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

Abstract

This invention discloses a modeling method for the phase shift model of each subcarrier in an intelligent reflecting surface (IRS)-assisted downlink orthogonal frequency division multiple access system, as well as a system optimization method. First, the IRS phase shift at multiple frequencies is calculated at a sufficient number of center frequency phase points. A quadratic function curve with coefficients related to frequency is used to fit the relationship between the phase shift and the center frequency phase shift, thus obtaining a function of the center frequency phase shift and other frequency phase shifts. Based on the designed phase shift model, an optimization problem is constructed to optimize the IRS center frequency phase shift matrix, subcarriers, and power allocation, maximizing the system's sum and rate. Finally, this invention transforms the original problem into a convex problem and solves it using successive convex approximation and alternating optimization methods. Simulation results demonstrate that, compared to optimization schemes assuming the same IRS phase shift on all subcarriers within the transmission band, the scheme optimized under the phase shift model presented in this invention achieves a higher practically achievable sum and rate under actual IRS phase shift conditions.

Description

Technical Field

[0001] This invention relates to the field of information and communication, specifically to the phase shift model and system optimization method in an IRS-assisted OFDMA system. Background Technology

[0002] With the increasing demand for mobile communication services, 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 surface (IRS) to improve the performance of wireless communication systems has become one of the hot research topics in academia. IRS is a surface composed of a large number of low-cost passive reflecting units. Each reflecting unit can independently control the phase shift of the incident signal reflection, and can achieve a certain degree of control over the wireless communication propagation environment [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 research has 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 wirelesscommunications: Challenges and opportunities[J].IEEE Wireless Communications,2021,28(2):136-143].

[0003] Orthogonal Frequency Division Multiplexing (OFDM) is a multi-carrier modulation technique [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 resistance to multipath interference. Orthogonal Frequency Division Multiple Access (OFDMA) is a multiple access technology developed from OFDM. It achieves multi-user communication by dynamically allocating subcarriers to multiple users and can effectively overcome wireless channel fading, achieving higher spectrum utilization. It is one of the key technologies in 4th and 5th generation mobile communication systems. Resource allocation in OFDMA systems is a crucial factor in ensuring fairness among users and influencing system performance, and it is one of the important research topics in academia [Rhee W, Ciofi 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 (Intermediate Reliability System) to OFDM and OFDMA systems, and utilizing the IRS to intelligently control the propagation environment, can significantly improve system performance. Currently, some literature has studied the performance analysis, channel estimation, and optimization design of IRS-assisted OFDM systems.The literature [Yang Y, Zheng B, Zhang S, et al. Intelligent reflecting surfacemeets OFDM: Protocol design and rate maximization[J].IEEE Transactions on Communications, 2020, 68(7): 4522-4535] proposes an IRS-assisted Single Input Single Output (SISO) OFDM communication system. It utilizes the channel correlation between adjacent IRS reflecting units to propose an IRS reflecting unit grouping method to reduce the overhead of channel training and estimation. Furthermore, it maximizes the achievable rate by jointly optimizing the power allocation between subcarriers and the IRS reflection coefficient based on the estimated Channel State Information (CSI). 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] proposes an IRS reflection mode to improve the efficiency of channel estimation for IRS-assisted SISO-OFDM systems, and designs a low-complexity reflection coefficient optimization algorithm based on the estimated CSI to maximize the average reachable 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] analyzes the correlation between rate maximization and mean square error minimization for IRS-assisted downlink multiple user multiple input single output (MU-MISO) OFDM systems, and designs an efficient joint algorithm of transmit beamforming and IRS reflection coefficient to maximize the system average rate.The 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] proposes a passive beamforming scheme to maximize the minimum user rate for IRS-assisted downlink OFDMA communication systems. This scheme adjusts the IRS reflection coefficient at different time slots within each channel coherence block and serves only a subset of users in each time slot, achieving higher passive beamforming gain through multi-user diversity.

