Symbiotic radio system design and optimization method based on intelligent reflection surface

Abstract

The invention discloses a transmission scheme design and performance optimization method of a symbiotic radio system based on an intelligent reflection surface. In the scheme, the intelligent reflection surface assists the multi-antenna base station to communicate with a main user, and meanwhile, the intelligent reflection surface serves as a backscattering device to generate a secondary signal and transmit information to a secondary user. The intelligent reflection surface controls the on-off of the reflection unit in an on-off keying mode, modulation and scattering of base station reflection signals are achieved, and a secondary user carries out secondary symbol detection through an energy detection method. On the premise of ensuring the transmission rate of main user transmission, joint optimization is performed on a base station beam forming vector and a phase shift matrix of an intelligent reflection surface so as to minimize the error probability of scattering transmission. An original optimization problem is a non-convex problem and is converted and solved by adopting a positive semidefinite relaxation method, an alternating iterative optimization method and other methods. Compared with a conventional symbiotic radio transmission scheme, the scheme provided by the invention has a higher primary transmission rate and a lower secondary transmission bit error rate.

Description

Technical Field

[0001] The invention relates to the technical field of wireless communication, in particular to designing a symbiotic radio system based on a smart reflective surface, and jointly optimizing a beamforming vector at a base station and a phase shift matrix of the smart reflective surface. Background Art

[0002] The large-scale commercial use of 5G technology has pushed the Internet of Things into a new era, making the Internet of Everything possible [LI B, QIANZ, LIU L, et al. Computation Offloading for Edge Computing in RIS-Assisted Symbiotic Radio Systems [J]. IEEE Transactions on Network Science and Engineering, 2023, 10 (6): 4033-4045]. In order to widely deploy billions of IoT devices with sensing, computing and wireless communication capabilities, it is necessary to solve the two key problems of spectrum scarcity and energy supply. Backscattering technology is one of the key technologies to achieve low-power communication. Symbiotic Radio (SR) is based on backscattering communication. It can not only efficiently utilize spectrum resources, but also has the characteristics of ultra-low power consumption and sustainability. It is a green communication method [DAI Z, LIR, XU J, et al. Rate-region characterization and channel estimation for cell-free symbiotic radio communications [J]. IEEE Transactions on Communications, 2022, 71 (2): 674-687.]. In the SR system, the backscatter device (BD) acts as a secondary transmitter, modulates the signal received from the primary transmitter to generate a secondary signal, and sends it to the secondary receiver in the form of reflection, thereby sharing spectrum and energy resources [LIANG YC, ZHANG Q, WANG J, et al. Backscatter communication assisted by reconfigurable intelligent surfaces [J]. Proceedings of the IEEE, 2022, 110 (9): 1339-1357.]. In addition, according to the length of the secondary symbol period, the relationship between the primary transmission and the secondary transmission can be divided into two modes: symbiotic and parasitic. When the secondary symbol period is much longer 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 composed of the primary transmission link and the scattering transmission link, eliminate the interference caused by the secondary symbol to the primary transmission, and the scattering link can become an additional, usable multipath link to improve the performance of the primary transmission.At this time, the main transmission and the secondary transmission are in a symbiotic relationship [Zhang Q, Zhou HC, Liang YC, 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 equivalent to the primary symbol period, the main transmission receiver cannot eliminate the impact of the secondary transmission on the main transmission, and the secondary symbol will interfere with the main transmission. The secondary transmission and the main transmission are in a parasitic relationship [LONG R, LIANG YC, 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. Under the condition of satisfying 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 the SR system, due to the double fading of the secondary transmission link, the received signal power of the secondary receiver is very low, and the transmission performance is greatly restricted. Intelligent Reflecting Surface (IRS) is a RF signal reflection device composed of multiple low-cost, passive reflection units. The reflection phase shift and amplitude can be intelligently controlled by changing the parameters of each reflection unit of IRS [YUAN X, ZHANG YJA, SHI Y, et al. Reconfigurable-intelligent-surface empowered wireless communications: Challenges and opportunities [J]. IEEE Wireless Communications, 2021, 28 (2): 136-143.]. Introducing IRS in wireless communication systems can improve the signal propagation environment, reduce transmission losses, and improve the energy efficiency of the system. The controllable reflection characteristics of IRS make it very suitable as a BD in the SR system. In the symbiotic relationship SR system based on IRS, not only can the secondary transmission be achieved by controlling the reflection characteristics of IRS, but also the performance of the primary transmission can be improved. Many literatures have studied this. The paper [ZHANG Q, LIANG YC, POOR H V. Reconfigurable intelligent surface assisted MIMO symbiotic radio networks [J]. IEEE Transactions on Communications, 2021, 69 (7): 4832-4846.] applies IRS to the MIMO SR system, generates a secondary binary phase shift keying (BPSK) modulated signal by controlling the phase shift matrix of the IRS, and uses the secondary transmission signal to enhance the transmission quality of the primary transmission link, thus achieving mutual symbiosis between the primary and secondary transmissions. Under the constraints of the signal-to-noise ratio of the secondary transmission and the average rate of the primary transmission, the paper minimizes the transmission power of the BS by jointly optimizing the beamforming vector of the BS and the IRS phase shift matrix.Reference [ZHOU H, KANG X, LIANGY C, et al. Cooperative beamforming for reconfigurable intelligent surface-assisted symbiotic radios [J]. IEEE Transactions on Vehicular Technology, 2022, 71 (11): 11677-11692.] proposes an SR system optimization scheme using IRS as BD for both perfect and imperfect channel state information (CSI). Under perfect CSI conditions, the BS transmit power is minimized by jointly optimizing the BS beamforming vector and the IRS phase shift matrix; under imperfect CSI conditions, a 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 paper [WANG J, LIANG YC, 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 reflection unit to generate a secondary signal. It also provides a reflection link for the macro user to improve the transmission performance between the macro base station and the macro user. The paper proposes two secondary multi-user transmission schemes, space division multiple access and time division multiple access, and minimizes the system power consumption by optimizing the phase shift matrix of IRS and the beamforming vector of the macro base station. The literature [XU ​​X, LIANG YC, YANG G, et al. Reconfigurable intelligent surface empowered symbiotic radio overbroadcasting signals [J]. IEEE Transactions on Communications, 2021, 69(10): 7003-7016.] studies an IRS-based SR downlink broadcast communication system, in which the IRS assists the BS to send broadcast signals to multiple primary receivers, and at the same time generates a secondary BPSK modulated signal by adjusting the IRS phase shift matrix to transmit secondary information to the IoT receiver, sharing the main transmission spectrum and power resources.The literature presents an optimization algorithm for minimizing BS transmit power by jointly optimizing the BS beamforming and the IRS phase shift matrix. Summary of the invention

