Non-cellular network symbol error rate analysis and optimization method based on PAM and QAM modulation

Abstract

The invention provides a non-cellular network symbol error rate analysis and optimization method based on PAM and QAM modulation. The method comprises the following steps: establishing a non-cellular network model based on a Rayleigh fading channel; performing channel estimation by using a minimum mean square error method based on the constructed network model; based on the constructed network model, signal detection is carried out by using a maximum ratio merging method; based on the constructed network model, calculating symbol error rates of PAM and QAM modulation of the user; and constructing an optimization problem for minimizing the maximum symbol error rate in all users according to the calculated user symbol error rate, and designing an optimization strategy for cooperatively controlling the user transmission power coefficient. The symbol error rate calculation method disclosed by the invention can provide theoretical guidance for researching the reliability performance of a cellular-free network under different modulation schemes, and the designed optimization method can obviously improve the symbol error rate performance of a user with the worst performance under relatively low calculation complexity.

Description

Technical Field

[0001] The present invention relates to the field of wireless communication technology, and in particular to a method for analyzing and optimizing symbol error rate of a non-cellular network based on PAM and QAM modulation. Background Art

[0002] At present, with the continuous development of mobile Internet and various communication technologies, 5G networks based on cellular structures have been widely used, and various applications related to 5G networks have penetrated into all aspects of people's lives. According to the 53rd "Statistical Report on the Development of China's Internet", as of December 2023, my country's mobile Internet access traffic will reach 301.5 billion GB, and the average weekly Internet access time per person will be 26.1 hours; among the usage time of major applications, the total time of online videos, short videos, and online live broadcasts, which have high requirements for network quality, accounts for more than a quarter; in addition, the number of cellular Internet of Things terminal users of the three basic telecommunications companies has reached 2.332 billion households. With such a large number of device connections and user needs, coupled with the continuous in-depth development of "5G+" applications such as autonomous driving, virtual reality, telemedicine, and industrial automation, the current problems of 5G networks are becoming increasingly prominent.

[0003] In traditional cellular networks, since wireless signals inevitably attenuate rapidly as distance increases, people are prone to encounter problems such as poor cell edge signal quality, high interference, and frequent cell switching when using cellular networks. On this basis, people have proposed a cell-free network. In a cell-free network, a large number of distributed access points (APs) with multiple antennas are distributed in a wide area. They are connected to the central processing unit (CPU) through a fronthaul network and provide services to users with the same time and frequency resources. As a potential solution for the next generation of wireless communication technology, it eliminates the concept of cells and inter-cell interference, and is expected to solve the problems of poor cell edge signal quality and high interference that people encounter when using cellular networks, and has broad development potential.

[0004] As a potential solution for the next generation of wireless communication technology, the research on non-cellular networks is of great significance. At present, most research works only study the spectrum efficiency, energy efficiency, transmission rate, power and other indicators of non-cellular networks, but there is little research on the calculation and optimization of symbol error rate, a key indicator of system reliability, especially the calculation and optimization of symbol error rate when the system adopts PAM and QAM modulation. Summary of the invention

[0005] According to the technical problems raised above, a symbol error rate analysis and optimization method for a non-cellular network based on pulse amplitude modulation (PAM) and quadrature amplitude modulation (QAM) modulation is provided, which effectively improves the symbol error rate performance of the worst performing users.

[0006] The technical means adopted by the present invention are as follows:

[0007] A method for analyzing and optimizing symbol error rate of a non-cellular network based on PAM and QAM modulation, comprising:

[0008] S1. Establish a non-cellular network model based on Rayleigh fading channel;

[0009] S2. Based on the constructed network model, the minimum mean square error method is used to perform channel estimation;

[0010] S3, based on the constructed network model, use the maximum ratio combining method to perform signal detection;

[0011] S4. Based on the constructed network model, calculate the symbol error rate of the user's PAM and QAM modulation;

[0012] S5. Based on the calculated user symbol error rate, construct an optimization problem to minimize the maximum symbol error rate among all users, and design an optimization strategy for collaboratively controlling the user's transmit power coefficient.