[0004] Currently, a few studies have investigated IRS reflection models in broadband systems and system optimization problems based on broadband phase shift models. 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 amplitude, phase shift, and frequency of reflected signals in IRS-assisted SISO-OFDM systems, and proposes a mathematical model for the IRS reflection coefficient in broadband systems. Based on this model, subcarrier power allocation and the IRS reflection coefficient are jointly optimized to maximize the average user rate. Simulation results show that optimization using this practical model can achieve better performance in practical systems than optimization schemes based on ideal models. However, the mathematical model proposed in this paper is too complex, resulting in high optimization complexity. Based on the research in the literature [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], a simplified IRS reflection model is proposed for IRS-assisted MU-MISO-OFDM systems when the bandwidth-to-carrier frequency ratio is less than 5%. Based on this model, a more efficient algorithm is designed to jointly optimize the transmit beam and the IRS reflection beam. Simulation results show that in practical systems, the optimization algorithm based on this model can also achieve higher data rates. Summary of the Invention

[0005] The purpose of this invention is to provide a design method for a broadband phase shift model and system optimization in an IRS-assisted OFDMA system to improve system performance and data rate. This method first proposes a simple yet relatively accurate mathematical model to describe the phase shift of the IRS for different subcarriers in a broadband system. Based on this, for an IRS-assisted multi-user OFDMA system, with the goal of maximizing user performance and data rate, optimizations are made to the IRS phase shift, inter-user subcarrier allocation, and power allocation.

[0006] To achieve the above objectives, this invention adopts the following technical solution: First, considering the correlation between IRS reflection phase shift and signal frequency, a mathematical model based on a quadratic function is presented to model the phase shift of the IRS reflection unit at different frequencies and the center frequency phase shift. Based on this, a joint optimization problem is proposed to maximize the system and rate of the IRS center frequency phase shift matrix, OFDMA subcarriers, and power allocation. Then, this optimization problem is decomposed into two subproblems: IRS phase shift optimization and subcarrier and power allocation optimization. The IRS phase shift optimization subproblem is transformed into a convex problem using a successive convex approximation method before being solved, while the subcarrier and power allocation optimization subproblem is solved using a greedy algorithm and a water-filling algorithm. Finally, an alternating optimization algorithm is used to iteratively optimize the IRS center frequency phase shift matrix and the subcarrier and power allocation until convergence is achieved.

[0007] The specific steps are as follows:

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

[0009] (2) With the goal of maximizing system and rate, construct an optimization mathematical model for the phase shift matrix of IRS center frequency, OFDMA subcarrier and power allocation under the constraints of minimum user rate and total base station transmit power;

[0010] (3) The optimization problem is transformed into two sub-problems: IRS center frequency phase shift optimization and subcarrier and power allocation optimization.

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

[0012] (5) Subcarrier and power allocation are obtained iteratively using greedy algorithm and water-filling algorithm;

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

[0014] Compared with existing related research, the present invention has the following beneficial technical effects: (1) Among the literature related to IRS in OFDM systems that can be retrieved, 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 assume that the reflection amplitude and phase shift of each reflection element of the IRS are the same for broadband signals in the entire transmission frequency band, but this is inconsistent with the actual reflection characteristics of the IRS. In fact, the amplitude and phase response of the reflection unit of the 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) Currently, a few studies have investigated the IRS reflection model in broadband systems and the system optimization problem based on the broadband phase shift model. For example, the literature [Cai W, Li H, Li M, et al. Practical modeling and beamforming for intelligent reflectioning 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, and it will make the optimization problem very difficult to solve when applied to the optimization of IRS-assisted OFDM systems. This invention uses a quadratic function curve with coefficients related to frequency to fit the relationship between phase shift and 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) This invention maximizes the system and rate by jointly optimizing the IRS center frequency phase shift matrix, OFDMA subcarriers and power allocation. In view of the difficulty in finding 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 achieved, thereby improving the system performance. (4) After simulation verification, the results show that the scheme with IRS and optimized phase shift matrix has a significantly higher sum and rate than 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 and rate under actual IRS phase shift conditions. Attached Figure Description

[0015] Figure 1 This is a communication system model of the present invention;

[0016] Figure 2 The equivalent circuit for an IRS element;

[0017] Figure 3 The curve shows the phase shift of the IRS as a function of the center frequency.

