An optimal power allocation method for maximizing system capacity based on random modulation

Abstract

The application discloses an optimal power allocation method for maximizing system capacity based on random modulation, which comprises the following steps: after a signal is randomly modulated, a discrete lookup table of the MMSE curve of the signal is established; an optimization model is established, so that the area surrounded by the inverse function of the MMSE function of the cross-domain orthogonal approximate message passing and the coordinate axis is maximized, and the optimal power allocation scheme for maximizing the limited capacity of the system is obtained; the inverse function of the MMSE function is obtained through the discrete lookup table, and the optimal power allocation scheme for maximizing the system capacity is obtained by solving the optimization model by using a convex optimization tool. The application can provide the optimal power allocation scheme for maximizing the replica limited capacity in a communication system with almost any discrete input in almost any actual channel.

Description

Technical Field

[0001] This invention relates to the field of signal power allocation, and more particularly to an optimal power allocation method based on random modulation to maximize system capacity. Background Technology

[0002] Since the Channel State Information (CSI) is not known in the assumptions of random unitary matrix coding modulation systems, the transmitted signal is typically only simply averaged and distributed at the transmitter, leading to suboptimal performance in practical communication systems. Therefore, to achieve optimal communication performance, it is necessary to distribute the transmitted signal power using an optimal power allocation scheme, given the known CSI. Common existing power allocation schemes include those based on Singular Value Decomposition (SVD) of the channel matrix and those based on specific detectors.

[0003] However, both power allocation methods have their own drawbacks: Channel matrix SVD-based power allocation schemes mainly include Gaussian water-filling for Gaussian signals and Mercury water-filling for ordinary discrete signals. These power-filling methods require transforming the complex linear channel into multiple parallel single-input-single-output (SISO) sub-channels using SVD, and then performing optimal power-filling on each sub-channel to maximize channel capacity. However, this power allocation scheme requires designing multiple channel codes that achieve optimal capacity in each additive white Gaussian noise (AWGN) sub-channel, resulting in excessively high complexity in the encoding and decoding scheme design. Furthermore, power-filling only guarantees optimal system capacity and does not achieve optimal maximum a posteriori (MAP) detection performance. Typical power allocation schemes based on specific detectors include iterative detectors based on Linear Minimum Mean Square Error (LMMSE) and iterative detectors based on Belief Propagation (BP) (early versions of the OAMP / VAMP iterative detector). The former aims to maximize the capacity of a Multiple-Input Multiple-Output (MIMO) system through power allocation, while the latter aims to minimize the total transmit power while achieving the target Bit Error Rate (BER). However, both of these detector-based power allocation schemes involve matrix inversion operations in calculating LMMSE, resulting in excessively high time complexity, making them difficult to apply to practical large-scale communication systems. Summary of the Invention

[0004] The purpose of this invention is to address the shortcomings of existing technologies by proposing an optimal power allocation method based on random modulation to maximize system capacity.

[0005] The objective of this invention is achieved through the following technical solution: an optimal power allocation method for maximizing system capacity based on random modulation, the method comprising the following steps:

[0006] After the signal is randomly modulated, a discrete lookup table of the MMSE curve of the signal is established; an optimization model is established to maximize the area enclosed by the variational function of the cross-domain orthogonal approximate message passing and the inverse function of the MMSE function of the transmitted signal with the coordinate axes, which is the optimal power allocation scheme for maximizing the system's limited capacity; the inverse function of the MMSE function is obtained through the discrete lookup table, and the optimal power allocation scheme for maximizing the system capacity is obtained by solving the optimization model using convex optimization tools.

[0007] Furthermore, the establishment of the discrete lookup table for the signal MMSE curve specifically includes:

[0008] The input set of the MMSE function is obtained by uniform sampling within a defined interval. Then the output set is calculated using the MMSE function. Save collection Φ s ={(ρ i ,v i )}, As a discrete lookup table for the MMSE curve of a signal.