[0013] Furthermore, in step S1, the non-cellular network model is established as follows:

[0014]

[0015] Among them, g lk represents the channel vector between the lth AP and the kth user, represents the small-scale fading coefficient of the Rayleigh distribution, which is an independent and identically distributed Gaussian vector relative to l and k; β lk Represents the large-scale fading coefficient, which is composed of shadow fading and path loss.

[0016] Further, step S2 specifically includes:

[0017] S21. Calculate the uplink pilot signal received by the lth AP. The calculation formula is as follows:

[0018]

[0019] In order for each AP to obtain channel state information from different users, each user needs to send uplink pilot sequences to all APs, and these pilot sequences satisfy when k = j, When k≠j, The conditions include: represents the uplink pilot sequence, τ represents the length, and p p represents the pilot transmission power of the user; N p,l ∈C N×τ represents the additive Gaussian white noise at the lth AP, and each element in the noise matrix obeys an independent and identical distribution in represents the Gaussian noise power during the transmission of the pilot sequence;

[0020] S22, based on the uplink pilot signal received by the lth AP, perform channel estimation on the pilot signals from different users, and convert the uplink pilot signal y p,l The inner product calculation with the pilot sequence is as follows:

[0021]

[0022] S23, calculate the channel g between the lth AP and the kth user lk The minimum mean square error estimate is calculated as follows:

[0023]

[0024] In the above formula, the channel estimation It includes N independent and identically distributed Gaussian variables, and all variables obey the following Gaussian distribution:

[0025]

[0026] in,

[0027] S24. According to the property of minimum mean square error estimation, the channel estimation error between the lth AP and the kth user is Channel Estimation are independent of each other, and All elements in are independent and identically distributed where ξ lk =β lk -γ lk .

[0028] Furthermore, step S3 specifically includes:

[0029] S31. In the uplink data transmission phase, all users send data signals to different APs, and the data signal received by the lth AP is calculated as follows:

[0030]

[0031] Among them, s k represents the signal sent by the kth user, p u and η k denote the transmission power and power control coefficient of user k respectively, and satisfy 0≤η k Power constraint condition of ≤1; n l represents the additive Gaussian white noise vector received at the lth AP, and each element is independent and identically distributed in represents the Gaussian noise power during uplink data transmission;

[0032] S32, when the maximum ratio combining method is used to detect the received signal, the data signal y received by the lth AP is l With detection vector Multiply them, and send the multiplied signals to the CPU for processing. At this time, the signal collected by the CPU for the kth user is:

[0033]

[0034] in, ε k represents the equivalent noise received by the kth user,

[0035] S33, will Defined as the transmission gain of the kth user's desired signal, and then using the moment matching method, ρ k The probability density function of is approximately Gamma distribution, as follows;

[0036]

[0037] in,

[0038] Further, step S4 specifically includes:

[0039] S41, when the user selects M-ary PAM modulation, all users start from the symbol {-M PAM +1,-M PAM +3,…,M PAM -1} select the sending signal, where M PAM Indicates the modulation order of M-ary PAM modulation;

[0040] In order to obtain the symbol error rate expression of M-ary PAM modulation, we can analyze and obtain and Approximately obeys complex Gaussian distribution in,

[0041] From the code element {-M PAM +1,-M PAM +3,…,M PAM -1}, select send signal, get The probability density functions of the real and imaginary parts are:

[0042]

[0043] Based on the formula and ε k ,k=1,2,…,K’s probability density function is expressed as:

[0044]

[0045] in express The jth row of can be expressed as:

[0046]

[0047] In the above formula, z = Cross_add (x, y) is the value of x∈C 1×M and y∈C 1×N All elements in the cross addition operation are performed, and the resulting elements are combined into a new vector z∈C 1×MN ;

