Intelligent reflecting surface auxiliary short packet communication method in electromagnetic interference environment

Abstract

A short packet communication method assisted by an intelligent reflecting surface in an electromagnetic interference environment is characterized in that in a reflective intelligent reflecting surface assisted two-user non-orthogonal multiple access system, the intelligent reflecting surface assists remote users in communication, and a wireless access point sends a short data packet to the two users to realize high-reliability and low-delay communication; an electromagnetic interference source exists in the system, and transmitting power of the electromagnetic interference source and characteristics of transmission channels from the electromagnetic interference source to an intelligent reflecting surface and two users are assumed to be known; the method comprises the following steps: firstly, determining signal to interference plus noise ratio statistical characteristics of decoding of two users by utilizing statistical channel state information; secondly, determining an average block error rate of the two users under a fading channel according to a short packet communication related formula; and finally, under the reliability constraint, determining the optimal power distribution coefficient and the minimum common block length of the system. According to the invention, high-reliability and low-delay communication is realized.

Description

Technical Field

[0001] The present invention relates to a method for optimizing the design of a reflective intelligent reflecting surface (IRS)-aided short-packet communication system in an environment with electromagnetic interference, belonging to the field of new-generation mobile communication technologies. Background Art

[0002] Ultra-Reliable and Low-Latency Communication (URLLC) is one of the main application scenarios of future mobile communication technologies, aiming to provide ultra-high reliability (above 99.999%) and ultra-low latency (≤1 ms). How to achieve URLLC remains one of the difficulties faced by the current wireless communication field.

[0003] Technologies such as short-packet communication, IRS, and Non-orthogonal Multiple Access (NOMA) are regarded as key technologies to achieve URLLC. Short-packet communication refers to the communication in which the block length of data is very short, usually only hundreds of bits. Therefore, short-packet communication can effectively reduce the system transmission delay (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.). IRS consists of a large number of programmable passive units, which can actively adjust the reflection or transmission of incident waves. IRS-aided communication improves the communication quality by changing the wireless propagation environment (Q. Wu, S. Zhang, B. Zheng, et al. “Intelligent reflecting surface-aided wireless communications: A tutorial,” IEEE Trans. Commun., vol. 69, no. 5, pp. 3313-3351, May 2021.). In a multi-user scenario, NOMA technology is considered to be one of the most promising multiple access technologies, which significantly improves the spectrum efficiency by allowing different users to share the same time-frequency resources.

[0004] The Chinese invention patent with the publication number CN115442816B discloses a method for realizing reflective IRS-assisted NOMA short-packet communication. For the two-user scenario, it designs the system using statistical channel state information and proposes a NOMA power allocation and transmission block length optimization algorithm. The Chinese invention patent with the publication number CN116170856A discloses a design method for a simultaneous transmission and reflection IRS-assisted NOMA short-packet communication system. It optimally designs the coefficients of the simultaneous transmission and reflection IRS, NOMA power allocation, and transmission block length for the two-user scenario using statistical channel state information to achieve URLLC. The above research on IRS-assisted NOMA short-packet communication assumes no additional electromagnetic interference in the transmission environment. In an actual wireless communication system, in addition to being affected by fading and Gaussian white noise, the communication system is often affected by co-channel interference signals. Since the IRS can not only enhance the useful signal but also enhance the interference signal, when there is co-channel interference, the performance of the IRS-assisted NOMA short-packet communication system designed in an environment without additional electromagnetic interference deteriorates severely. It is necessary to redesign parameters such as NOMA power allocation and transmission block length of the IRS-assisted NOMA short-packet communication system for the electromagnetic interference environment to achieve URLLC.

[0005] Currently, there is relatively little research on how to optimally design an IRS-assisted NOMA short-packet communication system to achieve URLLC in an environment with electromagnetic interference. Therefore, it is very necessary to study the optimal design of an IRS-assisted NOMA short-packet communication system to achieve URLLC in an environment with electromagnetic interference. Summary of the Invention

[0006] The present invention provides an intelligent reflecting surface-assisted short-packet communication method in an electromagnetic interference environment to achieve high-reliability and low-latency communication URLLC.

[0007] The object of the present invention is achieved by the following technical solutions:

[0008] An intelligent reflecting surface-assisted short-packet communication method in an electromagnetic interference environment, the specific implementation steps are as follows:

[0009] Step A: Establish a reflecting intelligent reflecting surface (IRS)-assisted downlink two-user non-orthogonal multiple access (NOMA) short-packet communication system. The system includes a single-antenna wireless access point (AP), two single-antenna users: a near user UE1, a far user UE2, and a reflecting IRS with N passive elements. Among them, AP communicates directly with the near user UE1 through the direct link AP-UE1, and AP communicates with the far user UE2 through the cascaded channel with the help of the reflecting IRS. The cascaded channel includes two communication links, namely AP-IRS and IRS-UE2. At the same time, an electromagnetic interference source will affect the received signals of UE1, the reflecting IRS, and UE2 respectively. There is an electromagnetic interference source in the system. Assume that the transmission power of the electromagnetic interference source and the transmission channel characteristics from the electromagnetic interference source to the reflecting IRS and the two users are known.

