A method for designing and optimizing a symbiotic radio system based on intelligent reflecting surfaces

Abstract

The application discloses a transmission scheme design and performance optimization method of a symbiotic radio system based on an intelligent reflecting surface. In the scheme, the intelligent reflecting surface assists a multi-antenna base station to communicate with a primary user, and simultaneously generates a secondary signal as a backscattering device to transmit information to a secondary user. The intelligent reflecting surface controls the switch of a reflecting unit through on-off keying to realize modulation and scattering of the reflected signal of the base station, and the secondary user detects the secondary symbol by using an energy detection method. On the premise of ensuring the transmission rate of the primary user transmission, the beamforming vector of the base station and the phase shift matrix of the intelligent reflecting surface are jointly optimized to minimize the error probability of the scattering transmission. The original optimization problem is a non-convex problem, which is transformed and solved by adopting a semi-positive definite relaxation method and an alternating iterative optimization method. Compared with a conventional symbiotic radio transmission scheme, the scheme provided by the application has a higher primary transmission rate and a lower secondary transmission bit error rate.

Description

TECHNICAL FIELD

[0001] The present application relates to the technical field of wireless communication, in particular to a symbiotic radio system based on intelligent reflecting surface, and joint optimization of beamforming vectors at base station and phase shift matrix of intelligent reflecting surface. BACKGROUND

[0002] The large-scale commercialization of 5G technology has ushered in a new era for the Internet of Things, making it possible for everything to be connected. To widely deploy billions of Internet of Things devices with sensing, computing, and wireless communication capabilities, two key issues need to be addressed: spectrum scarcity and energy supply. Backscatter technology is one of the key technologies for achieving low-power communication, and Symbiotic Radio (SR) is based on backscatter communication, which not only efficiently utilizes spectrum resources but also has ultra-low power consumption and sustainability, making it a green communication method. In an SR system, backscatter devices (BDs) act as secondary transmitters, modulating the received primary transmitter signals to generate secondary signals, which are transmitted to secondary receivers in the form of reflections, achieving the sharing of spectrum and energy resources. In addition, according to the length of the secondary symbol period, the relationship between primary and secondary transmissions can be divided into two modes: symbiotic and parasitic. When the secondary symbol period is much larger than the primary symbol period, the receiver of the primary transmission can estimate the secondary symbol in each secondary symbol period or the channel coefficient of the composite link formed by the primary transmission link and the scattering transmission link, eliminating the interference of the secondary symbol on the primary transmission, and the scattering link can become an additional and exploitable multipath link, improving the performance of the primary transmission.At this time, the primary transmission and the secondary transmission are symbiotic [Zhang Q, Zhou HC, Liang Y C, et al. Channel capacity of RIS-assisted symbiotic radios with imperfect knowledge of channels [J]. IEEE Transactions on Cognitive Communications and Networking, 2024, 10(3): 938-952.]. When the secondary symbol period is comparable to the primary symbol period, the primary transmission receiver cannot eliminate the influence of the secondary transmission on the primary transmission, and the secondary symbol will interfere with the primary transmission, and the secondary transmission and the primary transmission are parasitic [LONG R, LIANG Y C, GUO H, et al. Symbiotic radio: A new communication paradigm for passive Internet of Things [J]. IEEE Internet of Things Journal, 2019, 7(2): 1350-1363.]. At present, the main research work in the SR system is to reduce the system power consumption and improve the system transmission rate by optimizing the base station (BS) beamforming vector. For example, the literature [WU T, JIANG M, ZHANG Q, et al. Beamforming design in multiple-input-multiple-output symbiotic radio backscatter systems [J]. IEEE Communications Letters, 2021, 25(6): 1949-1953] studies the downlink SR system using a single-antenna BD as a secondary transmitter in a multiple-input-multiple-output system, and under the condition of meeting the minimum secondary transmission capacity constraint, the sum capacity of the primary and secondary transmissions is maximized by optimizing the BS beamforming vector.