[0048] Based on ρ k The probability density function and ε k , k=1,2,…,K probability density function, the symbol error rate expression of M-ary PAM modulation of the kth user is approximated as:

[0049]

[0050] in, Γ(x) represents the gamma function, 2F1(α,β;γ;x) represents the Gaussian hypergeometric function;

[0051] S42, when the user selects M-ary quadrature amplitude modulation, all users select the code element {Cross_add(Amplitude QAM ,i×Amplitude QAM )} selects the sending signal, where M QAM represents the modulation order of M-ary QAM modulation, and

[0052] In order to obtain the symbol error rate expression of M-ary QAM modulation, The probability density functions of the real and imaginary parts are:

[0053]

[0054] Based on the formula and The probability density function of the real and imaginary parts is obtained as follows: k ,k=1,2,…,the probability density function of the real and imaginary parts of K is:

[0055]

[0056] in, express The jth row of can be expressed as:

[0057]

[0058] Based on ρ k The probability density function of M-ary QAM modulation and the equivalent noise ε k ,k=1,2,…,K, the probability density function of the real and imaginary parts, the symbol error rate expression of the M-ary QAM modulation of the kth user is approximated as:

[0059]

[0060] Among them, c1=1.09500814703333, c2=0.75651138383854, and:

[0061]

[0062] Among them, D n (x) represents a parabolic cylinder function.

[0063] Furthermore, step S5 specifically includes:

[0064] S51, when the user transmission power coefficient η is satisfied k ,0≤η k Under the constraint of ≤1, the optimization problem of minimizing the maximum symbol error rate among users is expressed as:

[0065]

[0066] st0≤η k ≤1,k=1,2,…,K

[0067] S52, taking the expectation of the signal to interference noise ratio as a new objective function, as follows:

[0068]

[0069] in, Respectively represent the transmission signals of M-ary PAM and QAM modulation;

[0070] S53, based on the formula in step S52, convert the formula in step S51 as follows:

[0071]

[0072] st0≤η k≤1,k=1,2,…,K

[0073] in, Respectively represent the expected transmission signal power of M-ary PAM and QAM modulation

[0074] S54, introduce the slack variable t, and transform the formula in step S53 as follows:

[0075]

[0076] st0≤η k ≤1,k=1,2,…,K

[0077] The above equation is a standard geometric programming problem, which can be effectively solved using convex optimization tools to obtain a set of suboptimal power control coefficients to minimize the maximum symbol error rate of all users.

[0078] Compared with the prior art, the present invention has the following advantages:

[0079] 1. The present invention provides a method for analyzing and optimizing the symbol error rate of a non-cellular network based on PAM and QAM modulation, which can analyze the symbol error rate of a non-cellular network using PAM and QAM modulation under Rayleigh fading channels and non-ideal state information, and provide theoretical guidance for optimizing the reliable performance of non-cellular networks under different modulation modes.

[0080] 2. The present invention provides a method for analyzing and optimizing the symbol error rate of a non-cellular network based on PAM and QAM modulation, which can improve the user symbol error rate performance by adjusting the power coefficient while reducing the overall energy consumption of the system, which is helpful to promote the practical application of non-cellular networks in the future.

[0081] Based on the above reasons, the present invention can be widely promoted in fields such as wireless communication. BRIEF DESCRIPTION OF THE DRAWINGS

[0082] In order to more clearly illustrate the embodiments of the present invention or the technical solutions in the prior art, the drawings required for use in the embodiments or the description of the prior art will be briefly introduced below. Obviously, the drawings described below are some embodiments of the present invention. For ordinary technicians in this field, other drawings can be obtained based on these drawings without paying creative labor.

[0083] Figure 1 The figure is a flow chart of the method of the present invention.

[0084] Figure 2 This is a model structure of a non-cellular network to which the solution of the present invention is applicable.

