Large-scale SIMO system optimization method

Abstract

The invention discloses a large-scale SIMO system optimization method, and the method comprises the steps: S1, carrying out the zero-forcing ZF preprocessing of a received signal at a receiving end, so as to eliminate the channel correlation; s2, detecting the received signal subjected to zero forcing ZF preprocessing by adopting a fast asymptotic ML detector; s3, deducing a paired error probability PEP between adjacent constellation points corresponding to the fast asymptotic ML detector; and S4, performing optimization design on the PAM constellation based on the minimum PEP so that the constellation structure can be dynamically adjusted along with system parameters. Aiming at the problem of difficulty in performance analysis and optimization caused by complex energy distribution of received signals under a channel correlation condition, the method is obviously superior to a traditional fixed equidistant constellation scheme, and a simulation result shows that the scheme provided by the invention can enable an SIMO system to be more reliable and better in performance under a correlation Rayleigh fading channel.

Description

Technical Field

[0001] The present invention relates to the technical field of massive machine communication, and particularly to an optimization method for a massive SIMO system. Background Art

[0002] In the 6G framework proposed by the International Telecommunication Union in 2023, the enhancement of massive machine-type communication (mMTC) and ultra-reliable low-latency communication (URLLC) is emphasized, which are respectively extended to massive communication and extremely reliable low-latency communication. Machine-type communication can be divided into mMTC and critical machine-type communication. The latter is the integration of ultra-reliable low-latency communication and massive communication, and the demand in fields such as industrial Internet of Things and intelligent transportation is increasing day by day. 6G needs to exceed 5G in terms of reliability, latency, and connection density to support a large number of MTC terminals.

[0003] Massive antenna technology is considered the key to achieving URLLC. Its high spatial diversity gain has significant advantages, but existing technologies mostly adopt coherent detection that relies on accurate channel state information (CSI). This has problems in the actual application of URLLC. The simultaneous access of a large number of terminals leads to a sharp increase in the computational complexity of CSI estimation. Traditional methods are difficult to meet the real-time requirements, and short data packets further exacerbate the channel estimation overhead. Terminal mobility and dynamic environmental changes also make accurate CSI estimation extremely difficult, and traditional methods are difficult to track the rapidly changing channel in a timely manner. Low signal-to-noise ratio or pilot contamination will affect the accuracy of CSI. Therefore, in order to improve the spectral efficiency while avoiding high-complexity channel estimation, researchers have proposed non-coherent communication schemes in massive antenna systems. The non-coherent scheme combined with massive antennas can transmit information without relying on instantaneous CSI, and at the same time has the same asymptotic performance as the coherent scheme. Compared with the coherent scheme, the performance advantage and easy implementation of the non-coherent scheme in harsh scenarios make it one of the candidate schemes for future communication systems.

[0004] In the actual propagation environment, due to limited antenna spacing and / or limited scattering environment, channel correlation is almost inevitable, which will significantly affect the energy detection performance, especially in a massive SIMO system, the influence of channel correlation is more prominent. In a non-coherent massive SIMO system with channel correlation, how to achieve fast and reliable energy signal detection, how to conduct accurate performance analysis, and how to design an optimal modulation constellation are still problems that need to be deeply studied. Summary of the Invention

[0005] The object of the present invention is to address the above problems and provide an optimization method for large-scale SIMO systems.

[0006] To achieve the above object, the technical solution of the present invention is as follows:

[0007] An optimization method for large-scale SIMO systems, the steps of which are as follows:

[0008] S1. At the receiving end, perform zero-forcing (ZF) preprocessing on the received signal to eliminate channel correlation;

[0009] S2. Detect the received signal preprocessed by ZF using a fast asymptotic maximum likelihood (ML) detector;

[0010] S3. Deduce the pairwise error probability (PEP) between adjacent constellation points corresponding to this fast asymptotic ML detector;

[0011] S4. Optimally design the PAM constellation based on minimizing the PEP so that the constellation structure can be dynamically adjusted according to system parameters.