[0003] In SR systems, the performance of the secondary transmission is greatly restricted due to the double fading of the secondary transmission link, which results in a very low received signal power at the secondary receiver. Intelligent reflecting surface (IRS) is a radio frequency signal reflecting device composed of a large number of low-cost, passive reflecting elements, which can intelligently control the reflecting phase shift and amplitude by changing the parameters of each reflecting element of IRS [YUAN X, ZHANG Y J A, SHI Y, et al. Reconfigurable-intelligent-surface empowered wireless communications: Challenges and opportunities [J]. IEEE Wireless Communications, 2021, 28(2): 136-143.]. The introduction of IRS in wireless communication systems can improve the propagation environment of signals, reduce the loss in transmission, and improve the energy efficiency of the system. The controllable reflecting characteristics of IRS make it very suitable as BD in SR systems. In the symbiotic relationship SR system based on IRS, not only can the secondary transmission be realized by controlling the reflecting characteristics of IRS, but also the performance of the primary transmission can be improved. Many literatures have studied this. Literature [ZHANG Q, LIANG Y C, POOR H V. Reconfigurable intelligent surface assisted MIMO symbiotic radio networks [J]. IEEE Transactions on Communications, 2021, 69(7): 4832-4846.] applies IRS to a multiple-input multiple-output SR system, generates a secondary binary phase shift keying (BPSK) modulated signal by controlling the phase shift matrix of IRS, and at the same time, uses the secondary transmission signal to enhance the transmission quality of the primary transmission link, realizing the mutual symbiosis of primary transmission and secondary transmission. Under the constraints of the signal-to-noise ratio of the secondary transmission and the average rate of the primary transmission, the literature minimizes the transmit power of the BS by jointly optimizing the beamforming vector of the BS and the phase shift matrix of the IRS.The literature [ZHOU H, KANG X, LIANG Y C, et al. Cooperative beamforming for reconfigurable intelligent surface-assisted symbiotic radios[J]. IEEE Transactions on Vehicular Technology, 2022, 71(11): 11677-11692.] proposes to use IRS as the SR system optimization scheme for BD in two cases of perfect and imperfect channel state information (CSI) obtained. Under the perfect CSI condition, the BS transmit power is minimized by jointly optimizing the BS beamforming vector and the IRS phase shift matrix. Under the imperfect CSI condition, the bounded channel error model is used to describe the CSI error, and the worst-case BS transmit power is minimized by jointly optimizing the BS beamforming vector and the IRS phase shift matrix. The literature [WANG J, LIANG Y C, PEI Y, et al. Reconfigurable intelligent surface as a micro base station: A novel paradigm for small cell networks[J]. IEEE Transactions on Wireless Communications, 2022, 22(4): 2338-2351.] proposes a multi-user downlink transmission scheme using IRS as a secondary scattering base station. IRS reflects the signal transmitted by the macro base station and controls the phase shift of the reflecting elements to generate a secondary signal, while also providing a reflection link for macro users to improve the transmission performance between the macro base station and the macro users. The literature proposes two secondary multi-user transmission schemes, spatial division multiple access and time division multiple access, and minimizes the system power consumption by optimizing the phase shift matrix of the IRS and the beamforming vector of the macro base station. The literature [XU X, LIANG Y C, YANG G, et al. Reconfigurable intelligent surface empowered symbiotic radio over broadcasting signals[J]. IEEE Transactions on Communications, 2021, 69(10): 7003-7016.] studies the SR downlink broadcast communication system based on IRS, in which the IRS assists the BS to transmit broadcast signals to multiple primary receivers, and generates secondary BPSK modulated signals by adjusting the phase shift matrix of the IRS to transmit secondary information to the Internet of Things receivers, sharing the primary transmission spectrum and power resources.The document gives an optimization algorithm for minimizing the BS transmit power by jointly optimizing the BS beamforming and the IRS phase shift matrix. SUMMARY

[0004] The application aims to provide a design and optimization method of downlink symbiotic radio system based on intelligent reflecting surface, to improve system performance and transmission efficiency. The method first constructs a communication system model, introduces intelligent reflecting surface as a backscattering device, uses on-off keying to control the switch of the reflecting unit, generates secondary signals and scatters them to secondary users. The secondary users use energy detection method to detect the secondary symbols to ensure effective reception of signals.

[0005] To achieve the above-mentioned purpose, the application adopts the following technical scheme: first, construct a communication system model and derive the bit error rate formula of the secondary symbol, take the minimum bit error rate of the secondary symbol as the optimization goal, and construct an optimization mathematical model under the constraints of the minimum average rate of the primary user and the total transmit power of the base station. Then, the optimization problem is converted into two optimization sub-problems of the base station beamforming vector and the intelligent reflecting surface phase shift matrix, and the two sub-problems are solved by using convex optimization solver and Gaussian randomization method respectively. Finally, the intelligent reflecting surface phase shift matrix and the base station beamforming vector are iteratively optimized by using the alternating optimization algorithm until convergence is reached.

[0006] The specific steps are as follows:

[0007] (1) Analyze the signal transmission process and construct a communication system model: on the basis of the conventional symbiotic radio system, introduce intelligent reflecting surface as a backscattering device, use on-off keying to control the switch of the reflecting unit, generate secondary signals and scatter them to secondary users, and the secondary users use energy detection method for symbol detection;

[0008] (2) Derive the bit error rate formula of the secondary symbol, take the minimum bit error rate of the secondary symbol as the optimization goal, and construct an optimization mathematical model under the constraints of the minimum average rate of the primary user and the total transmit power of the base station;

[0009] (3) Convert the optimization problem into two sub-problems of intelligent reflecting surface phase shift matrix optimization and base station beamforming vector optimization;

[0010] (4) In the case of fixing the base station beamforming vector, the optimization sub-problem is converted into a convex problem, and then the intelligent reflecting surface phase shift matrix is obtained by using convex optimization solver and Gaussian randomization method;

[0011] (5) In the case of fixing the intelligent reflecting surface phase shift matrix, the optimization sub-problem is converted into a convex problem, and then the base station beamforming vector is obtained by using semi-definite relaxation and Gaussian randomization method;

[0012] (6) The phase shift matrix of the intelligent reflecting surface and the base station beamforming vector are iteratively solved by using an alternating optimization algorithm until convergence is reached.