[0085] Figure 3A simulation diagram of the relationship between user symbol error rate and transmission power provided in an embodiment of the present invention.

[0086] Figure 4 A simulation diagram of the relationship between the user symbol error rate and different power schemes provided in an embodiment of the present invention. DETAILED DESCRIPTION

[0087] In order to enable those skilled in the art to better understand the scheme of the present invention, the technical scheme in the embodiments of the present invention will be clearly and completely described below in conjunction with the drawings in the embodiments of the present invention. Obviously, the described embodiments are only part of the embodiments of the present invention, not all of the embodiments. Based on the embodiments of the present invention, all other embodiments obtained by ordinary technicians in this field without creative work should fall within the scope of protection of the present invention.

[0088] It should be noted that the terms "first", "second", etc. in the specification and claims of the present invention and the above-mentioned drawings are used to distinguish similar objects, and are not necessarily used to describe a specific order or sequence. It should be understood that the data used in this way can be interchanged where appropriate, so that the embodiments of the present invention described herein can be implemented in an order other than those illustrated or described herein. In addition, the terms "including" and "having" and any variations thereof are intended to cover non-exclusive inclusions, for example, a process, method, system, product or device that includes a series of steps or units is not necessarily limited to those steps or units that are clearly listed, but may include other steps or units that are not clearly listed or inherent to these processes, methods, products or devices.

[0089] like Figure 1 As shown, the present invention provides a non-cellular network symbol error rate analysis and optimization method based on PAM and QAM modulation, including:

[0090] S1. Establish a non-cellular network model based on Rayleigh fading channel;

[0091] S2. Based on the constructed network model, the minimum mean square error method is used to perform channel estimation;

[0092] S3, based on the constructed network model, use the maximum ratio combining method to perform signal detection;

[0093] S4. Based on the constructed network model, calculate the symbol error rate of the user's PAM and QAM modulation;

[0094] S5. Based on the calculated user symbol error rate, construct an optimization problem to minimize the maximum symbol error rate among all users, and design an optimization strategy for collaboratively controlling the user's transmit power coefficient.

[0095] During specific implementation, as a preferred embodiment of the present invention, the following is established: Figure 2 The non-cellular network shown in FIG. 1 is composed of a CPU, L APs, and K single-antenna users, where each AP is configured with N antennas and satisfies the condition LN>>K. It is assumed that all APs and users are uniformly and randomly distributed in a large service area, and each AP is connected to a CPU with high computing power through a perfect backhaul link, and uses the same time-frequency resources to provide communication services for all users. In step S1, the non-cellular network model established is as follows:

[0096]

[0097] Among them, g lk represents the channel vector between the lth AP and the kth user, represents the small-scale fading coefficient of the Rayleigh distribution, which is an independent and identically distributed Gaussian vector relative to l and k; β lk Represents the large-scale fading coefficient, which is composed of shadow fading and path loss. Since the large-scale fading coefficient changes slowly, it is usually assumed to be known. The large-scale fading coefficient model between the lth AP and the kth user is:

[0098]

[0099] in, and σ sh denote the shadow fading and the standard deviation of the shadow fading, respectively, and and σ sh =8dB. Path loss PL lk The three-slope model is used for modeling, which is specifically expressed as follows:

[0100]

[0101] Among them, d lk represents the distance between the lth AP and the kth user; d0 and d1 represent two distance constants, which are set to d0 = 10m and d1 = 50m respectively; L is the height h of the AP relative to the carrier frequency f. AP and the user's height h user The related constants are specifically modeled as:

[0102]

[0103] Where, f = 1900MHz, h AP =15m and h user =1.65m.

