Phase shift model in IRS-assisted OFDMA system and system optimization method

Abstract

The invention discloses a modeling method of each subcarrier phase shift model in an intelligent reflecting surface (IRS) assisted downlink orthogonal frequency division multiplexing multiple access system, and a system optimization method. The method comprises the following steps: firstly, calculating the IRS phase shift quantity at a plurality of frequencies under a sufficient number of center frequency phase points, and fitting the relationship between the phase shift and the center frequency phase shift and the frequency by adopting a quadratic function curve with coefficients related to the frequency, so as to obtain a function of the center frequency phase shift and other frequency phase shifts; based on the designed phase shift model, the optimization problems of optimizing an IRS center frequency phase shift matrix, subcarrier and power distribution and maximizing the system and rate are constructed. And finally, an original problem is converted into a convex problem through successive convex approximation, alternate optimization and other methods, and the convex problem is solved. Simulation results prove that compared with an optimization scheme which assumes that the phase shifts of the IRS on all subcarriers in a transmission band are the same, the scheme which is optimized under the phase shift model provided by the invention can obtain a higher actual reachable sum rate under an actual IRS phase shift condition.

Description

Technical Field

[0001] The invention relates to the field of information communication, and in particular to a phase shift model and a system optimization method in an IRS-assisted OFDMA system. Background Art

[0002] As society's demand for mobile communication services continues to grow, mobile communication networks need to provide higher quality services to more users. Improving transmission rate and spectrum efficiency has always been an important issue in the research and development of mobile communication systems [Qiao L, Zhang J, Gao Z, et al. Massive access in media modulation based massive machine-type communications [J]. IEEE Transactions on Wireless Communications, 2021, 21 (1): 339-356]. In recent years, the application of intelligent reflecting surfaces (IRS) to improve the performance of wireless communication systems has been one of the hot issues in academic research. IRS is a surface composed of a large number of low-cost passive reflection units. Each reflection unit can independently control the phase shift of the incident signal reflection, which can achieve control of the wireless communication propagation environment to a certain extent [Wu Q, Zhang R. Towards smart and reconfigurable environment: Intelligent reflecting surface aided wireless network [J]. IEEE Communications Magazine, 2019, 58 (1): 106-112]. By applying IRS, the performance of wireless communication systems in complex communication environments can be effectively improved and the system energy consumption can be reduced. Existing related studies have shown that with the assistance of IRS, the coverage of wireless networks can be significantly expanded, and the spectrum efficiency and energy efficiency can also be significantly improved [Yuan X, Zhang YJ A, Shi Y, et al. Reconfigurable-intelligent-surface empowered wireless communications: Challenges and opportunities [J]. IEEE Wireless Communications, 2021, 28(2): 136-143].

[0003] Orthogonal Frequency Division Multiplexing (OFDM) is a multi-carrier modulation technology [Lau CC, Zoltowski M D. Reduced dimension equalizer and interference canceller for MIMO-OFDM [C]. IEEE Military Communications Conference (MILCOM). San Diego, USA: IEEE, 2008: 1-7], which can effectively enhance the system's ability to resist multipath interference. Orthogonal Frequency Division Multiple Access (OFDMA) is a multiple access technology developed from OFDM technology. It achieves multi-user communication by dynamically allocating subcarriers to multiple users, and can effectively overcome the fading of wireless channels and obtain higher spectrum utilization. It is one of the key technologies in the 4th and 5th generation mobile communication systems. Resource allocation in OFDMA system is an important factor to ensure fairness among users and affect system performance, and is one of the important research topics in academia [Rhee W, Cioffi J M. Increase in capacity of multiuser OFDM system using dynamic subchannel allocation [C]. IEEE 51st vehicular technology conference proceedings (VTC). Tokyo, Japan: IEEE, 2000, 2: 1085-1089]. Applying IRS in OFDM and OFDMA systems and using IRS to intelligently control the propagation environment can significantly improve system performance. At present, there are some literatures that study performance analysis, channel estimation and optimization design in IRS-assisted OFDM systems.Reference [Yang Y, Zheng B, Zhang S, et al. Intelligent reflecting surface meets OFDM: Protocol design and rate maximization [J]. IEEE Transactions on Communications, 2020, 68 (7): 4522-4535] proposes an IRS reflection unit grouping method for the IRS-assisted single-input single-output (SISO) OFDM communication system by utilizing the channel correlation between adjacent IRS reflection units to reduce the overhead of channel training and estimation. Furthermore, the power allocation between subcarriers and the IRS reflection coefficient are jointly optimized based on the estimated channel state information (CSI) to maximize the achievable rate. Reference [Zheng B, Zhang R. Intelligent reflecting surface-enhanced OFDM: Channel estimation and reflection optimization [J]. IEEE Wireless Communications Letters, 2019, 9 (4): 518-522] For the IRS-assisted SISO-OFDM system, an IRS reflection mode is designed to improve the efficiency of channel estimation, and based on the estimated CSI, a low-complexity reflection coefficient optimization algorithm is designed to maximize the average achievable rate. Reference [Li H, Liu R, Liy M, et al. IRS-enhanced wideband MU-MISO-OFDM communication systems [C]. IEEE Wireless Communications and Networking Conference (WCNC). Seoul, South Korea: IEEE, 2020: 1-6] For the IRS-assisted downlink multiple user multiple input single output (MU-MISO) OFDM system, the correlation characteristics of sum rate maximization and mean square error minimization are analyzed, and an efficient joint algorithm of transmit beamforming and IRS reflection coefficient is designed to maximize the system average sum rate.Reference [Yang Y, Zhang S, Zhang R. IRS-enhanced OFDMA: Joint resource allocation and passive beamforming optimization [J]. IEEE Wireless Communications Letters, 2020, 9 (6): 760-764] proposes a passive beamforming scheme for IRS-assisted downlink OFDMA communication system to maximize the minimum user rate. This scheme adjusts the IRS reflection coefficient at different time slots within each channel coherent block and only serves some users in each time slot, thus achieving higher passive beamforming gain through multi-user diversity.