[0013] Further, the method of using the intelligent reflecting surface as a backscattering device and the secondary user energy detection in step (1) detects the secondary symbol, specifically including: first, the intelligent reflecting surface contains M reflecting units, each of which can independently control its phase shift. The intelligent reflecting surface receives the primary transmission signal from the base station, and generates the secondary symbol by adjusting the on and off state of the reflecting unit to achieve effective information transmission to the secondary user. The period of the secondary symbol is L times of the primary symbol period, and in a secondary symbol period, the secondary user calculates the energy value in each primary symbol period by energy sampling and accumulation on the received scattered signal, and compares the accumulated energy value with the preset decision threshold. If the accumulated energy value is higher than the decision threshold, the secondary symbol is determined to be 1; if it is lower than the decision threshold, it is determined to be 0. The value of the optimal decision threshold is obtained by taking the derivative of the bit error rate expression with respect to λ and setting the derivative equal to 0, specifically

[0014]

[0015] Further, the Gaussian randomization method in step (4) is specifically: in the case of fixed base station beamforming vector, assuming that the solution obtained after using the convex optimization solver to solve the sub-problem is V opt , if its rank is 1, then perform eigenvalue decomposition on V opt , assuming that the obtained non-zero eigenvector is , then can be obtained from

[0016]

[0017] If the rank of V opt is not 1, an approximate solution can be obtained by using the Gaussian randomization method. The specific steps are: first, perform eigenvalue decomposition on V opt , to obtain V opt =UΣ, where U is a matrix composed of the eigenvectors of V opt , and Σ is a diagonal matrix whose diagonal elements are composed of the eigenvalues of V opt . Randomly generate U M+1-dimensional complex Gaussian random vectors r(u), where u∈{1,2,…,U}, and obtain from r(u) and

[0018]

[0019] where represents the M+1th element, and obviously Then replace V in the average rate constraint of the primary user in the optimization subproblem with and judge whether the constraint is satisfied. If yes, put into the feasible solution set. After all the random vectors are processed, select the feasible solution with the largest from the feasible solution set as the . M+1th element of v opt to obtain the M-dimensional column vector v opt . opt H . opt .

[0020] ​Compared with the existing related research, the present application has the following beneficial technical effects: (1) Among the currently retrievable related literatures on symbiotic radio systems based on intelligent reflective surfaces, such as [ZHOU H, KANG X, LIANG Y C, et al. Cooperative beamforming for reconfigurable intelligent surface-assisted symbiotic radios [J]. IEEE Transactions on Vehicular Technology, 2022, 71 (11): 11677-11692] and [WANG J, LIANG Y C, PEI Y, et al. Reconfigurable intelligent surface as a micro base station: A novel paradigm for small cell networks [J]. IEEE Transactions on Wireless Communications, 2022, 22 (4): 2338-2351.], most of the researches adopt the method of binary phase shift keying to modulate and generate secondary symbols, and the interference of the primary transmission symbol needs to be eliminated before the secondary symbol detection. This not only restricts the decoding of the secondary symbol to the correct decoding of the primary symbol, but also increases the reception processing complexity and power consumption at the secondary user. The method of the present application does not need to decode the primary symbol first, but directly detects the secondary symbol through the energy detection method, simplifying the processing process. (2) The present application adopts the on-off keying modulation method, reduces the processing complexity of the secondary user, avoids the detection and cancellation of the primary symbol, so that the secondary user can directly detect the symbol through the energy detection method. (3) The present application jointly optimizes the beamforming vector of the base station and the phase shift matrix of the intelligent reflective surface to minimize the bit error rate of the secondary transmission. In view of the difficulty in finding the optimal solution for non-convex problems, an alternating iterative optimization algorithm is proposed to convert the original problem into a convex problem for solving until convergence is reached, thereby improving the system performance. (4) After simulation verification, the results show that, compared with the single-antenna backscattering device scheme, the intelligent reflective surface phase shift matrix random phase shift scheme and the maximum ratio transmission precoding scheme for the beamforming vector of the base station, the scheme proposed in the present application not only significantly improves the average rate of the primary user, but also realizes a lower bit error rate of the secondary transmission. BRIEF DESCRIPTION OF DRAWINGS

[0021] Figure 1 The communication system model of the present application;

[0022] Figure 2The process of convergence of the alternating iterative algorithm proposed in the application;

[0023] Figure 3 The influence of the maximum transmission power of the base station on the secondary symbol bit error rate;

[0024] Figure 4 The influence of the ratio L of the secondary symbol period to the primary symbol period on the secondary symbol bit error rate and the average rate of the primary user;

[0025] Figure 5 The influence of the number of base station antennas on the secondary symbol bit error rate and the average rate of the primary user;

[0026] Figure 6 The influence of the number of reflective elements of the intelligent reflecting surface on the secondary symbol bit error rate. DETAILED DESCRIPTION

[0027] The SR system model based on IRS studied in the application is shown in Figure 1 The system consists of a BS, an IRS, a PU and a SU. The BS is equipped with N transmit antennas, the IRS contains M reflective elements, and the user is configured with a single antenna. The symbol rate of the primary transmission is much larger than that of the secondary transmission. It is assumed that L primary symbols can be transmitted within one secondary symbol period, i.e. s T p = L × T p , L >> 1, where T s is the primary symbol period and T s is the secondary symbol period. It is assumed that all channels are block flat fading channels, and the channel state remains unchanged at least within one secondary symbol period T s . There is no direct transmission link between the BS and the SU due to the obstruction of obstacles. The channel coefficient matrix or vector between the BS and the IRS, the BS and the PU, the IRS and the PU, and the IRS and the SU are denoted as The phase shift matrix of the IRS is where ζ m ∈ [0, 1] and θ m ∈ [0, 2π] are the reflection amplitude and reflection phase shift of the mth reflective element, m ∈ {1, 2, …, M}. In order to achieve maximum reflection gain, the reflection amplitude of the IRS reflective element is set to 1 in the application.