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

[0011] Step C: According to the channel parameters and the number of IRS units N, the reflecting IRS performs optimal continuous phase adjustment based on the statistical channel state information, and analyzes and gives the distribution characteristics of the instantaneous SINR. The specific implementation is as follows:

[0012] The end-to-end channel gains from AP to UE1 and from AP to UE2 are |g 0 | 2 and |G| 2 , respectively. The end-to-end channel gains from the electromagnetic interference source to UE1 and to UE2 are |g 5 | 2 and |H| 2 , respectively. Where |·| represents the modulus of a complex number or the absolute value of a real number, and g 0 , G, g 5 and H represent the end-to-end channel fading coefficients from AP to UE1, from AP to UE2, from the electromagnetic interference source to UE1, and from the electromagnetic interference source to UE2, respectively. When optimal continuous phase adjustment is adopted, according to the central limit theorem, |G| follows a Rice distribution, and its average power and Rice factor are and where β 0 represents the path loss at a reference distance of 1 meter, β represents the path loss exponent, and d 1is the distance from the AP to the center of the reflective IRS, \(d\) 2 is the distance from the center of the reflective IRS to UE2, \(K\) 1 and \(K\) 2 is the Rice factor, \(K\) c \(=(K\) 1 + 1)(K\) 2 + 1); \(H\) follows a circularly symmetric complex Gaussian distribution with mean 0 and variance where \(d\) 3 and \(d\) 4 are the distances from the electromagnetic interference source to the center of the reflective IRS and UE2 respectively; since both \(H\) and \(g\) 5 follow circularly symmetric complex Gaussian distributions, so \(|H|\) 2 and \(|g\) 5 |\) 2 follow gamma distributions with shape parameter 1 and scale parameters \(\mu\) y and \(\mu\) 5 respectively, where \(\mu\) 5 \(=\beta\) 0 \(d\) 5 -β and \(d\) 5 represents the distance from the electromagnetic interference source to UE1; both \(|G|\) and \(|g\) 0 |\) follow Rice distributions, so \(|G|\) 2 and \(|g\) 0 |\) 2 both follow a mixed gamma distribution, and their probability density functions are respectively and where \(I\) and \(V\) represent the summation order, and are the weight coefficients,

[0013] \(\Gamma(\cdot)\) represents the gamma function, \(K\) 0 is the Rice factor, represents the mean operation, \(d\) 0 is the distance from the AP to UE1;

[0014] According to the probability density functions of the above channel gains, the cumulative distribution functions of the instantaneous SINR \(\gamma\) 12 , \(\gamma\) 11 , \(\gamma\) 22 can be obtained, that is

[0015]

[0016] where is the cumulative distribution function of \(\gamma\) lι \((l, \iota\in\{1, 2\})\), \(P\)I Denote the transmission power of the electromagnetic interference source, is the power allocation coefficient corresponding to UE1, satisfying P represents the transmission power of the AP, 2 F 1 (·) represents the Gaussian hypergeometric function, and γ(·) represents the lower incomplete gamma function;

[0017] Step D: Calculate the average block error rate (BLER) expressions of the two users according to the formulas in short-packet communication;

[0018] Step E: According to the expressions calculated in Step D, further solve for the NOMA optimal power allocation coefficient and the minimum common block length under the reliability constraint.

[0019] Furthermore:

[0020] The specific implementation of Step A is as follows:

[0021] Model the channel coefficients: The communication links AP-UE1, AP-IRS, and IRS-UE2 have the same path loss exponent β and the small-scale fading follows the Rice distribution. The channel coefficient between AP and UE1 is expressed as ), the channel coefficient between AP and the nth (n ∈ {1, 2,..., N}) unit of the reflective IRS is expressed as ), and the channel coefficient between the nth unit of the reflective IRS and UE2 is expressed as ), where and represent the corresponding line-of-sight transmission components, and are the corresponding non-line-of-sight transmission components, which follow the circularly symmetric complex Gaussian distribution with a mean of 0 and a variance of 1; and represent the channel coefficients from the electromagnetic interference source to the nth unit of the reflective IRS, UE2, and UE1 respectively, where h 3n 、h 4 and h 5 follow the circularly symmetric complex Gaussian distribution with a mean of 0 and a variance of 1.