[0012] As an improvement to the above technical solution, consider a large-scale SIMO system where the base station of the system has N receiving antennas and a single-antenna terminal transmits signals to the base station in the uplink. To avoid channel estimation problems, an energy-based non-coherent detector is used, which does not rely on channel state information (CSI). When the number of antennas is large enough, its performance can approach coherent detection. In a correlated channel, the transmitted signal s comes from an optimal PAM constellation containing L different power levels, denoted as {E1, E2,..., E L}. To maximize the distance between constellations, without loss of generality, let E1 = 0, and these power levels are arranged in ascending order, i.e., 0 = E1 < E2 < … < E L}. The transmitted signal s is equally likely to be selected from this PAM constellation, i.e., where i = 1, 2,..., L. In addition, assume that the PAM constellation satisfies the average power constraint: where P T is the average power. The signal passes through a correlated Rayleigh fast-fading channel, and the channel coefficients are denoted as h = [h1, h2,..., h N T , where h i represents the channel coefficient at the i-th receiving antenna. Assume that the channel coefficients follow a complex Gaussian distribution with a mean of 0 and a correlation matrix of R, denoted as The channel correlation matrix R is known to both the transmitter and the receiver, and the exponential correlation model is adopted:

[0013]

[0014] where [R] m，n ​Denote the (m, n)-th element of R, ρ is the complex correlation coefficient between adjacent antennas, and 0 ≤ |ρ| < 1. The received signal vector at the receiver is expressed as y = [y1, y2,..., y N T , where y i represents the signal received at the i-th receiving antenna. The received signal model can be expressed as:

[0015] y = hs + n

[0016] where, n = [n1, n2,..., n N T is an additive white Gaussian noise (AWGN) vector, whose elements are independent and identically distributed complex Gaussian random variables with zero mean and variance σ 2 , that is

[0017] In addition, we define the signal-to-noise ratio (SNR) of the system as SNR = P T / σ 2 . Also, the instantaneous channel coefficient h is not available at the transmitter or the receiver and may change to other values in the next time slot. This assumption is to eliminate the channel estimation / feedback overhead to achieve the ultra-low latency required for IIoT communication, especially for fast fading channels. However, the channel statistical information such as the mean and variance of the channel and the noise variance are assumed to be known for optimal constellation design.

[0018] As an improvement to the above technical solution, in the step S1, the zero-forcing ZF preprocessing matrix is where represents the transpose of; simplification can obtain The received signal after preprocessing is expressed as The noise after preprocessing is expressed as Since R is a real symmetric matrix, the mean of the noise after preprocessing is zero, and the covariance matrix is For simplicity of expression, define and

[0019] The received signal after preprocessing is expressed as:

[0020] where, and σ 2 is the noise variance.

[0021] As an improvement to the above technical solution, in the step S2, the received signal after preprocessing follows a complex Gaussian distribution, that is where E​​i is the power of the i-th constellation point in the PAM constellation. The probability density function (PDF) is where is the conditional i probability density function of given E Based on the Bayesian decision theory, the optimal decision rule is to select the signal energy that maximizes the posterior probability: Using Bayes' formula, we have: Since the prior probability P(E ) of each signal energy is the same, i.e., The objective function can then be simplified to: Substituting the expression of

[0022]

[0023] The asymptotic ML detector is: where is the corresponding equivalent channel gain, the equivalent noise variance on all channels is σ 2 ; N represents the number of receiving antennas; E i is the power of the i-th constellation point; is the signal after detection, estimation, and decision; is the received signal of the modulus.