[0004] There are a few papers that study the IRS reflection model in broadband systems and the system optimization problem based on the broadband phase shift model. The paper [Cai W, Li H, Li M, et al. Practical modeling and beamforming for intelligent reflecting surface aided wideband systems [J]. IEEE Communications Letters, 2020, 24 (7): 1568-1571] studies the relationship between the amplitude, phase shift and frequency of the reflected signal for the IRS-assisted SISO-OFDM system, and proposes a mathematical model of the IRS reflection coefficient in the broadband system. Based on this model, the subcarrier power allocation and the IRS reflection coefficient are jointly optimized to maximize the average user rate. Simulation results show that the optimization using this practical model can achieve better performance in the actual system than the optimization scheme based on the ideal model. However, the mathematical model proposed in this paper is too complex and the optimization complexity is very high. Reference [Li H, Cai W, Liu Y, et al. Intelligent reflecting surface enhanced wideband MIMO-OFDM communications: From practical model to reflection optimization [J]. IEEE Transactions on Communications, 2021, 69 (7): 4807-4820] Based on the research work in this reference, a simplified IRS reflection model is proposed for the IRS-assisted MU-MISO-OFDM system when the bandwidth to carrier frequency ratio is less than 5%. Based on this model, a more effective algorithm is designed to jointly optimize the transmit beam and the IRS reflection beam. Simulation results show that in actual systems, the optimization algorithm based on this model can also achieve a higher rate. Summary of the invention

[0005] The purpose of the present invention is to provide a broadband phase shift model and system optimization design method in an IRS-assisted OFDMA system to improve the system sum rate. The method first proposes a simple but relatively accurate mathematical description model for the phase shift of different subcarriers by IRS in a broadband system. On this basis, for an IRS-assisted multi-user OFDMA system, with the goal of maximizing the user sum rate, the IRS phase shift, subcarrier allocation between users, and power allocation are optimized.

[0006] In order to achieve the above-mentioned purpose, the present invention adopts the following technical scheme: first, in view of the correlation between the IRS reflection phase shift and the signal frequency, a mathematical modeling of the phase shift at different frequencies of the IRS reflection unit and the center frequency phase shift based on a quadratic function is given. On this basis, a joint optimization problem of the IRS center frequency phase shift matrix, OFDMA subcarrier and power allocation that maximizes the system and rate is proposed. Then, by decomposing the optimization problem into two sub-problems of IRS phase shift optimization and subcarrier and power allocation optimization, the IRS phase shift optimization sub-problem is converted into a convex problem using a successive convex approximation method and then solved, and the subcarrier and power allocation optimization sub-problem is solved using a greedy algorithm and a water injection algorithm. Finally, the alternating optimization algorithm is used to iteratively optimize the IRS center frequency phase shift matrix and the subcarrier and power allocation until convergence is reached.

[0007] The specific steps are as follows:

[0008] (1) Constructing a communication system model: Based on the conventional IRS-assisted OFDMA system, a relatively simple but relatively accurate mathematical model is proposed to describe the relationship between the phase shift of different subcarriers and the phase shift of the center frequency according to the correlation between the IRS reflection phase shift and the signal frequency.

[0009] (2) Taking system and rate maximization as the optimization goal, an optimization mathematical model for IRS center frequency phase shift matrix, OFDMA subcarrier and power allocation is constructed under the constraints of user minimum rate and base station total transmission power.

[0010] (3) Convert the optimization problem into two sub-problems: IRS center frequency phase shift optimization and subcarrier and power allocation optimization;

[0011] (4) Obtain the IRS center frequency phase shift matrix using variable relaxation and successive convex approximation method;

[0012] (5) Use the greedy algorithm and water injection algorithm to iteratively obtain subcarrier and power allocation;

[0013] (6) Use the alternating iterative algorithm to solve the IRS center frequency phase shift matrix and subcarrier and power allocation.

[0014] Compared with the existing related research, the present invention has the following beneficial technical effects: (1) In the literature related to IRS in OFDM system, such as [HAN Yi, CHEN Yan, WANG Beibei, et al. Time-reversal massive multipath effect: a single-antenna "massive MIMO" solution [J]. IEEE Transactions on Communications, 2016, 64 (8): 3382-3394.], most of them assume that the reflection amplitude and phase shift of each reflection element of IRS for broadband signals within the entire transmission band are the same, but this is inconsistent with the actual IRS reflection characteristics. In fact, the amplitude and phase responses of the reflection unit of IRS to signals of different frequencies are different. These ideal assumptions will cause non-negligible performance loss in the actual system, because the ideal model cannot accurately capture the reflection response of the actual IRS. Therefore, the present invention proposes an IRS phase shift mathematical model that is closer to the actual characteristics. (2) At present, there are a few papers that study the IRS reflection model in broadband systems and the system optimization problem based on the broadband phase shift model. For example, the paper [Cai W, Li H, Li M, et al. Practical modeling and beamforming for intelligent reflecting surface aided wideband systems [J]. IEEE Communications Letters, 2020, 24 (7): 1568-1571] proposes an IRS phase shift mathematical model that is close to the actual characteristics, but the formula is very complex. When applied to the optimization of the IRS-assisted OFDM system, it makes it very difficult to solve the optimization problem. The present invention uses a quadratic function curve related to the coefficient and frequency to fit the relationship between the phase shift and the center frequency phase shift and frequency, ensuring that the phase shift error is relatively small while significantly reducing the difficulty of solving the optimization problem. (3) The present invention jointly optimizes the IRS center frequency phase shift matrix, OFDMA subcarriers and power allocation to maximize the system and rate. 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 the sum rate of the scheme using IRS and optimizing the phase shift matrix is ​​significantly higher than that of the scheme without IRS and the scheme with random IRS phase shift values; compared with the scheme assuming that all subcarriers have the same phase shift, the proposed scheme can achieve a higher sum rate under the actual IRS phase shift conditions. BRIEF DESCRIPTION OF THE DRAWINGS