[0022] The specific implementation of Step B is as follows:

[0023] The received signals at UE1 and UE2 are respectively:

[0024]

[0025] where is the NOMA superimposed signal sent by the AP, sl represents the power - normalized signal sent by the AP to UE1, s I represents the power - normalized interference signal emitted by the electromagnetic interference source;

[0026] G 1 =[g 11 , g 12 ,..., g 1N , G 2 =[g 21 , g 22 ,..., g 2N T and G 3 =[g 31 , g 32 ,…, g 3N respectively represent the channel coefficient matrices between the AP and the reflective IRS, between the reflective IRS and UE2, and between the electromagnetic interference source and the reflective IRS. [g 21 , g 22 ,..., g 2N T represents the transpose of the vector [g 21 , g 22 ,..., g 2N . θ represents the phase - shift matrix of the reflective IRS, which is represents a diagonal matrix with as diagonal elements, and φ n represents the phase - shift value of the n - th unit of the reflective IRS. When the optimal continuous phase - adjustment strategy is adopted arg(·) represents the complex - angle - seeking function; w 1 and w 2 represent additive complex Gaussian white noise with a mean of 0 and a variance of ;

[0027] Furthermore, it can be obtained that the end - to - end channel fading coefficients G between the AP and UE2 and H between the electromagnetic interference source and UE2 are respectively:

[0028]

[0029] The AP uses statistical channel state information for system design. When , according to the NOMA principle, the AP allocates a small power - allocation coefficient to the user with a large channel gain. Therefore UE1 needs to correctly decode and remove the signal s 2 of UE2 first, and then decode its own signal s 1 . However, since UE2 is allocated a larger power coefficient, it can regard s 1 as an interference signal and directly decode its own signal s​​2 ; Therefore, the UE1 decodes the signal s 2 and s 1 and the SINRs of the UE2 decoding the signal s 2 are respectively:

[0030]

[0031] The specific implementation of step D is as follows:

[0032] According to the short-packet communication related formula, when the given signal-to-interference-plus-noise ratio γ, the short data packet block length size T d and the short data packet BLER ε are given, the maximum achievable rate of the short data packet, in units of bits per symbol, is approximately expressed as:

[0033]

[0034] where C(γ) = log 2 (1 + γ) represents the Shannon capacity, V(γ) = (1 - (1 + γ) -2 )(log 2 e) 2 represents the channel divergence, Q -1 (·) represents the inverse function of;

[0035] Assume that the physical layer information rates of the two users are R ι = F ι / T d , where F ι represents the number of information bits; The instantaneous BLERs of the UE1 decoding the signals s 2 , s 1 and the UE2 decoding the signal s 2 are approximately expressed as

[0036] According to the instantaneous BLER and the instantaneous SINR, the average in the fading channel is expressed as:

[0037]

[0038] where, represents the probability density function of γ lι ;

[0039] According to the approximation of, the average in the fading channel is further expressed as:

[0040]

[0041] where

[0042] Furthermore, by using the Gauss-Chebyshev integration method, we can obtain:

[0043]

[0044] where J is the approximation order of the Gauss-Chebyshev integration,

[0045] Therefore, the average BLER of UE1 and UE2 is:

[0046]

[0047] where and are respectively:

[0048]

[0049] The specific implementation of step E is as follows:

[0050] Express the target BLER of the two users as Determine the optimal power allocation coefficient and the minimum common block length. The specific steps for determining the optimal power allocation coefficient and the minimum common block length are as follows:

[0051] 1.1 Given the system parameters N, K 0 , K 1 , K 2 , d 0 , d 1 , d 2 , d 3 , d 4 , d 5 , β 0 , β, P, P I , F 1 , F 2 and Initialize the block length T d , and limit the block length within [M min , M max . Let T - = M min , T + = M max ;

[0052] 1.2 Substitute the block lengths T - , T + into the average BLER formula to calculate the corresponding average of the two users

[0053] 1.3 If the calculated average BLER satisfies or Let the minimum block length be T min = -1, which means there is no solution;

[0054] 1.4 If the calculated average BLER satisfies both and then let the minimum block length T min = M min ;

[0055] 1.5 If the above conditions are not met, under the condition that T + - T - ≠ 1, let Calculate the corresponding average and represents the ceiling function;

[0056] 1.6 When and then let otherwise let

[0057] 1.7 Update T - or T + , continue from step 1.5 to 1.6 until T + - T - = 1 to stop the iteration, and the minimum block length T min = T + ;

[0058] 1.8 Select a step size of Δ to traverse the value range of, repeat steps 1.1 to 1.7 to obtain the minimum block length T min corresponding to each power allocation coefficient, then let the corresponding power allocation coefficient is the optimal power allocation coefficient where min(·) represents calculating the minimum element in an array.

[0059] The core of the present invention lies in firstly deriving the closed - form expression of the cumulative distribution function of the instantaneous SINR of two - user decoding in an electromagnetic interference environment, and further deriving the closed - form expression of the average BLER. Finally, under the reliability constraint, URLLC is achieved by jointly optimizing the NOMA power allocation coefficient and the minimum common block length. BRIEF DESCRIPTION OF THE DRAWINGS

[0060] Figure 1 is the system model of the present invention;

[0061] Figure 2 is the logic flow chart of the present invention;

[0062] Figure 3 For the relationship between the minimum common block length and the optimal power allocation coefficient when the transmission power P of the electromagnetic interference source, i.e., there is no electromagnetic interference, in the present invention, where N = 64, β I = 0, where N = 64, β 0 = -20 dB, K 0 = K 1 = K 2 = 5, d 0 = 30 m, d 1 = 50 m, d 2 = 60 m, d 3 = d 4 = d 5 = 50 m, β = 2, P = 55 dBm, F 1 = F 2 = 200;