[0004] The purpose of the present invention is to provide a design and optimization method for a downlink symbiotic radio system based on a smart reflective surface to improve system performance and transmission efficiency. The method first constructs a communication system model, introduces a smart reflective surface as a backscattering device, and uses an on-off keying method to control the switch of the reflective unit to generate a secondary signal and scatter it to a secondary user. The secondary user uses an energy detection method to detect the secondary symbol to ensure effective reception of the signal.

[0005] To achieve the above purpose, the present invention adopts the following technical solutions: First, a communication system model is constructed and the bit error rate formula of the secondary symbol is derived. Taking the minimization of the secondary symbol bit error rate as the optimization goal, an optimization mathematical model is constructed under the constraints of the minimum average rate of the primary user and the total transmission power of the base station. Then, the optimization problem is transformed into the optimization sub-problems of the base station beamforming vector and the smart reflection surface phase shift matrix, and the two sub-problems are solved respectively by using a convex optimization solver and a Gaussian randomization method. Finally, an alternating optimization algorithm is used to iteratively optimize the smart reflection surface phase shift matrix and the base station beamforming vector until convergence is reached.

[0006] The specific steps are as follows:

[0007] (1) Analyze the signal transmission process and construct a communication system model: Based on the conventional symbiotic radio system, a smart reflective surface is introduced as a backscattering device. The on-off keying method is used to control the switch of the reflective unit to generate a secondary signal and scatter it to the secondary user. The secondary user uses the energy detection method to perform symbol detection.

