Electromagnetic interference under transmission reflection type intelligent reflecting surface assisted short packet communication method

Abstract

The application discloses a method for short packet communication assisted by a transmissive and reflective intelligent reflecting surface under electromagnetic interference. The transmissive and reflective intelligent reflecting surface assists a multi-antenna wireless access point in transmitting short packet signals to two single-antenna users under electromagnetic interference to realize high-reliability and low-latency communication. Firstly, based on statistical channel state information, under the phase constraint condition of the transmissive and reflective intelligent reflecting surface, a primary and secondary phase configuration strategy is adopted to deduce the probability distribution characteristics of end-to-end channel gains between an interference source, the wireless access point and the two users. Secondly, the statistical characteristics of decoding signal-to-interference-and-noise ratios at the two users are determined under electromagnetic interference. Finally, a closed-form solution of average block error rates of the two users is given, and power allocation coefficients and transmissive and reflective coefficients are jointly optimized to realize optimal system transmission block length under the reliability constraint of the two users. The application maximizes the use of communication resources to realize high-reliability and low-latency communication under electromagnetic interference.

Description

Technical Field

[0001] This invention relates to a short packet communication method for Non-orthogonal Multiple Access (NOMA) assisted by a Simultaneously Transmitting and Reflecting-Intelligent Reflecting Surface (STAR-IRS), belonging to the field of next-generation mobile communication technology. Background Technology

[0002] Ultra-Reliable and Low-Latency Communication (URLLC) is one of the main application scenarios for future mobile communication technologies, aiming to provide ultra-high reliability (above 99.999%) and ultra-low latency (≤1 millisecond). Achieving URLLC is one of the current challenges in the field of wireless communication. Short packet communication is a key technology for realizing URLLC, effectively reducing system transmission latency by transmitting short data packets (Y.Yu, H.Chen, et al. "On the Performance of Non-Orthogonal Multiple Access in Short-Packet Communications," IEEE Commun. Lett., vol.22, no.3, pp.590–593, Mar.2018.). However, due to the limited data block length in short packet communication, the proportion of pilot overhead available for channel estimation is significantly reduced, ultimately leading to a decrease in system transmission reliability. To compensate for the limitations of short packet communication systems in terms of transmission reliability, intelligent reflective surfaces (IRS) are often introduced into the system to assist in achieving URLLC.

[0003] IRS can reconstruct the wireless channel propagation environment, allowing the received signal to vary according to specific communication needs, thereby increasing system capacity, expanding signal transmission coverage, and improving system transmission reliability. IRS can be divided into pure reflective IRS and STAR-IRS. Compared to pure reflective IRS, STAR-IRS can achieve full-space coverage of the signal by simultaneously transmitting and reflecting the incident signal (X. Mu, Y. Liu, et al. "Simultaneously Transmitting and Reflecting (STAR) IRS Aided Wireless Communications," IEEE Trans. Wireless Commun., vol. 21, no. 5, pp. 3083-3098, May 2022.). Furthermore, in order to further improve the spectral efficiency and system capacity of wireless communication systems, multiple access technologies are often used in the design of wireless communication systems. Non-orthogonal multiple access (NOMA) technology is considered to be the most promising multiple access technology. It significantly improves spectral efficiency by allowing different users to share the same time and frequency resources (B. Makki, K. Chitti, A. Behravan, et al., "A Survey of NOMA: Current Status and Open Research Challenges", IEEE Open J. Commun. Soc., vol. 1, pp. 179-189, 2020.).

[0004] The aforementioned technologies can effectively improve the transmission performance of communication systems. However, in the design of practical communication systems, the impact of signal interference cannot be ignored. When electromagnetic interference is present, the energy of the interfering signal can reach the receiving end through the system transmission link, thereby reducing the end-to-end signal-to-interference-plus-noise ratio (SINR) of the system and significantly affecting the communication performance of the system. Therefore, the impact of electromagnetic interference will inevitably be discussed in the performance analysis of wireless communication systems.

[0005] Chinese invention patent CN115442816A discloses a method for implementing NOMA short packet communication with a reflective IRS-assisted system. It designs the system using statistical channel state information for a two-user scenario and proposes an algorithm for NOMA power allocation and transmission block length optimization. Chinese invention patent CN116170856A discloses a design method for a NOMA short packet communication system with a simultaneous transmission reflective IRS-assisted system. It uses statistical channel state information to optimize the coefficients of the simultaneous transmission reflective IRS, NOMA power allocation, and transmission block length for a two-user scenario to achieve URLLC. Both of the above IRS-assisted NOMA short packet communication studies assume no additional electromagnetic interference in the transmission environment. In actual wireless communication systems, in addition to being affected by fading and Gaussian white noise, communication systems are often affected by co-channel interference signals. Since IRS can amplify both useful and interfering signals, the performance of IRS-assisted NOMA short-packet communication systems designed in environments without additional electromagnetic interference deteriorates significantly when co-channel interference is present. Therefore, it is necessary to redesign parameters such as NOMA power allocation and transmission block length of the IRS-assisted NOMA short-packet communication system to achieve URLLC in electromagnetic interference environments. Currently, research on how to achieve URLLC by optimizing STAR-IRS-assisted NOMA short-packet communication systems in complex scenarios with electromagnetic interference is still limited. Therefore, researching the optimized design of STAR-IRS-assisted NOMA short-packet communication systems under electromagnetic interference environments is of significant practical importance for improving the reliability and low-latency performance of wireless communication systems. Summary of the Invention

[0006] This invention provides a short packet communication method assisted by a transmission-reflection type intelligent reflector under electromagnetic interference. By jointly optimizing the NOMA power allocation coefficient, STAR-IRS transmission-reflection coefficient and transmission block length, high-reliability and low-latency communication is achieved.