[0009] Furthermore, the variational function for the cross-domain orthogonal approximate message passing is:

[0010]

[0011] Where v represents the variance of the linear estimator input as The posterior variance of LMMSE at that time

[0012] Furthermore, the optimization model is specifically as follows:

[0013]

[0014] p i ≥0, i=1,…,N.

[0015] Among them, v low P is the preset lower limit of the input v. sum Represents the total transmission power, min{η SE (v,p),mmse -1 (v)} The approximate value is obtained by the bisection method.

[0016] Furthermore, the min{η SE (v,p),mmse -1 (v)}n is approximated using the bisection method, including:

[0017] The search interval for the bisection method is determined to be (0,1). As The search value;

[0018] Start the loop; if the search interval length is greater than the preset precision range, then... The value is taken from the midpoint of the interval; if the length of the search interval is within the precision range, the search stops.

[0019] Conditional judgment, if If the accuracy is within the specified range, then stop the search. Greater than the precision range ∈, when When the lower limit of the search interval is set to the midpoint of the original search interval, the next iteration begins. When this happens, the upper limit of the search interval is set to the midpoint of the original search interval;

[0020] Calculate after the loop ends As η SE The approximate value of (v,p) is obtained from the discrete lookup table, which yields mmse. -1 The approximate value of (v) is finally obtained as min{η}. SE (v,p),mmse -1 The approximate value of (v)}.

[0021] Furthermore, in the random modulation, it is achieved by randomly transforming the signal x = Ξs. A linear system with random modulation is defined as follows:

[0022] y = Ax + n = AΞs + n

[0023] Where AΞ is the equivalent channel matrix and Ξ is the random transformation matrix.

[0024] Furthermore, the equivalent channel matrix is ​​a universal matrix, satisfying the following conditions:

[0025] AΞ is spectrally convergent and possesses a bounded spectral norm, satisfying the following conditions:

[0026] For any fixed constant And constants ∈>0, we have

[0027]

[0028] Furthermore, the random transformation matrix comprises:

[0029] The random transformation matrix is ​​the QR decomposition matrix of the Haar matrix or the IID Gaussian matrix;

[0030] The random transformation matrix is ​​constructed by multiplying the random permutation matrix Π with the unitary matrix T, where T is selected as the discrete Fourier transform matrix, the Hadamard-Walsh transform matrix, the discrete sine transform matrix, or the normalized IID Gaussian transform matrix.

[0031] The random transformation matrix is ​​constructed using a multi-level row permutation unitary matrix, denoted as Ξ = Π1T1Π2T2…Π L T L , where each pair {∏ l ,T l All of them are randomly selected.

[0032] The beneficial effects of this invention are as follows: This invention ensures that the theoretical SE curve of the CD-OAMP algorithm matches the MSE curve in the actual iteration in the random transform domain. Furthermore, it utilizes the property that the variational function of CD-OAMP has the same fixed point as the SE curve to guarantee that the replica-constrained capacity of CD-OAMP can correctly represent the channel capacity of the actual system. Based on this premise, this invention proposes an optimal power allocation scheme that maximizes the replica-constrained capacity in communication systems with almost any discrete input in almost any actual channel, based on the CD-OAMP / MAMP detection algorithm. In addition, designing channel coding with achievable actual capacity under this power allocation scheme no longer requires complex channel coding schemes like the previous power watering method based on channel SVD; and since the CD-MAMP detection algorithm does not require matrix inversion operations and can effectively utilize the sparsity characteristics of the channel, the detection complexity is greatly reduced. Attached Figure Description

[0033] Figure 1 This is a block diagram of random modulation used in embodiments of the present invention;

[0034] Figure 2 This is a flowchart of the CD-MAMP algorithm used in the embodiments of the present invention;

[0035] Figure 3 This is a schematic diagram of the replica-limited capacity mentioned in the embodiments of the present invention. The area of ​​the shaded part is numerically equal to the replica-limited capacity.