[0008] (2) The bit error rate formula of the secondary symbol is derived, and the optimization mathematical model is constructed under the constraints of the minimum average rate of the primary user and the total transmission power of the base station, with the minimization of the secondary symbol bit error rate as the optimization goal;

[0009] (3) The optimization problem is transformed into two sub-problems: optimization of the smart reflection surface phase shift matrix and optimization of the base station beamforming vector;

[0010] (4) When the base station beamforming vector is fixed, the phase shift matrix of the smart reflection surface is obtained by converting the optimization subproblem into a convex problem and then using a convex optimization solver and a Gaussian randomization method.

[0011] (5) When the smart reflection surface phase shift matrix is ​​fixed, the beamforming vector of the base station is obtained by transforming the optimization subproblem into a convex problem and then using semi-positive definite relaxation and Gaussian randomization method;

[0012] (6) An alternating optimization algorithm is used to iteratively solve the smart reflection surface phase shift matrix and the base station beamforming vector until convergence is reached.

[0013] Furthermore, step (1) uses the intelligent reflecting surface as a backscattering device and the secondary user uses an energy detection method to detect the secondary symbol, which specifically includes: first, the intelligent reflecting surface includes M reflecting units, and each reflecting unit can independently control its phase shift. The intelligent reflecting surface receives the main transmission signal from the base station, and generates secondary symbols by adjusting the on and off states of the reflecting units to achieve effective information transmission to the secondary users. The period of the secondary symbol is L times the period of the main symbol. Within a secondary symbol period, the secondary user samples and accumulates the energy of the received scattered signal, calculates the energy value within each main symbol period, and compares these accumulated energy values ​​with a preset decision threshold. If the accumulated energy value is higher than the decision threshold, the secondary symbol is judged to be 1; if it is lower than the decision threshold, it is judged 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] Furthermore, the Gaussian randomization method in step (4) is specifically as follows: in the case of a fixed base station beamforming vector, assuming that the solution obtained by solving the subproblem using a convex optimization solver is V opt , if its rank is 1, then for V opt Perform eigenvalue decomposition and assume that the non-zero eigenvectors obtained are It can be obtained by the following formula get

[0016]

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

[0018]

[0019] in Represents the M+1th element, obviously there is Then use V in the average rate constraint of the primary user in the optimization subproblem to Replace to determine whether the constraint is satisfied. If satisfied, After all random vectors are processed, select the feasible solution from the feasible solution set. The largest feasible solution is Will Remove the M+1th element of to obtain the M-dimensional column vector v opt , and finally according to Θ opt =diag((v opt ) H ) to obtain the IRS phase shift matrix Θ opt .

[0020] Compared with the existing related research, the present invention has the following beneficial technical effects: (1) Currently, relevant literature on the research of symbiotic radio systems based on intelligent reflective surfaces can be retrieved, such as [ZHOU H, KANG X, LIANG YC, 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 YC, 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 studies use binary phase shift keying to modulate and generate secondary symbols, and the interference of the main transmission symbols must be eliminated before the secondary symbol detection. This not only makes the decoding of the secondary symbols restricted by the correct decoding of the main symbols, but also increases the reception processing complexity and power consumption at the secondary user. The method of the present invention does not need to decode the main symbol first, and directly detects the secondary symbol through the energy detection method, which simplifies the processing process. (2) The present invention adopts an on-off keying modulation method to reduce the processing complexity of the secondary user, avoid the detection and cancellation of the main symbol, and enable the secondary user to directly perform symbol detection through the energy detection method. (3) The present invention minimizes the bit error rate of the secondary transmission by jointly optimizing the beamforming vector of the base station and the phase shift matrix of the smart reflection surface. In view of the fact that it is difficult to find the optimal solution for non-convex problems, an alternating iterative optimization algorithm is proposed to transform the original problem into a convex problem for solution 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 smart reflection surface phase shift matrix random phase shift scheme and the base station beamforming vector using the maximum ratio transmission precoding scheme, the scheme proposed by the present invention not only significantly improves the average rate of the main user, but also achieves a lower secondary transmission bit error rate. BRIEF DESCRIPTION OF THE DRAWINGS

[0021] Figure 1 A communication system model of the present invention;

[0022] Figure 2The process of convergence of the alternating iterative algorithm proposed by the present invention;

