CN115551062A

CN115551062A - Hybrid time division power division energy acquisition relay scheme of RIS-NOMA downlink

Info

Publication number: CN115551062A
Application number: CN202211159727.5A
Authority: CN
Inventors: 段玮; 谷晓会; 章国安; 姜衍; 季彦呈
Original assignee: Nantong University
Current assignee: Nantong University
Priority date: 2022-09-22
Filing date: 2022-09-22
Publication date: 2022-12-30

Abstract

The invention discloses a hybrid time division power division energy harvesting relay scheme of a RIS-NOMA downlink.A cell user center server serves as a relay to help cell edge users and supports Synchronous Wireless Information and Power Transmission (SWIPT) protocol and RIS passive beam forming of hybrid Time Switching (TS) and power division (PS). First, a closed expression of the outage probability and the best and worst case are derived. To gain further insight, we also investigated the diversity order and high signal-to-noise ratio (SNR) slope of the associated outage probability. Simulation and numerical results show that the scheme has certain improvement compared with the performances of Orthogonal Multiple Access (OMA), uncoordinated non-orthogonal multiple access (NOMA) and coordinated NOMA without RIS. In addition, the scheme obtains higher diversity gain by using more transmitting antennas and RIS units.

Description

Hybrid time division power division energy collection relay scheme of RIS-NOMA downlink

Technical Field

The invention relates to a mixed time division power division energy acquisition relay scheme of an RIS-NOMA downlink, belonging to the technical field of wireless networks.

Background

In recent years, the application of RIS (reconfigurable intelligent surface) based technology to the fields of vehicle-mounted networks, terahertz communication, physical Layer Security (PLS), and the like has received much attention. The RIS-assisted system consists of a series of smart surface units, each of which can absorb energy and/or change the phase of the incident signal independently. By appropriate adjustment of the reflection angle and/or amplitude factor of the RIS element, the electromagnetic signal can be reconfigured for wireless transmission. In particular, the use of optimized or random phases on the reflective elements can achieve significant beamforming gain for multiple users. In addition, as can be seen from the comparison of the performance of the RIS-assisted network and the relay-assisted network, the performance of the RIS-assisted network is significantly improved as the number of RIS units increases.

To further improve spectral and energy efficiency, by integrating NOMA and RIS technologies, RIS can enhance the power level of cell edge user equipment (users), while cell center user equipment treats reflected signals as interference. For RIS assisted NOMA networks following a rayleigh fading profile, the total transmit power is minimized and the associated Bit Error Rate (BER) is calculated. The method is characterized in that a RIS auxiliary NOMA network fading algorithm based on fairness is provided under the influence of concerned fading environment on the RIS authorized network. However, for direct links and/or reflected links, the general assumptions of rayleigh fading and rice fading are not realistic for such systems, as the RIS can be flexibly deployed on buildings that are fixed to the strong line-of-sight (LoS) path of the base station. To demonstrate the performance of the RIS, the RIS auxiliary link is modeled herein using Nakagami-m fading, where m =1 and m >1 represent line-of-sight LoS and non-line-of-sight (NLoS) links, respectively.

On the other hand, the above studies have focused on fairness or on improving the spectrum efficiency of the NOMA network, and meanwhile, while ensuring user fairness, there are few studies on improvement of reception reliability. To avoid this fairness problem while ensuring the reliability of cell edge terminals, the use of cooperative relay transmission is a possible solution. By using cell center users as relays, cooperative NOMA can significantly improve system performance and rate. The results of the study also show that the outage performance of the coordinated NOMA scenario can exceed that of the non-coordinated NOMA scenario even in the case of incomplete CSI and incomplete Successive Interference Cancellation (SIC).

In order to realize the cooperative relay transmission of users in the cell center, the simultaneous wireless information and energy transmission (SWIPT) is an energy-saving technology. Specifically, the cooperative NOMA and the SWIPT protocol are combined, so that a cell center user can process own data and forward required information of cell edge users, and diversity gain is not damaged by using the SWIPT compared with the traditional NOMA. In recent years, application of SWIPT in a relay system of a Multiple Input Multiple Output (MIMO) relay node with Energy Harvesting (EH) is studied to improve energy harvesting of the relay node. Specifically, the relay node collects energy according to a radio frequency signal transmitted by a source node through a Time Switching (TS) protocol, and pre-codes information by fully utilizing the collected energy and forwards the information to a destination node. In addition, two Power Split (PS) and time handover based protocols are proposed, demonstrating tradeoffs at different source power levels. Meanwhile, the Transmit Antenna Selection (TAS) scheme provides an effective solution for eliminating the additional power consumption, hardware complexity and training overhead caused by the MIMO technology by reducing the radio frequency chains without damaging the benefits of the MIMO system. Therefore, the introduction of antenna selection and RIS technology is a necessary approach to improve low complexity outage probability and ergodicity and rate in conjunction with NOMA systems.

Disclosure of Invention

In view of the above problems with the prior art, the present invention provides a hybrid time-division power-division energy-harvesting relay scheme for RIS-NOMA downlink, thereby improving performance through basic integration of power domain NOMA and RIS technologies by studying the performance of the system in the downlink.