[0018] Figure 4 This describes the convergence process of the successive convex approximation algorithm proposed in this invention.

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

[0020] Figure 6 This relates to the effect of transmit power on the actual achievable rate and the theoretical rate.

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

[0022] Figure 8 The impact of user numbers on user base and speed; Detailed Implementation

[0023] The IRS-assisted downlink OFDMA communication system studied in this invention is as follows: Figure 1 As shown. The system comprises 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... Subcarrier set denoted as The IRS reflective unit set is denoted as All channels are frequency-selective multipath fading channels, denoted as L. 1,k L2 represents the number of delay taps in the direct channel between the base station and user k and the channel between the base station and the IRS. 2,k This represents the number of delay taps in the channel between the IRS and user k. The time-domain channel impulse response of the direct link from the base station to user k is denoted as... in The l-th delay tap coefficient is represented by ; the time-domain channel impulse response matrix from the base station to each reflection unit of the IRS is denoted as . in The vector is composed of the l-th delay tap coefficients of each reflection unit channel from the base station to the IRS; the time-domain channel impulse response matrix from the IRS to user k is denoted as... in, It is a vector composed of the l-th delay tap coefficients from each reflection unit of the IRS to the user's k-th channel.

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

[0025]

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

[0027] Each subcarrier is allocated to only one user, defined as c. k,n Assign indicators to subcarriers; if the nth subcarrier is assigned to user k, then c k,n =1, otherwise c k,n =0, obviously there is Let P k,n ≥0 indicates that the power allocated by the base station to the nth subcarrier of the kth user should not exceed the maximum allowable power P. tol Ignoring the rate loss due to cyclic prefix insertion in each OFDM symbol, the achievable rate for the k-th user is:

[0028]

[0029] In the formula σ 2 Let V be the variance of the channel noise with a complex Gaussian distribution.

[0030] Current research on IRS-assisted OFDM systems often assumes that the phase shift of each OFDM subcarrier signal is the same when the IRS reflects the signal, i.e., Φ1=Φ2=…=Φ NIn fact, depending on the structure and composition of the IRS reflector, its phase shift for signals of different frequencies is different.

[0031] The emitting unit of an IRS is typically a printed circuit board with uniformly distributed reflective elements, which can be equivalently modeled as a parallel resonant circuit, such as... Figure 2 As shown. The impedance of the IRS unit is

[0032]

[0033] Where 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] As known from the reflection phase shift formula, the reflection phase shift can be adjusted by changing the value of capacitor C, and the reflection phase shift is related to the frequency of the incident signal. For a given capacitor value, the reflection phase shift of the IRS is different for signals of different frequencies. 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 intelligentsurfaces (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 Within a range of 2.4 GHz and a bandwidth of B = 100 MHz, the center frequency f is adjusted by changing the value of capacitor C. c Phase shift θ at point c It varies within the range of -π to +π. Figure 3 The changes in phase shift at different frequencies with respect to the center frequency are shown, indicating that the amount of phase shift is different at different frequencies.

[0038] observe Figure 3By examining multiple curves showing the relationship between IRS phase shift and center frequency phase shift at different frequencies, it can be observed that they closely resemble quadratic curves. However, the curvature of these quadratic curves differs at different frequencies. Therefore, this invention considers using a quadratic function curve with coefficients related to frequency to fit the relationship between phase shift, center frequency phase shift, and frequency. Firstly, the formula is used... By calculating the IRS phase shift at multiple frequencies at a sufficient number of center frequency phase points, and then using a fitting tool to fit the frequency-related coefficients of the quadratic function, the function expression of the center frequency phase shift and other frequency phase shifts can be obtained. The IRS of the circuit parameters obtained using this method 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 frequency-dependent quadratic curve. This model will be used in the subsequent optimization problem modeling of this invention to describe the phase shift of the IRS at different frequencies.