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

[0024] Figure 4 is the effect 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 This is the effect of the number of reflective elements on the secondary symbol bit error rate of the smart reflective surface. DETAILED DESCRIPTION

[0027] The SR system model based on IRS studied in this invention is as follows: Figure 1 As shown in Figure 1, the system consists of a BS, an IRS, a PU, and a SU. The BS is equipped with N transmitting antennas, the IRS contains M reflecting elements, and the user is equipped with a single antenna. The symbol rate of the primary transmission is much greater than the symbol rate of the secondary transmission. Assuming that L primary symbols can be transmitted in one secondary symbol period, that is, T s =L×T p , L>>1, where T p is the main symbol period, T s is the secondary symbol period. Assuming that all channels are block flat fading channels, at least in one secondary symbol period T s The internal channel state remains unchanged. Due to the obstruction of obstacles, there is no direct transmission link between BS and SU. The channel coefficient matrices or vectors between BS and IRS, BS and PU, IRS and PU, and IRS and SU are respectively recorded as The phase shift matrix of IRS is where ζ m ∈[0,1] and θ m ∈[0,2π] is the reflection amplitude and reflection phase shift of the mth reflection element, m∈{1,2,…,M}. In order to achieve the maximum reflection gain, the reflection amplitude of the IRS reflection element is set to 1.

[0028] IRS reflects the signal transmitted by BS, generates a secondary OOK signal by controlling the on and off of the reflection unit and sends it to SU, and controls the reflection phase shift of each reflection unit to enhance the strength of the main transmission signal. The secondary symbol is denoted as s, s = 1 or s = 0. The lth primary symbol transmitted in a secondary symbol period is denoted as x[l], where l∈{1,…,L}, The lth symbol received by PU can be expressed 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, and 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 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 in a secondary symbol period is very small, ignoring the impact of pilot symbols on the transmission rate. 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 a mean of 0 and a variance of 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 values ​​are respectively

[0041]

[0042]

[0043] Among them, x r [l] and x i [l] are the real and imaginary parts of the main transmission symbol x[l], both of which obey a Gaussian distribution with a mean of 0 and a variance of 1 / 2. s,r The conditional mean and conditional variance of [l] are

[0044]

[0045]

[0046] Similarly, we can get E(y s,i [l]|s=1)=0 and Therefore, when s = 1, y s,r [l] and y s,i [l] has a mean of 0 and a variance of Gaussian distribution.

[0047] SU converts a secondary symbol period T s The energy of the L symbol samples in the sample is accumulated to obtain the detection statistic:

[0048]

[0049] The detection statistic Q when s=0 is the sum of the squares of 2L independent and identically distributed Gaussian variables, which is a random variable that obeys the central chi-square distribution, and its probability density function is

[0050]

[0051] in, represents the full gamma function.

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

[0053]

[0054] SU compares the detection statistic Q with the decision threshold to make a decision. The decision criterion is:

[0055]

[0056] When the secondary transmission symbol is s=0, the probability of misjudgment is

[0057]

[0058] in, represents 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 minimize the bit error rate, which can be obtained by e Find the derivative with respect to λ and set the derivative equal to 0 to obtain the optimal λ:

[0064]

[0065] According to P e From the expression of , it can be known that 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 invention considers minimizing the bit error rate of the secondary transmission under the condition of satisfying the average transmission rate of the primary transmission. The optimization problem can be formulated as

[0066] P1:

[0067] stC1:

[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 main transmission to be no less than R min , C2 constrains the BS's transmission power to not exceed P max , C3 constrains the reflection amplitude coefficient of the IRS reflection unit to be 1.

[0071] According to P e From the expression, we can know that the bit error rate P e The signal power at SU when s = 1 Since Γ(a,x) is a monotonically decreasing function of x, the signal power The larger the bit error rate P e Therefore, the optimization goal of P1 can be changed to maximize the signal power of SU when s=1, that is,

[0072] P2:

[0073] stC1:

[0074] C2:

[0075] C3:|Θ m,m |=1,m∈{1,2,…,M}

[0076] The objective function and constraints of P2 are both non-convex functions, and the optimization variables are coupled with each other, so it is very difficult to solve directly and needs to be transformed first. Since it is difficult to jointly solve the BS's transmit beamforming vector w and the IRS's phase shift matrix Θ, the optimization problem P2 is first decomposed into two sub-problems that optimize w and Θ respectively, and then the solution to the original problem is obtained by alternately iterating the two sub-problems.