[0024] The fast asymptotic ML detector is:

[0025] where the analytical expression of the threshold is:

[0026] As an improvement to the above technical solution, in the step S3, when the transmission energy is E i , the probability of misdetection as E j is: The total probability of error is the sum of the probabilities of error between all adjacent signals

[0027] Note that all constellations in the energy-based constellation are on a straight line, so the probability of error mainly depends on the probability of decision error between adjacent constellations; for simplicity of analysis, the average PEP of the fast asymptotic ML detector between adjacent constellations is analyzed, where L is the modulation order of the PAM constellation and N is the number of receiving antennas;

[0028] Using the cumulative distribution function (CDF) of the chi-square distribution: where Γ(a, x) is the incomplete gamma function;

[0029]

[0029] From E i The probability of error detection at E i+1 is: From E i The probability of error detection at E i-1 is: where T i is the analytical expression of the threshold;;

[0030] The average pairwise error probability is obtained as

[0031] As an improvement to the above technical solution, in the step S4, while minimizing the PEP and satisfying the average power constraint, minimizing the average PEP is transformed into a Lagrangian optimization problem:

[0032]

[0033] where, E i is the power magnitude of the i-th constellation point, and P T is the average power;

[0034] Construct the Lagrangian function

[0035]

[0036] where λ is the Lagrange multiplier;

[0037] For Take the partial derivative and set it equal to zero, take the partial derivative of the Lagrange multiplier and set it equal to zero, then

[0038]

[0039] Adopt the gradient descent method or Newton's method to solve the non-linear equations to iteratively solve the optimal constellation {E i} and λ.

[0040] Compared with the prior art, the present invention includes but is not limited to the following advantages and positive effects:

[0041] The present invention provides a large-scale SIMO system optimization method for non-coherent large-scale SIMO system optimization, which can achieve the same beneficial effects as the non-coherent single-user constellation optimization method in the SIMO system. This method minimizes the average PEP and uses the Lagrangian method to further iteratively solve the optimal PAM constellation. Compared with the traditional equally spaced constellation scheme, the proposed constellation scheme has a lower PEP, and as the number of receiver antennas or the signal-to-noise ratio increases, its performance gain is more significant.

[0042] The traditional equal-spacing constellation scheme exhibits an error performance floor effect in the medium to high signal-to-noise ratio (SNR) region, while the pairwise error probability (PEP) of the proposed scheme can continuously decrease as the SNR increases. This indicates that, in the absence of instantaneous channel information, the proposed constellation scheme still achieves a certain diversity gain. Through verification, when the channel correlation coefficient is zero, i.e., the channels are uncorrelated, the scheme of this application remains effective. The proposed optimized design can adaptively adjust the constellation points according to the strength of channel correlation, thus better adapting to the changes in the channel. Brief Description of the Drawings

[0043] To more clearly illustrate the technical solutions in the embodiments of the present invention or the prior art, the following will briefly introduce the drawings required for the description of the embodiments or the prior art. Obviously, the drawings in the following description are only some embodiments of the present invention. For those of ordinary skill in the art, without creative efforts, other drawings can also be obtained based on these drawings.

[0044] Figure 1 It is a schematic diagram of the SIMO system model of the present invention;

[0045] Figure 2 It is a flowchart of the communication method for a large-scale SIMO system in the embodiment of the present invention;

[0046] Figure 3a It is a schematic diagram comparing the performance of the optimized constellation scheme for minimizing PEP and the traditional equal-spacing constellation scheme with respect to SNR when the number of antennas N = 128 and ρ = 0.5 in the embodiment of the present invention;

[0047] Figure 3b It is a schematic diagram comparing the performance of the optimized constellation scheme for minimizing PEP and the traditional equal-spacing constellation scheme with respect to the number of antennas N when the SNR = 10 and ρ = 0.5 in the embodiment of the present invention;

[0048] Figure 4 It is a performance comparison of the optimized constellation scheme for minimizing PEP and the traditional equal-spacing constellation scheme with respect to the channel correlation coefficient ρ in the embodiment of the present invention;

[0049] Figure 5 It is a constellation diagram of the optimized constellation scheme for minimizing PEP and the traditional equal-spacing constellation scheme with respect to the channel correlation coefficient ρ when the modulation order L = 8 in the embodiment of the present invention. Detailed Description of the Preferred Embodiments

[0050] Next, the technical solutions in the embodiments of the present invention will be clearly and completely described in conjunction with the accompanying drawings in the embodiments of the present invention. Obviously, the described embodiments are only a part of the embodiments of the present invention, rather than all the embodiments. Based on the embodiments of the present invention, all other embodiments obtained by those of ordinary skill in the art without making creative efforts, any modifications, equivalent replacements, improvements, etc., shall be included in the protection scope of the present invention.

