A performance analysis method for outage probability and ergodic capacity of STAR-RIS-assisted NOMA system under hardware damage

Abstract

The present invention discloses a method for analyzing the outage probability and ergodic capacity performance of a Simultaneous Transmitting and Reflecting Reconfigurable Intelligent Surface (STAR‑RIS)-assisted Non‑Orthogonal Multiple Access (NOMA) system under hardware damage. For the STAR‑RIS-assisted NOMA system, hardware damage is considered, a system model is constructed under a Ricean channel, and the signal-to-noise distortion ratio, the approximate expressions of the outage probability and ergodic capacity of the system, as well as the asymptotic expression of the ergodic capacity under high signal-to-noise ratio are given. It is verified by simulation that the performance analysis method proposed in the present invention can effectively evaluate the performance of the system.

Description

Technical field:

[0001] The present invention belongs to the field of mobile communications and relates to a performance analysis method for a mobile communication system, in particular to an outage probability and ergodic capacity performance analysis method for a STAR-RIS assisted NOMA system. Background technology:

[0002] STAR-RIS is a surface that contains a large number of low-cost reflection and transmission units. It is placed between the base station and the user. Each unit can independently reflect and transmit the incident signal, change its amplitude and phase, and adjust the communication environment. Through appropriate adjustments, the reflected or transmitted signals can be superimposed on each other to enhance the desired signal power at the receiver. STAR-RIS can be densely deployed, adjustable and low-energy, without the need for complex interference management between passive STAR-RIS. Compared with traditional reconfigurable intelligent surfaces (RIS), users must be on the same side as the transmitter to receive the reflected signal from the RIS, while STAR-RIS allows the incident signal to be received by the user end through both reflection and transmission, so the coverage range can be extended to 360 degrees.

[0003] Reference 1 (Coverage Characterization of STAR-RIS Networks: NOMA and OMA [J]. IEEE Communications Letters, 2021, 25 (9): 3036-3040) studied the optimization problem of maximizing the coverage of STAR-RIS. Reference 2 (STAR-RISs: Simultaneous Transmitting and Reflecting Reconfigurable Intelligent Surfaces [J]. IEEE Communications Letters, 2021, 25 (9): 3134-3138) proposed the hardware model of STAR-RIS, as well as the channel models in the near field and far field, analyzed the outage probability and diversity gain of the STAR-RIS system, and compared it with the traditional RIS.

[0004] Existing related research mainly focuses on the analysis and optimization of some performance indicators of the STAR-RIS-assisted NOMA system, but they are all based on the assumption that the transmitter, receiver and STAR-RIS surface are in an ideal state, and there is a lack of research on the STAR-RIS-assisted NOMA system under the condition of hardware damage. Summary of the invention:

[0005] In order to more accurately analyze the performance of the STAR-RIS-assisted NOMA system under hardware damage, the present invention proposes a channel model, obtains the user's signal-to-noise distortion ratio and probability density function, and gives approximate expressions for the user's interruption probability and ergodic capacity under hardware damage, as well as an asymptotic expression for the ergodic capacity under high signal-to-noise ratio.

[0006] To achieve the above object, the present invention adopts the following technical solution: a method for analyzing the interruption probability and ergodic capacity performance of a STAR-RIS-assisted NOMA system under hardware damage, the specific steps of which are:

[0007] S1. Establish a STAR-RIS-assisted NOMA system model, in which a single-antenna base station communicates with two single-antenna users through STAR-RIS. STAR-RIS is a uniform planar array consisting of M components. The base station transmits the superimposed resources of the two users in the same time and frequency resources.

[0008] S2, STAR-RIS assisted NOMA system, For STAR-RIS and users The Rice channel between is the transmission matrix with phase noise, is the Ricean channel between the base station and STAR-RIS, and the user's signal-to-noise-plus-distortion-ratio (SNDR) is:

[0009]

[0010] Among them, p k represents the power allocated to user k, p s represents the total power, λ(k)∈{0,1} represents the decoding order, satisfying λ(t)+λ(r)=1, k tx , k rx is the hardware damage coefficient, is Gaussian white noise, Indicates other users;

[0011] S3. According to the user's signal-to-noise distortion ratio and probability density function, the approximate expression of the interruption probability is obtained:

[0012]

[0013] where γ tha , a∈{1,2} is the preset signal-to-noise ratio, is the variance;

[0014] Get an approximate expression for the traversal capacity:

[0015]

[0016] where y 1，i is the Laguerre polynomial L n The i-th root of (x), weight

[0017] The asymptotic expression for the ergodic capacity at high signal-to-noise ratio is obtained:

[0018]

[0019] The present invention has the following beneficial effects:

[0020] The present invention takes hardware damage into consideration when modeling, so the analysis results obtained are more in line with the actual situation; the user's signal-to-noise distortion ratio and probability density function are obtained, providing a basis for the analysis of system performance indicators; in addition, the analysis method proposed in the present invention can obtain the user's interruption probability and traversal capacity, providing a convenient and effective way for performance evaluation and comparison of systems of the same type. Description of the drawings:

[0021] Figure 1 This is a performance analysis step diagram of the STAR-RIS-assisted NOMA system of the present invention.