[0015] Figure 1 A communication system model of the present invention;

[0016] Figure 2 is the equivalent circuit of the IRS element;

[0017] Figure 3 It is the curve of IRS phase shift changing with center frequency phase shift;

[0018] Figure 4 It is the convergence process of the successive convex approximation algorithm proposed by the present invention;

[0019] Figure 5 The impact of transmission power on users and rates;

[0020] Figure 6 It is the influence of transmission power on the actual achievable rate and theoretical rate.

[0021] Figure 7 The impact of the number of IRS units on users and rates;

[0022] Figure 8 The impact of the number of users on the user and rate; DETAILED DESCRIPTION

[0023] The IRS-assisted downlink OFDMA communication system studied in the present invention is as follows: Figure 1 As shown in Figure 1, the system includes a single-antenna base station, an IRS, and K single-antenna users. The number of IRS reflection units is M, and the number of orthogonal subcarriers in the OFDMA system is N. The user set is denoted as The subcarrier set is denoted as The IRS reflection unit set is denoted as All channels are frequency selective multipath fading channels, denoted by L 1,k and L2 represent the number of delay taps between the direct channel between the base station and user k and the channel between the base station and the IRS, L 2,k represents the number of delayed taps of the channel between IRS and user k. The time domain channel impulse response of the direct link from the base station to user k is recorded as in represents the lth delay tap coefficient; the time domain channel impulse response matrix from the base station to each reflection unit of the IRS is recorded as in is the vector of the lth delayed tap coefficients of the channel from the base station to each reflection unit of the IRS; the time domain channel impulse response matrix from the IRS to user k is recorded as in, It is a vector composed of the lth delay tap coefficients from each IRS reflection unit to user k channel.

[0024] Assume that the cyclic prefix length N added to each OFDM symbol CP Not less than max(L1,k ,L 2,k ,L2), so the frequency response of the direct link from the base station to user k is The frequency response of the base station to IRS link is The frequency domain channel from IRS to user k is in Represents the N-th order discrete Fourier transform matrix. and The mth column of is the frequency response of the channel between the mth reflection unit of the IRS and the base station and user k. Let Φ n =diag(φ 1,n ,φ 2,n ,…,φ M,n ) represents the phase shift matrix of the M reflection units of the IRS for the signal transmitted on the nth subcarrier, where φ m,n represents the reflection phase shift of the signal transmitted on the nth subcarrier by the mth reflection unit. The subchannel gain coefficient of the channel synthesized by the direct link and the reflection link between the base station and user k on the nth subcarrier is

[0025]

[0026] in express The nth element of express The nth column of express The nth column of .

[0027] Each subcarrier is assigned to only one user, and c is defined k,n is the subcarrier allocation indicator. If the nth subcarrier is allocated to user k, then c k,n =1, otherwise c k,n =0, obviously Let P k,n ≥0 indicates the power of the nth subcarrier allocated by the base station to the kth user. The total transmission power of all subcarriers should not exceed the maximum power allowed P tol Ignoring the rate loss due to cyclic prefix insertion in each OFDM symbol, the achievable rate for the kth user is

[0028]

[0029] Where σ 2 is the variance of the complex Gaussian distributed channel noise.

[0030] In the current research on IRS-assisted OFDM systems, it is often assumed that the phase shift of each OFDM subcarrier signal by IRS when reflecting the signal is the same, that is, Φ1=Φ2=…=Φ NIn fact, depending on the structure and composition of the IRS reflection unit, its phase shift for signals of different frequencies is different.

[0031] The transmitting unit of IRS is usually a printed circuit board with uniformly distributed reflective elements, which can be equivalently modeled as a parallel resonant circuit, such as Figure 2 The impedance of the IRS unit is

[0032]

[0033] Among them, L1, L2, C, and R represent the metal plate inductance, outer layer inductance, effective capacitance, and loss resistance respectively.

[0034] The reflection phase shift of the IRS element is

[0035]

[0036] Where Z0=377Ω is the free space impedance, and ∠A represents the phase angle of the complex number A.