[0051] Embodiment 1: Non-coherent large-scale SIMO system communication method:

[0052] Figure 1 It is a schematic diagram of the SIMO system model of the present invention, where SIMO is the abbreviation of single input multiple output, that is, the SIMO system is a single input multiple output system. As Figure 1 shown, this embodiment gives a technical solution of a non-coherent large-scale SIMO system communication method. Consider a base station of a large-scale SIMO system with N receiving antennas, and a single-antenna terminal transmits signals to the base station in the uplink. To avoid the problem of channel estimation, an energy-based non-coherent detector is adopted. This detector does not need to rely on channel state information (CSI). When the number of antennas is large enough, its performance can be close to coherent detection. In a correlated channel, the transmitted signal s comes from an optimal PAM constellation containing L different power levels, denoted as {E1, E2,..., E L}.

[0053] To maximize the distance between constellations, without loss of generality, let E1 = 0, and these power levels are arranged in ascending order, that is, 0 = E1 < E2 <... < E L . The transmitted signal s is equally likely to be selected from this PAM constellation, that is where i = 1, 2,..., L. In addition, it is assumed that the PAM constellation satisfies the average power constraint: where P T is the average power. The signal passes through a correlated Rayleigh fast-fading channel, and the channel coefficients are represented as h = [h1, h2,..., h N T , where h i represents the channel coefficient at the i-th receiving antenna. It is assumed that the channel coefficients follow a complex Gaussian distribution with a mean of 0 and a correlation matrix of R, denoted as The channel correlation matrix R is known to both the transmitter and the receiver, and an exponential correlation model is adopted:

[0054]

[0055] where [R] m，n ​Denote the (m, n)-th element of R, ρ is the complex correlation coefficient between adjacent antennas, and 0 ≤ |ρ| < 1. The received signal vector at the receiver is denoted as y = [y1, y2,..., y N T , where y i denotes the signal received at the i-th receive antenna. The received signal model can be expressed as:

[0056] y = hs + n

[0057] where, n = [n1, n2,..., n N T is the additive white Gaussian noise (AWGN) vector, whose elements are independent and identically distributed complex Gaussian random variables with zero mean and variance σ 2 , that is In addition, we define the signal-to-noise ratio (SNR) of the system as SNR = P T / σ 2 . Also, the instantaneous channel coefficient h is not available at the transmitter or receiver and may change to other values in the next time slot. This assumption is to eliminate the channel estimation / feedback overhead to achieve the ultra-low latency required for IIoT communication, especially for fast-fading channels. However, the channel statistical information such as the mean and variance of the channel and the noise variance is assumed to be known for optimal constellation design.

[0058] Perform zero-forcing ZF preprocessing on the received signal y to eliminate the correlation, and obtain the preprocessed received signal Perform signal detection on the preprocessed signal through a maximum likelihood (ML) detector to obtain the detected signal

[0059] Figure 2 is the flowchart of the communication method for a large-scale SIMO system in an embodiment of the present invention. As Figure 2 shown, the specific steps are: S1. At the receiver, perform zero-forcing ZF preprocessing on the received signal y to eliminate the channel correlation, and obtain the preprocessed received signal S2. Based on the asymptotic analysis of the maximum likelihood (ML) detector, use a fast asymptotic ML detector to detect the zero-forcing ZF preprocessed received signal;

[0060] ​​S3. Deduce the pairwise error probability (PEP) between adjacent constellation points corresponding to the fast asymptotic ML detector; S4. Optimize the PAM constellation based on minimizing the PEP so that the constellation structure can be dynamically adjusted according to system parameters. This method optimizes the signal transmitted to the receiving end through an optimized PAM constellation scheme that considers minimizing the PEP, so that the receiving end of the SIMO system can adopt an energy-based fast ML detector, making the communication system more reliable and having better performance. This method also sets up signal preprocessing at the receiving end and a fast non-coherent maximum likelihood detector, and optimizes from both the user transmitting end and the receiving end respectively.

