In this article, we optimize the powers associated to Non Orthogonal Multiple Access (NOMA) users, sensing and harvesting duration for Cognitive Radio Networks (CRN). The secondary source harvests energy from node A signal. Then, it senses the channel to detect primary source. Then, the secondary source transmits a signal that is reflected by Intelligent Reflecting Surfaces (IRS) so that all reflections have a zero phase at any user. A set Ii of reflectors are associated to user Ui. The use of M = Mi = 512, 256, 128, 64, 32, 16, 8 reflectors per user offers 45, 42, 39, 36, 33, 30, 27 dB gain

IRS are used to maximize the throughput of wireless systems as all reflections have a zero phase at the destination [

In this article, we optimize NOMA powers, sensing and harvesting durations to maximize the throughput. After energy harvesting from node A signal, secondary source SS senses the channel to detect primary activity. When no activity is detected, the secondary source transmits a signal that is reflected by IRS so that all reflections have a zero phase at any NOMA user. A set Ii of reflectors are associated to user Ui. The use of M = Mi = 512, 256, 128, 64, 32, 16, 8 reflectors per user offers 45, 42, 39, 36, 33, 30, 27 dB gain

Next section optimizes the NOMA powers, sensing and harvesting durations. Section 3 improves the energy harvesting process using IRS. Section 4 gives some results and Section 5 concludes the paper.

In

The harvested energy is given by
_{A} = E_{A}/Ts is the power of A, Ts is the symbol duration, f is channel gain from A to SS, L_{0} = T/Ts. We can write E(|f|^{2}) = 1/dAS_{S}^{ple} where d_{XY} is the distance from X to Y and ple is the path loss exponent.

The symbol energy of S_{S} is computed as:

In _{S} is equal to
_{i} < 1 is the power allocated to Ui such that 0 < PO_{1} < PO_{2} < ⋯< PO_{K} < 1 and

Let hp be the channel from S_{S} to p-th IRS reflector. Let gp be the channel from p-th IRS reflector to Ui. Ii is a set of reflectors associated to Ui and contains Mi = |Ii| reflectors. We have: E(|hp|^{2}) = 1/dSSIRS^{ple}. Furthermore, we have E(|gp|^{2}) = 1/dIRSUi^{ple}.

We have hp = apexp(−jbp) where ap = |hp|. E(aq) = Γ(m + 0.5)/[Γ(m)^{2}) = 1/d_{SSIRS}^{ple} [^{2}) = 1/d_{IRSUi}^{ple} [

The phase of p-th reflector is equal to [

The received signal at Ui is given by

In

Using

Fi follows a Gaussian distribution with mean mFi = Mi Γ(m + 0.5)^{2}/[Γ(m)^{2}d_{SSIRS}^{ple/2}d_{IRSUi}^{ple/2}] and variance σFi^{2} = M/[d_{SSIRS}^{ple}d_{IRSUi}^{ple}][1−Γ(m + 0.5)^{4}/Mi^{2}/Γ(m)^{4}]. Therefore, Fi^{2} has a non-central-chisquare distribution with degree of freedom one. For Rayleigh channels, |f|^{2} has also a central-chisquare distribution with degrees of freedom 2 m. Therefore, Yi is the product of a non-central and a central chisquare random variables and we have [_{n,m}^{p,l}(x) is the Meijer G-function.

We deduce

Ui performs Successive Interference Cancelation (SIC) and detects first s_{K} since PO_{K} > PO_{i}. The corresponding SINR is

The contribution of the detected symbol sK is removed and Ui estimates s_{K−1} with the following SINR

The process is continued by detecting sl with SINR

The probability of an outage event at Ui is computed as
_{Yi}(y) is provided in

The Packet Error Probability (PEP) at Ui is equal to [_{0} is defined as [

The total throughput is equal to

The powers of NOMA users, sensing and harvesting durations μ and ζ are optimized as follows:

_{1} contains P reflectors between A to SS to enhance the energy harvesting process. IRS_{2} is between SS and users Ui with Mi reflectors to improve the throughput.

When energy harvesting uses IRS, we have

The mean and variance of C are equal to

We deduce

The variable Yi should be replaced by Zi written as

Zi is the product of two non central chisquare r.v. Therefore, we have [

_{i}, μ and ζ.

In

In this article, we optimized the powers of NOMA users, sensing and harvesting duration for CRN. Secondary source senses the channel over (1−μ)ζT s to detect primary activity. If no activity is detected, SS broadcasts a signal during (1−μ)(1−ζ)T s to NOMA users. The signal is reflected by Intelligent Reflecting Surfaces (IRS) towards K users. A set Ii of reflectors is associated to user Ui. The use of M = Mi = 512, 256, 128, 64, 32, 16, 8 reflectors per user offers 45, 42, 39, 36, 33, 30, 27 dB gain