[0077] The optimization subproblem when the BS transmit beamforming vector w is fixed is:

[0078] P3:

[0079] stC1:

[0080] C3:|Θ m,m |=1,m∈{1,2,…,M}

[0081] definition Rewrite P3 as

[0082] P4:

[0083] stC4:

[0084] C5:|v m |=1,m∈{1,2,…,M}

[0085] P4 is a non-homogeneous quadratic constrained quadratic programming problem that needs to be transformed into a convex optimization problem. Definition Where 0 is a column vector whose elements are all 0, And order Obviously, V±0, Rank(V)=1. By rewriting the objective function in P4 as tr(VR1), constraining v in C5 m Replace with V m,m , and order The non-convex constraint C4 can be rewritten as P4 can be converted to

[0086] P5:

[0087] stC6:

[0088] C7:|V m,m |=1,m∈{1,2,…,M}

[0089] C8:V±0

[0090] C9:Rank(V)=1

[0091] In the optimization problem P5, except for the constraint Rank(V)=1, which is still a non-convex constraint, all other constraints are already convex constraints, and the objective function is also a convex function. After relaxation, removing the constraint C9 in P5, it becomes a convex optimization problem, which can be solved using the convex problem solving algorithm or convex optimization solver. Assume that the solution obtained after solving the optimization problem is V opt , if its rank is 1, then for V opt Perform eigenvalue decomposition and assume that the non-zero eigenvectors obtained are It can be obtained by the following formula get

[0092]

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

[0094]

[0095] in Represents the M+1th element, obviously there is Then use V in the average rate constraint of the primary user in the optimization subproblem to Replace to determine whether the constraint is satisfied. If satisfied, After all random vectors are processed, select the feasible solution from the feasible solution set. The largest feasible solution is Will Remove the M+1th element of to obtain the 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] Constraint C13 in the optimization problem P7 is non-convex. By performing semi-positive definite relaxation and removing constraint C13, we can get a standard convex semi-positive definite programming problem, which can be solved using existing solution algorithms or convex optimization solvers. Assume that the solution of the optimization problem after semi-positive definite 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, convergence factor ε that controls the end of the iteration, number of Gaussian randomizations U, initialization of the beamforming vector at the beginning of the algorithm

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

[0109] (2) Fixed w = w (k-1) , solve problem P3, and get solution V (k) , for V (k) Perform eigenvalue decomposition and Gaussian randomization to obtain according to Get v (k) , and then according to v (k) Get Θ (k) .

[0110] (3) Fixed Θ = Θ (k) , solve problem P6, and get the solution W (k) , for W (k) Perform eigenvalue decomposition and Gaussian randomization to obtain w (k) .

[0111] (4) According to the 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 present invention will be further described in detail below with reference to the accompanying drawings. Unless otherwise specified, in the simulation, the number of base station antennas N = 3, the number of reflection units of the IRS M = 20, and the minimum average rate requirement of the primary user is R min =2bit / s / Hz, Gaussian randomization times U = 10 4 , P max =30dBm, L=20. The position of each node in the system is described by three-dimensional coordinates in meters (m), where the base station coordinates are (0,0,20), the IRS coordinates are (0,30,10), the primary user coordinates are (30,0,0), and the secondary user coordinates are (0,40,0). The channel between each node is a Rice fading channel, 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] in is the path loss, L0 = -30dB represents the path loss at a reference distance of 1 meter, α BI is the path loss exponent, dBI is the distance between BS and IRS; β BI is the Rice fading factor; G LoS G represents 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; NLoS is the channel coefficient matrix of the non-line-of-sight transmission part, and each element in the matrix is ​​a complex Gaussian random variable with zero mean and unit variance. Similarly, the models of the IRS-user channel and the BS-user channel are similar, and the channel coefficient vectors are

[0117]

[0118]

[0119]

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

[0121] The simulation also provides the results of the following three benchmark schemes 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 that of solving the optimization subproblem P6 of the present invention; (2) Benchmark Scheme 2 - IRS Random Phase Shift Scheme: The amplitude ζ of the elements in the phase shift matrix Θ of the IRS is m are all 1, the phase shift is θ m Randomly select a value from [0,2π], where m∈{1,2,…,M}, and the beamforming vector of the base station is obtained by a method similar to the method for solving the optimization problem P6 of the present invention; (3) Benchmark solution 3 - PU-MRT solution: The beamforming vector of the BS adopts MRT precoding and is the channel coefficient vector between the BS and the PU The conjugate transpose of , the phase shift matrix of IRS is obtained by a method similar to that of the present invention for solving the optimization problem P3.