[0044] With bandwidth B, number of subcarriers N, and center frequency f c In an OFDMA system, the frequency of the nth subcarrier is Where Δf represents the sub-channel bandwidth. When the phase shift of the center frequency of the m-th unit of the IRS is set to θ... c,m When, its phase shift with respect to the nth subcarrier is Therefore, the difference between the IRS phase shift of the m-th reflecting element at the n-th subcarrier frequency and its corresponding IRS phase shift at the center frequency is .

[0045]

[0046] Thus, θ(θ) is obtained 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 The center frequency f c The IRS phase shift diagonal matrix below,

[0049] This invention aims to maximize the sum rate of all users in the system while ensuring the minimum rate for each user. It jointly optimizes the phase shift of each IRS unit, the allocation of subcarriers among users, and the power allocation on the subcarriers. As described in the previous section, the phase shift of each subcarrier in the IRS is determined by the phase shift at the center frequency; therefore, the optimization variable is the center frequency phase shift θ. c,m Subcarrier allocation indicator c k,n With power allocation factor P k,n ,in The optimization problem is

[0050]

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

[0052] The direct solution to the optimization problem P1 is very difficult. This invention decomposes it into two sub-problems. Sub-problem one is to optimize the phase shift of the IRS given the subcarrier and power allocation. Sub-problem two is to optimize the subcarrier and power allocation given the IRS phase shift. By iteratively optimizing between the two sub-problems, the solution to the original optimization problem P1 is finally obtained.

[0053] Given a fixed subcarrier and power allocation, the optimization subproblem for optimizing the phase shift of each IRS cell is as follows:

[0054]

[0055] The objective function of optimization problem P1.1 is non-convex, and the expression for the IRS reflection phase shift is quite complex. According to the formula... The relationship between the phase shift matrix of each subcarrier IRS and the phase shift matrix of the center frequency is expressed in the logarithmic function of the objective function. Rewritten 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, requiring handling. Definition For z n (α n ,β n )exist Performing a first-order Taylor expansion at that point, we obtain...

[0058]

[0059] Among them, if and only if When the equality sign is taken. exist gradient at z n (α n ,β n )exist The gradients at each point are the same. The constraints in P1.2 are... Replace it with its lower bound to get

[0060]

[0061] This problem is already a convex problem and can be solved using solution tools. The tightness of its lower bound and the expansion point... The choice of ε is related to the accuracy of the optimization results, so iterative methods are needed to improve the accuracy. 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) The constraints in the optimization problem P1.3 Set as The optimal solution is obtained by using CVX to solve this optimization problem.

[0067] (4) Update

[0068] (5) From 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 it to the optimal value obtained in the previous iteration, according to the formula Calculate the phase shift matrix Φ for each subcarrier n α n and β n The initial values ​​are respectively The real and imaginary parts of the . In the u1-th iteration, the constraints of the optimization problem P1.3 are... and Set it to the optimal solution obtained in the previous iteration. and The optimization problem is solved using CVX to 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. When the relative increase in the sum rate is less than the preset convergence factor, the iterative optimization is considered to have converged, the iteration ends, and the center frequency phase shift matrix Φ obtained in the last iteration is output. c * .

[0072] In the IRS phase shift matrix Φ n Under certain conditions, the synthesized channel response from the base station to each user Therefore, the subproblem of optimizing subcarriers and power allocation is determined to be...

[0073]

[0074] in,

[0075] The optimization of subcarrier and power allocation is divided into two steps. First, the greedy algorithm and the water-filling 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 reach the minimum rate constraint. If it does not meet the constraint, the subcarrier allocation is adjusted and the power is re-optimized.