In order to achieve the purpose, the invention adopts the technical scheme that: a hybrid time-division power-split energy harvesting relay scheme for RIS-NOMA downlink, comprising the steps of:

step S1: establishing a dual-user MISO-NOMA downlink system model, wherein a BS with K antennas is simultaneously connected with a cell-centered single-antenna user (named as user N) and a 1 cell-edge single-antenna user (named as user F); by dividing users in a cell into groups and configuring an RIS with M reflective elements, relay transmission between two users is assisted by creating passive beamforming, user N acquires energy by mixing TS and PS protocols and acts as a DF relay between BS and user;

step S2: analyzing the OP of the cell edge user to further perform interruption performance analysis, wherein the OP is defined as the probability that the instantaneous data rate of the user is lower than a predefined target data rate;

s3, analyzing the interruption performance of the K-th power of the exponential function to obtain further insight;

and step S4, demonstrating the interrupt performance of the proposed RIS assisted cooperative transmission scheme in the dual-user NOMA system by giving sufficient simulation and numerical results.

Further, in the first step, the relay scheme specifically includes:

step S11, firstly considering a time block with duration T, wherein the time block consists of three sub-blocks, user N obtains energy in the first sub-block with duration alpha T, and alpha is more than or equal to 0 and less than 1, which represents the block time ratio of EH; through power splitting, user N simultaneously obtains a second block of information with energy and decoding duration (1- α) T/2, where 0 ≦ ρ <1 denotes the power splitting ratio of EH, the remaining (1- ρ) is used for information decoding, and then, in a third sub-block of (1- α) T/2 duration, user N forwards the information to user F with all the energy collected;

step S12, according to the time frame of the TS/PS mixed EH protocol, the considered downlink transmission of the dual-user cooperation NOMA system can be divided into two stages, wherein the first stage carries out direct information transmission and EH in a first sub-block and a second sub-block, and the second stage carries out RIS assisted cooperative relay transmission in a third sub-block; the second and third sub-blocks are assigned to the same duration, and during the cooperative relay transmission phase, the BS remains silent when user N communicates with user F according to the half-duplex protocol.

Further, the system model first provides channel statistics for the proposed RIS assisted collaborative NOMA network, which is used to evaluate outage probability in the following section;

the effective channel gain scheme of user F is specifically as follows:

wherein the BS transmits a signal of let h _iT Representing the channel coefficients of the BS antenna i to the user T, where i =1, · · ·, K and T ∈ N, F; considering a strongly scattering environment, h is given by the fact that the channel from BS to user N and user F is subject to rayleigh fading _iT Modelled as independent co-distributions with zero mean and square difference λ _ST Complex gaussian random variables of (a); additive White Gaussian Noise (AWGN) n at the receiving antenna and user T _aT Using zero mean and zero variance sigma respectively ² _aT And n _cT Zero mean, zero variance σ ² _cT Represents; therefore, the channel gain | h _XY | ² Obey an exponential distribution, i.e. the Probability Density Function (PDF)

Wherein X belongs to 1, K, Y belongs to N, F, lambda _XY Represents the average channel gain; in addition, | h _XY | ² Can be written as

Wherein d is _XY Represents the distance between two nodes, a unit is meter, epsilon is path loss index, d ₀ For the purpose of reference to the distance,

is d ₀ The average signal power attenuation at (a);

wherein, the signal transmitted by the user N represents the RIS auxiliary relay transmission

Is a phase shift momentThe number of the arrays is determined,

wherein phi _m Is the phase shift acting on the mth element of the RIS; is provided with

Channel coefficients for user N to user F, user N to RIS and RIS to user F links, respectively, where all links follow Nakagami-m fading;

the RIS reflectance can be written as:

in the formula h _0,m 、h _r,m Respectively m-th element is h ₀ 、h _r (ii) a It is assumed that these connections experience a Nakagami-m fade, i.e. | h _NF |～Nakagami(1,1)，|h _o，m |～Nakagami(m ₀ 1) and | h _r，m |～ Nakagami(m _F 1), wherein m ₀ And m _F Is the corresponding distribution parameter;

thus, by setting the phase shift of the RIS to φ _m ＝arg(h _NF )-arg(h _0，m ，h _r，m ) The maximum received power at user F can be obtained; thus, for the relayed signal received at user F, the effective channel gain can be written as

Wherein "l _NF ”、“l ₀ "and" l _r "the path loss of user N to user F, user N to RIS and RIS to user F links, respectively; by using h _NF 、h ₀ And h _r Can respectively convert the worst and the best of the effective channel gain into

And

element h of the channel matrix ₀ And h _r Dependent fading parameter m ₀ And m _F Respectively, obey the Nakagami distribution. Then, by using the properties of the random variables, it is possible to obtain

Wherein

Therefore, the worst case of effective channel gain can be expressed as

Where Γ (,) represents the Gamma distribution:

on the other hand, the best case distribution of the effective channel gain matrix for user F upon receiving signals reflected from users N and RIS can be expressed as

Wherein

Further, the first downlink transmission stage of the dual-user cooperative NOMA system in step S12 specifically includes:

suppose BS selects antenna i for information direct transmission; user N and user F information x required by the problem in considering the power domain NOMA system _n And x _F As a superposition, respectively

Then the first block, p, at the beginning of antenna selection i is played _N And p _F The power distribution coefficients N and F representing the problem satisfy | h respectively according to the principle of NOMA _iN | ² ＞|h _iF | ² ，0＜p _N ＜p _F ，p _N +p _F ＝1；

For broadcast transmission, the information received at user N may be written as

Wherein

Considering the TS and PS hybrid EH protocol, the total energy harvested by user N can be expressed as:

E _iN ＝ηP _S |h _iN | ² αT+ηρP _S |h _iN | ² (1-α)T/2 (10)

where 0 < eta <1 represents energy conversion efficiency, 0 < rho <1 represents power division ratio for energy collection, | h _iN | ² Represents the channel gain between antenna i and user N; the signal received at user N for Information Decoding (ID) may be represented as

Wherein

According to the NOMA principle, user N first pairs x with the SIC principle _F Decoding is performed and then x is subtracted from the received signal _F Get the desired information, i.e. x _N (ii) a Thus, coding x _F The signal-to-interference-plus-noise ratio (SINR) at user N can be written as:

decoding x at user N _N May be expressed as:

for user F, the information it receives from BS (from antenna i) can be expressed as:

wherein

Compared with user N, since x _F Higher transmit power is allocated so that user F can decode the information he wants directly, so x in the superimposed NOMA signal _N Processing as noise; thus, the decoding x received at user F _F Can be written as

Further, the second downlink transmission stage of the dual-user cooperative NOMA system in step S12 specifically includes:

let all the energy collected by user N be used to support relaying, as shown in [30] and [31 ]. Thus, for a relayed signal, the transmit power of user N may be determined by:

considering further the DF relay protocol, the signals received at subscribers F to RIS and subscriber N can be written as

Wherein

Is a coherent combined channel from user N to RIS that can be found in equation (2),

denotes x _F A re-encoded version of (a);

from equations (16) and (17), x is transmitted for user N _F Decoding is performed, and the received signal-to-noise ratio at user F can be written as

Wherein

Finally, user F combines the signal directly transmitted by BS antenna i with the cooperative relay signal of user, N and RIS by using Selective Combining (SC) technique; thus, the achievable signal-to-noise ratio at user, F, can be expressed as

Further, the performance of cooperative relay transmission depends on the successful decoding x of user N _F The probability of (d); thus, the end-to-end signal-to-noise ratio at user F can be written as

The instantaneous transmission rate achieved by user F in combination with antenna i can be:

the scheme takes the optimal interruption performance as a target, and selects the user F antenna with the maximum instantaneous transmission rate; thus, the criteria for TAS are expressed as

Further, the analyzing the interruption performance of the OP of the cell edge user in step S2 specifically includes:

let R _th，N And R _th，F (bits/s/Hz) indicates that the target data rates for user N and user F, respectively, are:

definition of

According to the TAS criterion in equation (22), the OP of user F can be expressed as:

wherein

Indicates successful decoding x _F A signal-to-noise ratio threshold. (ii) a

Theorem 1. The worst-case closed expression for the OP of user F can be found in equation (24), where Ks (·) is a modified Bessel function of some order;

it is proved that the worst case of the OP of the user F can be written as shown by equation (23)

It can be seen that the probability events in equation (25) are not mutually exclusive due to the presence of the random variable Y; thus, conditions act on

Can be re-expressed as:

also, consider

Can be expressed as:

when the temperature is higher than the set temperature

For gamma ₂ In the case of < theta, let

Can be expressed as:

due to the fact that

When the temperature is higher than the set temperature

When, define

When the temperature is higher than the set temperature

When, define

For the

When it is used, order

Through algebraic steps, xi ₁ Can be written as

To further simplify the above integration, a trinomial coefficient is used

Hence, xi ₁ Can be expressed as:

in the formula (30) I ₁ Can be further expressed as

Can be obtained as I in formula (31) ₂ Integral of (2)

For I in equation (31) ₃ Integral due to inequality

Result in

For the

Standing in the end, can use

In view of

Xi, xi ₂ Can be expressed as

Binding xi ₁ Xi and xi ₂ The OP of the user F is obtained, and the proof of theorem 1 is completed;

theorem 2 suppose γ ₂ The best case for the closed expression of user F OP can be given by equation (35):

it is proved that theorem 2 is easily proved, similar to theorem 1.

Further, the step S3 specifically includes:

consider the approximation in the high signal-to-noise state as:

for the sake of simplicity, let

When PS → ∞ is reached,

therefore, in the high signal-to-noise ratio region,

and

can be covered with

Substitution; then, there are

Wherein

In addition, the low-order incomplete Gamma function can be expanded into

Wherein

Rounding the shape parameter to the nearest integer;

when x → ∞ is reached, e ^-a/x 1-a/x, the user F is solved,

the worst case for asymptotic OP is:

based on the trinomial coefficients, the integral in equation (37) can be

The method is widely developed:

using a similar calculation procedure in theorem 1 proving, in equation (38)

Can be further expressed as:

can be simplified into:

will be provided with

Substitution into (37) gives

In the same way, the user F,

the optimum for asymptotic OP of (a) can be given by equation (42):

next, the achievable diversity gain of the proposed scheme is studied with emphasis, and mathematically, the diversity gain D can be expressed as

Wherein

Representing the signal-to-noise ratio, the bit error rate P _e Is a function of the signal-to-noise ratio; by using the probability of interruption P _out Alternative bit error rate, diversity gain is noted

Thus, by observing the slope of OP, the diversity order of user F can be derived from the following proposition.

Proposition 1 based on the approximate results of the equations, (41) and (42), the order of diversity can be determined; with the support of RIS assisted cooperative relaying NOMA network, the worst and best case of user F diversity order is given

Wherein

And

a non-negative constant; thus, equations (45) and (46) show that the slope of the OP for the proposed scheme is in the high SNR region

The curves are in direct proportion;

the results of propositions 2 (45) and (46) show that,

and

the larger the diversity order, the higher the interrupt performance is indicated by increasing the number of RIS units.