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

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

[0124] Figure 4The changes of the secondary transmission bit error rate and the main transmission average rate of each scheme with the ratio L of the secondary symbol period to the main symbol period are given. The figures show the results obtained by simulation. It can be seen that the bit error rate decreases as the size of L increases. This is because SU adopts the energy detection method. The detection statistic when s=0 is the accumulated noise energy, and when s=1 is the accumulated noise energy and signal energy. When L increases, the accumulated number of samples increases. Obviously, when s=1, the accumulated energy increases more than when s=0. Therefore, the increase in L reduces the probability of detection errors. Compared with the comparison scheme, the bit error rate of the scheme of the present invention decreases at the highest rate as L increases. This is because the scheme of the present invention jointly optimizes the BS beamforming and the IRS phase shift matrix, so that when L increases, the accumulated signal energy at the SU increases more. From Figure 4 It can also be seen that the average rate of PU in the scheme of the present invention 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 2bit / s / Hz. This is mainly attributed to the joint optimization of base station precoding and IRS phase shift in the scheme of the present invention. While minimizing the probability of SU detection errors, it can also enable the signal of the reflected link at the PU to achieve partial coherent superposition with the signal of the direct link, thereby improving the received signal power of 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 relatively limited. In the IRS random phase shift scheme, the phase shift of each transmitting unit is randomly selected, and the phases of the reflected signals and direct link signals received by the PU are random, and coherent superposition cannot be achieved. The improvement of the received signal power of the PU is small, and the average rate is lower than that of the scheme of the present invention. In contrast, the PU average rate of the PU-MRT scheme is the highest. This is because in the PU-MRT scheme, the BS adopts MRT precoding for the direct link, which is the optimal precoding for the main transmission. The received signal power at the PU is the highest among all schemes, so the main transmission rate is also the highest. In addition, the average rate of the main transmission under all schemes basically does not change with L, and is significantly higher than the minimum constraint value of 2bit / s / Hz. This is because when the channel does not change, the change of L does not affect the optimization result and has no effect on the main transmission. Since the present invention does not consider the overhead of estimating the composite link in the main transmission, the main transmission rate remains unchanged when L changes.

[0125] Figure 5The secondary transmission bit error rate and the average rate of the main transmission of each scheme are given as the number of BS antennas changes. The results given in the figure are all simulated results. With the increase of the BS's transmitting antennas, there is a greater degree of spatial freedom, which can more accurately control the signal beam, increase the signal power at the IRS, and then increase the strength of the reflected link signal at the SU, and increase the signal power when s=1, thereby reducing the probability of detection error. At the same time, the enhancement of the signal power at the IRS can also enhance the strength of the reflected link signal 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 present invention is lower than that of the PU-MRT scheme, and decreases faster with the increase of the number of transmitting antennas. This is because the BS beamforming in the PU-MRT scheme is an MRT scheme that maximizes the signal power of the direct link, and does not consider the reflection link. Therefore, the reflection link signal power increases very little with the increase of the number of BS transmitting antennas. The scheme of the present invention jointly optimizes the beamforming at the BS and the phase shift matrix at the IRS to maximize the signal power of the reflection link. 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 in the number of BS transmit antennas can also improve the performance of the main transmission. The main transmission rate of all schemes increases with the increase in the number of transmit antennas. However, MRT is optimal for the main transmission, so MRT is the optimal precoding for the multiple-input single-output system. Therefore, the main transmission rate of the PU-MRT scheme based on the main transmission link increases the fastest when the number of transmit antennas increases. Moreover, as the number of transmit antennas increases, the increase in array gain and diversity gain of the main transmission link brought by multiple antennas is more obvious than that of other schemes. Therefore, the main transmission rate of the PU-MRT scheme also increases the fastest.

