NOMA with Adaptive Transmit Power Using Intelligent Reflecting Surfaces
1 Information Technology Department, Saudi Electronic University, Riaydh, Saudi Arabia
2 University of Carthage, SUPCOM-COSIM, Ariana, 2083, Tunisia
* Corresponding Author: Raed Alhamad. Email:
Computer Systems Science and Engineering 2023, 45(2), 2059-2070. https://doi.org/10.32604/csse.2023.032610
Received 23 May 2022; Accepted 24 June 2022; Issue published 03 November 2022
AbstractIn this article, we use Intelligent Reflecting Surfaces (IRS) to improve the throughput of Non Orthogonal Multiple Access (NOMA) with Adaptive Transmit Power (ATP). The results are valid for Cognitive Radio Networks (CRN) where secondary source adapts its power to generate low interference at primary receiver. In all previous studies, IRS were implemented with fixed transmit power and previous results are not valid when the power of the secondary source is adaptive. In CRN, secondary nodes are allowed to transmit over the same band as primary users since they adapt their power to minimize the generated interference. Each NOMA user has a subset of dedicated reflectors. At any NOMA user, all IRS reflections have the same phase. CRN-NOMA using IRS offers 7, 13, 20 dB gain vs. CRN-NOMA without IRS for N = 8, 16, 32 reflectors. We also evaluate the effects of primary interference. The results are valid for any number of NOMA users, Quadrature Amplitude Modulation (QAM) and Rayleigh channels.
Intelligent Reflecting Surfaces (IRS) are a good candidate for sixth generation 6G networks [1–3]. IRS phases are adjusted so that reflections have a zero-phase at all users [4–7]. IRS has been suggested for optical communications [8–10] and Millimeter Wave (mmWave) systems [11,12]. Experimental results of IRS have been presented in [13–15]. A practical implementation of IRS can be found in [16,17] were phase shifts can be continuous or quantized. Machine learning algorithms can be used to optimize the performance of IRS [18,19]. A real time cutting model using finite element was proposed in . A fast and accurate tissue simulation model was discussed in . Device to Device (D2D) communications for the fifth generation and beyond was studied in .
IRS can be used to reflect the transmitted signal to NOMA users. The source combines of symbols of K NOMA users. This signal is reflected by RIS toward K users. The weakest user detects its signal and considers the rest of signals as noise. The strongest user detects weakest user signal. Then, it removes it and continue the detection process of remaining users that are ranked from the weakest to the strongest one. IRS was implemented when the transmitter has a fixed transmit power in [1–19]. In all previous studies [1–19], IRS were implemented with fixed transmit power and previous results are not valid when the power of the secondary source is adaptive. In CRN, secondary nodes are allowed to transmit over the same band as primary users since they adapt their power to minimize the generated interference. In this paper, we derive the throughput of NOMA using IRS and adaptive transmit power.
In this article, we propose to:
– Compute the throughput of CRN using NOMA and IRS where the secondary source has an adaptive power. Each secondary NOMA user has a given set of reflectors.
– We derive the statistics of Signal to Noise Ratio (SNR) as well as Signal to Interference plus Noise Ratio (SINR). We study the effects of primary interference. CRN-NOMA using IRS offers 7, 13, 20 dB gain versus CRN-NOMA without IRS for N = 8, 16, 32 reflectors.
– Two algorithms are discussed to rank the NOMA users.
Next section gives the throughput when there are two users. Section 3 generalizes the results to CRN-NOMA with K users. Section 4 discusses the obtained results. The paper is concluded in last section.
Fig. 1 depicts the network model with two secondary users, a Source (SS), a Primary Receiver and Transmitter and PR and PT. SS adapts its power to have a small interference at PR. We consider Rayleigh channels. Let be the channel from SS to k-th reflector of IRS. λ = 1/dSS, IRSple dX, Y is the distance from X to Y and ple is the path loss exponent. We can write ak = cke−j Φk where ck = |ak|.
Let be the channel from k-th reflector to i-th user U(i). . We can write where . Let I(i) be the set of reflector’s of U(i). The phase of k-th reflector dedicated to U(i) in set I(i) given by
The transmitted symbol by SS is written as
where s(i) is the symbol of U(i), poi is the power of U(i), po1 + po2 = 1 and 1 > po2 > po1 > 0.
