different RFs. Fig. 4 shows a view of the
equivalent matrix of the s-AP graph in step 2 of DONSA, which is one of the
main elements of this framework.

Figure 4: The equivalent matrix of the s-AP graph in step 2 of DONSA.

Step 4- Obtaining the final results of the desired problem: Let us now
consider the first $N_{s}$ elements of the output of the Hungarian algorithm,
which are related to the final response for the sources. If the output content
associated with a source is from new vertices, it means that in the optimal
solution of the desired problem, this source will not be connected to any node
of the network. For other sources, in the final optimal assignment, each
source whose output element content corresponds to:
\- A $(Rel-RF^{M2M}-BS-RF^{M2B})_{output}$ quadruple means that the source
must use the specified RF interfaces to send data to the intended BS via the
specified Rel,
\- A $(BS-RF^{M2B})_{output}$ pair means that the source must use the
specified RF interface to send data directly to the intended BS.

Algorithm 1 presents the pseudo code of DONSA.

Algorithm 1 Pseudo code of DONSA

1: Inputs: No. machines, No. BSs, No. M2M and M2B RF interfaces, and the data
rate between devices,

2: Step 1: 1’th Transformation (the selection problem to a
k-AP)$\Rightarrow$Output: Obtained k-AP,

3: Step 2: 2’th Transformation (k-AP to a s-AP)$\Rightarrow$Output: Equivalent
matrix to the s-AP graph,

4: Step 3: Solving the obtained s-AP by Hungarian
algorithm$\Rightarrow$Output: The output vector of the Hungarian algorithm,

5: Step 4: Obtaining the final results$\Rightarrow$Output: Final assignment.

Time Complexity (TC): Examining TC of steps, as previous works [3, 10], it is
observed that the bottleneck is the Hungarian algorithm that if its input
matrix size$=n\times n$ then TC$=O(n^{3})$ [12]. Therefore, TC of DONSA is
equal to $O(n^{3})$, where $n=N_{s}+N^{M2M}_{t}N^{M2B}_{t}N_{r}N_{b}$, if
$N_{s}\geq N_{b}Q_{BS}$,and otherwise
$n=N^{M2M}_{t}N^{M2B}_{t}N_{r}N_{b}+N_{b}Q_{BS}$.

##  IV Simulation Results

The simulations were implemented in M2MSim [10] with 200 runs on a device with
a 4-core Intel Xeon and 4 GB of RAM. An uplink network cell with default size
$500\times 500$ and 1 BS in the middle of the cell, $N^{M2M}_{t}=3$ M2M RF
interfaces, Z-Wave, Bluetooth, and WiFi (as a broadband RF with more BW than
other M2M RF interfaces under consideration), and $N^{M2B}_{t}=3$ M2B RF
interfaces, NBIoT, LTE-M, and LTE (as a broadband RF with more BW than other
M2B RF interfaces under consideration), is simulated. Also, path loss exponent
$\beta=4$, shadowing (dB) and small scale fading (dB) are modeled by
$\mathcal{N}(0,64)$ and $Rayleigh(1)$, respectively. In this paper, Average
Data Rate (ADR) of sources, No. Unmatched Sources (NUS), and Average Execution
Time (AET) of the generalized framework of DONSA using WiFi, Bluetooth, and
Z-Wave as M2M RFs and LTE, LTE-M, and NBIoT as M2B RFs (DONSA_WBZ-LMN) is
compared to the following algorithms in 3 scenarios: DiTOSA_L[10]: the optimal
direct transmission to BS with LTE, SORSA_W-L[3]: the optimal relay selection
with static M2M (WiFi) and M2B (LTE) RF interface setting, and
DORSA_WBZ-L[10]: DORSA with WiFi, Bluetooth, and Z-Wave as M2M RFs and LTE as
M2B RF.

In all cases of Fig. 5 is observed that the simultaneous use of the BW
capacity of all M2M and M2B RF interfaces in DONSA_WBZ-LMN improves the ADR
and NUS compared to other algorithms. As can be seen in Fig. 5(a) related to
Scenario 1, As the No. sources increases and the No. relays decreases, the
available bandwidth is divided among a number of them. For this reason, with
the increase in the No. sources and more requests than the BS capacity, BW has
not been allocated to some of them, and as a result, ADR charts have a
downward trend and NUS charts have an upward trend after reaching the maximum
BW capacity in each algorithm. However, it is observed that DONSA has improved
ADR (by an average of 13%) and NUS (by 1.9%) by increasing the BS connection
capacity. In Scenario 2 (Fig. 5(b)), increasing the cell radius reduces the
No. RFs with the required coverage range for long-distance machines.
Therefore, it is only possible to use fewer RFs (such as LTE-M and NB-IoT)
with lower supported data rates, and this has led to a downward trend in the
ADR. In addition, since the sources requests are the same (= 200 (kHz)) and is
supported by all RFs, algorithms that use only one M2M RF (LTE) will not be
able to serve at least 50 sources. In contrast, with the simultaneous use of
all RFs and the increase of BS connection capacity, ADR (by an average of
117%) and NUS (by 5.3%) have improved. Fig. 5(c), related to scenario 3, shows
that As long as all RFs are usable, the ADR is incremental, but from the point
on requested BW = 300 MHz onwards, the No. RFs that can support requested BW
decreases, and the chart trend decreases. This process continues until the end
of the chart, where, according to the requested BW, a maximum of 1 source is
connected to the BS. Therefore, where the requested BW varies from $20(kHz)$
to $20(MHz)$, machines are supported by 3, 2, or 1 M2B interfaces, NUS in
DONSA improves by a maximum of about 14.7% and an average of 2.9%. Finally,
the ADR obtained in DONSA improves by an average of 11.1%. The 95% confidence
interval of ADR for DONSA graphs in three scenarios are CI[$(1.28\times
10^{6})\pm 0.09\%$], CI[$(5.24\times 10^{5})\pm 0.4\%$], and CI[$(1.23\times
10^{6})\pm 0.4\%$], respectively. The trendline of AET in DONSA for all
scenarios is less than calculated TC($O(n^{3})$). Maximum AET in scenarios (1,
2, and 3), are equal to 431(ms), 1.1(s), and 1.8(s), respectively.

(a) Scenario 1: No.machines=300, req.BW=200(kHz), cell radius=500(m).

(b) Scenario 2: No.sources=150, No.relays=150, req.BW=200(kHz).

(c) Scenario 3: No.sources=150, No.relays=150, cell radius=500(m).

Figure 5: ADR and NUS vs. No. sources, cell radius, and the requested BW of
sources in different Scenarios with 200 simulation runs.

##  V Conclusion and Future Works

A generalized framework for dynamic optimal M2M and M2B RF interface setting
and next-hop selection for sources with the similar requested BW was proposed
in an IoT network. Using this framework, machines RF equipment may be used
more efficiently. The simulations show that using this method improved the
data rate of network sources up to 117% in different scenarios. The result can
be used to evaluate subsequent algorithms in this field as an upper bound. In
addition, in the future, our proposed algorithm can be compared with other
solvers to find the optimal solution. Also, practical decentralized algorithms
can be designed for dynamic RF interface setting in next-hop selection with
lower time complexity in real networks. Furthermore, algorithms can be
provided in situations where sources have a variety of requested BW.

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