[0036] Figure 4 When using a CD-MAMP detector for signal detection in a random modulation linear system, the maximum bit rate that the system can achieve under different power distributions is compared with that of a Gaussian signal after Gaussian water injection. Detailed Implementation

[0037] The specific embodiments of the present invention will be further described in detail below with reference to the accompanying drawings.

[0038] This invention provides an optimal power allocation method based on random modulation to maximize system capacity, making the CD-MAMP / OAMP algorithm applicable to any real-world channel matrix; the preliminary explanations and corresponding parameter interpretations are as follows:

[0039] like Figure 1As shown, this embodiment uses a power allocation matrix. in p i ≥0, P sum This represents the total transmitted power. Specifically, in practical applications, the signal s on the transmitter is first processed by the RT matrix Ξ, and then through the matrix ∑ P Perform RT domain power allocation, and finally multiply by the unitary matrix V on the left, that is...

[0040] y = AV∑ P Ξs+n,

[0041] Where A=U∑ A V H Therefore, both sides are multiplied by matrix U on the left. H You can get it later

[0042]

[0043] in

[0044] The idea behind this power allocation scheme can be summarized as follows:

[0045] Diagonalize the channel matrix A using the unitary matrix V;

[0046] Using the power allocation matrix Σ P Optimize the effective channel matrix AVΣ P The distribution of singular values ​​of Ξ.

[0047] The randomness of the effective channel matrix is ​​enhanced by using a semi-random matrix Ξ.

[0048] It is important to note the equivalent channel AV∑ for the transmitted symbol s. P Ξ still possesses right-unitary invariance, therefore CD-MAMP / OAMP detection can be directly applied to signal detection in this power-division random modulation system.

[0049] The premise of implementing this invention is that the receiving end uses the CD-OAMP / MAMP algorithm to recover the signal; such as Figure 2 As shown, the CD-MAMP detection algorithm specifically includes: the CD-MAMP detector framework incorporates a memory linear detector (MLD) γ t (·), RT and IRT, and the memory nonlinear detector (MNLD) φ(·). From t=1 and start

[0050] in and It is A H A polynomial of A, and has

[0051]

[0052] Without loss of generality, we assume and The norm is finite. Also, assume γ t (·) and φ t (·) is Lipschitz continuous.

[0053] According to the asymptotic IID Gaussianity, γ t The output covariances of (·) and φ(·) can be obtained by the following formula: when N→∞

[0054]

[0055]

[0056] Where X = x·1 T S = s·1 T The dimension of a vector depends on the dimensions of x and s; G t =[g1,…,g t ] and Z t =[z1,…,z t ] is a column-directed IID Gaussian and row-directed joint Gaussian matrix, and is independent of x and s. The covariance matrix satisfies make To simplify the description, the state evolution (SE) of CD-MAMP can be written as:

[0057]

[0058] Based on the CD-MAMP framework, a CD-BO-MAMP detector can be proposed. From t=1 and The specific process begins as follows:

[0059]

[0060] in Where λ min and λ max They are AA H The minimum and maximum eigenvalues. Meanwhile... These are optimization variables used to ensure that the CD-MAMP algorithm achieves maximum replica a posteriori optimality.

[0061] The implementation of this embodiment is as follows: the system has an arbitrary channel matrix and arbitrary discrete inputs, the system scale is relatively large, and it is expected that the system capacity will be optimized through power allocation.

[0062] The specific steps are as follows:

[0063] S1. Initialize the randomly modulated parameters and establish a discrete lookup table for the MMSE curve of the signal;

[0064] In this embodiment, the specific details of random modulation are as follows:

[0065] Given a random unitary matrix Ξ and a signal vector s, if the equivalent channel matrix AΞ ​​belongs to the universal class matrix

[23] , then Ξs and Ξ H s are respectively called the random transformation (RT) and the inverse random transformation (IRT) of s. Similarly, Ξ and Ξ H These are referred to as the RT matrix and the IRT matrix, respectively. The universal matrix must satisfy the following condition:

[0066] AΞ is spectrally convergent and possesses a bounded spectral norm, satisfying the following conditions:

[0067] For any fixed constant And constants ∈>0, we have

[0068]

[0069] Theoretically, only unitary matrices randomly selected from the entire feasible region are strictly optimal; however, experimental results show that most randomly generated unitary matrices are good modulation matrices, so easily implemented random unitary matrices can be chosen, such as:

[0070] The matrix Ξ can be the QR decomposition matrix of either the Haar matrix or the IID Gaussian matrix;

[0071] A matrix Ξ can be constructed by multiplying a random permutation matrix Π with a unitary matrix T, i.e., Ξ = ΠT, where T can be a discrete Fourier transform (DFT) matrix, a Hadamard-Walsh transform matrix, a discrete sine transform matrix, or a normalized IID Gaussian transform matrix.

[0072] The matrix Ξ can also be constructed using a multi-level row permutation unitary matrix, represented as Ξ = Π1T1Π2T2…Π L T L Each pair of {Π l ,T l All of them are randomly selected.

[0073] Random modulation is achieved by using RT on the signal, that is:

[0074] x=Ξs

[0075] When there is random modulation in a standard linear system, we have

[0076] The linear constraint Γ: y = Ax + n,

[0077] The random transformation T: x = Ξs,

[0078] The non - linear constraint Φ: s ∼ P S (s).

[0079] Where Ξ M×1 is an RT matrix of dimension N×N, A M×N is an arbitrary channel matrix of dimension M×N, s N×1 is the transmitted signal of dimension N×1, n M×1 is the channel noise, P S (s) is the probability distribution of the input signal vector s.

[0080] Random modulation obtains the maximum diversity gain by allowing each transmitted signal symbol to fully experience the fading of each path on the channel matrix, ensuring the performance of signal recovery; furthermore, through random modulation, the matrix AΞ exhibits right - unitary invariance, so AMP - like detection algorithms can reach the replica minimum mean - square error / bit - error rate limit (replica MMSE / BER limit), thus achieving Bayesian optimality; at the same time, since Ξ is a unitary matrix, the matrix (AΞ) H AΞ and A H The eigenvalue distributions of A are the same, so random modulation does not change the replica minimum mean - square error MMSE, replica MAP BER, and replica - limited capacity of the original standard linear system.

[0081] S11. The parameter initialization includes:

[0082] Let the known noise variance be ρ 2 、the total power P sum 、the actual channel matrix A M×N ; The eigenvalues of the matrix A H A are i = 1,…,N, where when min{M,N}<i≤N Specify the lower integration limit v low = 10 -4 and the precision parameter ∈ = 10 -15 (Theoretically, the smaller these two numbers are, the higher the calculation precision. However, in the actual algorithm, a trade - off needs to be made between precision and operation time, so these two parameters need to be adjusted according to actual needs. During experiments, v low = 10 -4 , ∈ = 10 -15The effect is quite remarkable, and the running time is within an acceptable range.

[0083] S12. Establish a discrete lookup table for the MMSE curve of a signal: Since the inverse function of the MMSE of most signals has a very complex expression, a discrete lookup table for the MMSE curve of a signal is first established to simplify the calculation:

[0084]

[0085] in The set is obtained by using the interval (0, ρ) up ) obtained by uniform sampling on ) ρ up The value needs to be large enough to ensure that its corresponding MMSE value is small enough, that is... At the same time, we usually adjust the sampling interval to make To ensure calculation accuracy.

[0086] Simply put, it involves first sampling to obtain the set {ρ} i Then, v is calculated using the MMSE function. i ,Right now

[0087] v i =mmse(ρ i ),

[0088] Then save the collection Φ s ={(ρ i ,v i )}, This is equivalent to establishing a discrete lookup table for the MMSE curve of the signal: You can use v i The value can be directly looked up to obtain the corresponding ρ. i =mmse -1 (v i The value of ) does not need to be found without determining the inverse function mmse. -1 The expression.

