1. Introduction
Wireless communication systems can be classified into two fundamental categories, namely humanuserbased and machineuserbased from the perspective of 5G use cases and applications [
1,
2]. Current technology gives priority to humanbased communications. However, the emerging idea of Massive MachineType Communications (mMTC) such as Internet of Things (IoT), vehicletovehicle (V2V), vehicletoinfrastructure (V2I), control of autonomous vehicles and smart cities with millions of sensors poses various demands for the nextgeneration networks [
3,
4,
5]. mMTC, where a large number of machine users sporadically communicate with a given base station (BS), leads to asynchronous uplink transmission associated with multiuser interference (MUI). Hence, handling of asynchronous impairments is expected to be one of the most challenging problems for mMTC networks [
2,
3,
6].
Orthogonal frequency division multiplexing (OFDM) has been well studied by academia in the last two decades [
7]. It has been shown that OFDM is robust against intersymbol interference (ISI) with the aid of cyclic prefix (CP), which turns the linear convolution with the channel into a circular convolution [
8]. However, OFDM is severely effected from intercarrier interference (ICI) due to loss of subcarrier orthogonality.
In multiuser OFDM, the users must be aligned in the time and frequency domains in order to maintain the orthogonality between the subcarriers. However, multiuser time alignment is infeasible in asynchronous mMTCbased systems, since signals transmitted from the users at different distances from the BS arrive with different time delays. Time misalignment causes ICI between the users. Furthermore, it is expected that the impact of MUI becomes significant when different power levels are assigned to the machine users, with respect to the applications or used cases [
9]. Even if equal power is distributed to the users, as far as signals travel through different paths, power misalignment occurs at the BS.
In literature, 5G candidate waveforms including filter bank multicarrier (FBMC), generalized frequencydivision multiplexing (GFDM) and universal filtered multicarrier (UFMC) are studied to relax MUI by suppressing outofband emission (OOBE) [
2,
10,
11,
12]. Moreover, inserting guardbands between the users is used to further suppress OOBE [
9,
13]. However, filtering process increases the system complexity and use of guardbands reduce spectral efficiency. In [
14], a new perspective is presented to reduce MUI by clustering of the channel impulse response.
Recently, the proliferation of index modulation (IM) has introduced new research perspectives for 5G wireless systems [
15]. At first, IM has been presented as spatial modulation technique (SM) for multipleinput multipleoutput (MIMO) systems to convey information by antenna indices [
16]. The notion of IM is also extended to OFDM and named as OFDM with index modulation (OFDMIM), which carries information not only by data symbols but also by the indices of active subcarriers [
17,
18]. In contrast to conventional OFDM, not all subcarriers are utilized in OFDMIM. In
Figure 1, a simple example is illustrated for an OFDMIM subblock consisting of eight subcarriers, where three of them are activated to convey data symbols. Extra bits are carried by the indices of active subcarriers to compensate inefficient use of spectrum. In addition, fractional subcarrier activation brings in diversity order as well as less energy consumption [
15]. Hence, OFDMIM provides a flexible and adaptive structure which can be optimized by considering the demands of nextgeneration communication systems.
Mapping incoming bits to the subcarrier indices is one of the flexible properties of OFDMIM. In the literature, three subcarrier mapping schemes (SMS) have been proposed to improve error performance and to reduce complexity of the OFDMIMbased systems. Lookup table (LUT) is the first technique used as a mapping scheme, which uses same storage table at both transmitter and receiver [
18]. However, it is not practical for large OFDMIM subblock sizes. Therefore, Combinatorial method (COM), which does not require storage table, is proposed in [
18]. Due to nonuniform subcarrier activation, COM leads to an unequal protection of the transmitted information bits that makes ultimate error performance worse. Hence, equiprobable subcarrier activation (ESA) technique is proposed in [
19]. It is observed an enhancement up to 1.9 dB on error rate performance by using ESA for noisy multipath fading channels.