[0028] The IRS reflects the signal transmitted by the BS, generates a secondary OOK signal by controlling the opening and closing of the reflective elements and transmits it to the SU, and controls the reflection phase shift of each reflective element to enhance the strength of the primary transmission signal. The secondary symbol is denoted as s, s = 1 or s = 0. The lth primary symbol transmitted within one secondary symbol period is denoted as x[l], where l ∈ {1, …, L}, The lth symbol received by the PU can be represented as

[0029]

[0030] in, represents the BS transmit beamforming vector, is the channel noise. The present invention considers the scenario where the secondary symbol period is much longer than the primary symbol period, that is, L>>1. In this scenario, the primary transmission transmitter can send a small amount of pilot signals at the beginning of each secondary symbol period. The primary transmission receiver estimates the channel coefficient of the composite link composed of the primary transmission link and the scattered transmission link in each secondary symbol period based on the received pilot symbols. In this way, the secondary scattered transmission link becomes another link outside the primary transmission link. Therefore, according to y p [l] The signal-to-noise ratio when decoding the main symbol at the PU is

[0031]

[0032] The achievable information transmission rate is

[0033]

[0034] Here, we consider that L is large, and the proportion of pilot symbols in the main transmission symbol sequence within a secondary symbol period is very small, so the impact of pilot symbols on the transmission rate is ignored. The signal-to-noise ratio and transmission rate are related to the value of the secondary symbol s. Assuming that the probability of s = 1 and 0 is 1 / 2, the average achievable rate of the main transmission link is

[0035]

[0036] The lth symbol received by SU is

[0037]

[0038] in, is the channel noise.

[0039] SU uses energy detection method to detect the secondary symbol, first in a secondary symbol period T s The main transmission symbol period T p The received signal is sampled periodically and the energy is accumulated. The energy accumulation value is the detection statistic. When the secondary symbol s = 0, the SU received signal contains only the channel noise n s [l], the real and imaginary parts are recorded as n r [l] and n i [l], all have mean 0 and variance Gaussian distribution.

[0040] When the secondary symbol s=1, the SU received signal contains the symbol sent by the BS and the channel noise. The real and imaginary parts of the received symbol sample are

[0041]

[0042]

[0043] where x r [l] are the real and imaginary parts of the primary transmitted symbol x[l], respectively, and are Gaussian distributed with mean 0 and variance 1 / 2. y i [l] are the real and imaginary parts of the primary transmitted symbol x[l], respectively, and are Gaussian distributed with mean 0 and variance 1 / 2. y s,r The conditional mean and conditional variance of y

[0044]

[0045]

[0046] Similarly, E(y s,i [l]|s=1) = 0 and Var(y Thus, y s,r [l] and y s,i [l] are Gaussian distributed with mean 0 and variance .

[0047] The SU accumulates the energy of L symbol samples within one secondary symbol period T s to obtain the detection statistic as

[0048]

[0049] The detection statistic Q for s = 0 is the sum of squares of 2L independent and identically distributed Gaussian variables, and is a random variable following a central chi-square distribution with 2L degrees of freedom. Its probability density function is given by

[0050]

[0051] where denotes the complete gamma function.

[0052] Similarly, the detection statistic Q for s = 1 is also a random variable following a central chi-square distribution, and its probability density function is given by

[0053]

[0054] The SU makes a decision by comparing the detection statistic Q with a decision threshold. The decision rule is given by

[0055]

[0056] The probability of false alarm when the secondary transmitted symbol is s = 0 is given by

[0057]

[0058] where, denotes the upper incomplete gamma function.

[0059] When s = 1, the probability of misjudgment is

[0060]

[0061] Assuming that the probability of s = 1 or 0 is 1 / 2, the bit error rate is

[0062]

[0063] The decision threshold λ should make the bit error rate minimum, which can be obtained by taking the derivative of P e with respect to λ and setting the derivative equal to 0 to obtain the optimal λ as

[0064]

[0065] According to the expression of P e , the average rate of the primary transmission and the error probability of the secondary transmission are related to the BS beamforming vector w and the IRS phase shift matrix Θ. The present application considers minimizing the bit error rate of the secondary transmission under the condition of satisfying the average transmission rate of the primary transmission, and the optimization problem can be formulated as

[0066] P1:

[0067] s.t.C1:

[0068] C2:

[0069] C3:|Θ m,m |=1,m∈{1,2,…,M}

[0070] In the optimization problem P1, C1 constrains the average rate of the primary transmission to be no less than R min , C2 constrains the transmit power of the BS to be no more than P max , and C3 constrains the reflection amplitude coefficient of the IRS reflection unit to be 1.