[0007] The objective of this invention is achieved through the following technical solution:

[0008] A short packet communication method assisted by a transmission-reflection type intelligent reflector under electromagnetic interference is described in the following steps:

[0009] Step A: Establish a downlink two-user non-orthogonal multiple access (NOMA) short packet communication system assisted by a simultaneously transmitting and reflecting intelligent reflective surface (STAR-IRS). This system includes an access point (AP) with one M-antenna, two single-antenna users (UE-1 and UE-2), and a STAR-IRS with N (N>1) passive elements. UE-1 is the transmitting user, and UE-2 is the reflecting user. Due to obstruction, the AP can only communicate with the users with the assistance of the STAR-IRS. The system includes an electromagnetic interference source that affects the received signal of the STAR-IRS. Assume that the location, transmission power, and transmission channel characteristics from the electromagnetic interference source to the STAR-IRS are known.

[0010] Step B: Based on the system model established in Step A, derive the received signals of the two users under electromagnetic interference environment; determine the order of continuous interference cancellation based on statistical channel state information, and further write out the instantaneous signal-to-interference-plus-noise ratio (SINR).

[0011] Step C: Based on the channel parameters, the number of wireless access point antennas M, and the number of STAR-IRS units N, the STAR-IRS performs phase adjustment based on statistical channel state information according to the Primary-Secondary Phase-Shift Configuration (PS-PSC) strategy, and analyzes and provides the distribution characteristics of instantaneous SINR; its specific implementation is as follows:

[0012] The channel coefficient from AP to STAR-IRS is Given a complex number field, the channel coefficients from STAR-IRS to UE-l (l∈{1,2}) are: The channel coefficient from the electromagnetic interference source to the STAR-IRS is Then the end-to-end channel coefficient from AP to UE-1 is: The end-to-end channel coefficient from the interference source to UE-1 is Where ξ l Let A represent the transmission and reflection coefficients of STAR-IRS, respectively. H This represents the conjugate transpose of matrix A. This represents the phase offset matrix designed for UE-1, where diag{·} represents a diagonal matrix with the elements within the brackets as diagonal elements, and φ n,lf represents the phase offset value from the nth STAR-IRS unit to UE-1. l This represents the power-normalized beamforming vector of the AP pointing to the UE-l, and G l It can be written as G l =A 1,l +A 2,l +A 3,l +A 4,l ,and

[0013]

[0014]

[0015] Where β0 is the path loss at a unit reference distance of 1 meter, κ0 and κ l For the path loss exponent, K0 and K l Let d0 and d be Rice factors. l These are the distances from the AP to the STAR-IRS and from the STAR-IRS to the UE-1, respectively. M (AoD0) is the antenna array response vector, and AoD0 is the transmit angle from the AP to the STAR-IRS. and Represents the line-of-sight component. and Indicates the non-line-of-sight component; A 2,l and A 3,l Follows the pattern of having a mean of 0 and variances of 1 / 2 and 1 / 2 respectively. and The complex Gaussian distribution, when the number of IRS units is large, according to the central limit theorem, A 4,l It can be approximated as having a mean of 0 and a variance of 0. The complex Gaussian distribution, For cascaded channel G l The phase error, according to the PS-PSC strategy (J.Xu, Y.Liu, et al., "STAR-RISs: A Correlated T&R Phase-Shift Model and Practical Phase-Shift Configuration Strategies," IEEE J.Sel. Topics Signal Process., vol.16, no.5, pp.1097-1111, Aug.2022.), when l=2, has: and Then we can obtain When l=1 The interval is [-2] -1 π,2 -1The uniform distribution of π can, when the number of IRS units is large, achieve the desired effect. If A is approximated as a complex Gaussian random variable, then A 1,1 The real and imaginary parts of the equation respectively follow the mean of . variance is Gaussian distribution and mean are variance is , where a is a Gaussian distribution. e,1 and b e,1 They are respectively (a M (AoD0)f1 H The real and imaginary parts of ) Based on the above analysis, G can be calculated. l The probability distribution of , where the real and imaginary parts respectively follow the mean of . variance is Gaussian distribution and mean are variance is Gaussian distribution, and

[0016]

[0017] in Similarly Wherein, κ3 represents the path loss index. This is a non-line-of-sight component. When the number of IRS elements is large, B 1,l and B 2,l Follows the pattern of having a mean of 0 and variances of 1 / 2 and 1 / 2 respectively. and The complex Gaussian distribution of H is further obtained. l Follows the pattern with mean 0 and variance of The complex Gaussian distribution is obtained. According to the moment matching theorem, the end-to-end channel gain |G| from AP to UE-l (l∈{1,2}) can be obtained. l | 2 Obeying shape parameters Scale parameter is The gamma distribution, the end-to-end channel gain |H from the interference source to UE-l (l∈{1,2}) l | 2 Obtains a shape parameter of 1 and a scale parameter of [missing information]. The gamma distribution of , where |·| represents the modulus of the complex number or the absolute value of the real number,

[0018]

[0019] And there are

[0020]

[0021]

[0022] in, This represents the mean operation. and This represents the operations of taking the real part and taking the imaginary part, from which γ is obtained. 1,1 γ 2,1 and γ 2,2 The cumulative distribution functions are respectively

[0023]

[0024] in,

[0025]

[0026] P represents the total power of the AP's transmitted signal, α l P represents the power allocation factor of UE-l. I Indicates the power of the interference signal; For the power of additive complex white Gaussian noise, W (a,b) (x) is the Whittaker W function and Represents the confluence hypergeometry function. This represents the gamma function.

[0027] Step D: Calculate the average block error rate (BLER) for both users according to the formula in short packet communication.

[0028] Step E: Based on the expressions calculated in Step D, under reliability constraints, further solve for the optimal power allocation coefficient, optimal transmission and reflection coefficient, and optimal transmission block length of NOMA.