The signal at U(i) given by
n(i) is an additive Gaussian r.v. with variance N0 and ESS is SS symbol energy defined as
Emax is the maximum symbol energy, I is the interference threshold and gSSPR is channel coefficient between SS and PR. SS verifies interference constraints as
Using (1), we obtain
Weak user U(2) estimates s(2) with SINR
The probability of an outage event at U(2) is given by
where the Cumulative Distribution Function (CDF) of , , is provided in Appendix A. U(1) detects s(2) as po2>po1 with SINR
Then U(1) removes s(2) and demodulates s(1) with SNR
The probability of an outage event at U(1) is computed as
The Packet Error Probability (PEP) of U(i) is given by
L is packet length and
The throughput of U(i) is given by
The total throughput (TThr) is given by
We maximize the total throughput as follows
3.1 Ranking Using Average Gains
The network model is depicted in Fig. 2. It contains PT, PR, SS and K secondary NOMA users. U(i) has the i-th maximum average channel gain between SS and NOMA users. Let P be defined as
N(j) is the number of IRS reflectors of U(j).
NOMA symbol is written as
where po1 + po2 = 1 and 1>po2>po1 > 0.
The received signal at U(i) is written as
U(i) detects sK as poK > poi with SINR
Then U(i) performs Successive Interference Cancelation (SIC), removes sK to detect sK−1 with SINR
U(i) detects sp with SINR
The probability of an outage event at U(i) is computed as
The PEP at U(i) is equal to
where W0 is defined in (15)
The throughput of U(i) is given by
The total throughput (TThr) is given by
We maximize the total throughput as follows
3.2 Ranking Using Instantaneous Gains
Let Ui(1) be the strongest user with largest instantaneous channel gain B(i):
Let Ui(K) be the weakest user :
Let Ui(q) be q-th ranked user:
The CDF of is given by
where 1 ≤ mi ≤ N for i = 1,…,N. m1¹m_2 ¹… mN, mq < mq + 1<…< mK and PB^(i)(x) is given in Appendix A.
The PEP and throughput can be computed as Section 3.1 where we have to replace PB(q)(x) by PBi(q)(x) given in (35).
4 Effects of Primary Interference
The SINR is computed as
The probability of an outage at U(i) is computed as
is the average interference. The PEP and throughput are computed using (37).
Fig. 3 shows the total throughput for CRN-NOMA for K = 2, for I = 1 16 Quadrature Amplitude Modulation (QAM), dIRSU(i) = 1,1.5 i = 1,2 Packet length is L = 200.. IRS allows 6, 12, 18 dB vs. CRN-NOMA without IRS for N = 8, 16, 32.
Fig. 4 shows the throughput for different values of I, 16QAM modulation and N = 8 reflectors. As I increases as the throughput improves since SS can increase its power while verifying interference constraints.
Fig. 5 shows that NOMA with IRS for N = 64 offers better performance than Orthogonal Multiple Access (OMA) and NOMA without IRS for 16QAM and two users. At high average SNR, the throughput of OMA is half that of NOMA.
Fig. 6 depicts the effects of primary interference when there are two users, N = 8, 16 reflectors per user for 16QAM Modulation. The parameters are dPTU(i) = 1,0.9, 0.5,0.6. We notice that the performance degrades as PT is close to NOMA users since there is more interference.
Fig. 7 depicts the total throughput for 16-QAM modulations for two users and N = 8, 16 reflectors. Ranking using instantaneous channel gains offers the best throughput.
In this article, we computed the PEP and throughput of NOMA with adaptive transmit power and IRS. IRS are deployed to enhance data reception at all users. CRN-NOMA using IRS offers 7, 13, 20 dB gain vs. the absence of IRS for N = 8, 16, 32. We have also derived the SNR and SINR statistics.
Funding Statement: The authors extend their appreciation to the Deanship of Scientific Research at Saudi Electronic University for funding this research work through the Project Number 8093.
Conflicts of Interest: The authors declare that they have no conflicts of interest to report regarding the present study.
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Appendix A: CDF of B(i)
The variance and mean of A(i) are and . B(i) is equal to
where λSSPR = E(|gSSPR|2), E(.) is the expectation operation and gSSPR is the channel coefficient between SS and PR. When I/|gSSPR|2>Emax, we have
where Qm(.,.) is the Generalized Marcum Q-function.
When I/|gSSPR|2<Emax , and we have