[0089] S2. Establish an optimization model:

[0090] The optimal power allocation scheme that maximizes the system's limited capacity can be obtained by solving the following optimization problem:

[0091]

[0092] p i ≥0, i=1,…,N.

[0093] Obj(v,p,Φ s ) is a user-defined function whose purpose is to find min{η} using the binary search method. SE (v,p),mmse-1 (v)} approximation (due to Since there is no explicit expression, a binary search is needed to find the value of the function when the input is v. SE (·) is the variational function of CD-OAMP, expressed as:

[0094]

[0095] It can be proven Since is a concave function of p, this optimization problem is also a convex optimization problem, which can be solved directly using the convex optimization tools in MATLAB. The function Obj(v,p,Φ) s The pseudocode example is as follows:

[0096]

[0097]

[0098] The explanations for each key line of code are as follows:

[0099] 1: The search interval for the bisection method is determined to be (0,1), because the maximum value of the MMSE after power normalization is 1.

[0100] 2: Start the loop, and stop the search if the length of the search interval is within the precision range.

[0101] 3: Use the bisection method to find the midpoint of the interval.

[0102] 4. Conditional judgment: If the search value and the target value are within the precision range, the search stops. The principle is:

[0103] inverse function It has an explicit expression, so the input... Then, an output value can be directly calculated using an explicit expression. When this output value is sufficiently close to v, it is equivalent to... Then correspondingly there would be Therefore, we can obtain The search value.

[0104] 5: Exit the loop if the condition is met.

[0105] 6: When This indicates that the search value is not precise enough, and Less than v, because

[0106] Since it is monotonically increasing, the lower limit of the search interval is set to the midpoint of the original search interval to raise the lower limit of the search interval, allowing... It becomes larger in the next cycle, thus making it Become larger to reduce

[0107] 7: See above.

[0108] 8: Corresponding The situation, principle and The situation is similar.

[0109] 9: See above.

[0110] 10: End judgment.

[0111] 11: End of loop.

[0112] 12: Calculate η SE Approximate value of (v,p)

[0113] 13: By finding set Φ s The closest value to the input v i To find mmse -1 (v) Closer It is important to note that It may not be all ρ i The closest to mmse -1 (v) because the slope of the function changes with v, the smaller v is, the larger the slope, mmse -1 (v) will change more rapidly, which could very likely lead to a larger v. larger (v larger ρ corresponding to -v>0) smaller =mmse -1 (v larger (a value that is smaller but closer to v) smaller (v smaller -v<0 and

[0114] v larger -v>vv smaller ) corresponding to ρ larger =mmse -1 (v smaller It is closer to mmse -1 (v)), but it is indeed close enough.

[0115] 14: Output min{η SE (v,p),mmse -1 The approximate value of (v)}.

[0116] S3. Solving the optimization model: Use the convex optimization toolbox to find the convex optimization problem.

[0117]

[0118] pi ≥0, i=1,…,N.

[0119] The solution p * .

[0120] like Figure 3 As shown in the embodiment of the above-described optimal power allocation method for maximizing replica-constrained capacity based on random modulation, the technical principle includes:

[0121] The replica-limited capacity of each transmission symbol in a power-allocated linear system is

[0122]

[0123] in The optimal power allocation scheme that maximizes the system's limited capacity can be obtained by solving the following optimization problem.

[0124] max p C MIMO (p),

[0125]

[0126] p i ≥0, i=1,…,N.

[0127] According to the capacity-area theorem, the capacity C... MIMO Can be re-represented as

[0128] C MIMO (p)=∫0 1 min{η SE (v,p),mmse -1 (v)}dv

[0129] Where η SE (·) is the variational function of CD-OAMP, expressed as:

[0130]

[0131] The reason for this transformation is that the SE of CD-OAMP includes an orthogonalization operation, making the orthogonalized error no longer locally MMSE optimal. This complicates the analysis of limited capacity and achievable rate using the I-MMSE lemma. This difficulty can be overcome using the variational transformation function of CD-OAMP, which preserves the same fixed point as the SE of CD-OAMP.