[0029] Further:

[0030] The specific implementation of step A is as follows:

[0031] Modeling Channel Coefficients: The channel coefficients between the AP and STAR-IRS are expressed as follows: The channel coefficients between STAR-IRS and UE-l are expressed as follows: Let be the antenna array response vector, t∈{M,N}, λ be the carrier wavelength, d=0.5λ be the spacing between STAR-IRS elements, and θ be the transmit angle or arrival angle of the corresponding channel. This represents the line-of-sight component of the corresponding link, where AoA0 and AoD0 are the angle of arrival and transmission angle from the AP to the STAR-IRS, respectively, and AoD... l Indicates the transmission angle from STAR-IRS to UE-1; These are the non-line-of-sight components of the corresponding links, and they respectively obey... and in This indicates that the mean is μ and the variance is σ. 2 The complex Gaussian distribution, I a Let a represent an identity matrix of size a; This represents the channel coefficient from the electromagnetic interference source to the STAR-IRS, where To obey The non-line-of-sight components; In STAR-IRS assisted communication, in order to meet the constraints that the impedance and magnetoresistance should be purely imaginary under passive and lossless conditions, the reflection and transmission coefficients of STAR-IRS have the following relationship with the corresponding phase coefficients: This condition, also known as the phase adjustment-related constraint, restricts the reflection and transmission phase coefficients of STAR-IRS to meet certain conditions.

[0032] The specific implementation of step B is as follows:

[0033] The received signal at UE-1 is:

[0034] y1=G1s+H1s I +w

[0035] Assuming UE-2 is closer to STAR-IRS, the instantaneous SINRγ of UE-1 decoding x1 is obtained according to the NOMA principle. 1,1 for:

[0036]

[0037] Meanwhile, the expression for the received signal at UE-2 is:

[0038] y2=G2s+H2s I +w

[0039] UE-2 initially treats x2 as interference with decoding x1. At this point, the instantaneous SINRγ of UE-2 decoding x1... 2,1 for:

[0040]

[0041] If x1 is successfully decoded, then x1 is removed and x2 is decoded again. At this time, the instantaneous SINRγ of UE-2 decoding x2 is... 2,2 for:

[0042]

[0043] in The AP transmits a short packet signal with a total power of P, α l Let x represent the power allocation coefficient for the corresponding user and satisfy α1 + α2 = 1. l This represents the power normalization signal sent by the AP to UE-l, s IP represents the power-normalized interference signal emitted by the electromagnetic interference source. I Indicates the power of the interference signal; w indicates a mean of 0 and a variance of 0. Additive complex Gaussian white noise.

[0044] The specific implementation of step D is as follows:

[0045] According to the relevant formulas for short packet communication, given the signal-to-interference-plus-noise ratio γ, the short packet block size T, and the short packet BLERε, the maximum achievable rate of short packets, in bits per symbol, is approximately expressed as:

[0046]

[0047] Where C(γ)=log2(1+γ) represents the Shannon capacity, and V(γ)=(1-(1+γ)) -2 (log2e) 2 Q represents the channel divergence. -1 (·)express The inverse function of .

[0048] Assume the maximum achievable rate of UE-1 is R. l =F l / T, where F l Indicates the number of UE-1 information bits; the corresponding instantaneous SINRγ l,j (j∈{1,2}) under UE-l decoding x j BLERε l,j Approximately expressed as

[0049]

[0050] Based on instantaneous BLER and instantaneous SINR, the average BLER in the fading channel is... Represented as:

[0051]

[0052] in, Indicates γ l,j The probability density function.

[0053] according to An approximation of the average value in the fading channel. Further expressed as:

[0054]

[0055] in

[0056] Further using the Gauss-Chebyshev integration method, we can obtain:

[0057]

[0058] Where M x Let be the approximate order of the Gauss-Chebyshev integral.

[0059] Therefore, the average BLER of UE-1 and UE-2 is:

[0060]

[0061] in and They are respectively:

[0062]

[0063]

[0064] The specific implementation of step E is as follows:

[0065] Represent the target BLER of the two users as Determine the optimal power allocation factor, optimal transmission block length, and optimal transmission / reflection factor. The specific steps for determining the optimal power allocation factor, optimal transmission / reflection factor, and optimal transmission block length are as follows:

[0066] 1.1 Given system parameters such as transmittance and reflection coefficients and power distribution coefficients, initialize the block length and limit it to [M]. min M max ],make

[0067] 1.2 will Substitute into the average BLER formula to calculate the corresponding average for the two users. 1.3 If the calculated average BLER satisfies or Let the minimum block length be T min =-1, which means there is no optimal solution in this case.

[0068] 1.4 If the calculated average BLER simultaneously satisfies and Let the minimum block length be T. min =M min .

[0069] 1.5 If none of the above conditions are met, then if the conditions are met... Under the condition that, let Calculate the corresponding average and This represents the floor function.

[0070] 1.6 When satisfied and Then let Otherwise

[0071] 1.7 Update or Continue with steps 1.5 to 1.6 until... Stop iteration, minimum block length

[0072] 1.8 Given the transmittance and reflectance coefficients, select a step size of δ to traverse the range α1, repeating steps 1.1 to 1.7 to obtain the block length T corresponding to each power allocation coefficient. min Then the minimum block length The corresponding power allocation coefficient is the optimal power allocation coefficient. min(·) calculates the minimum element in an array.

[0073] 1.9 Select a step size of δ to traverse the feasible range of ξ1, and repeat steps 1.1 to 1.8 to obtain the corresponding value for each transmission coefficient. So, the minimum common block length under the traversal of the transmission coefficients The corresponding transmittance is the optimal transmittance.