[0104] In specific implementation, as a preferred embodiment of the present invention, step S2 specifically includes:

[0105] S21. Calculate the uplink pilot signal received by the lth AP. The calculation formula is as follows:

[0106]

[0107] In order for each AP to obtain channel state information from different users, each user needs to send uplink pilot sequences to all APs, and these pilot sequences satisfy when k = j, When k≠j, The conditions include: represents the uplink pilot sequence, τ represents the length, and p p represents the pilot transmission power of the user; N p,l ∈C N×τ represents the additive Gaussian white noise at the lth AP, and each element in the noise matrix obeys an independent and identical distribution in represents the Gaussian noise power during the transmission of the pilot sequence;

[0108] S22, based on the uplink pilot signal received by the lth AP, perform channel estimation on the pilot signals from different users, and convert the uplink pilot signal y p,l The inner product calculation with the pilot sequence is as follows:

[0109]

[0110] S23, calculate the channel g between the lth AP and the kth user lk The minimum mean square error estimate is calculated as follows:

[0111]

[0112] In the above formula, the channel estimation It includes N independent and identically distributed Gaussian variables, and all variables obey the following Gaussian distribution:

[0113]

[0114] in,

[0115] S24. According to the property of minimum mean square error estimation, the channel estimation error between the lth AP and the kth user is Channel Estimation are independent of each other, and All elements in are independent and identically distributed where ξ lk =β lk -γ lk .

[0116] In specific implementation, as a preferred embodiment of the present invention, step S3 specifically includes:

[0117] S31. In the uplink data transmission phase, all users send data signals to different APs, and the data signal received by the lth AP is calculated as follows:

[0118]

[0119] Among them, s k represents the signal sent by the kth user, p u and η k denote the transmission power and power control coefficient of user k respectively, and satisfy 0≤η k Power constraint condition of ≤1; n l represents the additive Gaussian white noise vector received at the lth AP, and each element is independent and identically distributed in represents the Gaussian noise power during uplink data transmission;

[0120] S32, when the maximum ratio combining method is used to detect the received signal, the data signal y received by the lth AP is l With detection vector Multiply them, and send the multiplied signals to the CPU for processing. At this time, the signal collected by the CPU for the kth user is:

[0121]

[0122] In this embodiment, in order to recover the data signal sent by the kth user from the signal received by the AP, it is necessary to perform signal detection processing on the data of all APs. ε k represents the equivalent noise received by the kth user,

[0123] S33, will Defined as the transmission gain of the kth user's desired signal, and then using the moment matching method, ρ k The probability density function of is approximately Gamma distribution, as follows;

[0124]

[0125] in,

[0126] In specific implementation, as a preferred embodiment of the present invention, step S4 specifically includes:

[0127] S41, when the user selects M-ary PAM modulation, all users start from the symbol {-M PAM +1,-M PAM +3,…,M PAM -1} select the sending signal, where M PAM Indicates the modulation order of M-ary PAM modulation;

[0128] In order to obtain the symbol error rate expression of M-ary PAM modulation, we can analyze and obtain and Approximately obeys complex Gaussian distribution in,

[0129] From the code element {-M PAM +1,-M PAM +3,…,M PAM -1}, select send signal, get The probability density functions of the real and imaginary parts are:

[0130]

[0131] Based on the formula and ε k ,k=1,2,…,K’s probability density function is expressed as:

[0132]

[0133] in express The jth row of can be expressed as:

[0134]

[0135] In the above formula, z = Cross_add (x, y) is the value of x∈C 1×M and y∈C 1×N All elements in the cross addition operation are performed, and the resulting elements are combined into a new vector z∈C 1×MN ;

[0136] Based on ρ k The probability density function and ε k , k=1,2,…,K probability density function, the symbol error rate expression of M-ary PAM modulation of the kth user is approximated as:

[0137]

[0138] in,

[0139] Γ(x) represents the gamma function, 2F1(α,β;γ;x) represents the Gaussian hypergeometric function;

[0140] S42, when the user selects M-ary quadrature amplitude modulation, all users select the code element {Cross_add(Amplitude QAM ,i×Amplitude QAM )} selects the sending signal, where M QAM represents the modulation order of M-ary QAM modulation, and