Proposition 3 assume that the direct connection between user N and user F is the dominant component, where the path loss is l ₀ l _r ＜＜l _NF The order of diversity of best and worst case is the same; this indicates that the OP performance of user F is determined by both the number of active antennas at the BS and the number of passive antennas at the RIS.

Further, the simulation setting specific method in step 4 is as follows:

firstly, reasonably setting a power distribution coefficient; the power allocation factor is determined by the target data rates of user N and user F. Consider that cell-centric users need to decode x simultaneously _F And x _N Thus, the power allocation factor of the cooperative and non-cooperative NOMA systems is determined by the data rate required by user N; to simplify the notation, let

Decoding x in equation (12) for user N _F Can be re-expressed as

In equation (13), x is decoded at user N _N Can be re-expressed as

The user N decoding x can be calculated _F Achievable rate of

Users N to x _N Can be achieved by

The 1/2 factor appears in the equation; (49) And (50) since α =0, x is successfully decoded considering user N _F And x _N Is provided with

Wherein R is _th，F And R _th，N (bits/s/Hz) indicates that user N successfully decodes x _F And x _N A data rate threshold of; therefore, the power distribution coefficient can be obtained by the following formula

After some calculation, the formula (51) can be rewritten as

In order to further improve the OP performance of cell edge users, it may be considered that user F is a main user, and the priority service is implemented by allocating the maximum transmission power factor to user F; thus, users N and F are allocated power as

Proposition 4, in a mixed TS/PS framework, a power distribution and time division ratio and a NOMA user target rate are jointly determined;

for performance comparisons, the following protocol was chosen as a benchmark:

a. conventional OMA BS communicates with two users one after the other in two sub-blocks at the same time.

b. Non-cooperative NOMA the BS simultaneously signals two users over the entire time block.

c. Cooperative NOMA system without RIS in a cooperative NOMA system, a near-end user directly communicates information to a far-end user without the assistance of an RIS.

The beneficial effects of the invention are:

(1) A novel RIS auxiliary cooperative transmission scheme is provided for two-user MISO-NOMA system, the scheme selects a transmitting antenna with optimal reachable rate at the edge of a base station, NOMA-based transmission is carried out from the base station to a pair of terminals, and the RIS is deployed between the center of the base station and a cellular terminal to compensate large-scale path loss. Furthermore, with a hybrid TS and power split and energy harvesting receiver and the SWIPT protocol, the cell center users send the required signals to the cell edge users with the collected energy, a process aided by passive beamforming of the RIS.

(2) The achievable performance is characterized in terms of the OP of the intelligent terminal, taking into account the Nakagami fading and the user propagation between static channels with combined relayed signals. Specifically, we derive an exact and asymptotic closed-form expression of the best and worst case of the OP of the cell edge users. In addition, the algorithm also obtains diversity performance and high signal-to-noise ratio. The result shows that the diversity performance can be improved by increasing the number of active antennas of the antenna lattice and the number of passive antennas of the RIS module.

(3) The results show that this scheme significantly improves the outage performance for cell edge users compared to traditional OMA, uncoordinated NOMA, and coordinated NOMA without RIS system. The simulation result verifies the analysis of the people, and the result shows that 1) the increase of RIS element can improve OP; 2) The diversity gain is proportional to the number of base station antennas.

Drawings

FIG. 1 is a schematic diagram of the RIS assisted MISO-NOMA collaboration system architecture with two users of the present invention;

fig. 2 is a schematic diagram of a hybrid DF relaying scheme based on TS and PS SWIFT of the present invention;

FIG. 3 is a graphical illustration of a comparison of the effective channel gain results for a user N-RIS-user F link under simulation 105 of the present invention;

FIG. 4 is a graph illustrating the relationship between the outage probability of user F and the fraction time of EH α according to the present invention;

FIG. 5 is a view of the present invention;

FIG. 6 is a comparison diagram of the interruption performance of the cell edge users in different RIS directions according to the present invention;

FIG. 7 is a diagram illustrating the performance comparison of the present invention for user F with or without TAS;

fig. 8 is a diagram illustrating the interruption performance comparison of cell edge users when K =3 according to the present invention;

FIG. 9 is a schematic diagram of the diversity gain achieved by the RIS assisted cooperative NOMA system of the present invention;

fig. 10 is a schematic diagram of the diversity gain obtained by the scheme of the present invention when the numbers of α =0.3 and ρ =0.3 antennas are different.

Detailed Description

In order to make the objects, technical solutions and advantages of the present invention more apparent, the present invention is further described in detail below with reference to the accompanying drawings and examples. It should be understood, however, that the description herein of specific embodiments is only intended to illustrate the invention and not to limit the scope of the invention.

Unless defined otherwise, all technical and scientific terms used herein have the same meaning as commonly understood by one of ordinary skill in the art to which this invention belongs, and the terminology used herein in the description of the present invention is for the purpose of describing particular embodiments only and is not intended to be limiting of the present invention.

As shown in fig. 1, a considered dual-user MISO-NOMA downlink system, in which a BS with K antennas communicates with both cell-centric single-antenna users (named user N) and cell-edge single-antenna users (named user F) simultaneously. For simplicity we focus primarily on a two-terminal system, however, the proposed design can be applied to a multi-user scenario by dividing users in a cell into multiple groups. In addition, a RIS with M reflective elements is provided to facilitate relay transmissions between two users by creating passive beam forming. In this system, user N acquires energy through a hybrid TS and PS protocol and acts as a DF relay between BS and user F.

