In 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

Intelligent Reflecting Surfaces (IRS) are a good candidate for sixth generation 6G networks [

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 [

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.

^{ple} dX, Y is the distance from X to Y and ple is the path loss exponent. We can write a_{k} = c_{k}e^{−j Φk} where c_{k} = |a_{k}|.

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^{(i)} is the symbol of U^{(i)}, po_{i} is the power of U^{(i)}, po_{1} + po_{2 }= 1 and 1 > po_{2} > po_{1 }> 0.

The signal at U^{(i)} given by

n^{(i)} is an additive Gaussian r.v. with variance N_{0} and E_{SS} is SS symbol energy defined as

E_{max} is the maximum symbol energy, I is the interference threshold and g_{SSPR} is channel coefficient between SS and PR. SS verifies interference constraints as

Using

Weak user U^{(2)} estimates s^{(2)} with SINR

The probability of an outage event at U^{(2)} is given by^{(1)} detects s^{(2)} as po_{2}>po_{1} 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

The network model is depicted in ^{(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_{1} + po_{2 }= 1 and 1>po_{2}>po_{1 }> 0.

The received signal at U^{(i)} is written as

U^{(i)} detects s_{K} as po_{K }> po_{i} with SINR

Then U^{(i)} performs Successive Interference Cancelation (SIC), removes s_{K} to detect s_{K−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

The throughput of U^{(i)} is given by

The total throughput (TThr) is given by

We maximize the total throughput as follows

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 _{B^(i)}(x) is given in Appendix A.

The PEP and throughput can be computed as Section 3.1 where we have to replace P_{B(q)}(x) by P_{Bi(q)}(x) given in

The SINR is computed as

The probability of an outage at U^{(i)} is computed as

^{(i)} = 1,1.5 i = 1,2 Packet length is L = 200.. IRS allows 6, 12, 18 dB

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

The variance and mean of A(i) are ^{(i)} is equal to

We deduce_{SSPR} = E(|g_{SSPR}|^{2}), E(.) is the expectation operation and gSSPR is the channel coefficient between SS and PR. When I/|g_{SSPR}|^{2}>E^{max}, we have

where Q_{m}(.,.) is the Generalized Marcum Q-function.

When I/|g_{SSPR}|^{2}<E^{max} ,