[0037] It is known from the reflection phase shift formula that the reflection phase shift can be adjusted by adjusting the value of capacitor C, and the reflection phase shift is related to the frequency of the incident signal. For a given capacitance value, the reflection phase shift of IRS for signals of different frequencies is different. Taking the IRS reflection unit with parameters L1=2.5nH, L2=0.7nH, R=1Ω and C variable in the range of 0.47pF to 2.35pF given in the literature [Jung M, Saad W, Debbah M, et al. On the optimality of reconfigurable intelligent surfaces (RISs): Passive beamforming, modulation, and resource allocation [J]. IEEE Transactions on Wireless Communications, 2021, 20 (7): 4347-4363] as an example, at the center frequency f c =2.4GHz, bandwidth B = 100MHz, by adjusting the value of capacitor C, the center frequency f c The phase shift θ c Varies within the range of -π to +π. Figure 3 The variation of phase shift at different frequencies with the phase shift of the center frequency is given, and it can be seen that the phase shift amount at different frequencies is different.

[0038] observe Figure 3The curves of the relationship between the IRS phase shift and the center frequency phase shift at different frequencies show that they are very close to quadratic curves, but the curvature of the quadratic curves at different frequencies is different. Therefore, the present invention considers using a quadratic function curve related to the coefficient and frequency to fit the relationship between the phase shift and the center frequency phase shift and frequency. First, use the formula Calculate the IRS phase shift at multiple frequencies under a sufficient number of center frequency phase points, and then use the fitting tool to fit the function expression of the frequency-related coefficients in the quadratic function to obtain the function of the center frequency phase shift and other frequency phase shifts. The IRS of the above circuit parameters obtained by this method is at f c The quadratic function model of phase shift in a broadband system with B = 2.4 GHz and B = 100 MHz is:

[0039] θ(θ c ,f)=a1(f)θ c 2 +a2(f)θ c +a3(f)

[0040] a1(f)=2.012f-4.83

[0041] a2(f)=0.2303f+0.43

[0042] a3(f)=-16.59f+39.83

[0043] Where a1(f), a2(f) and a3(f) are the coefficients of the quadratic curve related to frequency. This model is used to describe the phase shift of IRS at different frequencies in the optimization problem modeling later in the present invention.

[0044] When the bandwidth is B, the number of subcarriers is N, and the center frequency is f c In the OFDMA system, the frequency of the nth subcarrier is Where Δf represents the subchannel bandwidth. When the center frequency phase shift of the mth unit of the IRS is set to θ c,m When , the phase shift of the nth subcarrier is Therefore, the difference between the IRS phase shift corresponding to the mth reflector element at the nth subcarrier frequency and its corresponding IRS phase shift at the center frequency is

[0045]

[0046] So we get θ(θ c,m ,f n )≈θ(θ c,m ,f c )+Δθ n , make The IRS phase shift matrix of the nth subcarrier can be expressed as

[0047]

[0048] where Φ c Indicates the center frequency f c The IRS phase shift diagonal matrix is:

[0049] The present invention considers jointly optimizing the phase shift of each unit of IRS, the allocation of subcarriers among users, and the power allocation on subcarriers, with the goal of maximizing the sum rate of all users in the system while ensuring the minimum rate of each user. As mentioned in the previous section, the phase shift of IRS on each subcarrier is determined by the phase shift at the center frequency, so the optimization variable of the optimization problem is the center frequency phase shift θ c,m , subcarrier allocation indicator c k,n and power allocation coefficient P k,n ,in The optimization problem is

[0050]

[0051] Among the constraints: (a) The rate of user k is constrained to be no less than R min,k ; (b) The constraint is that each subcarrier can only be allocated to one user; (c) The limit on the base station transmission power; (d) The range constraint of the center frequency phase shift.

[0052] It is very difficult to directly solve the optimization problem P1. The present invention decomposes it into two sub-problems. The first sub-problem is to optimize the phase shift of the IRS under the condition of given subcarrier and power allocation. The second sub-problem is to optimize the subcarrier and power allocation under the condition of given IRS phase shift. By alternating iterative optimization between the two sub-problems, the solution to the original optimization problem P1 is finally obtained.

[0053] When the subcarrier and power allocation are given, the optimization subproblem of optimizing the phase shift of each IRS unit is

[0054]

[0055] The objective function of the optimization problem P1.1 is non-convex, and the expression of the IRS reflection phase shift is relatively complicated. The relationship between the IRS phase shift matrix of each subcarrier and the center frequency phase shift matrix is ​​the logarithmic function of the objective function. Rewrite as Introducing auxiliary variable α n and β n , the optimization problem can be transformed into

[0056]

[0057] The constraints of this optimization problem are non-convex and need to be handled. Definition Right n (α n ,β n )exist Perform a first-order Taylor expansion at

[0058]

[0059] Among them, if and only if Take the equal sign. exist The gradient at z n (α n ,β n )exist The gradient at P1.2 is the same. Substituting its lower bound, we get

[0060]

[0061] This problem is already a convex problem and can be solved using the solver. The tightness of the lower bound is related to the expansion point The choice of also affects the accuracy of the optimization results, so it is necessary to improve the accuracy through iteration. The algorithm for solving the first subproblem based on successive convex approximation is shown in Algorithm 1, where u1 is the number of iterations and ε1 is the convergence factor.

[0062] Algorithm 1 IRS phase shift optimization algorithm

[0063] Initialization parameters: u1=0, Convergence factor ε1

[0064] (1) While.

[0065] (2)u1=u1+1.