[0141] In order to obtain the symbol error rate expression of M-ary QAM modulation, The probability density functions of the real and imaginary parts are:

[0142]

[0143] Based on the formula and The probability density function of the real and imaginary parts is obtained as follows: k ,k=1,2,…,the probability density function of the real and imaginary parts of K is:

[0144]

[0145] in, express The jth row of can be expressed as:

[0146]

[0147] Based on ρ k The probability density function of M-ary QAM modulation and the equivalent noise ε k ,k=1,2,…,K, the probability density function of the real and imaginary parts, the symbol error rate expression of the M-ary QAM modulation of the kth user is approximated as:

[0148]

[0149] Among them, c1=1.09500814703333, c2=0.75651138383854, and:

[0150]

[0151] Among them, D n (x) represents a parabolic cylinder function.

[0152] In specific implementation, as a preferred embodiment of the present invention, step S5 specifically includes:

[0153] S51, when the user transmission power coefficient η is satisfied k ,0≤η k Under the constraint of ≤1, the optimization problem of minimizing the maximum symbol error rate among users is expressed as:

[0154]

[0155] st0≤η k ≤1,k=1,2,…,K

[0156] S52. In this embodiment, the objective function in step S51 is a non-convex function involving a hypergeometric function, which is difficult to solve using existing convex optimization tools. However, there is a strong positive correlation between the symbol error rate and the signal to interference noise ratio. Therefore, the expectation of the signal to interference noise ratio is used as a new objective function, as follows:

[0157]

[0158] in, Respectively represent the transmission signals of M-ary PAM and QAM modulation;

[0159] S53, based on the formula in step S52, convert the formula in step S51 as follows:

[0160]

[0161] st0≤η k ≤1,k=1,2,…,K

[0162] in, Respectively represent the expected transmission signal power of M-ary PAM and QAM modulation

[0163] S54, introduce the slack variable t, and transform the formula in step S53 as follows:

[0164]

[0165] st0≤η k ≤1,k=1,2,…,K

[0166] The above equation is a standard geometric programming problem, which can be effectively solved using convex optimization tools to obtain a set of suboptimal power control coefficients to minimize the maximum symbol error rate of all users.

[0167] Example

[0168] In order to verify the effectiveness of the solution of the present invention, the following simulation experiments were carried out:

[0169] The specific simulation parameters without cellular network are:

[0170] For a non-cellular network with non-ideal information state under Rayleigh fading channel environment, the simulation scenario is set up in a square area of ​​500m×500m, with L=128 APs and K=15 users randomly distributed in it, and each AP is configured with N=8 antennas. In order to simulate a borderless area, 8 identical adjacent areas are set for the area where the simulation scenario is located. In addition, some parameters involved in the simulation are configured as follows: the transmission power of the uplink pilot signal is p p =30dBm; the transmission power of the uplink data signal is p u ; Noise power during transmission of uplink pilot signal and uplink data signal The length of the uplink pilot sequence τ=15; the power control coefficient of the user η=[η1,η2,…,η K ].

[0171] Figure 3 The relationship between the user symbol error rate and the transmission power is depicted. First, for 2PAM, 4PAM and 4QAM modulation, the symbol error rate expression is consistent with the Monte Carlo simulation results, which proves the correctness of the symbol error rate analytical expression. Then, by observing the simulation result graph, it can be seen that the symbol error rate performance of 2PAM is better than that of 4PAM and 4QAM, which shows that the low modulation order sacrifices the rate to enhance the reliability of the system. In addition, when the power is high, the symbol error rate performance of 4QAM is better than that of 4PAM. Finally, when the transmission power p u As it increases, the symbol error rate of different modulation modes will decrease and finally tend to a constant value, which shows that the continuous increase in power has limited performance improvement on the symbol error rate.