[0074] The core of this invention lies in: for the first time, under the consideration of electromagnetic interference and phase constraints, deriving the closed-form expression of the instantaneous SINR cumulative distribution function and the average BLER of STAR-IRS-assisted NOMA short packet communication; based on this, further realizing URLLC by jointly optimizing the NOMA power allocation coefficient, STAR-IRS transmission and reflection coefficient and the transmission block length under reliability constraints. Attached Figure Description

[0075] Figure 1 This is the system model of the present invention;

[0076] Figure 2 This is a logic flowchart of the present invention;

[0077] Figure 3 This invention relates to the relationship between the average BLER and AP transmit power of two users at different interference powers, where N = 128, M = 4, β0 = -30dB, κ0 = 2, κ1 = 2.5, κ2 = 2.5 and κ3 = 2.3. AoA0=π / 3, AoD0=π / 3, AoD1=π / 6, AoD2=2π / 3, d0=40 meters, d1=100 meters, d2=50 meters, d3=50 meters T=200, α1=0.8, ξ1=0.2, F1=F2=300;

[0078] Figure 4 This invention relates the optimal transmission block length and power allocation coefficients under different interference powers, where N = 128, M = 4, β0 = -30dB, P = 25dBm, κ0 = 2, κ1 = 2.5, κ2 = 2.5 and κ3 = 2.3. AoA0=π / 3, AoD0=π / 3, AoD1=π / 6, AoD2=2π / 3, d0=40 meters, d1=100 meters, d2=50 meters, d3=50 meters ξ1=0.2, F1=F2=300;

[0079] Figure 5 This diagram illustrates the relationship between the optimal transmission block length and transmission coefficient under different interference powers in this invention, where N = 128, M = 4, β0 = -30dB, P = 25dBm, κ0 = 2, κ1 = 2.5, κ2 = 2.5 and κ3 = 2.3. AoA0=π / 3, AoD0=π / 3, AoD1=π / 6, AoD2=2π / 3, d0=40 meters, d1=100 meters, d2=50 meters, d3=50 meters F1 = F2 = 300; Detailed Implementation

[0080] The present invention will be further described below with reference to the accompanying drawings, both in terms of theory and specific implementation.

[0081] Reference Figure 1 , Figure 2 A short packet communication method assisted by a transmission-reflection type intelligent reflector under electromagnetic interference is described below:

[0082] Step A: Establish a downlink two-user non-orthogonal multiple access (NOMA) short packet communication system assisted by a simultaneously transmitting and reflecting intelligent reflective surface (STAR-IRS). This system includes an access point (AP) with one M-antenna, two single-antenna users (UE-1 and UE-2), and a STAR-IRS with N (N>1) passive elements. UE-1 is the transmitting user, and UE-2 is the reflecting user. Due to obstruction, the AP can only communicate with the users with the assistance of the STAR-IRS. The system includes an electromagnetic interference source that affects the received signal of the STAR-IRS. Assume that the location, transmission power, and transmission channel characteristics from the electromagnetic interference source to the STAR-IRS are known.

[0083] The specific implementation of step A is as follows:

[0084] Modeling Channel Coefficients: The channel coefficients between the AP and STAR-IRS are expressed as follows: The channel coefficients between STAR-IRS and UE-l are expressed as follows: Let be the antenna array response vector, t∈{M,N}, λ be the carrier wavelength, d=0.5λ be the spacing between STAR-IRS elements, and θ be the transmit angle or arrival angle of the corresponding channel. This represents the line-of-sight component of the corresponding link, where AoA0 and AoD0 are the angle of arrival and transmission angle from the AP to the STAR-IRS, respectively, and AoD... l Indicates the transmission angle from STAR-IRS to UE-1; These are the non-line-of-sight components of the corresponding links, and they respectively obey... and in This indicates that the mean is μ and the variance is σ. 2 The complex Gaussian distribution, I a Let a represent an identity matrix of size a; This represents the channel coefficient from the electromagnetic interference source to the STAR-IRS, where To obey The non-line-of-sight components; In STAR-IRS assisted communication, in order to meet the constraints that the impedance and magnetoresistance should be purely imaginary under passive and lossless conditions, the reflection and transmission coefficients of STAR-IRS have the following relationship with the corresponding phase coefficients: This condition, also known as the phase adjustment-related constraint, restricts the reflection and transmission phase coefficients of STAR-IRS to meet certain conditions.

[0085] Step B: Based on the system model established in Step A, derive the received signals of the two users under electromagnetic interference conditions; determine the order of continuous interference cancellation based on statistical channel state information, and further write out the instantaneous signal-to-interference-plus-noise ratio (SINR). The specific implementation of Step B is as follows:

[0086] The received signal at UE-1 is:

[0087] y1=G1s+H1s I +w

[0088] Assuming UE-2 is closer to STAR-IRS, the instantaneous SINRγ of UE-1 decoding x1 is obtained according to the NOMA principle. 1,1 for:

[0089]

[0090] Meanwhile, the expression for the received signal at UE-2 is:

[0091] y2=G2s+H2s I +w

[0092] UE-2 initially treats x2 as interference with decoding x1. At this point, the instantaneous SINRγ of UE-2 decoding x1... 2,1 for:

[0093]

[0094] If x1 is successfully decoded, then x1 is removed and x2 is decoded again. At this time, the instantaneous SINRγ of UE-2 decoding x2 is... 2,2 for:

[0095]

[0096] in The AP transmits a short packet signal with a total power of P, α l Let x represent the power allocation coefficient for the corresponding user and satisfy α1 + α2 = 1. l This represents the power normalization signal sent by the AP to UE-l, s I P represents the power-normalized interference signal emitted by the electromagnetic interference source. I Indicates the power of the interference signal; w indicates a mean of 0 and a variance of 0. Additive complex Gaussian white noise.