Performance of OFDMIM is investigated under various impairments by researchers. In [
18], it is shown that OFDMIM under frequency selective fading channels impairment with high mobility is more robust than OFDM. Due to robustness against mobility, it is offered as a candidate for vehicle to X (V2X) communication systems [
20]. ICI stemming from carrier frequency offset (CFO) impairment is evaluated by introducing notions of intersubblock and intrasubblock interference for OFDMIM [
21]. It is observed that OFDMIM is superior to current technology when the signal is impaired by CFO. In [
22], both ICI and ISI is analyzed and mitigated using optimal tone spacing between adjacent subcarriers.
To the best of our knowledge, the performance of OFDMIM under asynchronous transmission has not been characterized or investigated. In this paper, OFDMIM is proposed as a candidate solution for uncoordinated mMTC networks. A novel subcarrier mapping scheme (ISA) is proposed to provide further enhancement of OFDMIM performance for asynchronous systems. It is compared with the current ESA and COM mapping methods. The comparison is performed for various OFDMIM subblock parameters to evaluate impact of flexibility properties of OFDMIM. Not only time misalignment but also power difference between the machine users is considered in this study. In addition, ICI analysis is performed and the performance of the OFDMIM is compared with conventional OFDM in the present of time and power offset between the users.
The remainder of this work is organized as follows.
Section 2 introduces the multiuser OFDMIM system model for asynchronous transmission. In
Section 3, ICI analysis is provided for OFDMIM. In
Section 4, existing SMS are revisited and a novel mapping technique is proposed. Numerical results are given in
Section 5. Finally, some concluding remarks are provided for OFDMIM technology with mMTC in
Section 6.
2. System Model
This section introduces an uplink system model where
U users independently communicate with the base station (BS) through a frequency selective channel. A simple uplink system example is presented in
Figure 2. Each user’s information is modulated with OFDMIM. A total of
N subcarriers is equally split between the users, and
${N}_{u}=\frac{N}{U}$ subcarriers are dedicated to
uth user, with
$1\le u\le U$. Assignment of OFDMIM subblocks to the users can be performed in two ways, either interleavedbased or localizedbased. Interleavedbased assignment mixes the users’ subblocks, while localizedbased assignment successively places each user’s subblocks, as visualized in
Figure 2.
In
Figure 3, time domain signal that belongs to
uth user is expressed as
${x}_{u}\left(n\right)$. It is assumed that
${x}_{1}\left(n\right)$, which reaches first to the BS, is considered to be reference signal for the BS. Each user’s signal arrives to the BS with a different time offset (TO)
${\u03f5}_{u}$ with respect to
${x}_{1}\left(n\right)$ since they can be placed at different distances from the BS or can be transmitted at different times. The transmitted signal from each user passes through its own channel
${h}_{u}\left(n\right)$. All the channels are uncorrelated with each other. Later, individual signals
${y}_{u}\left(n\right)$ transmitted from all the users is superimposed, and additive white Gaussian noise (AWGN)
$w\left(n\right)$ is added to the superimposed signal
$y\left(u\right)$. Due to the time misalignments, orthogonality between the machine users cannot be maintained anymore. Therefore, ICI between the users occurs and degrades the system performance.
Table 1 presents symbols used in the study and their descriptions. Further insights about asynchronous mMTC transmission with OFDMIM are given in following subsection.
OFDMIM Transmission Model
In this work, it is considered
N size OFDMIM block, where subcarriers are equally split into
G subblocks. Each subblock consists of
$s=\frac{N}{G}$ subcarriers and
v out of
s are selected to transmit
Mary data symbols with
$1\le v<s$. As mentioned in
Section 1, in contrast with conventional OFDM
$(v=s)$, not all subcarriers are utilized for
Mary symbols. Hence, the loss of spectral efficiency is compensated by the used subcarrier indices that convey additional information bits.