[0071] According to the expression of P e , the bit error rate P e is related to the signal power when s = 1 at the SU . Since Γ(a, x) is a monotonically decreasing function with respect to x, the larger the signal power , the smaller the bit error rate P e . Therefore, the optimization objective of P1 can be changed to maximize the signal power when s = 1 at the SU, that is,

[0072] P2:

[0073] s.t.C1:

[0074] C2:

[0075] C3:|Θ m,m |=1,m∈{1,2,…,M}

[0076] The objective function and constraints of P2 are non-convex, and the optimization variables are coupled with each other, which makes it difficult to solve directly. Therefore, P2 is decomposed into two sub-problems of optimizing w and Θ respectively, and the solution of the original problem is obtained by solving the two sub-problems through alternating iteration.

[0077] The optimization sub-problem when the BS transmit beamforming vector w is fixed is

[0078] P3:

[0079] s.t.C1:

[0080] C3:|Θ m,m |=1,m∈{1,2,…,M}

[0081] Define P3 can be rewritten as

[0082] P4:

[0083] s.t.C4:

[0084] C5:|v m |=1,m∈{1,2,…,M}

[0085] P4 is a non-homogeneous quadratic constraint quadratic programming problem, which needs to be transformed into the form of a convex optimization problem. Define where 0 is a column vector with all elements being 0, and let and let Obviously, V±0, Rank(V) = 1, by rewriting the objective function in P4 as tr(VR1), and replacing v m in the constraint C5 of P3 with V m,m , and let The non-convex constraint C4 can be rewritten as P4 can be transformed into

[0086] P5:

[0087] s.t.C6:

[0088] C7:|V m,m |=1,m∈{1,2,…,M}

[0089] C8:V±0

[0090] C9:Rank(V)=1

[0091] Optimization problem P5 is a convex optimization problem except that the constraint Rank(V) = 1 is still a non-convex constraint. The constraint C9 in P5 can be removed by relaxation, and the resulting optimization problem is a convex optimization problem which can be solved by using a convex optimization solver. Suppose the solution of the optimization problem is V opt , if the rank of V opt is 1, then V can be obtained from V by eigenvalue decomposition of V

[0092]

[0093] If the rank of V opt is not 1, an approximate solution can be obtained by using the method of Gaussian randomization. The specific steps are as follows: first, eigenvalue decomposition of V opt is performed to obtain V opt = UΣ, where U is a matrix composed of the eigenvectors of V opt , and Σ is a diagonal matrix whose diagonal elements are the eigenvalues of V opt . Randomly generate U M+1-dimensional complex Gaussian random vectors r(u), where u∈{1,2,…,U}, and obtain from r(u). Then obtain

[0094]

[0095] where represents the M+1th element, and obviously Then replace V in the average rate constraint of the main user in the optimization sub-problem with , and determine whether the constraint is satisfied. If it is satisfied, put into the feasible solution set. After all random vectors are processed, select the feasible solution with the maximum from the feasible solution set as Remove the M+1th element of to obtain an M-dimensional column vector vopt , and finally according to Θ opt =diag((v opt ) H ) to obtain the IRS phase shift matrix Θ opt .

[0096] The optimization subproblem when the IRS phase shift matrix Θ is fixed is

[0097] P6:

[0098] stC1:

[0099] C2: Except for constraint C2, all optimization subproblems P6 are non-convex. Let W = ww H , we know that W±0, Rank(W)=1, and then let The optimization problem P6 can be transformed into

[0100] P7:

[0101] stC10:

[0102] C11:tr(W)≤P max

[0103] C12:W±0

[0104] C13:Rank(W)=1

[0105] The constraint C13 in the optimization problem P7 is non-convex. By performing semi-positive relaxation and removing the constraint C13, we can obtain a standard convex semi-positive programming problem, which can be solved using existing solving algorithms or convex optimization solvers. Assume that the solution of the optimization problem after semi-positive relaxation is W opt , if its rank is 1, then perform eigenvalue decomposition on it, and the non-zero eigenvector is the solution w of the optimization problem P6 opt ; If W opt The rank is not 1, and the approximate solution of P6 can be obtained by using the Gaussian randomization method, which is the same as that obtained by V opt Get the approximate solution v opt similar.

[0106] Algorithm 1 Alternating Iteration Algorithm

[0107] Initialization parameters: number of iterations k = 0, the convergence factor ε that controls the end of the iteration, the number of Gaussian randomizations U, and the initialization of the beamforming vector at the beginning of the algorithm

[0108] (1) k = k + 1.

[0109] (2) Fix w = w (k-1) , solve problem P3 to get solution V (k) , perform eigenvalue decomposition and Gaussian randomization on V (k) to get According to get v (k) , and then according to v (k) get Θ (k) .

[0110] (3) Fix Θ = Θ (k) , solve problem P6 to get solution W (k) , perform eigenvalue decomposition and Gaussian randomization on W (k) to get w (k) .

[0111] (4) According to formula get P e (w (k) , Θ (k) ).

[0112] (5) Until

[0113] (6) Output w (k) , Θ (k) , P e (w (k) , Θ (k) ).