[0097] Step C: Based on the channel parameters, the number of wireless access point antennas M, and the number of STAR-IRS units N, the STAR-IRS performs phase adjustment based on statistical channel state information and a primary / secondary phase configuration strategy, analyzing and providing the distribution characteristics of instantaneous SINR; its specific implementation is as follows:

[0098] The channel coefficient from AP to STAR-IRS is Given a complex number field, the channel coefficients from STAR-IRS to UE-l (l∈{1,2}) are: The channel coefficient from the electromagnetic interference source to the STAR-IRS is Then the end-to-end channel coefficient from AP to UE-1 is: The end-to-end channel coefficient from the interference source to UE-1 is Where ξ l Let A represent the transmission and reflection coefficients of STAR-IRS, respectively. H This represents the conjugate transpose of matrix A. This represents the phase offset matrix designed for UE-1, where diag{·} represents a diagonal matrix with the elements within the brackets as diagonal elements, and φ n,l f represents the phase offset value from the nth STAR-IRS unit to UE-1. l This represents the power-normalized beamforming vector of the AP pointing to the UE-l, and G l It can be written as G l =A 1,l +A 2,l +A 3,l +A 4,l ,and

[0099]

[0100] Where β0 is the path loss at a unit reference distance of 1 meter, κ0 and κ l For the path loss exponent, K0 and K l Let d0 and d be Rice factors. l These are the distances from the AP to the STAR-IRS and from the STAR-IRS to the UE-1, respectively. M (AoD0) is the antenna array response vector, and AoD0 is the transmit angle from the AP to the STAR-IRS. and Represents the line-of-sight component. and Indicates the non-line-of-sight component; A 2,l and A 3,l Follows the pattern of having a mean of 0 and variances of 1 / 2 and 1 / 2 respectively. and The complex Gaussian distribution, when the number of IRS units is large, according to the central limit theorem, A 4,l It can be approximated as having a mean of 0 and a variance of 0. The complex Gaussian distribution, For cascaded channel G l The phase error, according to the PS-PSC strategy (J.Xu, Y.Liu, et al., "STAR-RISs: A Correlated T&R Phase-Shift Model and Practical Phase-Shift Configuration Strategies," IEEE J.Sel. Topics Signal Process., vol.16, no.5, pp.1097-1111, Aug.2022.), when l=2, has: and Then we can obtain When l=1 The interval is [-2] -1 π,2 -1 The uniform distribution of π can, when the number of IRS units is large, achieve the desired effect. If A is approximated as a complex Gaussian random variable, then A 1,1 The real and imaginary parts of the equation respectively follow the mean of . variance is Gaussian distribution and mean are variance is , where a is a Gaussian distribution. e,1 and b e,1 They are respectively (a M (AoD0)f1 H The real and imaginary parts of ) Based on the above analysis, G can be calculated. l The probability distribution of , where the real and imaginary parts respectively follow the mean of . variance is Gaussian distribution and mean are variance is Gaussian distribution, and

[0101]

[0102]

[0103] in Similarly Wherein, κ3 represents the path loss index. This is a non-line-of-sight component. When the number of IRS elements is large, B 1,l and B2,l Follows the pattern of having a mean of 0 and variances of 1 / 2 and 1 / 2 respectively. and The complex Gaussian distribution of H is further obtained. l Follows the pattern with mean 0 and variance of The complex Gaussian distribution is obtained. According to the moment matching theorem, the end-to-end channel gain |G| from AP to UE-l (l∈{1,2}) can be obtained. l | 2 Obeying shape parameters Scale parameter is The gamma distribution, the end-to-end channel gain |H from the interference source to UE-l (l∈{1,2}) l | 2 Obtains a shape parameter of 1 and a scale parameter of [missing information]. The gamma distribution of , where |·| represents the modulus of the complex number or the absolute value of the real number,

[0104]

[0105] And there are

[0106]

[0107] in, This represents the mean operation. and This represents the operations of taking the real part and taking the imaginary part, from which γ is obtained. 1,1 γ 2,1 and γ 2,2 The cumulative distribution functions are respectively

[0108]

[0109]

[0110] in,

[0111]

[0112] P represents the total power of the AP's transmitted signal, α l P represents the power allocation factor of UE-l. I Indicates the power of the interference signal; For the power of additive complex white Gaussian noise, W (a,b) (x) is the Whittaker W function and Show the hypergeometry of the confluence. Represents the gamma function;

[0113] Step D: Calculate the average block error rate (BLER) for both users using the formula in short packet communication. The specific implementation of step D is as follows:

[0114] According to the relevant formulas for short packet communication, given the signal-to-interference-plus-noise ratio γ, the short packet block size T, and the short packet BLERε, the maximum achievable rate of short packets, in bits per symbol, is approximately expressed as:

[0115]

[0116] Where C(γ)=log2(1+γ) represents the Shannon capacity, and V(γ)=(1-(1+γ)) -2 (log2e) 2 Q represents the channel divergence. -1 (·)express The inverse function of .

[0117] Assume the maximum achievable rate of UE-1 is R. l =F l / T, where F l Indicates the number of UE-1 information bits; the corresponding instantaneous SINRγ l,j (j∈{1,2}) under UE-l decoding x j BLERε l,j Approximately expressed as

[0118]

[0119] Based on instantaneous BLER and instantaneous SINR, the average BLER in the fading channel is... Represented as:

[0120]

[0121] in, Indicates γ l,j The probability density function.

[0122] according to An approximation of the average value in the fading channel. Further expressed as:

[0123]

[0124] in

[0125] Further using the Gauss-Chebyshev integration method, we can obtain:

[0126]

[0127] Where M x Let be the approximate order of the Gauss-Chebyshev integral.