[0061] Specifically, the large-scale SIMO system optimization method includes the following steps:

[0062] Consider a large-scale SIMO system where the base station of the system has N receiving antennas and a single-antenna terminal transmits signals to the base station in the uplink. To avoid the problem of channel estimation, an energy-based non-coherent detector is adopted. This detector does not need to rely on channel state information (CSI), and when the number of antennas is large enough, its performance can approach coherent detection. In a correlated channel, the transmitted signal s comes from an optimal PAM constellation containing L different power levels, denoted as {E1, E2,..., E L}. To maximize the distance between constellations, without loss of generality, let E1 = 0, and these power levels are arranged in ascending order, i.e., 0 = E1 < E2 < … < E L . The transmitted signal s is equally likely to be selected from this PAM constellation, i.e., where i = 1, 2,..., L. In addition, assume that the PAM constellation satisfies the average power constraint: where P T is the average power. The signal passes through a correlated Rayleigh fast-fading channel, and the channel coefficients are represented as h = [h1, h2,..., h N T , where h i represents the channel coefficient at the i-th receiving antenna. Assume that the channel coefficients follow a complex Gaussian distribution with a mean of 0 and a correlation matrix of R, denoted as The channel correlation matrix R is known to both the transmitter and the receiver, and the exponential correlation model is adopted:

[0063]

[0064] where [R] m，n represents the (m, n)-th element of R, ρ is the complex correlation coefficient between adjacent antennas, and 0 ≤ |ρ| < 1. The received signal vector at the receiving end is represented as y = [y1, y2,..., y N T , where y i ​​Denote the signal received at the \(i\)-th receiving antenna. The received signal model can be expressed as:

[0065] y = hs + n

[0066] where \(n=[n_1,n_2,\cdots,n N T is an additive white Gaussian noise (AWGN) vector, whose elements are independent and identically distributed complex Gaussian random variables with zero mean and variance \(\sigma 2 . That is In addition, we define the signal-to-noise ratio (SNR) of the system as SNR = P T / \(\sigma 2 . Also, the instantaneous channel coefficient \(h\) is not available at the transmitter or receiver and may change to other values in the next time slot. This assumption is to eliminate the channel estimation / feedback overhead to achieve the ultra-low latency required for IIoT communication, especially for fast fading channels. However, the channel statistics such as the mean and variance of the channel and the noise variance are assumed to be known for optimal constellation design.

[0067] S1: At the receiving end, perform zero-forcing (ZF) preprocessing on the received signal to eliminate channel correlation. The ZF preprocessing matrix is where denotes the transpose of The received signal after preprocessing is expressed as The noise after preprocessing is expressed as Since \(R\) is a real symmetric matrix, the mean of the preprocessed noise is zero, and the covariance matrix is For simplicity of expression, define and

[0068] The received signal after preprocessing is expressed as:

[0069] where and

[0070] The received signal after preprocessing follows a complex Gaussian distribution: where \(E i is the power of the \(i\)-th constellation point.

[0071] S2: For the received signal subjected to zero-forcing (ZF) preprocessing, use a fast ML detector for detection.