[0022] Figure 2 This is a system model diagram of the present invention.

[0023] Figure 3 It is a curve diagram of theoretical and simulated values ​​of user interruption probability and ergodic capacity when the number of STAR-RIS surface elements changes according to the present invention.

[0024] Figure 4 It is a curve diagram of the theoretical value and the simulated value of the user's interruption probability and ergodic capacity when the hardware damage factor changes in the present invention. Specific implementation method:

[0025] The present invention will be further described below in conjunction with the accompanying drawings.

[0026] 1. System Model

[0027] like Figure 1 As shown in Figure 1, the base station communicates with two single-antenna users via a STAR-RIS consisting of M elements. The T users and the base station are located on both sides of the STAR-RIS, and the R users and the base station are located on the same side of the STAR-RIS. We assume that the direct channel between the base station and the two users is blocked by an obstacle.

[0028] make Indicates STAR-RIS and user The Rician fading channel between:

[0029]

[0030] where d k represents the distance between STAR-RIS and user k, α RU ≥2 is the path loss index, ρ0 represents the path loss at a reference distance of 1 meter, and κ1 is the Ricean factor.

[0031] make Represents the Rice fading channel between the base station and STAR-RIS:

[0032]

[0033] Where d0 is the distance between the base station and STAR-RIS, α BR is the path loss exponent, and κ2 is the Rice factor.

[0034] Assuming that all elements on STAR-RIS have the same amplitude coefficients, the transmission and reflection factor matrices are:

[0035]

[0036] The amplitude satisfies And β t +β r ≤1, phase shift satisfies

[0037] Assume that there is phase noise on the STAR-RIS surface So the reflection and transmission factor matrices for:

[0038]

[0039] The phase noise of each element They obey the uniform distribution of [-π, π] respectively.

[0040] For the NOMA assisted communication system, the base station transmits the superimposed resources of two users in the same time and frequency resources. Assume s k represents the transmission signal of user k sent by the base station, and E[|s k | 2 ] = 1. Considering the hardware damage of the transmitter, the transmitter sends the superimposed signal of two users, and the transmitted signal can be expressed as:

[0041]

[0042] Where n tx The mean is 0 and the variance is Gaussian distribution. Where ps =p t +p r is the total transmit power, k tx It is a parameter representing the error vector magnitude (EVM) of the transmitter. According to the Long Term Evolution-Advanced (LTE-A) of the 3rd Generation Partnership Project (3GPP), the EVM value is in the range of [0.07, 0.175].

[0043] Considering the hardware impairment at the receiver, the received signal of user k can be expressed as:

[0044]

[0045] where n rx The mean is 0 and the variance is Gaussian distribution. rx is a parameter representing the magnitude of the receiver error vector. k is subject to the mean of 0 and the variance of Gaussian white noise.

[0046] 2. Signal-to-Noise-Distortion Ratio and Probability Distribution

[0047] To maximize the signal-to-noise ratio, optimize the phase The value of is:

[0048]

[0049] in Then the channel gain can be expressed as:

[0050]

[0051] Let binary variable λ(k)∈{0,1} represent the decoding order, satisfying λ(t)+λ(r)=1. Then the signal-to-noise-distortion ratio of user k is ( Indicates other users):

[0052]

[0053] When decoding, we take the R user as an example, as it has a better channel gain. Therefore, we decode the T user first, and then the R user. Then the SNDR of the T user and the R user is expressed as:

[0054]

[0055]

[0056] because It obeys the uniform distribution of [-π, π], then:

[0057]

[0058]

[0059] Rice fading channel |h i ||g k，i The mean and variance of | are:

[0060]

[0061] According to the expectation and variance formula of the product of independent random variables, we have:

[0062]

[0063]

[0064] Therefore, for T users, μ t =0, For R users, μ r =0,

[0065] Since the channels passing through different elements of STAR-RIS are independent of each other and obey the Rice distribution, according to the central limit theorem, when M is large enough, the distribution of the sum of random variables is approximately Gaussian. That is, make:

[0066]

[0067] X is a chi-square distribution with degrees of freedom n = 2. Therefore, the probability density function and cumulative distribution function of X are:

[0068]

[0069]