[0066] (3) Constrain the optimization problem P1.3 Set to Use CVX to solve the optimization problem and get the optimal solution

[0067] (4) Update

[0068] (5) By Φ c * Calculated as well as

[0069] (6) Until

[0070] (7) Output

[0071] In the first iteration, the center frequency phase shift matrix Φ c Set to the optimal value obtained in the previous iteration, according to the formula Calculate the phase shift matrix Φ of each subcarrier n , α n and β n The initial values ​​are In the u1th iteration, the constraints in the optimization problem P1.3 are and Set to the optimal solution obtained from the last iterative optimization and Use CVX to solve the optimization problem and obtain the optimal solution for this iteration and users and rates The sum rate obtained in this iteration is compared with the sum rate obtained in the previous iteration optimization. When the relative amount of the sum rate growth is less than the preset convergence factor, the iterative optimization is considered to have converged, the iteration is terminated, and the center frequency phase shift matrix Φ obtained in the last iteration optimization is output. c * .

[0072] In the IRS phase shift matrix Φ n Under certain conditions, the synthetic channel response from the base station to each user is is determined, the sub-problem of optimizing subcarrier and power allocation is

[0073]

[0074] in,

[0075] The optimization of subcarrier and power allocation is divided into two steps. First, the greedy algorithm and water injection algorithm are used to perform initial allocation and optimization with the goal of maximizing the system and rate. Then, it is checked whether the transmission rate of each user can meet the minimum rate constraint. If it does not meet the constraint, the subcarrier allocation is adjusted and the power is re-optimized.

[0076] During the initial allocation, the greedy algorithm is used to allocate subcarriers according to the gain of the composite channel of each user on the subcarrier. In order to obtain the highest system sum rate, the subcarrier is allocated to the user with the highest channel gain on the subcarrier, that is, when season

[0077] After subcarrier allocation is completed, the classic iterative water filling algorithm can be used to allocate subcarrier power. The power allocated to the nth subcarrier is

[0078]

[0079] where [x] + represents the maximum value between x and 0, and λ0 is the threshold value that satisfies the total power constraint.

[0080] The goal of subcarrier allocation and power allocation is to maximize the system and rate. After allocation, it may happen that the rate of a certain user does not reach the minimum rate. In order to ensure the minimum rate of each user, it is necessary to calculate the rate of each user after the initial allocation of subcarriers and power to determine whether there are users who do not meet the minimum rate requirements. If there are users whose minimum rate does not meet the requirements, find the user with the lowest rate that does not meet the minimum rate requirements, and try to allocate an additional subcarrier to this user. This user is denoted as k′. When adjusting the subcarrier allocation, first of all, it should be ensured that no new users who do not meet the minimum rate constraint are generated, and secondly, the impact on the system and rate should be minimized. First, for each user who meets the minimum rate constraint, find the subcarrier with the smallest channel gain among the subcarriers allocated to the user, denoted as n′. Calculate the achievable transmission rate of the user without including subcarrier n′. If the transmission rate can still meet the minimum rate constraint, n′ is added to the subcarrier set to be adjusted. Otherwise, the subcarriers allocated to this user will not be reduced. After all users that meet the minimum rate constraint are traversed, calculate The ratio of the subchannel gain of user k′ on each subcarrier to the subchannel gain of the user currently assigned to the subcarrier, and find the subcarrier n with the largest ratio * , and reassign it to user k'. This process can increase the transmission rate of user k' while minimizing the impact on the system and rate. After the subcarriers are reallocated, the water injection algorithm is used to optimize the power allocation, and this cycle is repeated until all users meet the minimum user rate requirement. The second subproblem solution algorithm based on the greedy algorithm and the water injection algorithm is shown in Algorithm 2, where Represents the set of users that meet the rate constraint before subcarrier adjustment.

[0081] Algorithm 2 Subcarrier and power allocation algorithm

[0082] Initialization parameters: c k,n =0,P k,n =0,

[0083]

[0084] (2) Use the water filling algorithm to allocate subcarrier power and obtain P k,n , Calculate the rate R of each user k ,

[0085] (3) Determine whether the rates of each user meet the minimum rate requirement. If yes, jump to (13).

[0086] (4)While.

[0087]

[0088] (9) n * Assign it to user k′ and update c k,n ,

[0089] (10) Use water injection method to optimize power distribution and update P k,n , Update each user's rate R k ,

[0090] (11)Until R k ≥R min,k ,

[0091] (12) Output c k,n ,P k,n ,

[0092] At the beginning of Algorithm 2, the greedy algorithm is used to allocate all subcarriers. Then, based on the subcarrier allocation, the water injection algorithm is used to allocate power to each subcarrier. The rate of each user is calculated, and the user with the lowest rate that does not meet the minimum rate requirement is found. An additional subcarrier is allocated to it, and the subcarrier power is allocated again using the water injection algorithm. The rate of each user is calculated again to check whether all meet the minimum rate constraint. This cycle is repeated until all user rates meet the minimum rate requirement.

[0093] The solution to the optimization problem P1 can be obtained by alternately iterating and solving subproblems P1.3 and P1.4. The complete solution algorithm is shown in Algorithm 3. In the algorithm, u2 is the number of iterations, and ε2 is the convergence factor that controls the end of the iteration. At the beginning of the algorithm, the initial rate of each user is 0, and the center frequency phase shift matrix Φ c First, randomly assign values, according to the formula The phase shift matrix Φ of each subcarrier is calculated n, call Algorithm 2 to perform subcarrier allocation and power allocation. Then start the alternating iterative optimization of the IRS phase shift matrix and subcarrier and power allocation. In each round of iteration, first fix the subcarrier and power allocation as the solution of the previous round of iterative optimization, call Algorithm 1 to optimize the IRS phase shift matrix; then call Algorithm 2 to optimize the subcarrier and power allocation based on the phase shift matrix obtained in this round of optimization. After each round of iteration, calculate the user sum rate and compare it with the user sum rate obtained in the previous round of iteration. When the relative value of the sum rate growth is less than the convergence factor, the iterative optimization process converges and the optimization ends.