In multiuser transmission, each user has a total of
${G}_{u}=\frac{{N}_{u}}{s}$ available subblocks to carry
${m}_{u}$ bit stream, with
$1\le {G}_{u}\le G$. When all the subcarriers are assigned to one user,
${G}_{u}$ equals to
G. Block diagram for asynchronous OFDMIM transmitter is shown in
Figure 4. Each OFDMIM subblock consists of
$p=\frac{{m}_{u}}{{G}_{u}}$ bit stream, which is divided into
${p}_{1}$ and
${p}_{2}$ bits. The indices of active subcarriers are defined from
${p}_{1}$ bit stream, while remaining
${p}_{2}$ bit stream is mapped to conventional
Mary symbols
$\{{d}_{1},\cdots ,{d}_{v}\}\in {M}_{ary}$, which are carried by the activated subcarriers. Division of the
p bit stream is illustrated by “IM” entity in
Figure 4. The indices of active subcarriers of
uth user for
lth subblock are defined as
where
${j}_{u}(l,v)\in [1,2,\cdots ,s]$ for
$l=1,\cdots ,{G}_{u}$. Thus, total number of conveyed bits per OFDMIM subblock is calculated as
where
$\lfloor .\rfloor $ and
$C(s,v)$ denote floor function and binomial coefficient, respectively. The number of transmitted bits per user is
lth subblock
${c}_{u}^{i}\left(l\right)$ belongs to
ith data block of
uth user is represented as
where
${c}_{u}^{i}(l,s)\in \{0,{M}_{ary}\}$.
${M}_{ary}$ represents the data symbols. Later, as illustrated by “Block Generator” in
Figure 4,
${G}_{u}$ subblocks are combined to form
ith data block of
uth user
${c}_{u}^{i}$ expressed as follow
$V=v{G}_{u}$ out of
${N}_{u}=s{G}_{u}$ subcarriers carry Mary symbols and the rest equal to zero. “IM” entity in
Figure 4 full demonstrates the process of generating the frequency domain data samples for
uth user.
Once
${c}_{u}^{i}$ is generated, it passes through the multiuser “Subblock assignment” (SA) entity, as in
Figure 4. SA performs either localized assignment or interleaved assignment for
${c}_{u}^{i}$, and inserts
N
${N}_{u}$ zeros to the subcarriers assigned to the other users. Then,
ith OFDMIM block of
uth user is generated as follow
Time domain samples for
ith block of
uth user are obtained by inverseFast Fourier Transform (IFFT) process shown in
Figure 4 as
A cyclic prefix (CP) with length L is appended to the beginning of
${x}_{u}^{i}\left(n\right)$ to prevent intersymbol interference (ISI) due to time dispersion of the channel [
8]. Time domain signal of
uth user
${x}_{u}\left(n\right)$ passes through multipath channel. The signal experiences Rayleigh fading. Channel impulse response coefficients between
uth user and the BS for
ith block are characterized as
where
${L}_{tap}$ denotes total number of taps,
r is the path index and
${\tau}_{r}$ is the delay of the
rth path. It is assumed that maximum excess delay of the channel is smaller than CP size, and path gains
${g}_{u}^{i}$ are Gaussian random variables with distribution
$\mathcal{C}\mathcal{N}(0,1/{L}_{tap})$. The signal
${x}_{u}\left(n\right)$ is received as
where ∗ denotes convolution process. At the BS, signal transmitted from all the machine users are superimposed as follow
$w\left(n\right)$ is AWGN with distribution of $\mathcal{C}\mathcal{N}(0,{N}_{o}/2)$.
At the receiver, time offset
${\u03f5}_{u}$ is removed from the superimposed signal to obtain the signal belonging to
uth user. Fast Fourier Transform (FFT) is applied to obtain the frequency domain samples
$Y\left(k\right)$. Then, deassignment process, which refers to the inverse process of the SA, is applied to get only
uth user data blocks
${c}_{u}$. The indices of active subcarriers are detected by using maximum likelihood (ML) or loglikelihood ratio (LLR) detectors. ML detector checks all the possible subcarriers combinations and information symbols to find the most optimum joint decision. LLR receiver first detects active subcarriers and then information symbols carried by the detected subcarriers are demodulated [
18].