[0126] Figure 6 The secondary transmission bit error rate is shown as the number of IRS reflective elements changes. The results are all obtained by simulation. It can be seen that except for the single-antenna BD scheme, the bit error rate of all schemes decreases as the number of IRS reflective elements increases. First, the more reflective elements there are in the IRS, the more reflection paths there are. Even without optimizing the IRS phase shift matrix, the received signal power of the PU and SU is increasing. Secondly, the increase in IRS elements provides greater spatial freedom for controlling the signal transmission of the reflection link. The synthesized signal power is larger after the IRS phase shift is optimized, so the signal power at the SU can be more significantly increased, reducing the bit error rate.

Claims

1. A design and optimization method for a symbiotic radio system based on a smart reflective surface, characterized in that: The following steps are involved: (1) Constructing a communication system model: Based on the conventional symbiotic radio system, a smart reflective surface is introduced as a backscattering device. The switch of the reflective unit is controlled by on-off keying to generate a secondary signal and scatter it to the secondary user. The secondary user detects the secondary symbol using an energy detection method. (2) The bit error rate formula of the secondary symbol is derived. Taking the minimization of the secondary symbol bit error rate as the optimization goal, an optimization mathematical model for the base station beamforming vector and the smart reflection surface phase shift matrix is ​​constructed under the constraints of the minimum average rate of the primary user and the total transmission power of the base station. (3) Convert the optimization problem into two sub-problems: base station beamforming vector optimization and smart reflection surface phase shift matrix optimization; (4) When the base station beamforming vector is fixed, the optimization subproblem is transformed into a convex problem, and then the phase shift matrix vector of the smart reflection surface is obtained by using a convex optimization solver and a Gaussian randomization method; (5) When the smart reflection surface phase shift matrix vector is fixed, the base station beamforming vector is obtained by converting the optimization subproblem into a convex problem and then using semi-positive definite relaxation and Gaussian randomization methods; (6) Use the alternating optimization algorithm to solve the smart reflection surface phase shift matrix vector and the base station beamforming vector.

2. The design and optimization method of a downlink symbiotic radio system based on a smart reflective surface according to claim 1, characterized in that: In step (1), the intelligent reflective surface is used as a backscattering device, and a secondary signal is generated by on-off keying and scattered to the secondary user, which can also provide a beneficial multipath link for the primary user and improve the primary transmission performance.

3. The design and optimization method of a downlink symbiotic radio system based on a smart reflective surface according to claim 1, characterized in that: When the secondary user cannot eliminate the interference of the primary symbol, the secondary user detects the secondary symbol using an energy detection method.

4. The design and optimization method of a downlink symbiotic radio system based on a smart reflective surface according to claim 1, characterized in that: The mathematical model in step (2) includes modeling the average transmission rate of the primary user and the bit error rate of the secondary user, as follows: The signal-to-noise ratio when decoding the main symbol at the primary user is: In the formula, represents the BS transmit beamforming vector; is the channel noise; and are the channel coefficient matrices or vectors between BS and IRS, BS and PU, and IRS and PU respectively; is the phase shift matrix of IRS, where ζ m ∈[0,1] and θ m ∈[0,2π] is the reflection amplitude and reflection phase shift of the mth reflection element; s is a secondary symbol, which can be 0 or 1. Assuming that the probability of s=1 and 0 is 1 / 2, the average achievable rate at the primary user is: The secondary user uses the energy detection method to detect the secondary symbol. It first samples the received signal with the main transmission symbol period as the period in a secondary symbol period and accumulates the energy. The energy accumulation value is the detection statistic. The SU accumulates the energy of L symbol samples in a secondary symbol period and obtains the detection statistic as Where n r [l] and n i [l] are n p The real and imaginary parts of [l]; y s,r [l] and y s,i [l] are the real and imaginary parts of the symbol sample value received at the secondary user when s = 1. When the secondary transmitted symbol is s = 0, the probability of misjudgment is Where λ is the decision threshold; Γ(x) and Γ(a,x) are the gamma function and the upper incomplete gamma function respectively. When the secondary transmission symbol is s=1, the probability of misjudgment is Assuming that the probability of s = 1 or 0 is 1 / 2, the bit error rate of the secondary symbol is 5. The design and optimization method of a downlink symbiotic radio system based on a smart reflective surface according to claim 1, characterized in that: The optimization mathematical model in step (2) takes the minimum average rate of the primary user and the total transmission power of the base station as constraints, and takes minimizing the secondary symbol bit error rate as the optimization goal. The optimization problem is constructed as follows: I m,m |=1,m∈{1,2,…,M} Where P max Represents the total transmission power of the base station, R min Indicates the minimum average rate of the primary user.