[0128] Therefore, the average BLER of UE-1 and UE-2 is:

[0129]

[0130] in and They are respectively:

[0131]

[0132]

[0133] Step E: Based on the expressions calculated in Step D, under reliability constraints, further solve for the optimal power allocation coefficient, optimal transmission and reflection coefficient, and optimal transmission block length for NOMA. The specific implementation of Step E is as follows:

[0134] Represent the target BLER of the two users as Determine the optimal power allocation factor, optimal transmission block length, and optimal transmission / reflection factor. The specific steps for determining the optimal power allocation factor, optimal transmission / reflection factor, and optimal transmission block length are as follows:

[0135] 1.1 Given system parameters such as transmittance and reflection coefficients and power distribution coefficients, initialize the block length and limit it to [M]. min M max ],make

[0136] 1.2 will Substitute into the average BLER formula to calculate the corresponding average for the two users. 1.3 If the calculated average BLER satisfies or Let the minimum block length be T min =-1, which means there is no optimal solution in this case.

[0137] 1.4 If the calculated average BLER simultaneously satisfies and Let the minimum block length be T. min =M min .

[0138] 1.5 If none of the above conditions are met, then if the conditions are met... Under the condition that, let Calculate the corresponding average and This represents the floor function.

[0139] 1.6 When satisfied and Then let Otherwise

[0140] 1.7 Update or Continue with steps 1.5 to 1.6 until... Stop iteration, minimum block length

[0141] 1.8 Given the transmittance and reflectance coefficients, select a step size of δ to traverse the range α1, repeating steps 1.1 to 1.7 to obtain the block length T corresponding to each power allocation coefficient. min Then the minimum block length The corresponding power allocation coefficient is the optimal power allocation coefficient. min(·) calculates the minimum element in an array.

[0142] 1.9 Select a step size of δ to traverse the feasible range of ξ1, and repeat steps 1.1 to 1.8 to obtain the corresponding value for each transmission coefficient. So, the minimum common block length under the traversal of the transmission coefficients The corresponding transmittance is the optimal transmittance. The specific implementation process of this invention is as follows:

[0143] A short packet communication method assisted by a transmission-reflection type intelligent reflector under electromagnetic interference is described in the following steps:

[0144] Step A: Construct a STAR-IRS-assisted downlink two-user NOMA short packet communication system consisting of an Access Point (AP) with M=4 antennas, two single-antenna users (UE-1 and UE-2), and a STAR-IRS with N=128 passive elements. UE-1 is a transmitting user, and UE-2 is a reflecting user. Line-of-sight links exist between the STAR-IRS, the two users, and the AP. The location of the electromagnetic interference source is known, and it will affect the received signal of the STAR-IRS through non-line-of-sight links. The path loss indices from the AP to the STAR-IRS and from the STAR-IRS to UE-1 (l∈{1,2}) are κ0 and κ1, respectively. l Furthermore, the small-scale fading follows a Rice distribution, and the distances between them are d0 and d... l K0, K l The Rice factor; the channel coefficients between the AP and STAR-IRS are expressed as... The channel coefficients between STAR-IRS and UE-l (l∈{1,2}) are expressed as follows: Let be the antenna array response vector, t∈{M,N}, λ be the carrier wavelength, d=0.5λ be the spacing between STAR-IRS elements, and θ be the transmit angle or arrival angle of the corresponding channel. Represents the line-of-sight component of the corresponding link, where AoD l Indicates the transmission angle from STAR-IRS to UE-1. These are the non-line-of-sight components of the corresponding links, and they respectively obey... and This represents the channel coefficient from the electromagnetic interference source to the STAR-IRS, where κ3 represents the path loss exponent between the electromagnetic interference source and the STAR-IRS, and d3 represents the distance between the electromagnetic interference source and the STAR-IRS. To obey The non-line-of-sight components. Where β0 represents the path loss at a reference distance of 1 meter, and β0 = -30 dB, d0 = 40 meters, d1 = 100 meters, d2 = 50 meters, d3 = 50 meters. κ0=2, κ1=κ2=2.5, κ3=2.3, AoA0=π / 3, AoD0=π / 3, AoD1=π / 6, AoD2=2π / 3.

[0145] Step B: Based on the system model established in Step A, derive the received signals of the two users under electromagnetic interference environment; determine the order of continuous interference cancellation based on statistical channel state information, and further write out the instantaneous SINR.

[0146] Step C: Based on the channel parameters, the number of wireless access point antennas M and the number of STAR-IRS units N, the STAR-IRS performs phase adjustment based on the statistical channel state information and the primary and secondary phase configuration strategy, and analyzes and gives the distribution characteristics of instantaneous SINR.

[0147] Step D: Calculate the average BLER expression for the two users according to the formula in short packet communication;

[0148] Step E: Based on the expression calculated in step D, under reliability constraints... With a step size Δ = 0.01, the relationship between the average BLER and the optimal power allocation coefficient, optimal transmission and reflection coefficient, and optimal transmission block length is further obtained through the bisection method and one-dimensional traversal search algorithm.

[0149] Figure 3 The relationship between the average BLER and AP transmit power for two users under different interference powers is presented. The simulation results for both users are consistent with the theoretical results, verifying the accuracy of the theoretical derivation. Figure 3 It can be seen that as the AP transmit power increases, the average BLER decreases, and compared with UE-1, the increase in interference power has a greater impact on the system transmission performance of UE-2. Figure 4 The relationship between the optimal transport block length and power allocation coefficient for different interference powers is given, by... Figure 4 The optimal power allocation factor and optimal transmission block length can be obtained under reliability constraints, such as in P I When the power density is 20 dBm, the optimal power allocation factor is α1 = 0.15, and the optimal transmission block length of the system is... Symbols; secondly, as interference power increases, more power needs to be allocated to UE-2 to achieve optimal overall system transmission block length, such as P. I When the interference power is 23 dBm, the optimal power allocation factor increases to α1 = 0.22; finally, the increase in interference power has a deteriorating effect on the system transmission block length, such as compared to P I Optimal transport block length for a system of 20 dBm P I When the value is 25dBm, the optimal transport block length of the system is: symbol. Figure 5 The relationship between the optimal transmit block length and the STAR-IRS transmission coefficient for different interference powers is given, from Figure 5 It can be found that the optimal transmission coefficient range or specific value under reliability constraints makes the system transmission block length optimal, such as in P I When ξ = 20dBm, it can reach ξ1∈[0.2,0.36] in the interval. The symbol, and as the interference power increases, the system transmission block length also increases, such as in P I When ξ = 25 dBm, it reaches its maximum value when ξ1 = 0.39. Symbols. As can be seen from the above examples, the intensity of electromagnetic interference has a significant impact on the system's transmit block length.