[0063] Figure 4 For the relationship between the minimum common block length and the optimal power allocation coefficient when there is electromagnetic interference and the transmission power P of the electromagnetic interference source is I = 25 dBm in the present invention, where N = 64, β 0 = -20 dB, K 0 = K 1 = K 2 = 5, d 0 = 30 m, d 1 = 50 m, d 2 = 60 m, d 3 = d 4 = d 5 = 50 m, β = 2, P = 55 dBm, F 1 = F 2 = 200. Specific implementation manners

[0064] The present invention will be further described below from both theoretical and specific implementation aspects with reference to the accompanying drawings.

[0065] Refer to Figure 1 , Figure 2 , an intelligent reflecting surface assisted short-packet communication method in an electromagnetic interference environment, and the specific implementation steps are as follows:

[0066] Step A: Establish a downlink two-user non-orthogonal multiple access (NOMA) short-packet communication system assisted by a reflective intelligent reflecting surface (IRS). The system includes a single-antenna wireless access point (AP), two single-antenna users: a near user UE1, a far user UE2, and a reflective IRS with N passive elements. Among them, the AP communicates directly with the near user UE1 through the direct link AP-UE1, and the AP communicates with the far user UE2 through the cascaded channel with the help of the reflective IRS. The cascaded channel includes two communication links, namely AP-IRS and IRS-UE2. At the same time, an electromagnetic interference source will affect the received signals of UE1, the reflective IRS, and UE2 respectively. There is an electromagnetic interference source in the system. Assume that the transmission power of the electromagnetic interference source and the transmission channel characteristics from the electromagnetic interference source to the reflective IRS and the two users are known.

[0067] Step B: According to the system model established in Step A, deduce the received signals of the two users in the electromagnetic interference environment. According to the statistical channel state information, determine the order of successive interference cancellation, and further write out the instantaneous signal-to-interference-plus-noise ratio (SINR).

[0068] Step C: Based on the channel parameters and the number of reflective IRS elements N, the reflective IRS performs optimal continuous phase adjustment based on the statistical channel state information, and analyzes and gives the distribution characteristics of the instantaneous SINR. The specific implementation is as follows:

[0069] The end-to-end channel gains from the AP to UE1 and from the AP to UE2 are |g 0 | 2 and |G| 2 , respectively. The end-to-end channel gains from the electromagnetic interference source to UE1 and to UE2 are |g 5 | 2 and |H| 2 , respectively, where |·| represents the modulus of a complex number or the absolute value of a real number, and g 0 , G, g 5 and H represent the end-to-end channel fading coefficients from the AP to UE1, from the AP to UE2, from the electromagnetic interference source to UE1, and from the electromagnetic interference source to UE2, respectively. When optimal continuous phase adjustment is adopted, according to the central limit theorem, |G| follows a Rice distribution, and its average power and Rice factor are and where β 0 represents the path loss at a reference distance of 1 meter, β represents the path loss exponent, and d 1is the distance from the AP to the center of the reflective IRS, \(d\) 2 is the distance from the center of the reflective IRS to UE2, \(K\) 1 , \(K\) 2 is the Rice factor, \(K\) c =(K 1 + 1)(K 2 + 1); \(H\) follows a circularly symmetric complex Gaussian distribution with a mean of 0 and a variance of where d 3 , \(d\) 4 are the distances from the electromagnetic interference source to the center of the reflective IRS and UE2 respectively; since both \(H\) and \(g\) 5 follow a circularly symmetric complex Gaussian distribution, so \(|H|\) 2 and \(|g\) 5 |\) 2 follow a gamma distribution with a shape parameter of 1 and scale parameters of \(\mu\) y and \(\mu\) 5 respectively, where \(\mu\) 5 =\(\beta\) 0 d 5 -β , \(d\) 5 represents the distance from the electromagnetic interference source to UE1; \(|G|\) and \(|g\) 0 |\) both follow a Rice distribution, so \(|G|\) 2 and \(|g\) 0 |\) 2 both follow a mixed gamma distribution, and their probability density functions are respectively and where \(I\) and \(V\) represent the summation order, and are the weight coefficients,

[0070] \(\Gamma(\cdot)\) represents the gamma function, \(K\) 0 is the Rice factor, represents the mean operation, \(d\) 0 is the distance from the AP to UE1;

[0071] According to the probability density functions of the above channel gains, the cumulative distribution functions of the instantaneous SINR \(\gamma\) 12 , \(\gamma\) 11 , \(\gamma\) 22 can be obtained, that is

[0072]

[0073]

[0074] where is \(\gamma\)lι (l, ι ∈ {1, 2}) cumulative distribution function, P I represents the transmission power of the electromagnetic interference source is the power allocation coefficient corresponding to UEl, satisfying P represents the transmission power of the AP 2 F 1 (·) represents the Gaussian hypergeometric function, γ(·) represents the lower incomplete gamma function;

[0075] Step D: Calculate the average block error rate Block ErrorRate, BLER expressions of the two users respectively according to the formulas in short-packet communication.