[0132] It can be proven Since it is a concave function of p, this optimization problem is also a convex optimization problem. However, because finding mmse... -1 (v) and ηSE The analytical expression for (v, p) is not easy. Therefore, it can be solved using the following approach:

[0133] Since v = mmse(ρ) is independent of p, we pre-compute a lookup table for mmse(ρ), where the values ​​of ρ are taken from the interval [0, ρ]. up A discrete set {ρ} uniformly distributed on [a] i}. Typically, we ensure that |{ρ i}|≥10 4 , and select ρ up Make mmse(ρ) up The value is small enough. Therefore, we can obtain the mmse through lookup tables and interpolation. -1 (v).

[0134] because about It is monotonically increasing, which means Since v is increasing, we obtain it through piecewise search. We initialize And set a small threshold ∈>0. For each iteration i≥1, and

[0135] if but

[0136] if but

[0137] Otherwise, stop the search and return.

[0138] Furthermore, experiments have shown that the following approximation of the objective function can significantly reduce the algorithm's complexity:

[0139]

[0140] Where v low It is an artificially set lower limit. During the experiment, v is set... low =10 -4 ,∈=10 -15 .

[0141] This invention achieves a perfect match between the theoretical SE curve and the MSE curve in the actual iteration of the CD-OAMP algorithm in the random transform domain. Furthermore, it leverages the property that the variational function of CD-OAMP coincides with the fixed point of the SE curve to ensure that the replica-constrained capacity of CD-OAMP accurately represents the channel capacity of the actual system. Based on this premise, this invention proposes an optimal power allocation scheme that maximizes the replica-constrained capacity in communication systems with almost any discrete input in virtually any real-world channel, using the CD-OAMP / MAMP detection algorithm.

[0142] like Figure 4 As shown, this embodiment also provides simulation results, specifically when the input is a QPSK signal, M=N=256, (J=8, K=4), P jk =5, ρ=0.6 and v=300km / h in a MIMO stochastic modulation linear system with parallelized SVD channel, using a CD-MAMP detector for signal detection, the maximum bit rate that the system can achieve under different power allocations (the solid red line in the middle represents the power allocation scheme that maximizes the replica-limited capacity, and the dashed red line represents the average power allocation scheme; the dark red at the bottom represents QPSK water injection based on parallelized SVD channel) is compared with the maximum bit rate that the Gaussian signal can achieve after Gaussian water injection;

[0143] The relevant time-varying multipath multiple-transmission multiple-receive (MIMO) channel used in the simulation is as follows:

[0144] Consider a time-varying multipath MIMO channel with J transmit antennas and K receive antennas. in The channel impulse response A between the j-th transmitting antenna and the k-th receiving antenna j,k [u,l] is

[0145]

[0146] Where u = 1, ..., M, l = 1, ..., K j,k L j,k P represents the maximum number of channel taps between the j-th transmit antenna and the k-th receive antenna. j,k T represents the maximum number of paths between the j-th transmit antenna and the k-th receive antenna. s A represents the system sampling interval. j,k,i , τ j,k,i and v j,k,i These correspond to the channel gain, delay, and Doppler shift of the i-th path between the j-th transmit antenna and the k-th receive antenna, respectively. When the transceiver employs a practical root-raised cosine (RRC) pulse shaping filter to control the signal bandwidth and suppress out-of-band emissions, P... rc(·) is the overall raised cosine roll-off filter. Meanwhile, A j,k,i It also includes the spatial correlation between antennas, i.e. in

[0147]

[0148] It is an independent and identically distributed complex Gaussian random matrix, C rx and It is made by R tx and R rx The correlation integer matrix obtained from the Cholesky decomposition is as follows: Matrix R tx and R rx The elements in are

[0149]

[0150] Where ρ tx ,ρ rx ∈[0,1) represents R respectively tx and R rx The correlation level, when ρ is set during simulation tx =ρ rx =ρ.

