1. Introduction
Non-orthogonal multiple access (NOMA) is a suitable technique to achieve the goals of the massive machine-type communication (mMTC) in the 5G wireless networks [
1]. NOMA serves multiple users in the same frequency band and time slot by assigning different transmit powers [
2]. At the base station (BS) of the downlink NOMA system, a composite signal is generated by superimposing the constellations of all users belonging to any particular cluster [
3]. At the receiver’s end, the desired signal for each user is detected from the composite signal using the successive interference cancellation (SIC) technique [
3]. By using NOMA, we can serve the massive connecting devices simultaneously, which is not possible if the network resources are shared in orthogonal ways [
1]. However, in NOMA, the transmit power levels for all users in a cluster are required to be sufficiently high to mitigate the AWGN noise and the interference due to signals of other users present in the same composite signal [
3]. Furthermore, the stand-alone NOMA downlink system does not have any control over the channel gain between BS and the users [
4]. If the channel quality is poor between the source and destination (due to long distances or obstacles), then there is no alternate path for communication to occur [
4]. One way to resolve the problem of poor channel quality is addressed in [
5], where the author has considered the NOMA downlink system for the relay-to-relay cooperative communication as a solution. Another way to handle these challenges in the downlink NOMA system is by using the RIS [
6].
The RIS is an array of a large number of passive reflecting meta-surfaces (called meta-atoms). The electromagnetic properties of these meta-atoms can be reconfigured to control the amplitude and phase shift of the reflected signal from each meta-atom to focus the beam at the desired location [
7]. Hence, RIS can control the radio environment intelligently [
8]. The main advantages of using RIS are as follows: (i) Each meta atom contributes to a separate path from RIS to the user [
9]. (ii) By adjusting the phase shift provided by the meta-atom to the reflected signal, constructive interference condition is achieved among the signals received from the different meta-atoms towards the desired user in a point-to-point communication model. This improves the SNR for the received signal. Consequently, the data rate of the user also increases. (iii) Another advantage of RIS is that if the direct path from BS to the user is blocked, then the system has a better coverage area by more indirect wireless paths from BS-RIS-User [
7].
From the current literature on NOMA, it has been observed that sum data rate (SR) maximization is a common problem to encounter [
10,
11]. But, the problem with the SR in the NOMA downlink system is that when power allocation is conducted to maximize the SR, the more and more the data-rate is increased for the highest channel gain (CG) user and the data rates of lower CG users do not increase significantly. During the literature survey, we found that in the stand-alone NOMA downlink system, although optimization work has been conducted to maximize SR, the lower CG users could not achieve the upper bound of their individual data rate (IDR).
The drawback of a stand-alone NOMA downlink cluster is that lower CG users could not achieve the upper bound of their IDRs. This drawback can be overcome in the RIS-assisted TDMA-NOMA point-to-point communication model by allocating a sufficient number of meta-atoms such that the SINR of each user becomes saturated to reach the upper bound of IDR.
There are two popular resource allocation strategies: one is concentrating on SR maximization [
11] and the other is focusing on fairness Index equalization [
12,
13,
14] for the IDRs of all users present in the NOMA downlink cluster. But the previous allocation strategy does not hit always the upper bound of IDRs for lower CG users and the later allocation strategy does not allow the highest CG user to increase its data rate beyond the lowest IDR of the cluster. So, the resource allocation strategy should be able to hit the upper bound of IDRs for lower CG users and then allow to increase in the IDR of the highest CG user.