[0094] Algorithm 3 Alternating Optimization Algorithm

[0095] Initialization parameter: Φ c [0] , u2=0, convergence factor ε2.

[0096] (1) Set Φ c =Φ c [0] , call Algorithm 2 to optimize subcarrier allocation and power allocation.

[0097] (2)While.

[0098] (3)u2=u2+1.

[0099] (4) Call Algorithm 1 to optimize the IRS reflection phase shift matrix and obtain Φ c .

[0100] (5) Calculate Φ n .

[0101] (6) Call Algorithm 2 to optimize subcarrier and power allocation.

[0102] (7) Calculate users and rates

[0103] (8) Until

[0104] (9) Output P k,n , c k,n , Φ n ,

[0105] The present invention will be further described in detail below in conjunction with the accompanying drawings. The number of subcarriers in the system is N=64, and the position of each node is described by a two-dimensional position in meters (m). The base station coordinates are (0,0), the IRS coordinates are (50,0), and the coordinates of each user are (50,10), (55,0), and (60,0). The channel between each node is a Rayleigh fading channel. The channel fading includes path loss and small-scale fading. The gain model of each path in the channel is an exponential attenuation model. The channel coefficient of the lth path from the base station to the user k channel is

[0106]

[0107] in is the path loss, L0 = -30dB represents the path loss at the reference distance of 1m, η BU is the path loss exponent, d BU is the distance between the base station and the user, is the normalized power gain of the lth tap, is the small-scale fading coefficient. Similarly, the vectors composed of the l-th path channel coefficients of the IRS to user k and the base station to IRS channels are

[0108]

[0109] in and is the small-scale fading coefficient, Set η in simulation BR =2.5,η RU =2.8,η BU =3.7, channel noise power σ 2 =-80dBm, user minimum rate constraint R min,k =0.1bit / s / Hz, the number of delay taps of the base station to user direct link, base station to IRS link and IRS to user link are set to L 1,k =6, L2=4, L 2,k =4. Convergence factor ε1=ε2=10 in Algorithms 1 and 3 -3 .

[0110] In order to evaluate the performance of the scheme of the present invention, it is compared with three benchmark schemes. Benchmark Scheme 1 - No IRS Scheme: No IRS is configured in the system, and subcarrier allocation and power allocation are performed according to the direct link from the base station to the user. The algorithm is similar to Algorithm 2 of this paper; Benchmark Scheme 2 - Random IRS Phase Shift Scheme: The center frequency phase shift matrix of the IRS is randomly generated, and the phase shift matrix of each subcarrier is obtained according to the phase shift model proposed in the literature [Cai W, Li H, Li M, et al. Practical modeling and beamforming for intelligent reflecting surface aided wideband systems [J]. IEEE Communications Letters, 2020, 24 (7): 1568-1571], and then subcarrier allocation and power allocation are performed, using Algorithm 2 of the present invention; Benchmark Scheme 3 - Literature [Yang Y, Zhang S, Zhang R. IRS-enhanced OFDMA: Joint resource allocation and passive beamforming optimization [J]. IEEE Wireless Communications Letters, 2020, 9(6): 760-764] Solution: Assuming that the IRS reflection phase shift is the same throughout the transmission band, the algorithm in the document is used to optimize the IRS phase shift. Since the document does not elaborate on the resource allocation of the OFDMA system, the subcarrier and power allocation adopts the algorithm 2 of the present invention. Figure 4 Except for , the results given in other simulation figures are the average values ​​of 500 sets of channel samples. In order to compare the performance of different schemes fairly, the sum rate of each scheme is based on the rate that can be obtained under the actual IRS phase shift characteristics.

[0111] Firstly, the convergence of Algorithm 1 in the solution proposed in the present invention is verified by simulation. Figure 4 The convergence curve of the iterative algorithm under a certain set of channel samples for 4 combinations of transmit power and number of IRS units when the number of users is 3 is given. It can be seen that the system and rate increase with the iteration and tend to converge after about 11 rounds of iteration. As the number of reflective elements M increases, the number of iterations required for convergence also increases.

[0112] Figure 5The variation of user sum rate with transmission power when the number of users is 3 and the number of IRS units is 32 is given. As can be seen from the figure, the user sum rate gradually increases with the increase of transmission power under the four schemes; the sum rate of the scheme equipped with IRS is higher than that of the scheme without IRS assistance, which proves that IRS can enhance system performance; the sum rate of the scheme with optimized IRS phase shift is significantly higher than that of the random IRS phase shift scheme, which shows that optimizing IRS phase shift is very important for improving system performance. The sum rate of the scheme of the present invention is higher than that of the benchmark scheme 3 because the IRS broadband phase shift model adopted by the present invention is very close to the actual phase shift characteristics. Figure 6 When the number of users is 3 and the number of IRS units is 32, the theoretical rates of the scheme of the present invention and the benchmark scheme 3 under their respective theoretical phase shift models are compared with the achievable rates under the actual phase shift characteristics. In the figure, the dotted lines are the theoretical rates that can be achieved by the two schemes under their respective phase shift models, and the solid lines are the rates that can be achieved under the actual phase shift characteristics. Benchmark scheme 3 assumes that the phase shift of IRS for all subcarriers is the same, and is optimized accordingly. The simulation results show that the system and rate of benchmark scheme 3 under the actual phase shift characteristics are significantly lower than its theoretical rate, and the decrease increases with the increase of the transmission power. When the transmission power P tol When it is 30dBm, the decrease is 14%. However, the sum rate under the actual phase shift characteristics of the scheme of the present invention is only about 3% lower than the theoretical sum rate. This result shows that if the correlation between the IRS phase shift and the signal frequency is not considered, the optimization scheme will have a significant performance degradation when applied to the actual system. The scheme of the present invention proposes a simple relationship model between phase shift and frequency. Although there is still a deviation from the actual phase shift characteristics, the scheme optimized under this phase shift model does not suffer much performance loss under the actual phase shift characteristics, and is suitable from the perspective of the trade-off between complexity and performance.