[0076] Step E: According to the expressions calculated in Step D, further solve for the NOMA optimal power allocation coefficient and the minimum common block length under the reliability constraint.

[0077] Furthermore:

[0078] The specific implementation of Step A is as follows:

[0079] Model the channel coefficients: The communication links AP-UE1, AP-IRS, and IRS-UE2 have the same path loss exponent β and the small-scale fading follows the Rice distribution. The channel coefficient between AP and UE1 is expressed as ), the channel coefficient between AP and the nth (n ∈ {1, 2, … N}) unit of the reflective IRS is expressed as ), the channel coefficient between the nth unit of the reflective IRS and UE2 is expressed as ), where and represent the corresponding line-of-sight transmission components and are the corresponding non-line-of-sight transmission components, following the circularly symmetric complex Gaussian distribution with a mean of 0 and a variance of 1; and represent the channel coefficients from the electromagnetic interference source to the nth unit of the reflective IRS, UE2, and UE1 respectively, where h 3n 、h 4 and h 5 follow the circularly symmetric complex Gaussian distribution with a mean of 0 and a variance of 1.

[0080] The specific implementation of Step B is as follows:

[0081] The received signals at UE1 and UE2 are respectively:

[0082]

[0083] where is the NOMA superimposed signal sent by the AP, s l represents the power-normalized signal sent by the AP to UEl, s I represents the power-normalized interference signal emitted by the electromagnetic interference source;

[0084] G 1 =[g 11 , g 12 ,..., g 1N , G 2 =[g 21 , g 22 ,..., g 2N T and G 3 =[g 31 , g 32 ,…, g 3N respectively represent the channel coefficient matrices between the AP and the reflective IRS, the reflective IRS and UE2, and the electromagnetic interference source and the reflective IRS. [g 21 , g 22 ,..., g 2N T represents the transpose of the vector [g 21 , g 22 ,..., g 2N . θ represents the phase shift matrix of the reflective IRS, which is represents the diagonal matrix with n as the diagonal elements. φ arg(·) represents the complex angle function; w 1 and w 2 represent additive complex Gaussian white noise with a mean of 0 and a variance of ;

[0085] Furthermore, it can be obtained that the end-to-end channel fading coefficient G between the AP and UE2 and the end-to-end channel fading coefficient H between the electromagnetic interference source and UE2 are respectively:

[0086]

[0087] The AP uses statistical channel state information for system design. When , according to the NOMA principle, the AP assigns a small power allocation coefficient to the user with a large channel gain. Therefore UE1 needs to correctly decode and remove the signal s of UE2 2 , and then decode its own signal s 1 , while UE2, due to being assigned a larger power coefficient, can use s​​1 Treat the interference signal as directly decoding its own signal s 2 ; Therefore, UE1 decodes the signal s 2 and s 1 and the SINR of UE2 decoding the signal s 2 are respectively:

[0088]

[0089] The specific implementation of step D is as follows:

[0090] According to the short-packet communication related formula, when the given signal-to-interference-plus-noise ratio γ, the short data packet block length size T d and the short data packet BLER ε are given, the maximum achievable rate of the short data packet, in units of bits per symbol, is approximately expressed as:

[0091]

[0092] where C(γ) = log 2 (1 + γ) represents the Shannon capacity, V(γ) = (1 - (1 + γ) -2 )(log 2 e) 2 represents the channel divergence, Q -1 (·) represents the inverse function of;

[0093] Assume that the physical layer information rate of the two users is R ι = F ι / T d , where F ι represents the number of information bits; UE1 decodes the signal s 2 , s 1 and the instantaneous BLER of UE2 decoding the signal s 2 is approximately expressed as

[0094] According to the instantaneous BLER and the instantaneous SINR, the average in the fading channel is expressed as:

[0095]

[0096] where, represents the probability density function of γ lι ;

[0097] According to the approximation of, the average in the fading channel is further expressed as:

[0098]

[0099] where Further using the Gauss-Chebyshev integration method, we can obtain:

[0100]

[0101] where J is the approximation order of the Gauss-Chebyshev integration.

[0102] Therefore, the average BLER of UE1 and UE2 is:

[0103]

[0104] where and are respectively:

[0105]

[0106] The specific implementation of step E is as follows:

[0107] Express the target BLER of the two users as Determine the optimal power allocation coefficient and the minimum common block length. The specific steps for determining the optimal power allocation coefficient and the minimum common block length are as follows:

[0108] 1.1 Given the system parameters N, K 0 , K 1 , K 2 , d 0 , d 1 , d 2 , d 3 , d 4 , d 5 , β 0 , β, P, P I , F 1 , F 2 and Initialize the block length T d , and limit the block length within [M min , M max . Let T - = M min , T + = M max ;