[0076] During initial allocation, a greedy algorithm is used to allocate subcarriers based on the gain of the synthesized channel for each user on the subcarrier. To obtain the highest system and rate, subcarriers are allocated to the user with the highest channel gain on that subcarrier, i.e., when... season

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

[0078]

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

[0080] Subcarrier and power allocation aim to maximize system performance and data rate. However, after allocation, some users may not reach their minimum data rate. To ensure the minimum data rate for each user, the data rate for each user needs to be calculated after the initial subcarrier and power allocation to determine if any users fail to meet the minimum data rate requirement. If such users exist, the user with the lowest data rate is identified, and an additional subcarrier is allocated to that user, denoted as k′. Subcarrier allocation adjustments should first ensure that no new users fail to meet the minimum data rate constraint, and secondly, minimize the impact on system performance and data rate. First, for each user meeting the minimum data rate constraint, the subcarrier with the lowest channel gain among the subcarriers allocated to that user is identified, denoted as n′. The achievable transmission rate for that user without subcarrier n′ is calculated. If the transmission rate still meets the minimum data rate constraint, n′ is added to the set of subcarriers to be adjusted. If the minimum rate constraint is satisfied, the number of subcarriers allocated to that user is not reduced. After all users satisfying the minimum rate constraint have been traversed, the calculation is performed. Find the subcarrier n with the largest ratio of the ratio of the subchannel gain of user k′ on each subcarrier to the subchannel gain currently allocated to that subcarrier. * The subcarrier is then reassigned to user k′, which increases the transmission rate of user k′ while minimizing the impact on the system and rate. After subcarrier reallocation, a water-filling algorithm is used to optimize power allocation, and this process is repeated until all users meet the minimum user rate requirement. The solution algorithm for the second subproblem based on the greedy algorithm and the water-filling algorithm is shown in Algorithm 2, where... This represents the set of users who meet the rate constraints 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) The subcarrier power allocation is performed using the water-filling algorithm to obtain P. k,n , Calculate the rate R for each user k ,

[0085] (3) Determine whether the rate of each user meets the minimum rate requirement. If so, skip to (13).

[0086] (4) While.

[0087]

[0088] (9) n * Reassign to user k′, update c k,n ,

[0089] (10) Optimize power distribution using the water injection method and update P k,n , Update the user rate R k ,

[0090] (11)Until R k ≥R min,k ,

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

[0092] Algorithm 2 begins by using a greedy algorithm to allocate all subcarriers. Then, based on the subcarrier allocation, a water-filling algorithm is used to allocate power to each subcarrier. The user rate is calculated, and the user with the lowest rate that does not meet the minimum rate requirement is identified. This user is then allocated one more subcarrier, and the water-filling algorithm is used again to allocate subcarrier power. The user rate is then calculated again, and it is checked whether all users meet the minimum rate constraint. This process is repeated until all user rates meet the minimum rate requirement.

[0093] The solution to optimization problem P1 can be obtained by iteratively 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 termination 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, assign values ​​randomly, then use the formula The phase shift matrix Φ of each subcarrier is calculated. nAlgorithm 2 is then invoked for subcarrier and power allocation. Alternating iterative optimization of the IRS phase shift matrix and subcarrier and power allocation then begins. In each iteration, the subcarrier and power allocation are first fixed as the solution from the previous iteration, and Algorithm 1 is invoked to optimize the IRS phase shift matrix. Then, based on the phase shift matrix obtained in this iteration, Algorithm 2 is invoked to optimize the subcarrier and power allocation. After each iteration, the user and rate sums are calculated and compared with those obtained in the previous iteration. When the relative increase in sum and rate is less than the convergence factor, the iterative optimization process converges, and the optimization ends.

[0094] Algorithm 3 Alternating Optimization Algorithm

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

[0096] (1) Set Φ c =Φ c [0] Algorithm 2 is then invoked 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) Φ is calculated 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 invention will now be described in further detail with reference to the accompanying drawings. The system has N = 64 subcarriers, and the positions of each node are described using two-dimensional coordinates in meters (m). The base station coordinates are (0,0), the IRS coordinates are (50,0), and the user coordinates are (50,10), (55,0), and (60,0), respectively. The inter-node channel is a Rayleigh fading channel, and the channel fading includes path loss and small-scale fading. The gain model for each path in the channel is an exponential attenuation model. The channel coefficient of the l-th path of the channel from the base station to user k is...