[0172] Figure 4 The maximum symbol error rate of users under different power schemes is depicted. First, compared with the full power algorithm, the proposed geometric programming algorithm and genetic algorithm can greatly reduce the symbol error rate of all users. Second, compared with the genetic algorithm, the geometric programming algorithm has better symbol error rate performance with lower computational complexity. In summary, compared with the other two algorithms, the proposed geometric programming algorithm is an excellent solution that combines the symbol error rate performance and computational complexity of various modulation schemes.

[0173] In summary, the above simulation results verify the accuracy of the symbol error rate calculated by the solution of the present invention, and also show that the optimization algorithm proposed in the present invention can effectively reduce the symbol error rate of the worst performing user while maintaining extremely low computational complexity.

[0174] Finally, it should be noted that the above embodiments are only used to illustrate the technical solutions of the present invention, rather than to limit it. Although the present invention has been described in detail with reference to the aforementioned embodiments, those skilled in the art should understand that they can still modify the technical solutions described in the aforementioned embodiments, or replace some or all of the technical features therein with equivalents. However, these modifications or replacements do not cause the essence of the corresponding technical solutions to deviate from the scope of the technical solutions of the embodiments of the present invention.

Claims

1. A method for analyzing and optimizing symbol error rate of non-cellular networks based on PAM and QAM modulation, characterized in that: include: S1. Establish a non-cellular network model based on Rayleigh fading channel; S2. Based on the constructed network model, the minimum mean square error method is used to perform channel estimation; S3, based on the constructed network model, use the maximum ratio combining method to perform signal detection; S4. Based on the constructed network model, calculate the symbol error rate of the user's PAM and QAM modulation; S5. Based on the calculated user symbol error rate, construct an optimization problem to minimize the maximum symbol error rate among all users, and design an optimization strategy for collaboratively controlling the user's transmit power coefficient.

2. According to claim 1, a method for analyzing and optimizing symbol error rate of a non-cellular network based on PAM and QAM modulation is characterized in that: In step S1, the non-cellular network model is established as follows: Among them, g lk represents the channel vector between the lth AP and the kth user, represents the small-scale fading coefficient of the Rayleigh distribution, which is an independent and identically distributed Gaussian vector relative to l and k; β lk Represents the large-scale fading coefficient, which is composed of shadow fading and path loss.

3. According to claim 1, a method for analyzing and optimizing symbol error rate of a non-cellular network based on PAM and QAM modulation is characterized in that: Step S2 specifically includes: S21. Calculate the uplink pilot signal received by the lth AP. The calculation formula is as follows: In order for each AP to obtain channel state information from different users, each user needs to send uplink pilot sequences to all APs, and these pilot sequences satisfy when k = j, When k≠j, The conditions include: represents the uplink pilot sequence, τ represents the length, and p p represents the pilot transmission power of the user; N p,l ∈C N×τ represents the additive Gaussian white noise at the lth AP, and each element in the noise matrix obeys an independent and identical distribution in represents the Gaussian noise power during the transmission of the pilot sequence; S22, based on the uplink pilot signal received by the lth AP, perform channel estimation on the pilot signals from different users, and convert the uplink pilot signal y p,l The inner product calculation with the pilot sequence is as follows: S23, calculate the channel g between the lth AP and the kth user lk The minimum mean square error estimate is calculated as follows: In the above formula, the channel estimation It includes N independent and identically distributed Gaussian variables, and all variables obey the following Gaussian distribution: in, S24. According to the property of minimum mean square error estimation, the channel estimation error between the lth AP and the kth user is Channel Estimation are independent of each other, and All elements in are independent and identically distributed where ξ lk =β lk -γ lk .