[0109] 1.2 Substitute the block lengths T - , T + into the average BLER formula to calculate the corresponding average of the two users 1.3 If the calculated average BLER satisfies or Let the minimum block length be T min =-1, indicating no solution;

[0110] 1.4 If the calculated average BLER satisfies both and then let the minimum block length T min =M min ;

[0111] 1.5 If none of the above conditions are met, and under the condition that T + -T - ≠1, let Calculate the corresponding average and represents the ceiling function;

[0112] 1.6 When and are satisfied, then let Otherwise, let

[0113] 1.7 Update T - or T + , and continue steps 1.5 to 1.6 until T + -T - =1 to stop the iteration, and the minimum block length T min =T + ;

[0114] 1.8 Select a step size of Δ to traverse the value range of , and repeat steps 1.1 to 1.7 to obtain the minimum block length T min corresponding to each power allocation coefficient. Then let The corresponding power allocation coefficient is the optimal power allocation coefficient where min(·) represents calculating the minimum element in an array.

[0115] The specific implementation process of the present invention is as follows:

[0116] An intelligent reflecting surface-assisted short-packet communication method in an electromagnetic interference environment, the specific implementation steps are as follows:

[0117] Step A: Construct a downlink two-user non-orthogonal multiple access system consisting of a single-antenna wireless access point (AP), two single-antenna users, and a reflective IRS with N = 64 passive elements. Among them, the near user UE1 communicates directly with the AP, and the far user UE2 communicates with the AP with the assistance of the reflective IRS. There is no direct line-of-sight link between the AP and UE2, and communication can only be achieved through the cascaded channel with the help of the reflective IRS. The cascaded channel includes two communication links, namely AP-IRS and IRS-UE2. There is a direct line-of-sight link AP-UE1 between the AP and UE1. At the same time, the electromagnetic interference source will affect the received signals of UE1, the reflective IRS, and UE2 respectively. The communication links AP-UE1, AP-IRS, and IRS-UE2 have the same path loss exponent β and the small-scale fading follows the Rice distribution, where β = 2. The channel coefficient between the AP and UE1 is expressed as ), the channel coefficient between the AP and the nth (n ∈ {1, 2,..., N}) element of the reflective IRS is expressed as ), and the channel coefficient between the nth element of the reflective IRS and UE2 is expressed as ), where β 0 represents the path loss at a reference distance of 1 meter, d 0 is the distance from the AP to UE1, d 1 is the distance from the AP to the center of the reflective IRS, d 2 is the distance from the center of the reflective IRS to UE2, K 0 , K 1 and K 2 are Rice factors, and represent the corresponding line-of-sight transmission components, and are the corresponding non-line-of-sight transmission components, which follow a circularly symmetric complex Gaussian distribution with a mean of 0 and a variance of 1. And β 0 = -20 dB, d 0 = 30 m, d 1 = 50 m, d 2 = 60 m, K 0 = K 1 = K 2 = 5; Define the average power of g 0 as where |·| represents the modulus of a complex number or the absolute value of a real number, represents the mean operation; and represent the channel coefficients from the electromagnetic interference source to the nth element of the reflective IRS, UE2, and UE1 respectively, where d 3 , d 4 and d5 are the distances from the electromagnetic interference source to the center of the reflective IRS, UE2, and UE1, respectively, h 3n , h 4 and h 5 follow a circularly symmetric complex Gaussian distribution with a mean of 0 and a variance of 1, and d 3 = d 4 = d 5 = 50 m.

[0118] Step B: Based on the system model established in Step A, derive the received signals of the two users in the electromagnetic interference environment; determine the order of successive interference cancellation according to the statistical channel state information, and further write out the instantaneous SINR;

[0119] Step C: Based on the channel parameters and the number N of reflective IRS units, the reflective IRS performs optimal continuous phase adjustment based on the statistical channel state information, and analyzes and gives the distribution characteristics of the instantaneous SINR;

[0120] Step D: Calculate the average BLER expressions of the two users respectively according to the formulas in short-packet communication;

[0121] Step E: According to the expressions calculated in Step D, under the reliability constraint step size Δ = 0.01, through the bisection method and the one-dimensional traversal search algorithm, further obtain the relationship between the average BLER, the optimal power allocation coefficient of NOMA, and the minimum common block length.

[0122] Assume that the AP transmit power P = 55 dBm and the noise power Figure 3 gives the transmit power P of the electromagnetic interference source I = 0, the minimum common block lengths under different power allocation coefficients. From Figure 3 it can be obtained that the optimal power allocation coefficient under the reliability constraint is the minimum common block length is Symbol, substituting the obtained optimal power allocation coefficient and the minimum common block length into the formula for calculating the average BLER of the two users when P I = 25 dBm, the average BLER of UE1 can be obtained as the average BLER of UE2 is both do not meet the reliability constraint, indicating that the NOMA power allocation and transmission block length designed in the electromagnetic interference-free environment are not applicable in the electromagnetic interference environment, and need to be redesigned for the electromagnetic interference environment. Figure 4 gives the transmit power P of the electromagnetic interference source I = 25 dBm, the minimum common block lengths under different power allocation coefficients. From Figure 4 it can be obtained that the optimal power allocation coefficient under the reliability constraint is the minimum common block length is Symbol, substitute the obtained optimal power allocation coefficient and the minimum common block length into P I When = 25dBm, substituting into the average BLER calculation formula for the two users, the average BLER of UE1 can be obtained as The average BLER of UE2 is Both satisfy the reliability constraint. It can be seen from the embodiments of the present invention that, compared with the electromagnetic interference - free environment, the minimum common block length required by the system in the electromagnetic interference environment increases significantly under the condition of satisfying the user reliability constraint.