[0106]

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

[0108]

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

[0110] To evaluate the performance of the proposed solution, it was compared with three benchmark solutions. Benchmark Solution 1 – No IRS: No IRS is configured in the system. Subcarrier allocation and power allocation are performed based on the direct link from the base station to the user. The algorithm is similar to Algorithm 2 in this paper. Benchmark Solution 2 – Random IRS Phase Shift Scheme: The center frequency phase shift matrix of the IRS is randomly generated. 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 reflectioning surface aided wideband systems[J]. IEEE Communications Letters, 2020, 24(7): 1568-1571]. Then, subcarrier allocation and power allocation are performed using Algorithm 2 of this paper. Benchmark Solution 3 – [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] Scheme: Assuming the IRS reflection phase shift is the same throughout the entire transmission band, the algorithm in this paper is used to optimize the IRS phase shift. Since this paper does not elaborate on the resource allocation of the OFDMA system, the subcarrier and power allocation adopts algorithm 2 of this invention. Except Figure 4 In addition, the results given in other simulation diagrams are averages based on 500 channel samples. To fairly compare the performance of different schemes, the sum rate of each scheme is based on the rate achievable under the actual IRS phase shift characteristics.

[0111] First, the convergence of Algorithm 1 in the proposed scheme of this invention is verified through simulation. Figure 4 The convergence curves of the iterative algorithm under a certain set of channel samples are presented when the number of users is 3, with 4 combinations of transmit power and IRS unit number. It can be seen that the system and rate increase with the iterations, and converge after approximately 11 iterations. The number of iterations required for convergence also increases with the increase of the number of reflecting elements M.

[0112] Figure 5The figure shows the variation of user and rate with transmit power when the number of users is 3 and the number of IRS units is 32. As can be seen from the figure, the user and rate gradually increase with increasing transmit power in all four schemes. The sum rate of the scheme equipped with IRS is higher than that without IRS assistance, proving 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, indicating that optimizing IRS phase shift is very important for improving system performance. The sum rate of the scheme in this invention is higher than that of the baseline scheme 3 because the broadband IRS phase shift model used in this invention is very close to the actual phase shift characteristics. Figure 6 With 3 users and 32 IRS units, the theoretical rates and achievable rates under actual phase shift characteristics of the proposed scheme and the baseline scheme 3 were compared under their respective theoretical phase shift models. In the figure, the dashed line represents the theoretically achievable rate of the two schemes under their respective phase shift models, and the solid line represents the achievable rate under actual phase shift characteristics. The baseline scheme 3 assumes that the phase shift of the IRS is the same for all subcarriers and is optimized accordingly. Simulation results show that the system and rate of the baseline scheme 3 under actual phase shift characteristics are significantly lower than its theoretical rate, and the decrease increases with the increase of transmit power. When the transmit power P tol At 30 dBm, the performance drop reaches 14%. However, the sum rate under the actual phase shift characteristics of the proposed solution is only about 3% lower than the theoretical sum rate. This result indicates that if the correlation between the IRS phase shift and the signal frequency is not considered, the optimized solution will experience a significant performance degradation when applied to practical systems. The proposed solution presents a simple model of the relationship between phase shift and frequency. Although it still deviates from the actual phase shift characteristics, the optimized solution under this model shows minimal performance loss under actual phase shift characteristics, making it a suitable compromise between complexity and performance.

[0113] Figure 7 The figure shows the user sum and rate as a function of the number of IRS units when the number of users is 3 and the transmit power is fixed at 30 dBm. As can be seen from the figure, except for the scheme without IRS assistance, the user sum and rate increase with the number of IRS units. This is because more IRS units mean more reflection paths, resulting in greater received signal power and better directivity of the passive beam. Since the IRS phase shift is not optimized, the random IRS phase shift scheme can only benefit from increased path size, thus its sum and rate increase rate is relatively low. However, the scheme of this invention and the baseline scheme 3, due to phase shift optimization, also benefit from improved passive beam directivity, resulting in a higher sum and rate growth rate.