[0113] Figure 7 The figure shows how the user sum rate changes with the number of IRS units when the number of users is 3 and the transmission power is fixed at 30dBm. As can be seen from the figure, except for the scheme without IRS assistance, the user sum rate of other schemes increases with the increase of the number of IRS units. This is because more IRS units mean more reflection paths, the greater the power of the received signal, and the better the directivity of the passive beam. Since the IRS phase shift is not optimized, the random IRS phase shift scheme can only benefit from the increase in the path, so the rate of increase of the sum rate is low. However, since the scheme of the present invention and the benchmark scheme 3 optimize the phase shift, they can also benefit from the improvement of the directivity of the passive beam, so the growth rate of the sum rate is higher.

[0114] Figure 8The variation of user sum rate when the number of IRS units is 32 and the transmission power is fixed at 30dBm, and the number of users changes, is given. In the simulation, users are uniformly and randomly distributed in the sector ring with the base station as the center, with an angle ranging from -30° to +30°, an outer circle radius of 60m, and an inner circle radius of 30m. 50 groups of user positions are randomly generated for each number of users, and the channel is randomly changed 200 times for each group of positions. The sum rate of 10,000 channel samples is simulated, and then the average sum rate under a certain number of users is obtained by averaging. As can be seen from the figure, the user sum rate under the four schemes will increase with the increase of the number of users. This is because the subcarrier allocation and power allocation between users are optimized. As the number of users increases, more multi-user diversity gain can be obtained.

Claims

1. A phase shift model and system optimization method in an IRS-assisted OFDMA system, comprising the following steps: (1) Constructing a communication system model: Based on the conventional IRS-assisted OFDMA system, a relatively simple but relatively accurate mathematical model is proposed to describe the relationship between the phase shift of different subcarriers and the phase shift of the center frequency according to the correlation between the IRS reflection phase shift and the signal frequency. (2) Taking system and rate maximization as the optimization goal, an optimization mathematical model for IRS center frequency phase shift matrix, OFDMA subcarrier and power allocation is constructed under the constraints of user minimum rate and base station total transmission power. (3) Convert the optimization problem into two sub-problems: IRS center frequency phase shift optimization and subcarrier and power allocation optimization; (4) Obtain the IRS center frequency phase shift matrix using variable relaxation and successive convex approximation method; (5) Use the greedy algorithm and water injection algorithm to iteratively obtain subcarrier and power allocation; (6) Use the alternating iterative algorithm to solve the IRS center frequency phase shift matrix and subcarrier and power allocation.

2. The phase shift model and system optimization method in the IRS-assisted OFDMA system according to claim 1, characterized in that: Step (1) The system is a multi-user OFDMA downlink communication system with an IRS assisted by a base station equipped with a single antenna, an IRS with M reflection units, and a user equipped with a single antenna. It is assumed that the base station can obtain channel state information and the channels are all frequency selective fading channels.

3. The phase shift model and system optimization method in the IRS-assisted OFDMA system according to claim 1, characterized in that: The mathematical model in step (1) is to fit the relationship between phase shift and center frequency phase shift and frequency using a quadratic function curve with coefficients and frequency. The transmitting unit of IRS is usually a printed circuit board with uniformly distributed reflective elements, which can be equivalently modeled as a parallel resonant circuit with an impedance of Where L1, L2, C, and R represent the metal plate inductance, outer layer inductance, effective capacitance, and loss resistance respectively; f represents the signal frequency. The reflection phase shift of the IRS element is Where Z0=377Ω is the free space impedance, and ∠A represents the phase angle of the complex number A. Taking the IRS reflection unit with parameters L1=2.5nH, L2=0.7nH, R=1Ω, and C variable in the range of 0.47pF to 2.35pF as an example, the reflection phase shift formula is used to calculate the IRS phase shift at multiple frequencies under a sufficient number of center frequency phase points, and then the fitting tool is used to fit the function expression of the frequency-related coefficients in the quadratic function to obtain the function of the center frequency phase shift and other frequency phase shifts. Using this method, the center frequency f c The quadratic function model of IRS phase shift θ in a broadband system with B = 2.4 GHz and bandwidth B = 100 MHz is: θ(θ c ,f)=a1(f)θ c 2 +a2(f)θ c +a3(f) a1(f)=2.012f-4.83 a2(f)=0.2303f+0.43 a3(f)=-16.59f+39.83 Among them, θ c represents the center frequency phase shift; a1(f), a2(f) and a3(f) are the coefficients of the frequency-dependent quadratic curve.