Claims

1. A method for electromagnetic interference (EMI) -under transmission reflection-type intelligent reflecting surface (IRS) -assisted short packet communication, the method comprising: The specific implementation steps are as follows: Step A, establishing a simultaneously transmitting and reflecting-intelligent reflecting surface (STAR-IRS) assisted downlink two-user non-orthogonal multiple access (NOMA) short packet communication system, the system comprising an M-antenna wireless access point (AP), two single-antenna users (UE-1 and UE-2) and a STAR-IRS with N (N>1) passive units, wherein UE-1 is a transmitting user and UE-2 is a reflecting user, and the AP can only communicate with the users with the assistance of the STAR-IRS due to obstruction shielding; the system contains an electromagnetic interference source which will affect the received signal of the STAR-IRS; it is assumed that the position, transmission power and transmission channel characteristics of the electromagnetic interference source to the STAR-IRS are known; Step B, according to the system model established in step A, the received signal of the two users in the electromagnetic interference environment is derived; according to the statistical channel state information, the order of successive interference cancellation is determined, and the instantaneous signal-to-interference-plus-noise ratio (SINR) is further written out; Step C, according to the channel parameters, the number of wireless access point antennas M and the number of STAR-IRS units N, the STAR-IRS adjusts the phase based on the statistical channel state information according to the primary-secondary phase-shift configuration (PS-PSC) strategy, and the distribution characteristics of the instantaneous SINR are analyzed and given; the specific implementation is as follows: The channel coefficient from the AP to the STAR-IRS is hAP→STAR-IRS= hAP→STAR-IRS,1+ hAP→STAR-IRS,2. The channel coefficient from the STAR-IRS to the UE-l (l e {1, 2}) is hSTAR-IRS→UE-l= hSTAR-IRS→UE-l,1+ hSTAR-IRS→UE-l,2. The channel coefficient from the EMI source to the STAR-IRS is hEMI→STAR-IRS= hEMI→STAR-IRS,1+ hEMI→STAR-IRS,2. The end-to-end channel coefficient from the AP to the UE-l is hAP→UE-l= hAP→STAR-IRS· hSTAR-IRS→UE-l. The end-to-end channel coefficient from the EMI source to the UE-l is hEMI→UE-l= hEMI→STAR-IRS· hSTAR-IRS→UE-l. where ξ l denote the transmission and reflection coefficients of the STAR-IRS, respectively, A H denotes the conjugate transpose of the matrix A, denotes the phase shift matrix designed for the UE-l, diag{·} denotes a diagonal matrix with the elements in the brackets as the diagonal elements, φ n,l denotes the phase shift value of the n-th STAR-IRS element to the UE-l, f l denotes the power-normalized beamforming vector of the AP pointing to the UE-l, and G l can be written as G l = A 1,l + A 2,l + A 3,l + A 4,l , and Where β0 is the path loss at a unit reference distance of 1 meter, κ0 and κ l For the path loss exponent, K0 and K l Let d0 and d be Rice factors. l These are the distances from the AP to the STAR-IRS and from the STAR-IRS to the UE-1, respectively. M (AoD0) is the antenna array response vector, and AoD0 is the transmit angle from the AP to the STAR-IRS. and Represents the line-of-sight component. and Indicates the non-line-of-sight component; A 2,l and A 3,l Follows the pattern of having a mean of 0 and variances of 1 / 2 and 1 / 2 respectively. and The complex Gaussian distribution, when the number of IRS units is large, according to the central limit theorem, A 4,l It can be approximated as having a mean of 0 and a variance of 0. The complex Gaussian distribution, For cascaded channel G l The phase error, according to the PS-PSC strategy, when l=2, has and Then we can obtain When l=1 The interval is [-2] -1 π,2 -1 The uniform distribution of π can, when the number of IRS units is large, achieve the desired effect. If A is approximated as a complex Gaussian random variable, then A 1,1 The real and imaginary parts of the equation respectively follow the mean of . variance is Gaussian distribution and mean are variance is , where a is a Gaussian distribution. e,1 and b e,1 They are respectively (a M (AoD0)f1 H The real and imaginary parts of ) Based on the above analysis, G can be calculated. l The probability distribution of , where the real and imaginary parts respectively follow the mean of . variance is Gaussian distribution and mean are variance is Gaussian distribution, and wherein Similarly wherein, κ3 represents a path loss exponent, is a non-line of sight component; when the number of IRS elements is large, B 1,l and B 2,l obeys a complex Gaussian distribution with mean 0 and variance and further, H l obeys a complex Gaussian distribution with mean 0 and variance ; according to the moment matching theorem, the end-to-end channel gain |G l | 2 obeys a Gamma distribution with shape parameter and scale parameter , the end-to-end channel gain |H l | 2 obeys a Gamma distribution with shape parameter 1 and scale parameter , wherein |·| represents the modulus of a complex number or the absolute value of a real number, And wherein denotes the mean operation, and denotes the take real part and take imaginary part operations, respectively, whereby γ 1,1 , γ 2,1 and γ 2,2 have cumulative distribution functions given by Wherein, P denotes the total power of the AP transmitted signal, a l denotes the power allocation factor of UE-l, P I denotes the interference signal power; W is the power of the additive complex Gaussian white noise, (a,b) (x) is the Whittaker W function and denotes the confluent hypergeometric function, denotes the gamma function; Step D, the average block error rate (BLER) expressions of the two users are calculated according to the formulas in short packet communication, respectively; Step E, according to the expressions calculated in step D, the NOMA optimal power allocation coefficient, the optimal transmitting and reflecting coefficient and the optimal transmission block length are further solved under the reliability constraint.