Claims

1. A short packet communication method assisted by an intelligent reflective surface in an electromagnetic interference environment, characterized in that: The specific implementation steps are as follows: Step A, establishing a reflective intelligent reflecting surface Intelligent Reflecting Surface, IRS-assisted downlink two-user non-orthogonal multiple access Non-orthogonal Multiple Access, NOMA short packet communication system, the system includes a single-antenna wireless access point Access Point, AP, two single-antenna users: near user UE1, far user UE2 and a reflective IRS with N passive units; The AP communicates directly with the near user UE1 through the direct link AP-UE1, and the AP communicates with the far user UE2 through a cascade channel with the help of a reflective IRS. The cascade channel includes two communication links, namely AP-IRS and IRS-UE2. The system includes an electromagnetic interference source, and it is assumed that the transmission power of the electromagnetic interference source, the transmission channel characteristics from the electromagnetic interference source to the reflective IRS and the two users are known. At the same time, the electromagnetic interference source will affect the receiving signals of UE1, the reflective IRS and UE2 respectively. Step B: According to the system model established in step A, derive the received signals of the two users in the electromagnetic interference environment; according to the statistical channel state information, determine the order of continuous interference elimination, and further write the instantaneous signal to interference plus noise ratio Signal to Interference plus Noise Ratio, SINR; Step C: According to the channel parameters and the number of reflective IRS units N, the reflective IRS performs optimal continuous phase adjustment based on statistical channel state information, and analyzes and gives the distribution characteristics of the instantaneous SINR; the specific implementation is as follows: The end-to-end channel gains from AP to UE1 and from AP to UE2 are |g0| 2 and |G| 2 , the end-to-end channel gains from the electromagnetic interference source to UE1 and UE2 are |g5| 2 and |H| 2 , where |·| represents the modulus of a complex number or the absolute value of a real number, g0, G, g5 and H represent the end-to-end channel fading coefficients from AP to UE1, AP to UE2, electromagnetic interference source to UE1, and electromagnetic interference source to UE2, respectively; when the optimal continuous phase adjustment is adopted, according to the central limit theorem, |G| obeys the Rice distribution, and its average power and Rice factor are and Where β0 represents the path loss at a reference distance of 1 meter, β represents the path loss exponent, d1 is the distance from the AP to the center of the reflective IRS, d2 is the distance from the center of the reflective IRS to UE2, K1 and K2 are Rice factors, and K c =(K1+1)(K2+1); H has a mean of 0 and a variance of A cyclically symmetric complex Gaussian distribution, where d3 and d4 are the distances from the electromagnetic interference source to the center of the reflective IRS and UE2, respectively; because both H and g5 obey cyclic symmetric complex Gaussian distribution, |H| 2 and |g5| 2 The shape parameter is 1 and the scale parameters are μ y and μ5 gamma distribution, where μ5=β0d5 -β , d5 represents the distance from the electromagnetic interference source to UE1; |G| and |g0| both obey Rice distribution, so |G| 2 and |g0| 2 All obey the mixed gamma distribution, and their probability density functions are and Where I and V represent the summation order, w i =ψ i Γ(i) / ξ i i and w v =ψ v Γ(v) / ξ v v is the weight coefficient, Γ(·) represents the gamma function, K0 is the Rice factor, represents the mean operation, d0 is the distance from AP to UE1; According to the probability density function of the above channel gain, the instantaneous SINRγ can be calculated 12 , γ 11 , γ 22 The cumulative distribution function of Among them, F γlι (·) is γ lι The cumulative distribution function of (l,ι∈{1,2}), P I Indicates the transmission power of the electromagnetic interference source, is the power allocation coefficient corresponding to UE1, satisfying P represents the transmit power of AP, 2F1(·) represents the Gaussian hypergeometric function, and γ(·) represents the lower incomplete gamma function; Step D, respectively calculating the average block error rate Block Error Rate, BLER expression of the two users according to the formula in the short packet communication; Step E: Based on the expression calculated in step D, the NOMA optimal power allocation coefficient and the minimum common block length are further solved under the reliability constraint.