As shown in FIG. 2, we consider a time block of duration T, consisting of three sub-blocks [23 ]. Wherein, the user N gets energy in the first sub-block with duration α T, where 0 ≦ α <1 denotes the block time fraction of EH. By power splitting, user N simultaneously obtains a second block of information with energy and decoding duration of (1- α) T/2, where 0 ≦ ρ <1 represents the power splitting ratio of the EH, and the remaining (1- ρ) is used for information decoding. Then, in the third sub-block of (1- α) T/2 duration, user N forwards the information to user F using all the energy collected.

According to the time frame of the TS/PS hybrid EH protocol shown in fig. 2, the downlink transmission of the considered dual-user cooperative NOMA system can be performed in two stages. The first stage carries out direct information transmission and EH in the first and second sub-blocks, and the second stage carries out RIS assisted cooperative relay transmission in the third sub-block. For simplicity we note that the second and third sub-blocks are assigned the same duration. In the cooperative relay transmission phase, the BS remains silent when user N communicates with user F according to the half-duplex protocol.

In this section, channel statistics information is first provided for the proposed RIS assisted cooperative NOMA network, which is used to evaluate outage probabilities in the following sections.

1) Signal transmitted by BS let h _iT Represents the channel coefficients of BS antenna i to user T, where i =1, · ·, K and T ∈ N, F. Considering a strongly scattering environment, h is given by the fact that the channel from BS to user N and user F is subject to rayleigh fading _iT Modelled as independent co-distributed with zero mean and variance λ _ST Complex gaussian random variables of (a). Additive White Gaussian Noise (AWGN) n at the receiving antenna and user T _aT Respectively using zero mean value and zero variance sigma ² _aT And n _cT Zero mean, zero variance σ ² _cT And (4) showing. Thus, the channel gain | h _XY | ² Obey an exponential distribution, i.e. the Probability Density Function (PDF)

Wherein X belongs to 1, K, Y belongs to N, F, lambda _XY The average channel gain is indicated. In addition, | h _XY | ² Can be written as

Wherein d is _XY Represents the distance between two nodes in meters, e is the path loss exponent, d ₀ For the purpose of reference to the distance,

is d ₀ The average signal power at (a) decays.

2) Signal transmitted by user N for RIS assisted trunking we mean

In order to phase-shift the matrix of the phase,

wherein phi _m Is the phase shift acting on the mth element of the RIS. Is provided with

User N to user F, user N to RIS and RIS to user, respectivelyChannel coefficients for the user F link, where all links follow Nakagami-m fading. Note that the RIS reflection coefficient can be written as

In the formula h _0,m 、h _r,m Respectively m-th element is h ₀ 、h _r . It is assumed that these connections experience a Nakagami-m fade, i.e. | h _NF |～Nakagami(1,1)，|h _0，m |～Nakagami(m ₀ 1) and | h _r，m |～Nakagami(m _F 1) where m is ₀ And m _F Are the corresponding distribution parameters.

In the proposed RIS assisted NOMA system, in order to improve the performance of user F, RIS is introduced. Thus, by setting the phase shift of the RIS to φ _m ＝arg(h _NF )-arg(h _0，m ，h _r，m ) The maximum received power at user F can be obtained by a simple application of its received amplitude. Thus, for a relayed signal received at user F, the effective channel gain can be written as

Wherein "l _NF ”、“l ₀ "and" l _r "the path loss for user N to user F, user N to RIS and RIS to user F links, respectively. By using h _NF 、h ₀ And h _r Independent co-distribution of the effective channel gains can be converted to [29 ] worst and best case respectively]

And

it is noted that the element h of the channel matrix ₀ And h _r With fading parameter m ₀ And m _F Respectively, obey the Nakagami distribution. Then, by using the properties of the random variables, it is possible to obtain

Wherein

Thus, the worst case of effective channel gain can be expressed as

Wherein Γ (·,) represents the Gamma distribution:

Wherein

To evaluate the approximated channel statistics, the best and worst case effective channel gains for user F are compared to the results from the simulation, and as shown in fig. 3, the worst and best case effective channel gains provide a lower and an upper bound, respectively, for the simulated channel gain.

This section analyzes the OP of cell edge users, where OP can be defined as the probability that the user's instantaneous data rate is below a predefined target data rate.

for simplicity of notation, we define

The OP of user F can be expressed as the TAS criterion in equation (22)

Wherein

Indicates successful decoding x _F A signal-to-noise ratio threshold of (c).

In this section, sufficient simulation and numerical results are given to demonstrate the interrupt performance of the proposed RIS assisted cooperative transport scheme in a dual-user NOMA system.