[0070] 3. Interruption Probability

[0071] When distributing power Substitute SNDR t , the interruption probability of T users is:

[0072]

[0073] Where R th1 is the information rate that needs to be achieved, is the preset signal-to-noise ratio. Substitute into the cumulative distribution function:

[0074]

[0075] When distributing power, ensure Substitute SNDR r , then the interruption probability of R users is:

[0076]

[0077] Where R th2 is the information rate that needs to be achieved, is the preset signal-to-noise ratio. Substitute into the cumulative distribution function:

[0078]

[0079] 4. Traversal Capacity

[0080] The SNDR and probability density function of T users are known. Substituting them, we can get the ergodic capacity of T users as:

[0081]

[0082] make Using Gauss-Laguerre integration:

[0083]

[0084] where y 1，i is the Laguerre polynomial L n The i-th root of (x), weight

[0085] The SNDR and probability density function of user R are known. Substituting them into the SNDR and probability density function, we can get the ergodic capacity of user R as follows:

[0086]

[0087] make Using Gauss-Laguerre integration:

[0088]

[0089] 5. Traversal Capacity at High SNR

[0090] At high signal-to-noise ratio

[0091] Therefore, the ergodic capacity of T users tends to:

[0092]

[0093] At high signal-to-noise ratio Therefore, the traversal capacity of an R user tends to be:

[0094]

[0095] The following Matlab simulation is used to verify the effectiveness of the STAR-RIS-assisted NOMA system performance analysis method under hardware damage proposed in this invention. The parameters are set as: d0 = 150m, d t =50m,d r =20m, path loss exponent α BR =α RU =2.2, reference path loss ρ0 = -30dB at 1m, noise power Rice factor κ1=κ2=8, preset signal-to-noise ratio γ th1 =γ th2 =2.

[0096] Figure 2 This is the change in the outage probability and traversal capacity of T and R users when the number of elements M on the STAR-RIS surface changes. As can be seen from the figure, with the increase in the number of elements M, at the same transmission power, the outage probability of T and R users decreases, the traversal capacity increases, and the system performance is better. The traversal capacity at a high signal-to-noise ratio is independent of the number of elements, which is consistent with the results of theoretical analysis. Therefore, in actual layout, we can increase the number of elements to obtain better system performance.

[0097] Figure 3 is the change of the interruption probability and ergodic capacity of T users and R users when the hardware damage factor changes, where k is assumed to be tx =k rx =k x As can be seen from the figure, as the hardware damage factor increases, at the same transmission power, the interruption probability of T users and R users increases, the traversal capacity decreases, and the system performance becomes worse. The traversal capacity under high signal-to-noise ratio will also be affected by the hardware damage factor. Therefore, in practical applications, we must try to minimize the adverse effects of hardware damage on system performance.

[0098] In summary, the performance analysis method proposed in this paper can effectively analyze the performance of the STAR-RIS-assisted NOMA system under hardware damage, and the simulation results fully demonstrate its effectiveness.

[0099] The above description is only a preferred embodiment of the present invention. It should be pointed out that a person skilled in the art can make several improvements without departing from the principle of the present invention, and these improvements should also be regarded as within the protection scope of the present invention.

Claims

1. A method for analyzing the outage probability and ergodic capacity performance of a STAR-RIS-assisted NOMA system under hardware damage, characterized in that: The following steps are involved: S1. A Simultaneous Transmitting and Reflecting Reconfigurable Intelligent Surface (STAR-RIS)-assisted Non-Orthogonal Multiple Access (NOMA) system model is established. In this system, a single-antenna base station communicates with two single-antenna users through STAR-RIS. STAR-RIS is a uniform planar array consisting of M components. The base station transmits the superimposed resources of the two users in the same time and frequency resources. S2. In the STAR-RIS assisted NOMA system, is the Ricean channel between STAR-RIS and user k∈K={t,r}, is the transmission matrix with phase noise, is the Ricean channel between the base station and STAR-RIS, and the user's signal-to-noise-plus-distortion-ratio (SNDR) is: Among them, p k represents the power allocated to user k, p s represents the total power, λ(k)∈{0,1} represents the decoding order, satisfying λ(t)+λ(r)=1, k tx , k rx is the hardware damage coefficient, is Gaussian white noise, Indicates other users; S3. According to the user's signal-to-noise distortion ratio and probability density function (PDF), the approximate expression of the interruption probability is obtained: where γ tha , a∈{1,2} is the preset signal-to-noise ratio, is the variance; Get an approximate expression for the traversal capacity: where y 1，i is the Laguerre polynomial L n The i-th root of (x), weight The asymptotic expression for the ergodic capacity at high signal-to-noise ratio is obtained:

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