[0114] The application will be described in further detail below with reference to the accompanying drawings. In the simulation, unless otherwise specified, the number of base station antennas N = 3, the number of reflecting elements of the IRS M = 20, the minimum average rate requirement of the primary user R min = 2 bit / s / Hz, the number of Gaussian randomization U = 10 4 , P max = 30 dBm, and L = 20. The positions of the nodes in the system are described by three-dimensional coordinates, with units of meters (m), wherein the coordinates of the base station are (0, 0, 20), the coordinates of the IRS are (0, 30, 10), the coordinates of the primary user are (30, 0, 0), and the coordinates of the secondary user are (0, 40, 0). The channels between the nodes are Rayleigh fading channels, and the channel fading includes path loss (large-scale fading) and small-scale fading. The model of the channel matrix from the base station to the IRS is

[0115]

[0116] wherein is the path loss, L0 = -30 dB represents the path loss at a reference distance of 1 meter, and α BI is the path loss exponent, dBI is the distance between BS and IRS; β BI is the Rician factor; G LoS denotes the channel coefficient matrix of the line-of-sight transmission part between BS and IRS, which is generated according to the azimuth and elevation angles of the transmitting antenna and the azimuth and elevation angles of the IRS; G NLoS is the channel coefficient matrix of the non-line-of-sight transmission part, each element in the matrix is a complex Gaussian random variable with 0 mean and unit variance. Similarly, the models of the channel between IRS and user and the channel between BS and user are similar, and the channel coefficient vectors are

[0117]

[0118]

[0119]

[0120] In the simulation, α BI = 2.2, α BP = α IP = α IS = 3.5, β BI = 2, β IP = β IS = β BP = 1. The channel noise power The convergence factor ε = 10 -3 in Algorithm 1. In the secondary transmission bit error rate simulation, each simulation value is 1000 groups of channel samples, and the bit error rate of 2x10 4 secondary symbols is transmitted under each channel sample.

[0121] The following three benchmark schemes are given in the simulation for performance comparison: (1) Benchmark Scheme 1 - Single Antenna BD Scheme: The secondary transmitter is a single antenna BD, there is no IRS in the system, and the beamforming vector of the base station is obtained by a method similar to solving the optimization sub-problem P6 of the application; (2) Benchmark Scheme 2 - IRS Random Phase Shift Scheme: The amplitude ζ m of the elements in the phase shift matrix Θ of the IRS is 1, and the phase shift θ m is randomly taken from [0, 2π], where m ∈ {1, 2, …, M}, and the beamforming vector of the base station is obtained by a method similar to solving the optimization problem P6 of the application; (3) Benchmark Scheme 3 - PU-MRT Scheme: The beamforming vector of the BS uses MRT precoding, which is the conjugate transpose of the channel coefficient vector between BS and PU, and the phase shift matrix of the IRS is obtained by a method similar to solving the optimization problem P3 of the application.

[0122] Figure 2The convergence process of the alternative iteration algorithm for solving problem P2 is given, and the bit error rate changes with the iteration number for a set of random channel samples with different maximum transmit power and different L when M=30 and N=4. After each iteration, the bit error rate is calculated according to the optimized w and Θ. It can be seen that the bit error rate decreases with the iteration, and basically converges after 2-3 iterations.

[0123] Figure 3 The bit error rate of the secondary transmission changes with the maximum transmit power of the BS. The theoretical bit error rate calculated according to the optimized w and Θ, and the simulation value of the bit error rate obtained by simulating the complete message transmission process under the beamforming and IRS phase shift are given in the figure. It can be seen that the simulation value under each scheme is consistent with the theoretical value, proving that the theoretical analysis of the error probability of the secondary transmission of the application is correct. The bit error rate of the single antenna BD scheme is the highest, and basically does not decrease with the increase of the transmit power. The bit error rate of the IRS random phase shift scheme is also high, and the decrease of the bit error rate with the increase of the transmit power is very slow. In these two schemes, there is double fading in the reflection link, and only one reflection link or the random phase of each reflection link makes the received reflection link signal power at the SU very low, even lower than the noise power, so the bit error rate is very high. In addition, the phase shift matrix of the IRS is optimized in the scheme of the application and the PU-MRT scheme, and the bit error rate is significantly lower than that of the single antenna BD scheme and the IRS random phase shift scheme, which shows that using the IRS with optimized phase shift as the BD in the SR system and optimizing the phase shift matrix of the IRS have very obvious effects on improving the performance of the system, because the number of reflection paths increases and the power of the signals transmitted through each reflection path is significantly increased after superposition at the SU, and also has a relatively obvious effect on improving the transmission quality of the main transmission link. The bit error rate of the PU-MRT scheme is significantly lower than that of the single antenna BD scheme and the IRS random phase shift scheme, and the bit error rate of the secondary transmission of the scheme of the application is the lowest, which is significantly lower than that of the single antenna BD scheme and the IRS random phase shift scheme, and also lower than that of the PU-MRT scheme, and decreases rapidly with the increase of the BS transmit power, and has the best performance. The PU-MRT scheme optimizes the IRS phase shift, but does not optimize the beamforming of the BS, and adopts the MRT beamforming which is optimal for the main transmission, but not optimal for the reflection link. The scheme of the application optimizes the BS beamforming and the IRS phase shift matrix jointly to maximize the signal power at the SU on the basis of satisfying the transmission rate of the main transmission, so that the bit error rate of the secondary transmission is lower.