4. The phase shift model and system optimization method in the IRS-assisted OFDMA system according to claim 1, characterized in that: The mathematical model in step (2) includes modeling the user transmission rate and the system sum rate, which is as follows: The subchannel gain coefficient of the channel synthesized by the direct link and the reflection link between the base station and user k on the nth subcarrier is in represents the frequency response of the direct link from the base station to user k The nth element of ; represents the frequency response of the link from IRS to user k The nth column of Φ n Represents the phase shift matrix of the M reflection units of the IRS for the transmission signal on the nth subcarrier; Represents the frequency response of the base station to IRS link The nth column of represents a subcarrier set; represents a user set; the superscript T represents the transpose operation of a vector or matrix. The achievable transmission rate of user k (k = 1, 2, ..., K) is where c k,n is the subcarrier allocation indicator. If the nth subcarrier is allocated to user k, then c k,n =1, otherwise c k,n =0;P k,n represents the power of the nth subcarrier allocated by the base station to the kth user; σ 2 is the noise variance of the channel. The system and rate are 5. The phase shift model and system optimization method in the IRS-assisted OFDMA system according to claims 1 and 4, characterized in that: The optimization mathematical model in step (2) takes the user minimum rate and the total transmission power of the base station as constraints, and takes the system and rate maximization as the optimization goal. The optimization problem is constructed as follows: s.t.R k ≥R min,k Among them, R k,min Indicates the minimum rate limit of the user; R k represents the achievable transmission rate of user k; P tol represents the total transmission power of the base station; θ c,m Represents the center frequency phase shift of the mth reflection unit; represents the IRS reflection unit set.

6. The phase shift model and system optimization method in the IRS-assisted OFDMA system according to claims 1 and 5, characterized in that: Step (3) converts the optimization problem into two optimization sub-problems: receiving filter and power allocation, which specifically include: (1) When the subcarrier and power allocation are given, the phase shift of each IRS unit is optimized to maximize the system sum rate, that is, (2) When the IRS phase shift matrix is ​​determined, the subcarrier and power allocation are optimized to maximize the system sum rate, that is, s.t.R k ≥R min,k In the formula 7. The phase shift model and system optimization method in the IRS-assisted OFDMA system according to claims 1 and 6, characterized in that: Step (4) uses variable relaxation and successive convex approximation method to obtain the IRS center frequency phase shift matrix, specifically including: first recursively obtain the relationship between the IRS phase shift matrix of the nth subcarrier and the center frequency phase shift matrix: in Δf represents the subchannel bandwidth; Φ c Indicates the center frequency f c The IRS phase shift diagonal matrix under ; Then introduce the slack variable and the relationship to transform the original non-convex optimization problem into where α n and β n is the slack variable. Finally, the first-order Taylor expansion is performed on the left side of the inequality constraint to transform the optimization problem into a convex problem, which can be solved using a convex optimization solver.

8. The phase shift model and system optimization method in the IRS-assisted OFDMA system according to claims 1 and 6, characterized in that: Step (5) uses the greedy algorithm and water injection algorithm to iteratively obtain the subcarrier and power allocation, specifically including: during the initial allocation, the greedy algorithm is used to allocate subcarriers according to the gain of the synthetic channel of each user on the subcarrier. In order to obtain the highest system and rate, the subcarrier is allocated to the user with the highest channel gain on the subcarrier, that is, when season After subcarrier allocation is completed, the classic iterative water filling algorithm is used to allocate subcarrier power. The power allocated to the nth subcarrier is where [x] + represents the maximum value between x and 0, and λ0 is the threshold value that satisfies the total power constraint. At this time, calculate the rate of each user, find the user with the lowest rate that does not meet the minimum rate requirement, and try to allocate an additional subcarrier to this user, and record this user as k'. When adjusting the subcarrier allocation, first, for each user that meets the minimum rate constraint, find the subcarrier with the smallest channel gain among the subcarriers allocated to this user, and record it as n'. Calculate the achievable transmission rate of this user without including subcarrier n'. If the transmission rate can still meet the minimum rate constraint, then put n' into the subcarrier set to be adjusted Otherwise, the subcarriers allocated to this user are not reduced. After all users that meet the minimum rate constraint are traversed, calculate The ratio of the subchannel gain of user k′ on each subcarrier to the subchannel gain of the user currently assigned to the subcarrier, and find the subcarrier n with the largest ratio * , and reassign it to user k′. After the subcarriers are reallocated, the water filling algorithm is used to allocate the subcarrier power, and the rates of each user are calculated again to check whether they all meet the minimum rate constraint. This cycle is repeated until all user rates meet the minimum rate requirement.

9. The phase shift model and system optimization method in the IRS-assisted OFDMA system according to claims 1, 7 and 8, characterized in that: Step (6) uses an alternating iterative algorithm to solve the IRS center frequency phase shift matrix and subcarrier and power allocation, specifically including: at the beginning of the algorithm, the initial rate of each user is 0, the center frequency phase shift matrix Φ c First, randomly assign values, according to the formula Φ n =b n Φ c vn The phase shift matrix Φ of each subcarrier is calculated n , call the greedy algorithm and water injection algorithm to perform subcarrier allocation and power allocation. Then start the alternating iterative optimization of IRS phase shift matrix and subcarrier and power allocation. In each round of iteration, the subcarrier and power allocation are first fixed as the solution of the previous round of iterative optimization, and the successive convex approximation algorithm is called to optimize the IRS phase shift matrix; then, according to the phase shift matrix obtained in this round of optimization, the greedy algorithm and water injection algorithm are called to optimize the subcarrier and power allocation. After each round of iteration, the user sum rate is calculated and compared with the user sum rate obtained in the previous round of iteration. When the relative value of the sum rate growth is less than the convergence factor, the iterative optimization process converges and the optimization ends.

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