[0072] The probability density function (PDF) is where is given \(E i under the condition that​ The probability density function. Based on Bayesian decision theory, the optimal decision rule is to select the signal energy that maximizes the posterior probability: Using Bayes' formula, we have: Since the prior probability P(E i ) of each signal energy is the same, that is Then the objective function can be simplified to: Substitute into the expression, and the equivalent objective function of the original ML detector is obtained as:

[0073]

[0074] The asymptotic ML detector is: where The corresponding equivalent channel gain is The equivalent noise variance on all channels is σ 2 ; N represents the number of receiving antennas; E i is the power of the i-th constellation point; is the signal after detection and estimation decision; is the received signal is the modulus value.

[0075] The asymptotic ML detector is:

[0076] The fast asymptotic ML detector is:

[0077] where the analytical expression of the threshold is:

[0078] It can be clearly seen that this fast detector avoids the high-dimensional (large-scale channel) matrix inversion and multiplication operations in the original ML detector, and the detection complexity is greatly reduced. It effectively reduces the detection complexity and processing delay, and can achieve fast detection of the received signal.

[0079] S3: Derive the pairwise error probability (PEP). When the transmitted energy is E i , the probability of misdetecting it as E j is:

[0080] The total error probability is the sum of the error probabilities between all adjacent signals Note that all constellations in the energy-based constellation are on a straight line, so the error probability mainly depends on the decision error probability between adjacent constellations. To simplify the analysis, analyze the average PEP of the fast asymptotic maximum likelihood detector between adjacent constellations,

[0081] Among them, L is the modulation order of PAM constellation, and N is the number of receiving antennas.

[0082] Using the cumulative distribution function (CDF) of the chi-square distribution: where Γ(a, x) is the incomplete gamma function. From E i The probability of error detection to E i+1 is: From E i The probability of error detection to Ei-1 is: where T i is the analytical expression of the threshold. At this time, the average pairwise error probability can be obtained as

[0083]

[0084] S4: Modulate using the optimal constellation that minimizes PEP. Optimal constellation calculation method:

[0085] Under the condition of satisfying the average power constraint, minimize the average PEP. This problem can be formulated as a Lagrangian optimization problem:

[0086]

[0087]

[0088] where, E i is the power magnitude of the i-th constellation point, and P T is the average power.

[0089] Furthermore, by constructing the Lagrangian function

[0090]

[0091] where λ is the Lagrange multiplier.

[0092] For Take the partial derivative and set it equal to zero; take the partial derivative of the Lagrange multiplier and set it equal to zero.

[0093]

[0094] Use numerical methods, such as the gradient descent method or the Newton method, to solve the nonlinear equations to iteratively solve the optimal constellation {E i} and λ.

[0095] Figure 3a and Figure 3bShows the relationship between the pairwise error probability (PEP), signal-to-noise ratio (SNR), and the number of receive antennas. Under the same system configuration, the PEP performance of the proposed scheme is compared with that of the equally spaced constellation scheme. To ensure the fairness of the comparison, the derived non-coherent ML detector and the fast asymptotic non-coherent ML detector are used for symbol detection. The experimental results show that, whether using the equally spaced constellation or the constellation proposed in this paper, the PEP performance of the fast asymptotic non-coherent ML detector is basically the same as that of the exact non-coherent ML detector. At the same time, the theoretically analyzed PEP curve is highly consistent with the results of Monte Carlo simulation, verifying the accuracy and effectiveness of the theoretical analysis. Compared with the traditional benchmark scheme, the proposed constellation scheme has a lower PEP, and its performance gain is more significant as the number of receiver antennas or SNR increases. In addition, it is observed that the traditional scheme exhibits an error performance floor effect in the medium and high SNR regions, while the PEP of the proposed scheme can continue to decrease as the SNR increases, indicating that the proposed constellation scheme still obtains a certain diversity gain in the absence of instantaneous channel information.

[0096] To further compare the PEP performance of the two schemes in a strongly correlated channel, Figure 4 Shows the relationship between the PEP curve and the channel correlation coefficient. The results show that as the channel correlation coefficient increases, the PEP performance of both schemes decreases, but the proposed scheme is always better than the traditional scheme. In addition, when the channel correlation coefficient is zero, that is, when the channel has no correlation, the proposed scheme is still effective.