Simulation setup

Firstly, reasonably setting the power distribution coefficient. The conventional approach is to set a fixed power distribution coefficient,randomly chosen under the NOMA principle, i.e. p _N ＜p _F ,p _N +p _F And =1. Another way to determine the coefficients is based on the target data rate of the user. In our simulation, the power division factor is given by user N and user F [36 ]]Is determined together with the target data rate of (c). Considering the cell-centric user needs to decode x simultaneously _F And x _N Therefore, the power allocation coefficient of the cooperative and non-cooperative NOMA systems is determined by the data rate required by the user N to ensure the fairness of the comparison. To simplify the notation, let

Decoding x in equation (12) for user N _F Can be re-expressed as

In equation (13), x is decoded at user N _N Can be re-expressed as

The user N decoding x can be calculated _F Achievable rate of

Users N to x _N Can be achieved by

The factor of 1/2 appears in the equation. (49) and (50) are due to α =0. Consider user N successfully decoding x _F And x _N We have

Wherein R is _th，F And R _th，N (bits/s/Hz) indicates that user N successfully decodes x _F And x _N The data rate threshold of (a). Therefore, the power distribution coefficient can be obtained by the following formula

After some calculation, the formula (51) can be rewritten as

In order to further improve the OP performance of cell edge users, it may be considered that user F is the main user, and the prioritized service is implemented by allocating the maximum transmit power factor to user F. Thus, users N and F are allocated power of

Proposition 4 in the hybrid TS/PS architecture, the power allocation and time division ratio should be determined together with the NOMA user target rate.

Some important simulation parameters are summarized in table 1:

TABLE 1

Simulation parameters

For performance comparisons, we chose the following scheme as a benchmark:

d. conventional OMA: the BS communicates with two users one after the other in two sub-blocks at the same time.

e. Non-cooperative NOMA: the BS simultaneously transmits NOMA signals to both users during the entire time block.

f. Cooperative NOMA system without RIS: in a cooperative NOMA system, a near-end user passes information directly to a far-end user without the assistance of a RIS.

B. Simulation result

Fig. 4 and 5 show the relationship of OP of the user F to the fractional time α and the fractional power ρ in EH. The solid and dashed lines represent the worst and best case analysis results, respectively. As we expect, the simulation results lie between the best and worst case, which validates our analysis. In fig. 4 and 5 we represent OPs for the proposed scheme as a function of a and p, respectively. It is readily seen that α has a stronger influence on the OP of the user F than ρ. In particular, fig. 4 shows that for a given p and different values of α, the OP of user F varies significantly. In contrast, fig. 5 shows that the OP of the user F varies within a limited range for a given value of α and different values of ρ. This can be explained by the fact that the outage performance of cell-edge users is determined by both direct and cooperative relay transmission, with fixed p and varying a having a significant impact on them, while fixed a and varying p only affect the performance of relay transmission. It can be seen from the results of fig. 4 that selecting an approximate power split ratio and time split ratio will help to achieve higher performance gains.

In graph V-B, we compare the outage performance of user F when the RIS is configured as cell center user and cell edge user, respectively. The results show that a smaller OP can be achieved when the RIS is designed as user F to improve relay transmission. The reason is that the OP of user F is successfully decoded x by user N and user F _F The probability of (c) is determined together, and if the cell center user is, the user N performing SIC should be subjected to large interference.

Fig. 7 shows the effect of the TAS scheme on OP, with random antenna selection as the reference scheme. Considering the mixed cooperative NOMA system based on SWIPT and RIS assistance, it can be seen that the performance of cell edge users is improved by improving the transmission signal-to-noise ratio, because in high signal-to-noise ratio areas, users have enough received power to successfully perform SIC. Furthermore, in the TAS criterion that maximizes the user F instantaneous data rate, the proposed RIS assisted cooperative transmission scheme has better interrupt performance, especially in case of full use of RIS. This is reasonable because the userThe OP of F is jointly determined by the direct transmission of BS and the relayed transmission of user N, and the RIS assisted relayed transmission successfully decodes x with user N _F Is related to the probability of (c).

In fig. 8, we provide a comparison between the proposed RIS assisted cooperative NOMA, legacy OMA and non-cooperative NOMA systems. For a fair comparison, the transmit antennas are randomly selected at the BS. In OMA systems, the BS communicates with two users one after the other in two sub-blocks at the same time. In a non-cooperative NOMA system, the entire time block is used to serve two users simultaneously. As shown in fig. 7, the conventional NOMA scheme improved cell-edge performance compared to the conventional OMA scheme. In addition, the RIS significantly increases the OP at user F, the greater the number of RIS elements, the greater the performance gain. This phenomenon illustrates that RIS will play an important role in OP performance at user F when the transmission between user N and user F experiences server fading or large path loss.

Fig. 9 shows the diversity gain obtained by the proposed RIS assisted cooperative NOMA system. It can be seen that the slope of the OP curve for user F is parallel to the best and worst case scenarios

The line of (c). A similar trend can be observed in fig. 10, where we plot the OPs of user F for different antenna counts. Obviously, for a given number of antennas, the curve slopes for the worst case optima of OPs are parallel, the diversity gain is proportional to the number of transmit antennas, which also validates proposition 1.

Aiming at a coordinated NOMA downlink system, the performance of a cell edge terminal is improved while the energy efficiency of a cell center terminal is ensured. Specifically, a novel RIS assisted cooperative transmission scheme is provided, a cell center terminal adopts SWIPT to support DF relay transmission, and the RIS is deployed between a cell edge and the cell center terminal to further enhance the relay transmission. In addition, the proposed scheme employs TAS in direct transmission and RIS passive beamforming design in relay transmission to optimize outage performance for cell edge users. Considering the mixed TS and PS SWIPT architecture, our best case and worst case channel statistics and OPs are derived in a closed form to characterize the system performance. More specifically, a closed form expression of OPs of cell edge users and corresponding asymptotic OPs are derived, and the validity thereof is verified through simulation. Simulation and numerical results show that the algorithm proposed herein has a significant improvement in cell edge user performance compared to traditional OMA, coordinated NOMA, and NOMA without RIS system.