3. ICI Analysis in OFDMIM Systems
Consider a system model which includes
$U=3$ users with 3 OFDMIM blocks to analyze ICI because of time offset
$\u03f5$ between the users. These users transmit sporadically in adjacent bands with different transmit power levels, as illustrated in
Figure 5a. For the sake of simplicity, it is assumed that equal time offset between the adjacent users. Notations of
$b1$,
$b2$ and
$b3$ in the figure denote first, second and third OFDMIM block, respectively.
In [
6], ICI model is calculated for OFDM systems under time misalignment. Besides time offset, the model is modified for uncoordinated OFDMIM systems by considering the fact that power difference between the machine users. In contrast to OFDM, only the active subcarriers of the users’ cause ICI in OFDMIM. Therefore, the indices of interferer subcarriers belong to
$\xi $.
In our calculations,
${ti}_{{u}_{y}}^{{u}_{x}}$ shows the interference coming from
${u}_{x}$th user to the
${u}_{y}$th user while
${ti}_{{u}_{x}}^{bl}$ denotes the interference caused by
lth block of
${u}_{x}$th user.
${\xi}_{u}$ denotes the active subcarrier indices of
uth user for all the subblocks.
Figure 5b shows the superimposed signal at the BS. As illustrated in the figure, time domain interference for the 2nd symbol of 2nd user
${ti}_{{u}_{2}}$ is calculated as
where
$t{i}_{{u}_{2}}^{{u}_{1}}=t{i}_{{u}_{1}}^{b2}+t{i}_{{u}_{1}}^{b3}$ and
$t{i}_{{u}_{2}}^{{u}_{3}}=t{i}_{{u}_{3}}^{b1}+t{i}_{{u}_{3}}^{b2}$, and they are expressed as
where
$\mathrm{\Delta}{p}_{12}$ and
$\mathrm{\Delta}{p}_{32}$ refers to power difference between the 1st and 2nd user, and the 3rd and 2nd user, respectively.
In the frequency domain, ICI
${I}_{2}$ is calculated by taking FFT for
$t{i}_{{u}_{2}}$, and it is expressed as
ICI for first user
${I}_{1}$ and third user
${I}_{3}$ is obtained as
As seen in the
Figure 5b, by considering both time and power offset
$t{i}_{{u}_{1}}^{{u}_{2}},t{i}_{{u}_{1}}^{{u}_{3}},t{i}_{{u}_{3}}^{{u}_{1}}$ and
$t{i}_{{u}_{3}}^{{u}_{2}}$ can be easily extracted as
In this paper, it is considered that subcarriers belong to
uth user are orthogonal to each other while machine users’ subcarriers are interfering with each other due to the time offset between them. For this reason, interference coming from other users to
uth user is mainly determined by its adjacent users’ edge subcarriers. Since the subcarriers are sinc functions in frequency domain, inner subcarriers’ sidelobes have less impact on the ICI compared to the edge subcarriers, as explained in [
13,
23,
24]. Therefore, more users can be considered, but the interference coming from users that are not adjacent with the
uth user becomes much smaller.
4. OFDMIM Subcarrier Mapping Schemes
In this section, the existing SMSs in the literature for OFDMIM are revised, and the proposed mapping scheme ISA is explained in details.
4.1. Existing SMSs
4.1.1. LUT
The method requires at both transmitter and receiver side a lookup table with the size
$d={2}^{{p}_{1}}$ to store all possible combinations of the active subcarrier indicies
$\xi $ with respect to
${p}_{1}$bit stream. An example of LUT with
${p}_{1}=2$,
$v=2$ and
$s=4$ is illustrated in
Table 2.