[0124] Figure 4The secondary transmission bit error rate and the primary transmission average rate of each scheme are given as the ratio L of the secondary symbol period to the primary symbol period changes. The results given in the figure are obtained by simulation. It can be seen that the bit error rate decreases as the value of L increases. This is because the SU uses energy detection, and the detection statistic is the cumulative noise energy when s = 0, and the cumulative noise energy and signal energy when s = 1. When L increases, the number of cumulative samples increases, and obviously, the cumulative energy when s = 1 increases more than when s = 0, so the probability of detection error decreases as L increases. Compared with the comparative schemes, the bit error rate of the scheme of the present application decreases at the highest rate as L increases, because the scheme of the present application jointly optimizes the BS beamforming and the IRS phase shift matrix, so that the cumulative signal energy at the SU increases more as L increases. From Figure 4 It can also be seen that the average rate of the PU of the scheme of the present application is higher than that of the IRS random phase shift scheme and the single antenna BD scheme, and is much higher than the required minimum rate value of 2 bit / s / Hz. This is mainly due to the joint optimization of the base station precoding and the IRS phase shift in the scheme of the present application, which minimizes the SU detection error probability while enabling the signal of the reflected link at the PU to be partially coherently superimposed with the signal of the direct link, thereby improving the received signal power at the PU. In the single antenna BD scheme, since the number of BD antennas is 1, the direction of the reflected signal cannot be controlled, and the improvement effect on the transmission performance of the PU is limited. In the IRS random phase shift scheme, the phase shift of each transmitting unit is randomly selected, and the phase of each reflected signal and the direct link signal received by the PU is random, and coherent superposition cannot be achieved, so the improvement of the received signal power at the PU is small, and the average rate is lower than that of the scheme of the present application. In contrast, the PU average rate of the PU-MRT scheme is the highest. This is because in the PU-MRT scheme, the BS uses MRT precoding for the direct link, which is the optimal precoding for the primary transmission, and the received signal power at the PU is the highest among all schemes, so the primary transmission rate is also the highest. In addition, the average rate of the primary transmission in all schemes does not change substantially with L, and is significantly higher than the minimum constraint value of 2 bit / s / Hz, because when the channel does not change, the change of L does not affect the optimization result, and has no effect on the primary transmission. Since the present application does not consider the overhead of estimating the composite link in the primary transmission, the primary transmission rate does not change when L changes.

[0125] Figure 5The secondary transmission error bit rate and the main transmission average rate change with the BS antenna number are given. The results given in the figure are obtained by simulation. With the increase of the BS transmitting antenna, there is more spatial freedom, which can more accurately control the signal beam, improve the signal power at the IRS, and further improve the signal strength of the reflection link at the SU, improve the signal power when s=1, and thus reduce the detection error probability. At the same time, the enhancement of the signal power at the IRS can also enhance the signal strength of the reflection link between the IRS and the PU, so the transmission rate of the main transmission link can also be improved. The bit error rate of the scheme of the application is less than that of the PU-MRT scheme, and decreases faster with the increase of the number of transmitting antennas, because the BS beamforming in the PU-MRT scheme is the MRT scheme that maximizes the signal power of the direct link, and the reflection link is not considered, so the reflection link signal power increases little with the increase of the number of BS transmitting antennas, while the scheme of the application jointly optimizes the beamforming at the BS and the phase shift matrix at the IRS, maximizes the signal power of the reflection link, and when the number of transmitting antennas increases, the signal power of the reflection link increases more, so the bit error rate decreases faster. Due to the improvement of array gain and diversity gain, the increase of BS transmitting antennas can also improve the performance of the main transmission, and the main transmission rate of all schemes increases with the increase of the number of transmitting antennas. But MRT is optimal for the main transmission, so MRT is the optimal precoding for the multiple-input single-output system, so the main transmission rate of the PU-MRT scheme based on the main transmission link increases fastest with the increase of the number of transmitting antennas, and with the increase of the number of transmitting antennas, the array gain and diversity gain of the main transmission link brought by multiple antennas are more obvious, so the increase of the main transmission rate of the PU-MRT scheme is also the fastest.

[0126] Figure 6 The change of the secondary transmission error bit rate with the number of IRS reflecting elements is given, and the results given in the figure are obtained by simulation. It can be seen that, except for the single antenna BD scheme, the error bit rate of all schemes decreases with the increase of the number of IRS reflecting elements. First, the more the number of reflecting elements of the IRS, the more the number of reflection paths, even without optimizing the IRS phase shift matrix, the received signal power of the PU and the SU is increasing. Second, the increase of the IRS elements provides more spatial freedom for controlling the signal transmission of the reflection link, and the signal power synthesized after the IRS phase shift optimization is larger, so it can more significantly increase the signal power at the SU and reduce the bit error rate.