1.1. Motivation and Contribution
Figure 1 shows the motivation behind the proposed work in this paper. Although the effectiveness of NOMA has largely been explored in the sum throughput maximization, the identification of IDR still remained an unexplored area. Previously, it has been shown that RIS can lead to an overall improvement in the data rate by enhancing the effective channel gain of the downlink NOMA system. When time division multiple access (TDMA) is clubbed with multiple RISs in a distributed RIS-assisted NOMA (TDMA-RIS-NOMA) downlink system, a point-to-point communication model is created between the access point-to-RIS-to-user device. Due to this point-to-point communication model, the optimization of the phase shifts provided by meta-atoms of each RIS is facilitated. The optimized phase shifts of meta-atoms maximize the equivalent channel gain between the access point to the user. In this scenario, the channel becomes saturated and signal-to-interference plus noise ratio (SINR) becomes a function of power coefficients only. In this study, the power coefficients are calculated to maximize the SINR of each user belonging to a NOMA cluster using a geometric progression-based power allocation method such that IDR reaches its upper bound. Our findings set an upper limit for IDR and are useful for planning the resource allocation to achieve the desired quality of service (QoS) requirements in a NOMA downlink cluster.
To the best of the authors’ knowledge and belief, no resource allocation strategy tries to achieve the upper bound on the IDRs of lower CG users and simultaneously increases the IDR of the highest CG in stand-alone NOMA and RIS-NOMA systems. This IDR maximization becomes important when the access point (AP) is radiating low transmit power, as in the case of internet-of-things (IoT) networks [
15].
Motivated by the above-mentioned points, this paper presents the TDMA-RIS-NOMA downlink system, where exploiting the upper bound of IDRs is possible with easy beam-forming and channel gain controlling. The main contributions from this paper are listed below:
A point-to-point beam-forming strategy is exploited in the TDMA-RIS-NOMA downlink cluster such that at any instant, one RIS is serving only one user device for downlink communication.
A geometric progression (GP)-based power coefficient allocation scheme is derived to find out the power coefficients of all the users belonging to an RIS-assisted downlink NOMA cluster for maximizing the IDRs of the users.
Distribution of data rate among the users of an RIS-NOMA downlink cluster is analyzed and an expression is derived to calculate the upper bound of IDRs.
Based on the upper bound of IDRs and QoS requirements, a clustering algorithm is proposed where we decide the cluster bandwidth and cluster size in the downlink NOMA-RIS system for different applications.
1.2. Paper Organization
The rest of the paper contains the system description in
Section 2 followed by problem formulation in
Section 3. The proposed scheme is elaborated in
Section 4, then
Section 5 contains the proposed algorithm. The complexity and convergence analysis of the proposed power allocation algorithm is done in
Section 6.
Section 7 explains the simulation results and briefly discusses the results obtained. Finally, the conclusion is written in
Section 8,
2. System Description
We consider a downlink TDMA-RIS-NOMA point-to-point communication system that contains one AP with a single antenna; ‘
M’ devices, each equipped with a single antenna; and ‘
n’ RIS made up of ‘
N’ meta-atoms, each as shown in
Figure 2.
There are ‘
n’ numbers of RIS present in the proposed system model, as shown in
Figure 1. We assume that the distances among the RISs are large enough to mitigate the possibility of interference from one RIS to another RIS. Here, the TDMA system is followed with ‘
m’ time slots. During one time slot, only one device is active in a TDMA group to access the corresponding RIS. Hence, a point-to-point communication model is formed between AP-RIS-user devices. One RIS is dedicated to one TDMA group.
The entire communication period
is divided into multiple equal duration time slots of ‘
t’ milliseconds, as in a TDMA system and shown in
Figure 3. During any time slot ‘
n’ devices are active from ‘
n’ different TDMA groups. These active ‘
n’ devices make a downlink NOMA cluster. There are
m devices in a TDMA group. Hence, there are ‘
m’ NOMA clusters. Each slot is assigned to a different cluster of user devices. The cluster formation is conducted as per the QoS (data-rates) requirements.
When a new time slot starts, only one user device is communicating through one RIS. The number of user devices active in any time slot is equal to the number of RIS deployed (
n) in the system. During the present time slot, these
n active devices receive a common broadcasted composite NOMA signal through different wireless channels (i.e., AP-to-RIS-to-user device). This received NOMA composite signal is decoded at the receiver (user device). The realization of time synchronization and frequency distribution among different resource blocks are conducted as described in [
16] for NB-IoT systems.