$\beta \left(z\right)$ denotes bit streams corresponding to each index combination
$\xi \left(z\right)$, with
$z\in [1,2\phantom{\rule{3.33333pt}{0ex}}...\phantom{\rule{3.33333pt}{0ex}}{2}^{{p}_{1}}]$. The size of lookup table significantly increases the system complexity with the increase of the
${p}_{1}$. Therefore, LUT scheme become infeasible for large
${p}_{1}$.
At the receiver, ML detector is used to make a joint decision for active subcarrier indices with
Mary data symbols [
18].
4.1.2. COM
In contrast to LUT method, storage tables at the transmitter and receiver are not required. It assigns a specific lexicographically ordered sequence
$J\left(z\right)=\{{\alpha}_{v},\phantom{\rule{3.33333pt}{0ex}}...,\phantom{\rule{3.33333pt}{0ex}}{\alpha}_{1}\}$ with
$\alpha \in \{0,\phantom{\rule{3.33333pt}{0ex}}...,\phantom{\rule{3.33333pt}{0ex}}s1\}$ for each possible index combination
$\xi \left(z\right)$. The
$\beta \left(z\right)$bit stream is converted to a natural number
E, which is converted to a specific
$J\left(z\right)$ sequence as follow
To select
$\alpha $ components, we start from the condition that satisfies
$E\ge C({\alpha}_{v},v)$ and then choose the maximal
${\alpha}_{v1}$ that satisfies
$EC({\alpha}_{v},v)\ge C({\alpha}_{v1},v1)$ until
$v=1$ and then the index combination is obtained as
$\xi \left(z\right)=J\left(z\right)+1$. Detailed information about COM can be found in [
18].
In the receiver, firstly $\xi \left(z\right)$ is identified for a given subblock by using LLR detector, and $J\left(z\right)=\xi \left(z\right)1$ is mapped to its corresponding decimal number E, which passes through bit to decimal converter to get $\beta \left(z\right)$ bit stream.
In
Figure 6a,b subcarrier activation probability is represented by the red line for COM scheme. As seen in the figures, initial subcarriers have higher usage probability in comparison to the last ones, especially for
$s=8$ and
$v=3$.
4.1.3. ESA
In contrast with COM method, ESA offers as much as possible equiprobable subcarrier activation opportunity as illustrated in
Figure 6a,b by the blue line [
19]. A small table named as adjacent subcarrier distance vector (ASDV) is present at both transmitter and receiver to find
$C(s1,v1)$ basic combinations
${\xi}_{b}$, which belongs to
$\xi $. By using column cyclic shift
$s1$ new active subcarrier combinations are generated from the
${\xi}_{b}$. The new combinations have the same ASDV with the corresponding basic pattern
${\xi}_{b}$. Note that some index combinations generated from cyclic shift of
${\xi}_{b}$s can be the same. In this case, ASDV considers only one from repeated patterns and disregards the rest. This idea successively is applied all over
${\xi}_{b}$ until we get all
${2}^{{p}_{1}}$ possible subcarrier combinations
$\xi $. Selection of the basic patterns
${\xi}_{b}$ are explained in [
19]. At the receiver side, LLR receiver is used to find
$\xi \left(z\right)$ that is mapped to
$\beta \left(z\right)$bit stream for a given subblock.
4.2. Proposed SMS: ISA
Aforementioned SMSs are designed for synchronous communication systems, which leads to equal noise power level at each subcarrier. Therefore, in this study new mapping scheme ISA, which stands for inner subcarrier activation, is proposed and explained to alleviate the ICI due to sporadic transmission in mMTC.
ISA scheme gives a higher activation probability to the subcarriers located at the center part of the OFDMIM subblock, as illustrated in
Figure 6a,b by the green line. OOBE coming from inner subcarrier is less than that of edge subcarriers [
23]. Therefore, each user experiences less interference from its adjacent users.