4. According to claim 1, a method for analyzing and optimizing symbol error rate of a non-cellular network based on PAM and QAM modulation, characterized in that: Step S3 specifically includes: S31. In the uplink data transmission phase, all users send data signals to different APs, and the data signal received by the lth AP is calculated as follows: Among them, s k represents the signal sent by the kth user, p u and η k denote the transmission power and power control coefficient of user k respectively, and satisfy 0≤η k Power constraint condition of ≤1; n l represents the additive Gaussian white noise vector received at the lth AP, and each element is independent and identically distributed in represents the Gaussian noise power during uplink data transmission; S32, when the maximum ratio combining method is used to detect the received signal, the data signal y received by the lth AP is l With detection vector Multiply them, and send the multiplied signals to the CPU for processing. At this time, the signal collected by the CPU for the kth user is: in, ε k represents the equivalent noise received by the kth user, S33, will Defined as the transmission gain of the kth user's desired signal, and then using the moment matching method, ρ k The probability density function of is approximately Gamma distribution, as follows; in, 5. The method for analyzing and optimizing symbol error rate of a non-cellular network based on PAM and QAM modulation according to claim 1, characterized in that: Step S4 specifically includes: S41, when the user selects M-ary PAM modulation, all users start from the symbol {-M PAM +1,-M PAM +3,…,M PAM -1} select the sending signal, where M PAM Indicates the modulation order of M-ary PAM modulation; In order to obtain the symbol error rate expression of M-ary PAM modulation, we can analyze and obtain and Approximately obeys complex Gaussian distribution in, From the code element {-M PAM +1,-M PAM +3,…,M PAM -1}, select send signal, get The probability density functions of the real and imaginary parts are: Based on the formula and ε k ,k=1,2,…,K’s probability density function is expressed as: in express The jth row of can be expressed as: In the above formula, z = Cross_add (x, y) is the value of x∈C 1×M and y∈C 1×N All elements in the cross addition operation are performed, and the resulting elements are combined into a new vector z∈C 1×MN ; Based on ρ k The probability density function and ε k , k=1,2,…,K probability density function, the symbol error rate expression of M-ary PAM modulation of the kth user is approximated as: in, Γ(x) represents the gamma function, 2F1(α,β;γ;x) represents the Gaussian hypergeometric function; S42, when the user selects M-ary quadrature amplitude modulation, all users select the code element {Cross_add(Amplitude QAM ,i×Amplitude QAM )} selects the sending signal, where M QAM represents the modulation order of M-ary QAM modulation, and In order to obtain the symbol error rate expression of M-ary QAM modulation, The probability density functions of the real and imaginary parts are: Based on the formula and The probability density function of the real and imaginary parts is obtained as follows: k ,k=1,2,…,the probability density function of the real and imaginary parts of K is: in, express The jth row of can be expressed as: Based on ρ k The probability density function of M-ary QAM modulation and the equivalent noise ε k ,k=1,2,…,K, the probability density function of the real and imaginary parts, the symbol error rate expression of the M-ary QAM modulation of the kth user is approximated as: Among them, c1=1.09500814703333, c2=0.75651138383854, and: Among them, D n (x) represents a parabolic cylinder function.

6. The method for analyzing and optimizing symbol error rate of a non-cellular network based on PAM and QAM modulation according to claim 1, characterized in that: Step S5 specifically includes: S51, when the user transmission power coefficient η is satisfied k ,0≤η k Under the constraint of ≤1, the optimization problem of minimizing the maximum symbol error rate among users is expressed as: s.t.0≤η k ≤1,k=1,2,…,K S52, taking the expectation of the signal to interference noise ratio as a new objective function, as follows: in, Respectively represent the transmission signals of M-ary PAM and QAM modulation; S53, based on the formula in step S52, convert the formula in step S51 as follows: s.t.0≤η k ≤1,k=1,2,…,K in, and Respectively represent the expected transmission signal power of M-ary PAM and QAM modulation S54, introduce the slack variable t, and transform the formula in step S53 as follows: s.t.0≤η k ≤1,k=1,2,…,K The above equation is a standard geometric programming problem, which can be effectively solved using convex optimization tools to obtain a set of suboptimal power control coefficients to minimize the maximum symbol error rate of all users.

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