Let denote the ith device of the lth cluster, which is scheduled in lth time slot. Further, N is the number of meta-atoms allocated to the device ‘’ such that these N meta-atoms are tuned to reflect the incoming signal from AP towards the user device ‘’. Let denote the channel coefficient between and rth meta-atoms of ith RIS allocated to . The indicates the channel gain between rth meta-atom of ith RIS allocated to and AP. Here, .
Assume
and
are the corresponding channel vectors for AP to RIS and RIS to the device
, respectively. The
and
have
N total RIS elements, which generate the maximum channel gain (CG). If the symbol
denotes the reflectivity-matrix of RIS for all
s, then equivalent channel gain
is given by
where
is
diagonal matrix for
ith device
.
and
are the
matrix containing the channel gain coefficients. The
denotes the transpose of matrix
.
The parameter is responsible for altering the amplitude of the reflected signal from the meta-atom.
The optimal value of phase shifts is calculated using the point-to-point downlink model
, which causes the in-phase addition of all the paths [
17,
18].
We assume that the positions of RISs and AP are fixed so the distance between RIS and AP is also fixed. The direct path between all the devices and AP is completely blocked and channel gain for direct paths is equal to zero. This yields,
For maximizing the amplitude of reflected signal, we put
in (
1) as unity. The
is computed as,
We assume the Rician fading channel model [
12] for channel gain calculation between AP to IRS and IRS to the mobile user.
The value of
parameter is taken equal to 3 and
and
are non-line-of-sight components of the corresponding paths and characterized by Rayleigh distributed random variables with unit variance and zero mean in (
4) and (
5).
and
are line-of-sight components of the corresponding paths and their value is taken as unity in this study. Direct paths from AP to devices are assumed to be missing due to signal blockage or longer distance, and communication occurs only via RIS to devices. A common frequency band is shared among the devices belonging to a NOMA cluster.
In this paper, our primary focus is to maximize the IDR when channel gains are already known. Hence, we assumed the perfect channel state information (CSI) and calculated the expression for IDRs. Although, the channel estimation is a complex task for the TDMA-RIS-assisted NOMA system, some channel estimation techniques [
19,
20] may be used to estimate the channels from AP-to-RIS and from RIS-to-user devices. The positions of RIS and AP are fixed.
The composite signal received at the
is given by,
where
is the received signal at
,
represents the additive white Gaussian noise (AWGN) with zero mean and
variance for all
s. Then the IDR of any user device inside the cluster can be given as,
where
is the individual data-rate (IDR) achieved by the device
in the system and
is the SINR corresponding to device
. The SINR of
ith user in a downlink NOMA cluster is given by
where
is total power allocated to the cluster,
is the power coefficient of
ith device in the
lth cluster.
is the variance of AWGN noise that represents the noise power.
6. Complexity and Convergence of Proposed Algorithm
We have compared the complexity in terms of flop count with the stand-alone NOMA system described by Ali et al. [
11]. The detailed analysis of the complexity of Ali et al. is conducted in [
22]. The flops are basically defined as any mathematical operation (like addition, subtraction, multiplication, and division) performed during the execution of algorithm [
23]. For the purpose of comparison, we have compared the proposed algorithm’s complexity with Ali et al. in
Table 2.
In the proposed algorithm, the complexity is calculated for the power allocation block only, i.e., step 14. We have calculated the initial 5 terms appearing in the GP for each power coefficient by putting
in (
24) and, hence, the number of additions required is equal to 4 for calculating any power coefficient. There are
n members in a cluster so we need to calculate
n power coefficients. The total add operations are equal to
during the power allocation. Similarly, the total multiplication operations required for power allocation are equal to
. Total number of flops required is
The power coefficients are calculated with the help of (
24). In (
24) the initial 5 terms only contribute significantly and subsequent terms are ignored as the value of the power coefficient converges until the third decimal place with the initial 5 terms only. Furthermore, the convergence of the proposed algorithm is proofed by the number of meta atoms Vs. IDR (in bits per second per Hertz) curve (
Figure 5) presented in the simulation result section. As the number of meta-atoms are increased, the IDR converges to its upper limit value. these upper limits of IDR are calculated and tabulated in
Section 4.1,
Table 1.