ISA scheme is based on the COM scheme, which directly maps $\beta \left(z\right)$ bits to subcarrier indices $\xi \left(z\right)$, and vise versa. As calculated in line 1 of Algorithm 1, a subblock with s subcarriers is divided into two parts, where first part and second part contains ${s}_{1}$ subcarriers and ${s}_{2}$ subcarriers, respectively. ${v}_{1}$ subcarriers and ${v}_{2}$ subcarriers are activated to carry data information symbols. Indices for ${v}_{1}$ active subcarriers ${\xi}_{1}\left(z\right)$ are selected by flipped version of COM method, which is calculated from line 4 through 6. Conventional COM method is used to select ${v}_{2}$ subcarrier indices ${\xi}_{2}\left(z\right)$ as shown in line 7. Consequently, indices of active subcarriers for $\beta \left(z\right)$ are composed of ${\xi}_{1}\left(z\right)$ and ${\xi}_{2}\left(z\right)$, as shown in line 8. In ISA, ${p}_{1}$ equals $\lfloor lo{g}_{2}\left(C({s}_{1},{v}_{1})\right)\rfloor +\lfloor lo{g}_{2}\left(C({s}_{2},{v}_{2})\right)\rfloor \le \lfloor lo{g}_{2}\left(C(s,v)\right)\rfloor $. This results in less spectral efficiency for some combinations of s and v.
Algorithm 1 ISA mapper. 
 1:
${s}_{1}=\lfloor s/2\rfloor $, ${s}_{2}=s{s}_{1}$ ▹ # of subcarriers for each part  2:
${v}_{1}=\lfloor v/2\rfloor $, ${v}_{2}=v{v}_{1}$ ▹ # of active subcarriers for each part  3:
$\beta \left(z\right)=\left(\right)open="["\; close="]">{\beta}_{1}\left(z\right)\phantom{\rule{3.33333pt}{0ex}}{\beta}_{2}\left(z\right)$ ▹ Incoming bit stream  4:
$c=\left(\right)open="["\; close="]">{s}_{1}1:1:0$  5:
${\xi}_{1}\left(z\right)=COM({\beta}_{1}\left(z\right),{s}_{1},{v}_{1})$  6:
${\xi}_{1}\left(z\right)=1+c\left({\xi}_{1}\left(z\right)\right)$ ▹ Flipped version of COM  7:
${\xi}_{2}\left(z\right)={v}_{1}+COM({\beta}_{2}\left(z\right),{s}_{2},{v}_{2})$ ▹ COM  8:
$\xi \left(z\right)=\left(\right)open="["\; close="]">{\xi}_{1}\left(z\right)\phantom{\rule{3.33333pt}{0ex}}{\xi}_{2}\left(z\right)$ ▹ Activated subcarrier indices

At the receiver, LLR detectors are used to know the active subcarrier indices $\xi \left(z\right)$, as shown in line 3 through 6 of Algorithm 2.
Algorithm 2 ISA demapper. 
 1:
${s}_{1}=\lfloor s/2\rfloor $, ${s}_{2}=s{s}_{1}$ ▹ # of subcarriers for each part  2:
${v}_{1}=\lfloor v/2\rfloor $, ${v}_{2}=v{v}_{1}$ ▹ # of active subcarriers for each part  3:
${c}^{{}^{\prime}}=\left(\right)open="["\; close="]">0:1:{s}_{1}1$  4:
${\xi}_{1}\left(z\right)=LLR({s}_{1},{v}_{1})$  5:
${\xi}_{1}\left(z\right)={\xi}_{1}\left(z\right)1,{\xi}_{1}\left(z\right)=sort\left({\xi}_{1}\left(z\right){,}^{\prime}ascen{d}^{\prime}\right)$  6:
${\xi}_{1}\left(z\right)={c}^{{}^{\prime}}\left({\xi}_{11}\right)$ ▹ Detecting active subcarrier indices for first $s1$ subcariers  7:
${\xi}_{2}\left(z\right)=LLR({s}_{2},{v}_{2})$ ▹ Detecting active subcarrier indices for last $s2$ subcariers  8:
${J}_{z1}={\xi}_{1}\left(z\right)1\to {E}_{1}\to {\beta}_{1}\left(z\right)\phantom{\rule{6.0pt}{0ex}}$  9:
${J}_{z2}={\xi}_{2}\left(z\right)1\to {E}_{2}\to {\beta}_{2}\left(z\right)\phantom{\rule{6.0pt}{0ex}}$  10:
$\beta \left(z\right)=\left(\right)open="["\; close="]">{\beta}_{1}\left(z\right)\phantom{\rule{3.33333pt}{0ex}}{\beta}_{2}\left(z\right)$ ▹ Bit stream

The receiver first calculates the LLR values with respect to each subcarrier as
where
$P\left({A}_{k}\right)$ and
$P\left(\overline{{A}_{k}}\right)$ denotes the probability of
kth subcarrier being active and inactive, respectively.