[0151] Other embodiments of this application will readily occur to those skilled in the art upon consideration of the specification and practice of the disclosure herein. This application is intended to cover any variations, uses, or adaptations of this application that follow the general principles of this application and include common knowledge or customary techniques in the art not disclosed herein. The specification and embodiments are to be considered exemplary only, and the true scope and spirit of this application are indicated by the claims.

[0152] It should be understood that the foregoing general description and the following detailed description are exemplary and explanatory only, and are not intended to limit this application. This application is not limited to the precise structures described above and shown in the accompanying drawings, and various modifications and changes can be made without departing from its scope. The scope of this application is limited only by the appended claims.

Claims

1. An optimal power allocation method for maximizing system capacity based on random modulation, characterized in that, The method includes the following steps: After the signal is randomly modulated, a discrete lookup table of the signal MMSE curve is established; an optimization model is established to maximize the area enclosed by the variational function of the cross-domain orthogonal approximate message passing and the inverse function of the MMSE function of the transmitted signal and the coordinate axis, which serves as the optimal power allocation scheme for maximizing the system's limited capacity. The inverse function of the MMSE function is obtained through a discrete lookup table. The optimal power allocation scheme that maximizes the system capacity is obtained by solving the optimization model using convex optimization tools.

2. The optimal power allocation method for maximizing system capacity based on random modulation according to claim 1, characterized in that, The discrete lookup table for establishing the MMSE curve of the signal specifically includes: The input set of the MMSE function is obtained by uniform sampling within a defined interval. Then, the output set is obtained by calculating using the MMSE function. Save collection As a discrete lookup table for the MMSE curve of a signal.

3. The optimal power allocation method for maximizing system capacity based on random modulation according to claim 1, characterized in that, The variational function for the cross-domain orthogonal approximate message passing is: This indicates that when the input variance of the linear estimator is The variance of the posterior estimate of LMMSE at time , where .

4. The optimal power allocation method for maximizing system capacity based on random modulation according to claim 3, characterized in that, The optimization model is specifically as follows: , , . in, Preset Enter the lower limit. Indicates the total transmission power. An approximate value is obtained using the bisection method.

5. The optimal power allocation method for maximizing system capacity based on random modulation according to claim 4, characterized in that, The The approximate value obtained by the bisection method includes: The search interval for the binary search method is determined to be (0,1). As The search value; Start the loop; if the search interval length is greater than the preset precision range... ,but The value is taken from the midpoint of the interval; if the length of the search interval is within the precision range, the search stops. Conditional judgment, if If the accuracy is within the specified range, then stop the search. Greater than the accuracy range ,when When the lower limit of the search interval is set to the midpoint of the original search interval, the next iteration begins. When this happens, the upper limit of the search interval is set to the midpoint of the original search interval; Calculate after the loop ends As The approximate value is obtained from the discrete lookup table. The approximate value is obtained, and finally... Approximate value.

6. The optimal power allocation method for maximizing system capacity based on random modulation according to claim 1, characterized in that, In the random modulation, the signal is randomly transformed. A linear system with random modulation is defined as follows: in Let be the equivalent channel matrix, and Ξ be the random transformation matrix.

7. The optimal power allocation method for maximizing system capacity based on random modulation according to claim 6, characterized in that, The equivalent channel matrix is ​​a universal matrix that satisfies the following conditions: It is spectrally convergent and possesses a bounded spectral norm, satisfying... ; For any fixed constant and constants ,have 。 8. The optimal power allocation method for maximizing system capacity based on random modulation according to claim 6, characterized in that, The random transformation matrix includes: The random transformation matrix is ​​the QR decomposition matrix of the Haar matrix or the IID Gaussian matrix; Random transformation matrix through random permutation matrix unitary matrix Multiplication To construct, in Choose the discrete Fourier transform matrix, the Hadamard-Walsh transform matrix, the discrete sine transform matrix, or the normalized IID Gaussian transform matrix; The random transformation matrix is ​​constructed using a multi-level row permutation unitary matrix, denoted as: , where each pair { They are all randomly selected.

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