7. Simulation Results and Discussion
Table 3 describes the simulation parameters. The AWGN noise power is calculated according to the
, where
is in dB,
is in dBm,
B is in Hz [
17].
Monte-Carlo simulations are performed for 100,000 samples and the average value of normalized IDR in bits per sec per Hertz is calculated for different cluster sizes. For RIS-NOMA simulations, the total transmit power (
) is taken as 23 dBm [
24]. For simulation of stand-alone NOMA without RIS system, the total transmit power is taken as 46 dBm [
11].
Table 1 and
Table 4 present the theoretical upper bounds of IDRs and the Monte-Carlo simulation results to verify the theoretical benchmark, respectively, for proposed GP-based power allocation in the RIS-NOMA downlink cluster with different cluster sizes. The results shown here validate the proposed hypothesis that each lower CG user (user 2 to user ‘n’) present in a NOMA downlink cluster cannot achieve the IDR higher than its upper bound benchmark, irrespective of higher channel gain or higher cluster power provided to it. The empty places in these tables are intentionally left blank to show that the cluster is already full and no more users can be accommodated in the cluster than the cluster size.
Similarly,
Table 5 shows the theoretical upper bound of IDRs for the magic matrix-based power allocation [
22] in RIS-NOMA downlink cluster and
Table 6 verifies the theoretical benchmark set in
Table 5 by showing Monte-Carlo simulation-based results in deep agreement with the benchmark of
Table 5. The results obtained in
Table 4 and
Table 6 again validate the proposed hypothesis about the upper bound of IDR for each lower CG user belonging to a NOMA downlink cluster.
Table 7 and
Table 8 highlight the simulation results for stand-alone NOMA downlink cluster without RIS for different cluster sizes, when Magic matrix-based power allocation [
22] and optimal power allocation [
11] have been performed, respectively. Now, if we compare the results obtained in
Table 4 and
Table 8, then it clearly shows that IDRs for all the users are better in RIS-NOMA as compared to stand-alone NOMA without RIS. The same conclusion can also be drawn by comparing the results of
Table 6 and
Table 7. This comparison shows that RIS-NOMA is better than NOMA without RIS for all cases of power allocation. A reduction of 23Dbm in total power is achieved in the RIS-NOMA system while improving the data-rates as compared to their non-RIS counter part.
Results of
Table 4 also show the optimality of the proposed GP-based power allocation technique for all users of the RIS-NOMA cluster because IDRs in
Table 4 are highest among
Table 5,
Table 6,
Table 7 and
Table 8.
As shown in
Figure 5, the saturation point is reached for all the lower CG users in the downlink NOMA clusters as the effective CG is increased. The highest CG user for RIS-NOMA cluster is not saturated with respect to effective CG. This fact is shown in the
Figure 6 where the number of meta-atoms is increased to enhance the effective CG. The curves for different cluster sizes are plotted in this graph. The graph shows that the IDR of the highest CG user increases as the effective CG increases.
The simulation results confirmed the analysis conducted in
Section 4. The data rate increases as the number of meta-atoms increases before the saturation point. After this point, as we increase the number of meta-atoms, the change in the data rate of the corresponding user is negligible and we can say that the user has reached the upper limit of the IDR.
The data rate of the highest CG user is not saturated with respect to its effective CG. The rest of the users belonging to the same NOMA cluster are saturated to a predefined value
, which is dependent on the power coefficients of the users. Simulation results for
are in agreement with (
14).