The above description is intended to be illustrative of the present invention and should not be taken as limiting the invention, as the invention is intended to cover any modification, equivalent replacement or improvement made within the spirit and scope of the present invention.

Claims

1. A hybrid time division power split energy harvesting relay scheme for RIS-NOMA downlink, comprising the steps of:

step S1: establishing a dual-user MISO-NOMA downlink system model in which a Base Station (BS) with K antennas is simultaneously associated with a cell-centric single-antenna user (named user N) and a cell-edge single-antenna user (named user F); by dividing users in a unit into groups and configuring an RIS with M reflecting elements, relay transmission between two users is assisted by generating passive beam forming, user N acquires energy by mixing TS and PS protocols and acts as DF relay between BS and user;

step S2: analyzing the OP of the cell edge users, and further performing interruption performance analysis, wherein the OP is defined as the probability that the instantaneous data rate of the users is lower than a predefined target data rate;

and S4, demonstrating the interrupt performance of the proposed RIS auxiliary cooperative transmission scheme in the dual-user NOMA system by giving sufficient simulation and numerical results.

2. A RIS-NOMA downlink hybrid time division power split energy harvesting relay scheme according to claim 1, wherein in said first step, the relay scheme is specifically:

step S11, firstly considering a time block with duration T, wherein the time block consists of three sub-blocks, a user N obtains energy in a first sub-block with duration alpha T, and alpha is more than or equal to 0 and less than 1, which represents the block time proportion of EH; through power splitting, user N simultaneously obtains a second block of information with energy and decoding duration (1- α) T/2, where 0 ≦ ρ <1 indicates the EH power split ratio, and the remaining (1- ρ) is used for information decoding, and then, in a third sub-block of (1- α) T/2 duration, user N forwards the information to user F using all the collected energy;

step S12, according to the time frame of TS/PS hybrid energy collection (EH) protocol, the downlink transmission of the considered dual-user cooperation NOMA system can be divided into two stages, wherein the first stage carries out direct information transmission and EH in a first sub-block and a second sub-block, and the second stage carries out RIS assisted cooperative relay transmission in a third sub-block; the second and third sub-blocks are assigned to the same duration, and the BS remains silent during the cooperative relay transmission phase when user N communicates with user F according to the half-duplex protocol.

3. A RIS-NOMA downlink hybrid time division power split energy harvesting relay scheme according to claim 1, characterized in that the system model first provides channel statistics of the proposed RIS assisted collaborative NOMA network, which is used to evaluate outage probability in the following subsections;

the effective channel gain scheme of user F is specifically as follows:

wherein the BS transmits a signal of let h _iT Representing the channel coefficients of BS antenna i to user T, where i =1, \ 8230;, K and T ∈ N, F; considering a strongly scattering environment, h, assuming that the channel from BS to user N and user F is subject to rayleigh fading _iT Modelled as independent co-distributed with zero mean and variance λ _ST Complex gaussian random variables of (a); additive White Gaussian Noise (AWGN) n at the receiving antenna and user T _aT Respectively using zero mean value and zero variance sigma ² _aT And n _cT Zero mean, zero variance σ ² _cT Represents; thus, the channel gain | h _XY | ² Obey an exponential distribution, i.e. the Probability Density Function (PDF)

Wherein X belongs to 1, \8230, K, Y belongs to N, F, lambda _XY Represents the average channel gain; in addition, | h _XY | ² Can be written as

is d ₀ The average signal power attenuation at (a);

In order to be a phase-shift matrix,

the RIS reflectance can be written as:

in the formula h _0,m 、h _r,m Respectively m-th element is h ₀ 、h _r (ii) a It is assumed that these connections experience a Nakagami-m fade, i.e. | h _NF |～Nakagami(1,1)，|h _0，m |～Nakagami(m ₀ 1) and | h _r，m |～Nakagami(m _F 1) where m is ₀ And m _F Is the corresponding distribution parameter;

therefore, by setting the phase shift of the RIS to φ _m ＝arg(h _NF )-arg(h _0，m ，h _r，m ) The maximum received power at user F can be obtained; thus, for a relayed signal received at user F, the effective channel gain can be written as

And

element h of the channel matrix ₀ And h _r With fading parameter m ₀ And m _F Respectively obeying a Nakagami distribution. Then, by using the properties of the random variables, it is possible to obtain

Wherein

Therefore, the worst case of effective channel gain can be expressed as

Wherein Γ (·,) represents the Gamma distribution:

Wherein

4. The hybrid time-division power-division energy-harvesting relay scheme of RIS-NOMA downlink of claim 2, wherein the specific steps of the first phase of downlink transmission of dual-user cooperative NOMA system in step S12 are:

suppose that the BS selects an antenna i to directly transmit information; in considering the power domain NOMA system, the number of users N required by the problem anduser F information x _n And x _F Respectively as a superposition

Then the first block, p, of the start of the antenna selection i is played _N And p _F The power distribution coefficients N and F representing the problem, following the principle of NOMA, satisfy | h respectively _iN | ² ＞|h _iF | ² ，0＜p _N ＜p _F ，p _N +p _F ＝1；

Wherein

E _iN ＝ηP _S |h _iN | ² dT+ηρP _S |h _iN | ² (1-α)T/2 (10)

wherein eta <1 > 0 represents energy conversion efficiency, rho <1 > 0 represents power division ratio of energy collection, | h _iN | ² Represents the channel gain between antenna i and user N; the signal received at user N for Information Decoding (ID) may be represented as