2. According to the intelligent reflective surface assisted short packet communication method in an electromagnetic interference environment according to claim 1, the specific implementation of step A is as follows: Modeling channel coefficients: The communication links AP-UE1, AP-IRS and IRS-UE2 have the same path loss index β and the small-scale fading follows the Rice distribution. The channel coefficient between AP and UE1 is expressed as The channel coefficient between the AP and the nth (n∈{1,2,…N}) unit of the reflective IRS is expressed as The channel coefficient between the nth unit of the reflective IRS and UE2 is expressed as in and represents the corresponding line-of-sight transmission component, and is the corresponding non-line-of-sight transmission component, which obeys a cyclically symmetric complex Gaussian distribution with a mean of 0 and a variance of 1; and represents the channel coefficients from the electromagnetic interference source to the nth unit of the reflective IRS, UE2 and UE1, respectively, where h 3n , h4 and h5 obey a circularly symmetric complex Gaussian distribution with a mean of 0 and a variance of 1.

3. According to the intelligent reflective surface assisted short packet communication method under electromagnetic interference environment of claim 1, the specific implementation of step B is as follows: The received signals at UE1 and UE2 are: in is the NOMA superposition signal sent by the AP, s l represents the power normalized signal sent by AP to UE1, s I Represents the power normalized interference signal emitted by the electromagnetic interference source; G1=[g 11 ,g 12 ,...,g 1N ],G2=[g 21 ,g 22 ,...,g 2N ] T and G3 = [g 31 ,g 32 ,…,g 3N ] represent the channel coefficient matrices between AP to reflective IRS, reflective IRS to UE2, and electromagnetic interference source to reflective IRS, respectively. [g 21 ,g 22 ,...,g 2N ] T Represents the vector [g 21 ,g 22 ,...,g 2N ] is the transpose of θ, and θ represents the reflection IRS phase offset matrix, which is Indicates is a diagonal matrix with diagonal elements, φ n Represents the phase offset value of the nth unit of the reflective IRS when the optimal continuous phase adjustment strategy is adopted arg(·) represents the complex angle function; w1 and w2 represent the mean and variance of 0. Additive complex Gaussian white noise; It can be further obtained that the end-to-end channel fading coefficient G between the AP and UE2 and the end-to-end channel fading coefficient H between the electromagnetic interference source and UE2 are respectively: AP uses statistical channel status information to design the system. According to the NOMA principle, the AP allocates a small power allocation coefficient to users with large channel gain, so UE1 needs to correctly decode and remove UE2's decoded signal s2 first, and then decode its own signal s1. Since UE2 is allocated a larger power coefficient, s1 can be regarded as an interference signal and directly decode its own signal s2. Therefore, the SINRs of UE1's decoded signals s2 and s1 and UE2's decoded signal s2 are:

4. According to the intelligent reflective surface assisted short packet communication method under electromagnetic interference environment of claim 1, the specific implementation of step D is as follows: According to the short packet communication related formula, when the signal-to-interference-noise ratio γ and the short data packet block length T are given d When the BLER of short packets is equal to 1, the maximum achievable rate of short packets is expressed in bits per symbol, which can be approximately expressed as: in, C(γ)=log2(1+γ) represents Shannon capacity, V(γ)=(1-(1+γ) -2 )(log2e) 2 represents the channel divergence, Q -1 (·)express The inverse function of Assume that the physical layer information rate of the two users is R ι =F ι / T d , where F ι represents the number of information bits; the instantaneous BLER of UE1 decoding signal s2, s1 and UE2 decoding signal s2 is approximately expressed as According to the instantaneous BLER and instantaneous SINR, the average BLER in the fading channel It is expressed as: in, Represents γ lι The probability density function of according to Approximation, average BLER in fading channel Further expressed as: in Further using the Gauss-Chebyshev integration method, we can get: Where J is the Gauss-Chebyshev integral approximation order, So the average BLER of UE1 and UE2 is: in and They are:

5. According to the intelligent reflective surface assisted short packet communication method in an electromagnetic interference environment of claim 1, the specific implementation of step E is as follows: The target BLER of the two users is expressed as Determine the optimal power allocation coefficient and the minimum common block length. The specific steps for determining the optimal power allocation coefficient and the minimum common block length are as follows: 1.1 Given system parameters N, K0, K1, K2, d0, d1, d2, d3, d4, d5, β0, β, P, P I , F1, F2 and Initialize block length T d , limit the block length to [M min ,M max ], let T - =M min , T + =M max ; 1.2 Set the block length to T - , T + Substitute into the average BLER formula to calculate the corresponding average BLER of 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 solution; 1.4 If the calculated average BLER satisfies both and Then let the minimum block length be T min =M min ; 1.5 If none of the above conditions are met, then + -T - ≠1, let Calculate the corresponding average BLER and represents the ceiling function; 1.6 When satisfied and Then Otherwise, 1.7 Update T - or T + , continue steps 1.5 to 1.6 until T + -T - =1 to stop the iteration, and the minimum block length T can be obtained min =T + ; 1.8 Select a step size of Δ to traverse the value interval of ζ1, repeat steps 1.1 to 1.7, and obtain the minimum block length T corresponding to each power allocation coefficient min , then let The corresponding power allocation coefficient is the optimal power allocation coefficient Where min(·) means calculating the minimum element in an array.

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