${N}_{0}^{\prime}={I}_{u}+{N}_{0}$ shows total distortion of the system due to both ICI and noise, and
${H}_{u}\left(k\right)$ is channel frequency response (CFR) for
uth user. After calculation of
$LLR$ values for a subblock,
v out of them with highest
$LLR$ define the active subcarriers. The subcarrier index patterns are converted to lexicographically ordered sequences
${J}_{z1}$ and
${J}_{z2}$. By using Equation (
21), these sequences are mapped to decimal numbers
${E}_{1}$ and
${E}_{2}$. Then,
${E}_{1}$ and
${E}_{2}$ undergo decimaltobit converter to obtain
${\beta}_{1}\left(z\right)$ and
${\beta}_{2}\left(z\right)$ bit streams as illustrated in line 7 and 8, respectively.
$\beta \left(z\right)$ bit stream is a concatenation of
${\beta}_{1}\left(z\right)$ and
${\beta}_{2}\left(z\right)$, as shown in line 9.
Due to the fact that proposed ISA mapper is based on COM mapper, ISA does not bring additional complexity to the system. Unlike LUT and ESA schemes, storage tables are not required for ISA. Moreover, ISA technique gives higher activation probability
$P\left({A}_{k}\right)$ to the inner subcarriers with low
${N}_{0}^{\prime}$ and vice versa. Therefore, the reliability of calculated LLR values is maximum for asynchronous transmission with the aid of ISA regarding to Equation (
22). In other words, detection performance of the active subcarriers under asynchronous transmission is increased by ISA.
5. Numerical Results and Discussion
This section is dedicated to evaluating the performance of OFDMIM and OFDMbased systems for asynchronous mMTC networks. Theoretical results for ICI due to both time offset and power difference between the users are first validated by computerbased simulations. Secondly, BER performance for OFDMIM with three different subcarrier mapping schemes including COM, ESA and ISA are shown to compare their performance for uncoordinated networks. In this study, we assume three users are sporadically transmitting to the BS. Available N = 120 subcarriers are equally split between the users. The system is tested over ${L}_{tap}$ = 10 tap frequencyselective Rayleigh fading channel. A CP size is adjusted as $L=30$ to prevent ISI for each user. BPSK modulation is used for the machine users. MATLAB software is used for the simulations.
In all simulations, two different subblock parameters are preferred to make a proper comparison between the subcarrier mapping methods. OFDMIM with ESA for subblock parameters
s = 8 and
v = 3 offers the best performance in comparison to COM, since it benefits the most from frequency selectivity of the channel. On the other hand, the performance of ESA becomes similar to COM for the parameters
s = 8 and
v = 4 due to loss of selectivity, which is caused by usage of almost all subcarrier combinations [
19]. In addition, two different time offset between the users are considered. Minimum and maximum time offset
$\u03f5$ are adjusted as 24 and
$(N+L)/2=75$, respectively. Power differences between the users obey uniform distribution in a range of 2 dB and 7 dB.