[0114] Figure 8The simulation presents the changes in user and rate of data under varying user numbers, with an IRS unit count of 32 and a fixed transmit power of 30 dBm. In the simulation, users are uniformly and randomly distributed within a sector ring centered on the base station, with angles ranging from -30° to +30°. The outer radius is 60 m, and the inner radius is 30 m. For each user number, 50 user locations are randomly generated, and the channel is randomly varied 200 times for each location. The simulation yields the sum rate of 10,000 channel samples, which are then averaged to obtain the average sum rate for a given user number. As shown in the figure, user and rate of data increase with the increase in the number of users in all four scenarios. This is due to the optimization of subcarrier allocation and power distribution among users; increasing the number of users allows for greater multi-user diversity gain.

Claims

1. Phase shift model and system optimization method in IRS-assisted OFDMA system, including the following steps: (1) Construction of the communication system model: Based on the conventional IRS-assisted OFDMA system, and according to the correlation between the IRS reflection phase shift and the signal frequency, a mathematical model describing the relationship between the phase shift of different subcarriers and the phase shift of the center frequency is proposed; the IRS reflection unit is modeled as a parallel resonant circuit with an impedance of... Where L1, L2, C, and R represent the plate inductance, outer layer inductance, effective capacitance, and loss resistance, respectively, and 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; for an IRS reflection unit with L1 = 2.5nH, L2 = 0.7nH, R = 1Ω, and C varying from 0.47pF to 2.35pF, the IRS phase shift at multiple frequencies at a sufficient number of center frequency phase points is calculated using this reflection phase shift formula. Then, the center frequency f is fitted using a fitting tool. c In a broadband system with a frequency of 2.4 GHz and a bandwidth of B = 100 MHz, the phase shift function of the IRS, with the frequency and center frequency as variables, 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 Where, θ c The center frequency phase shift is represented by a1(f), a2(f), and a3(f), which are frequency-dependent quadratic curve coefficients. (2) With the goal of maximizing system and rate, construct an optimization mathematical model for the phase shift matrix of IRS center frequency, OFDMA subcarrier and power allocation under the constraints of minimum user rate and total base station transmit power; (3) The optimization problem is transformed into two sub-problems: IRS center frequency phase shift optimization and subcarrier and power allocation optimization. (4) Obtain the phase shift matrix of the IRS center frequency by using variable relaxation and successive convex approximation methods; (5) Subcarrier and power allocation are obtained iteratively using greedy algorithm and water-filling algorithm; (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 equips the base station with a single antenna, the IRS has M reflection units, and the user is equipped with a multi-user OFDMA downlink communication system assisted by the IRS 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 described in step (2) includes modeling the user transmission rate and the system rate, as follows: The subchannel gain coefficient of the channel synthesized from the direct link and the reflection link between the base station and user k on the nth subcarrier is: in This represents the frequency response of the direct link from the base station to user k. The nth element, Φ represents the nth column of the frequency response matrix of the IRS to user k link. n This represents the phase shift matrix of the M reflection units of the IRS for the signal transmitted on the nth subcarrier; This represents the nth column of the frequency response matrix of the base station to IRS link. Represents the set of subcarriers. This represents a set of users, and the superscript T indicates the transpose operation of a vector or matrix. The achievable transmission rate of user k (k = 1, 2, ..., K) is Where c k,n Assign indicators to subcarriers; if the nth subcarrier is assigned to user k, then c k,n =1, otherwise c k,n =0, P k,n σ represents the power allocated by the base station to the nth subcarrier of the kth user. 2 Let V be the noise variance of the channel; the system and rate are...

4. The phase shift model and system optimization method in the IRS-assisted OFDMA system according to claim 1, characterized in that: The optimization mathematical model described in step (2) uses the minimum user rate and the total transmission power of the base station as constraints, and the optimization objective is to maximize the system and rate. The optimization problem is constructed as follows: s.t.R k ≥R min,k Among them, R min,k R represents the user's minimum rate limit. k P represents the achievable transmission rate of user k. tol θ represents the total transmission power of the base station. c,m This represents the phase shift of the center frequency of the m-th reflecting element. This represents the set of IRS reflective units.