2. The electromagnetic interference under the transmitting and reflecting type intelligent reflecting surface assisted short packet communication method according to claim 1, wherein the specific implementation of step A is as follows: Modeling Channel Coefficients: The channel coefficients between the AP and the STAR-IRS are denoted as The channel coefficients between the STAR-IRS and the UE-l are denoted as is the antenna array response vector, t e {M, N}, l is the carrier wavelength, d = 0.5l is the spacing of the STAR-IRS elements, and 0 is the transmit angle or the angle of arrival corresponding to the channel, denotes the line-of-sight component of the corresponding link, where AoA0, AoD0are the angle of arrival and the angle of departure from the AP to the STAR-IRS, respectively, and AoD l denotes the angle of departure from the STAR-IRS to the UE-l; is the non-line-of-sight component of the corresponding link and follows and where denotes a complex Gaussian distribution with mean p and variance 2 a denotes an identity matrix of size a; denotes the channel coefficients from the electromagnetic interference source to the STAR-IRS, where is the non-line-of-sight component following In STAR-IRS assisted communications, to satisfy the constraint that the electric impedance and the magnetic impedance should be purely imaginary under the passive and lossless condition, there is the following relationship between the reflection and transmission coefficients of the STAR-IRS and the corresponding phase coefficients: This condition is also called the phase adjustment related constraint condition, which limits the reflection and transmission phase coefficients of the STAR-IRS to satisfy ​ 3. The electromagnetic interference under the transmitting and reflecting type intelligent reflecting surface assisted short packet communication method according to claim 1, wherein the specific implementation of step B is as follows: The received signal at UE-1 is: y1 = G1s + H1s I +w Assume UE-2 is closer to STAR-IRS, so according to NOMA principle, the instantaneous SINR γ of UE-1 decoding x1 is 1,1 is: At the same time, the received signal expression of UE-2 is y2 = G2s + H2s I + w UE-2 first decodes x1 treating x2 as interference, in which case the instantaneous SINR γ of UE-2 decoding x1 is 2,1 where: If xi is successfully decoded, remove xi and decode x2, at which time UE-2 decodes the instantaneous SINR γ of x2 2,2 is: wherein is the total power of the AP transmitted Pshort packet signal, a l represents the power allocation coefficient of the corresponding user and satisfies a1+a2=1, x l represents the power normalization signal of the AP transmitted to UE-1, s I represents the power normalization interference signal of the electromagnetic interference source transmitted, P I represents the interference signal power; w represents the additive complex Gaussian white noise with mean 0 and variance .

4. The electromagnetic interference under the transmitting and reflecting type intelligent reflecting surface assisted short packet communication method according to claim 1, wherein the specific implementation of step D is as follows: According to the related formulas of short packet communication, when the signal-to-interference-plus-noise ratio γ, the short data packet block length T and the short data packet BLER ε are given, the maximum achievable rate of the short data packet is approximately represented as: wherein C(y) = log2(l + y) represents the Shannon capacity, V(y) = (1 - (1 + y) -2 )(log2e) 2 represents the channel dispersion, Q -1 (·) represents the inverse function of Assume the maximum achievable rate of UE-l is R l = F l / T, where F l denotes the number of information bits of UE-l; the corresponding instantaneous SINR γ l,j (j e {1,2}) under which UE-l decodes x j with BLER ε l,j is approximately given by According to the instantaneous BLER and the instantaneous SINR, the average is expressed as: wherein denotes the probability density function of γ l,j denotes the probability density function of γ According to the approximation, the average is further expressed as: wherein Further, the Gauss-Chebyshev integral method is used to obtain: where M x is the Gauss-Chebyshev integration approximation order, Therefore, the average BLER of UE-1 and UE-2 is: wherein and are respectively:

5. The method of claim 1, wherein the step E is implemented as follows: The target BLER of two users is expressed as The optimal power allocation coefficient, the optimal transmission block length and the optimal transmission-reflection coefficient are determined. The specific steps of determining the optimal power allocation coefficient, the optimal transmission block length and the optimal transmission-reflection coefficient are as follows: 1.1 Initialize block length under given system parameters of transreflectance, power distribution factor, etc. Restrict block length to [M min ,M max ] Let 1.2 Bring into the average BLER formula the corresponding average BLER of the two users 1.3 If the calculated average BLER satisfies or Let the minimum block length T min = -1, which means that there is no optimal solution in this case. 1.4 If the computed average BLER simultaneously satisfies and then let the minimum block length T min = M min ; 1.5 If none of the above conditions are met, under the condition that denotes the ceiling function.​​​ 1.6 Let and then let else let 1.7 Update or Continue steps 1.5 to 1.6 until Stop iteration, minimum block length 1.8 Repeat steps 1.1 to 1.7 with a step size of δ to traverse the range of α1, and obtain the block length T corresponding to each power allocation factor min Then the minimum block length is The corresponding power allocation factor is the optimal power allocation factor min(·) denotes the calculation of the minimum element in an array; 1.9 Selecting the step size as δ to traverse the feasible range of ξ1, repeating steps 1.1 to 1.8, obtaining the corresponding Then the minimum common block length under the traversed transmission coefficients is The transmission coefficient corresponding to it is the optimal transmission coefficient

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