6. The design and optimization method of a downlink symbiotic radio system based on a smart reflective surface according to claim 5, characterized in that: Since the bit error rate is related to the signal power at the secondary user when s=1. Since the gamma function is a monotonically decreasing function of x, the greater the signal power, the smaller the bit error rate. Therefore, the optimization goal can be changed from minimizing the secondary symbol bit error rate to maximizing the signal power at the secondary user when s=1, that is, I m,m |=1, m∈{1,2,…,M}.

7. The design and optimization method of a downlink symbiotic radio system based on a smart reflective surface according to claim 1, characterized in that: Step (3) converts the optimization problem into two sub-problems: base station beamforming vector optimization and smart reflection surface phase shift matrix optimization, which specifically includes: (1) When the BS transmit beamforming vector w is fixed, the smart reflection surface phase shift matrix Θ is optimized to minimize the secondary symbol bit error rate, that is, I m,m |=1,m∈{1,2,…,M} (2) When the IRS phase shift matrix Θ is fixed, the BS transmit beamforming vector w is optimized to minimize the secondary symbol bit error rate, that is, 8. The design and optimization method of a downlink symbiotic radio system based on a smart reflective surface according to claim 1, characterized in that: Step (4) of obtaining the smart reflective surface phase shift matrix vector by using a convex optimization solver and Gaussian randomization method specifically includes: Since the optimization subproblem is a non-homogeneous quadratic constrained quadratic programming problem, it needs to be transformed into a convex optimization problem. Definition Where 0 is a column vector whose elements are all 0, And order The optimization problem can be transformed into: In m,m |=1,m∈{1,2,…,M} Rank(V)=1 In the formula, After removing the Rank(V)=1 constraint, the optimization problem becomes a convex problem and can be solved using a convex optimization solver. opt The approximate solution of the phase shift matrix Θ of the smart reflective surface is obtained by Gaussian randomization method.

9. The design and optimization method of a downlink symbiotic radio system based on a smart reflective surface according to claim 1, characterized in that: Step (5) obtains the base station beamforming vector by semi-positive relaxation and Gaussian randomization, specifically: Since the optimization problem is a non-convex problem, let W = ww H , and then The optimization subproblem can be transformed into tr(W)≤P max Rank(W)=1 Then perform semidefinite relaxation and remove the constraint Rank(W) = 1, and you can get a standard convex semidefinite programming problem, which can then be solved using an existing solution algorithm or convex optimization solver. Assume that the solution to the optimization problem after semidefinite relaxation is W opt , if its rank is 1, then perform eigenvalue decomposition on it, and the non-zero eigenvector is the solution to the optimization subproblem; If the rank is not 1, Gaussian randomization can be used to obtain an approximate solution to the optimization subproblem.

10. The design and optimization method of a downlink symbiotic radio system based on a smart reflective surface according to claim 1, characterized in that: The alternating optimization algorithm for solving the smart reflection surface phase shift matrix vector and the base station beamforming vector in step (6) is specifically as follows: the beamforming vector w is initialized at the beginning of the algorithm. To ensure the feasibility of the initial iteration of the algorithm, w can be initialized using the maximum ratio transmit precoding according to the channel coefficient vector between the BS and the PU to maximize the received signal-to-noise ratio of the main transmission link. In each round of alternating iterative optimization of w and , the beamforming vector w is first fixed to the solution obtained in the previous round of iterative optimization, and the phase shift matrix Θ is optimized; then the phase shift matrix is ​​fixed to the solution obtained in this round of optimization, and the beamforming vector w is optimized. After both w and are optimized in this round, the bit error rate is calculated according to the following formula: When the relative difference in bit error rate between this iteration and the previous iteration is less than the convergence factor ε, the iteration ends.

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