5. The phase shift model and system optimization method in the IRS-assisted OFDMA system according to claim 1, characterized in that: Step (3) involves transforming the optimization problem into two sub-problems: the receiver filter and power allocation. Specifically, this includes: (1) Given a fixed subcarrier and power allocation, optimize the phase shift of each IRS unit to maximize the system and rate, i.e. (2) Given a fixed IRS phase shift matrix, optimize subcarrier and power allocation to maximize system performance and rate. s.t.R k ≥R min,k In the formula 6. The phase shift model and system optimization method in the IRS-assisted OFDMA system according to claim 1, characterized in that: Step (4) involves obtaining the IRS center frequency phase shift matrix using variable relaxation and successive convex approximation methods. Specifically, this includes: first, recursively obtaining the relationship between the IRS phase shift matrix of the nth subcarrier and the center frequency phase shift matrix. in △f represents the sub-channel bandwidth, Φ c The center frequency f c The IRS phase shift diagonal matrix below, By introducing slack variables and this relation, the original non-convex optimization problem is transformed into... Where α n and β n The variables are slack variables; finally, the first-order Taylor expansion of the left side of the inequality constraint is performed, transforming the optimization problem into a convex problem, which can be solved using a convex optimization solver.

7. The phase shift model and system optimization method in the IRS-assisted OFDMA system according to claim 1, characterized in that: Step (5) iteratively obtains subcarrier and power allocation using a greedy algorithm and a water-filling algorithm. Specifically, during the initial allocation, a greedy algorithm is used to allocate subcarriers based on the gain of the synthetic channel of each user on the subcarrier. To obtain the highest system and rate, the subcarrier is allocated to the user with the highest channel gain on that subcarrier, i.e., when... season After subcarrier allocation is completed, the classic iterative water-filling algorithm is used for subcarrier power allocation, and the power allocated to the nth subcarrier is... Where [x] + This indicates taking the maximum value between x and 0, where λ0 is the threshold value that satisfies the total power constraint. Calculate the rate for 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, denoted as k′. For each user that meets the minimum rate constraint, find the subcarrier with the smallest channel gain among the subcarriers allocated to this user, denoted as n′. Calculate the achievable transmission rate for this user without subcarrier n′. If the transmission rate still meets the minimum rate constraint, then add n′ to the set of subcarriers to be adjusted. If the minimum rate constraint is satisfied, the number of subcarriers allocated to that user is not reduced; after all users satisfying the minimum rate constraint have been traversed, the calculation is performed. Find the subcarrier n with the largest ratio of the ratio of the subchannel gain of user k′ on each subcarrier to the subchannel gain currently allocated to that subcarrier. * The subcarrier is then reassigned to user k′. After the subcarrier is reassigned, the subcarrier power is allocated using the water-filling algorithm. The rate of each user is recalculated, and it is checked whether the minimum rate constraint is met. This process is repeated until the rate of all users meets the minimum rate requirement.

8. The phase shift model and system optimization method in the IRS-assisted OFDMA system according to claim 1, characterized in that: Step (6) involves using an alternating iterative algorithm to solve for the IRS center frequency phase shift matrix and subcarrier and power allocation. Specifically, this includes: at the start of the algorithm, the initial rate for each user is 0, and the center frequency phase shift matrix Φ... c First, assign values ​​randomly, then use the formula The phase shift matrix Φ of each subcarrier is calculated. n The algorithm first uses a greedy algorithm and a water-filling algorithm to perform subcarrier and power allocation. Then, iterative optimization of the IRS phase shift matrix and subcarrier and power allocation is performed alternately. In each iteration, the subcarrier and power allocation are fixed as the solution of the previous iteration. The successive convex approximation algorithm is used to optimize the IRS phase shift matrix. Then, based on the phase shift matrix obtained in the current iteration, the greedy algorithm and the water-filling algorithm are used to optimize the subcarrier and power allocation. After each iteration, the user and rate are calculated and compared with the user and rate obtained in the previous iteration. When the relative value of the increase in the sum and rate is less than the convergence factor, the iterative optimization process converges and the optimization ends.

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