In
Figure 7, BER performance of existing SMSs and the ISA are simulated for synchronous communication, where all users arrive to the BS at the same time (
$\u03f5=0$).
Figure 7a shows the results for OFDMIM with
$(s=8,v=3)$. ESA mapper is superior to COM mapper as aforementioned. BER performance of ISA lies in between COM with (
${s}_{1}$,
${v}_{1}$) and COM with (
s,
v) because of subblock division property. Therefore, the performance of ISA is the best for low signaltonoise ratio (SNR). Its performance goes near to COM as SNR increases. In
Figure 7b, obtained results are illustrated for
$(s=8,v=4)$. The performance of ESA is similar to COM [
19].The performance of ISA is almost the same with ESA and COM for high SNR, while it outperforms for low SNR due to subblock division.
In
Figure 8, it is shown that theoretical calculations of ICI for both OFDMIM and conventional OFDM perfectly match with computerbased simulations. The simulation results are obtained under maximum time offset
$\u03f5=Max$ for 2nd user, who has less power in comparison to others. As seen in the figure, OFDMIM is exposed to less ICI thanks to partial subcarrier activation under asynchronous transmission. In the
Figure 8a, the most exposed to ICI is ESA, since it has higher probability of edge subcarrier usage as shown in
Figure 6a. COM experience minimum ICI for initial subcarriers due to lower usage probability of last subcarriers of the previous user. On the other hand, last subcarriers of subblock are exposed to maximum ICI due to higher usage probability of initial subcarriers of the following user. Proposed method ISA encounters less ICI because of its lower usage probability for edge subcarriers.The obtained ICI results are inversely proportional to the edge subcarrier usage probability within the subblock. According to activation probability for SMSs with (
$s=8$,
$v=4$) as in the
Figure 6b, ISA faces minimum ICI, as illustrated in
Figure 8b.
In
Figure 9, ICI analyzes on reference user are performed regarding different number of machine users with a fixed number of subcarriers per user. As seen in the
Figure 9a,b, nearly 0.5 dB more interference is observed for 6 users compared with 3 users case. For more than 6 users, there is a very slit increase in the ICI. Hence, the amount of the interference coming from far users proportionally decays with the increase in the number of users.
In
Figure 10, BER performances are obtained for 2nd user under time and power misalignment. In
Figure 10a,b, only time misalignment between the users is considered. As seen in the
Figure 10a, ISA with (
$s=8$,
$v=3$) has the best BER performance, but with a slight difference from ESA for
$\u03f5=Min$. Edge subcarrier activation probability for ESA is higher in comparison to COM and ISA, as shown in
Figure 6. Therefore, ICI coming from adjacent users to the 2nd user further increases for ESA. For
$\u03f5=Max$, the difference between the performances of SMSs is more obvious and ESA has the worst performance. COM has a slight better BER performance than ESA as observed in the
Figure 8b. ISA offers a much better BER performance for maximum time misalignment, since it has the smallest edge subcarrier activation probability associated with the lowest ICI. In
Figure 10b, OFDMIM with subblock parameters (
$s=8$,
$v=4$) is simulated. The performance of both ESA and COM become much worse than in
Figure 10a. For ISA with (
$s=8$,
$v=4$), subcarrier usage probability is more localized around the middle subcarriers than in the case of ISA with (
$s=8$,
$v=3$), as shown in
Figure 6. Moreover, equiprobable activation properties of ESA causes a destructive effect on the BER performance due to nonuniform distribution of ICI. For COM, less activation probability of one edge provides better protection against ICI caused by asynchronism between the users in time. In
Figure 10c,d, power difference between the users is also considered as well as time offset. The advantages of ISA against asynchronous transmission impairments are much more visible with the increase of ICI. Not only power difference but also increased number of active subcarriers within the OFDMIM subblock results in higher ICI. Therefore, ISA mapping scheme plays a key role for larger subcarrier activation ratio of
$v/s$ in asynchronous mMTC networks.