Claims

1. A method for design and optimization of symbiotic radio systems based on intelligent reflecting surfaces, characterized by: The method comprises the following steps: (1) constructing a communication system model: on the basis of a conventional symbiotic radio system, an intelligent reflecting surface is introduced as a backscattering device, an on-off keying control mode is used to control the switch of the reflecting unit, a secondary signal is generated and scattered to a secondary user, and when the secondary user cannot eliminate the interference of the primary symbol, an energy detection method is used to detect the secondary symbol; (2) the signal-to-noise ratio when the primary user decodes the primary symbol is wherein denotes the base station transmit beamforming vector, is the channel noise, and are the channel coefficient matrices or vectors between the base station and the intelligent reflecting surface, the base station and the primary user, and the intelligent reflecting surface and the primary user, respectively, is the phase shift matrix of the intelligent reflecting surface, where ζ m ∈ [0, 1] and θ m ∈ [0, 2π] are the reflection amplitude and reflection phase shift of the m-th reflecting element, s is the secondary symbol, which takes values 0 or 1; and the average achievable rate at the primary user is (3) the secondary user uses the energy detection method to detect the secondary symbol, first samples the received signal in a primary transmission symbol period within a secondary symbol period, and then accumulates the energy of L sample values to obtain a detection statistic where n r [l] and n i [l] are the real and imaginary parts of the noise, respectively, y s,r [l] and y s,i [l] are the real and imaginary parts of the received sample of the secondary user when s = 1, respectively; and the probability of false alarm when s = 0 wherein λ is a decision threshold, Γ(x) and Γ(a,x) are a gamma function and an upper incomplete gamma function respectively, and the error probability when s = 1 is the bit error rate of the secondary symbol is the optimal decision threshold λ is (4) taking the minimization of the bit error rate of the secondary symbol as an optimization objective, an optimization mathematical model about the base station beamforming vector and the phase shift matrix of the intelligent reflecting surface is constructed under the constraints of the minimum average rate of the primary user and the total transmission power of the base station; |Θ m,m | = 1, m e {1,2,...,M} where P max denotes the total transmit power of the base station, R min denotes the minimum average rate of the primary user; the optimization problem is further converted to maximize the received signal power of the secondary user at s = 1: (5) the optimization problem is converted into two sub-problems of base station beamforming vector optimization and intelligent reflecting surface phase shift matrix optimization; (6) when the base station beamforming vector is fixed, the optimization sub-problem is converted into a convex problem, and then the intelligent reflecting surface phase shift matrix vector is obtained by using a convex optimization solver and a Gaussian randomization method; (7) when the intelligent reflecting surface phase shift matrix vector is fixed, the base station beamforming vector is obtained by using a semi-definite relaxation and a Gaussian randomization method; (8) the intelligent reflecting surface phase shift matrix vector and the base station beamforming vector are solved by using an alternating optimization algorithm.

2. The method of claim 1, wherein: In step (1), the intelligent reflecting surface is used as a backscattering device, an on-off keying control mode is used to generate a secondary signal and scatter it to a secondary user, and a beneficial multipath link can also be provided for the primary user, thereby improving the primary transmission performance.

3. The method of claim 1, wherein: In step (5), the optimization problem is converted into two sub-problems of base station beamforming vector optimization and intelligent reflecting surface phase shift matrix optimization, which specifically includes: (1) under the condition that the base station transmission beamforming vector w is fixed, the intelligent reflecting surface phase shift matrix Θ is optimized to minimize the bit error rate of the secondary symbol, that is (2) under the condition that the intelligent reflecting surface phase shift matrix Θ is fixed, the base station transmission beamforming vector w is optimized to minimize the bit error rate of the secondary symbol, that is 4. The method of claim 1, wherein: The method for converting the optimization sub-problem into a convex problem and obtaining the smart reflecting surface phase shift matrix vector by a convex optimization solver and Gaussian randomization in step (6) specifically comprises: since the optimization sub-problem is a non-homogeneous quadratic constraint quadratic programming problem, it needs to be transformed into the form of a convex optimization problem; defining where 0 is a column vector with all elements being 0, and let and let the optimization problem is converted into |V m,m | = 1, m e {1, 2,..., M} Rank(V) = 1 wherein After removing the Rank(V) = 1 constraint, the optimization problem is a convex problem, which can be solved using a convex optimization solver; and then solving the optimization problem to obtain a solution V opt An approximate solution of the phase shift matrix Θ of the intelligent reflecting surface is obtained by a method of Gaussian randomization.

5. The method for design and optimization of a coexisting radio system based on smart reflective surfaces according to claim 1, characterized in that: The base station beamforming vector is obtained by the method of semi-positive relaxation and Gaussian randomization in step (7), and specifically, since the optimization problem is a non-convex problem, let W=ww H , and let The optimization sub-problem can be converted into tr(W) < P max Rank(W) = 1 After semi-definite relaxation, the constraint Rank(W) = 1 is removed, and a standard convex semi-definite programming problem is obtained, which can be solved by using existing convex optimization solvers; suppose the solution of the semi-definite relaxation optimization problem is W opt , if the rank of W is 1, then the non-zero eigenvector of W is the solution of the optimization sub-problem. If the rank is not 1, an approximate solution of the optimization sub-problem can be obtained by using a Gaussian randomization method.

6. The method of claim 1, wherein: The alternating optimization algorithm for solving the intelligent reflecting surface phase shift matrix vector and the base station beamforming vector in step (8) is specifically as follows: at the beginning of the algorithm, the beamforming vector w is initialized by using the maximum ratio transmission precoding based on the channel vector between the base station and the primary user; in each round of alternating iteration optimization of w and Θ, the beamforming vector w is first fixed as the solution obtained in the last round of iteration optimization, and the phase shift matrix Θ is optimized; then the phase shift matrix Θ is fixed as the solution obtained in the current round of optimization, and the beamforming vector w is optimized; after the optimization of w and Θ in each round, the secondary transmission bit error rate is calculated according to the following formula: When the relative difference between the bit error rates obtained in the current iteration and the previous iteration is less than the convergence factor ε, the iteration ends.

Images