Wherein

According to the NOMA principle, user N first pairs x with the Successive Interference Cancellation (SIC) principle _F Decoding and then subtracting x from the received signal _F To obtain the information it wants, i.e. x _N (ii) a Thus, coding x _F The signal-to-interference-plus-noise ratio (SINR) at user N can be written as:

decoding x at user N _N The received signal-to-noise ratio (SNR) of (d) may be expressed as:

for user F, the information it receives from the BS (from antenna i) can be expressed as:

wherein

5. The hybrid time-division power-division energy-harvesting relay scheme of RIS-NOMA downlink of claim 2, wherein the second stage of downlink transmission of dual-user cooperative NOMA system in step S12 comprises the specific steps of:

let all the energy collected by user N be used to support relaying, as shown in [30] and [31 ]. Thus, for a relayed signal, the transmit power of user N may be represented by:

Wherein

denotes x _F A re-encoded version of (a);

Wherein

6. The hybrid time-division power-division energy-harvesting relay scheme of RIS-NOMA downlink of claim 2, wherein the performance of cooperative relay transmission depends on user N successfully decoding x _F The probability of (d); thus, the end-to-end signal-to-noise ratio at user F can be written as

the scheme takes the optimal interruption performance as a target, and selects the user F antenna with the maximum instantaneous transmission rate; thus, the criterion for Transmit Antenna Selection (TAS) is expressed as

7. The hybrid time-division power-division energy harvesting relay scheme of RIS-NOMA downlink according to claim 2, wherein said analyzing the interruption performance of the OP of the cell edge user in step S2 is specifically:

definition of

According to the TAS criterion in equation (22), the OP for user F can be expressed as:

wherein

Indicates successful decoding x _F A signal-to-noise ratio threshold. (ii) a

Theorem 1. The worst-case closed expression of the OP of user F can be found in equation (24), where Ks (·) is a modified Bessel function of some order;

It can be seen that the probabilistic events in equation (25) are not mutually exclusive due to the presence of the random variable Y; thus, conditions act on

Can be re-expressed as:

also, consider

Can be expressed as:

when in use

For gamma ₂ In the case of < theta, let

Can be expressed as:

due to the fact that

When in use

When, define

When in use

When, define

For

When it is used, order

Through algebraic steps, xi ₁ Can be written as

To further simplify the above integration, trinomial coefficients are used

Hence, xi ₁ Can be expressed as:

in the formula (30) I ₁ Can be further expressed as

Can be obtained as I in the formula (31) ₂ Integral of

For I in equation (31) ₃ Integral due to inequality

Result in that

For the

Is established by

In view of

Xi, xi ₂ Can be expressed as

it is proved that theorem 2 is easily proved, similar to theorem 1.

8. A RIS-NOMA downlink hybrid time division power split energy harvesting relay scheme according to claim 1, characterized in that said step S3 specifically is:

consider the approximation at high signal-to-noise ratio:

for the sake of simplicity, let

When PS → ∞ is reached,

therefore, in the high signal-to-noise ratio region,

and

can be covered with

Substitution; then, there are

Wherein

In addition, the low-order incomplete Gamma function can be expanded into

Wherein

Rounding the shape parameter to the nearest integer;

when x → ∞ is reached, e ^-a/x Is approximately equal to 1-a/x, the user F is solved,

the worst case for asymptotic OP is:

based on the trinomial coefficients, the integral in equation (37) can be

The method is widely developed:

using a similar calculation procedure in theorem 1 proving, in equation (38)

Can be further expressed as:

can be simplified into:

will be provided with

Substitution into (37) gives

In the same way, the user

The optimum of the asymptotic OP of (a) can be given by equation (42):

Wherein

Thus, by observing the slope of OP, the diversity order of user F can be obtained by the following proposition;

proposition 1 based on the approximation results of the equations, (41) and (42), the order of diversity can be determined; with the support of RIS assisted cooperative relaying NOMA network, the worst and best case of user F diversity order is given

Wherein

And

is a non-negative constant; thus, equations (45) and (46) show that the slope of the OP of the proposed scheme is in the high SNR region

The curves are in direct proportion;

the results of propositions 2 (45) and (46) show that,

and

9. The hybrid time-division power-division energy harvesting relay scheme for the RIS-NOMA downlink according to claim 1, wherein the simulation setup in step 4 comprises the following specific methods:

firstly, reasonably setting a power distribution coefficient; the power allocation factor is determined by the target data rates of user N and user F. Consider that cell-centric users need to decode x simultaneously _F And x _N Thus, the power allocation coefficient for cooperative and uncooperative NOMA systems is determined by the data rate required by user N; to simplify the notation, let

X in user N decoding equation (12) _F Can be re-expressed as

In equation (13), x is decoded at user N _N Can be re-expressed as

The user N decoding x can be calculated _F Achievable rate of

Users N to x _N Can be achieved by

After some calculation, the formula (51) can be rewritten as

In order to further improve the OP performance of cell edge users, it may be considered that user F is taken as a main user, and the priority service is implemented by allocating the maximum transmission power factor to user F; thus, users N and F are allocated power of

for performance comparisons, the following protocol was chosen as a benchmark:

b. Non-cooperative NOMA-the BS simultaneously transmits NOMA signals to both users over a time block.

c. Cooperative NOMA system without RIS in a cooperative NOMA system, a near-end user passes information directly to a far-end user without the assistance of an RIS.