[0097] To more intuitively show the differences between the proposed constellation scheme and the traditional benchmark constellation, Figure 5 Shows the corresponding constellation structures under different correlation coefficients. It is clearly visible that the proposed optimized design can adaptively adjust the constellation points according to the strength of channel correlation, so as to better adapt to the changes of the channel.

[0098] Embodiment: Optimization method for PAM constellation in non-coherent large-scale SIMO system

[0099] This embodiment provides a technical solution for an optimization method for PAM constellation in a non-coherent large-scale SIMO system. This method determines the single-user PAM constellation in the non-coherent large-scale SIMO system and optimizes the PAM constellation by minimizing the PEP.

[0100] This method optimizes the PAM constellation by minimizing the PEP. First, calculate the PEP of the non-coherent large-scale SIMO system. Optimize the PAM constellation by minimizing the PEP and construct the Lagrangian function. Take the partial derivative and set it equal to zero; take the partial derivative of the Lagrange multiplier and set it equal to zero. Use numerical methods, such as the gradient descent method or Newton's method, to solve the non-linear equations to iteratively solve the optimal constellation {Ei} and λ.

[0101] This method minimizes the PEP of the SIMO system, and obtains the optimal PAM constellation design scheme corresponding to the fast ML detector under the minimized PEP criterion. The optimized constellation structure varies with the system parameters and is significantly different from the traditional fixed-spacing constellation. The proposed optimized design can adaptively adjust the constellation points according to the strength of channel correlation, so as to better adapt to the changes of the channel.

[0102] Since the specific steps of the non-coherent large-scale SIMO system PAM constellation optimization method in this embodiment have been described in detail in the embodiment of the non-coherent large-scale SIMO system PAM constellation optimization method, they will not be elaborated here.

Claims

1. An optimization method for a large-scale SIMO system, characterized in that: It includes the following steps: S1. At the receiving end, perform zero-forcing (ZF) preprocessing on the received signal to eliminate channel correlation; S2. Detect the received signal preprocessed by ZF using a fast asymptotic maximum likelihood (ML) detector; S3. Deduce the pairwise error probability (PEP) between adjacent constellation points corresponding to the fast asymptotic ML detector; S4. Optimally design the PAM constellation based on minimizing the PEP so that the constellation structure can be dynamically adjusted according to system parameters.

2. The optimization method for a large-scale SIMO system according to claim 1, characterized in that: In the step S1 described above, the channel is a relevant Rayleigh fast fading channel; based on a large-scale SIMO system with N receiving antennas, under the relevant Rayleigh fast fading channel, the transmitted signal s comes from an optimal PAM constellation containing L different power levels, denoted as {E1, E2,..., E L}; To maximize the distance between PAM constellations, without loss of generality, let E1 = 0, and these power levels are arranged in ascending order, i.e., 0 = E1 < E2 < … < E L ; The transmitted signal s is selected equally likely from this PAM constellation, i.e., where i = 1, 2, ..., L; Assume that the PAM constellation satisfies the average power constraint where P T is the average power; then the channel coefficients are expressed as h = [h1, h2,..., h N T , where h i represents the channel coefficient at the i-th receiving antenna;​ Assume that the channel coefficients follow a complex Gaussian distribution with a mean of 0 and a correlation matrix of R, denoted as The channel correlation matrix R is known to both the transmitter and the receiver, and the exponential correlation model is where [R] m，n denotes the (m, n)-th element of R, and ρ is the complex correlation coefficient between adjacent antennas; The received signal vector at the receiving end is represented as y = [y1, y2,..., y N T , where y i represents the signal received at the i-th receiving antenna;​ The received signal model can be expressed as: y = hs + n, where, n = [n1, n2,..., n N T is an additive white Gaussian noise vector, whose elements are independent and identically distributed complex Gaussian random variables with zero mean and variance of σ 2 , that is ​ Define the signal-to-noise ratio (SNR) of the system as SNR = P T / σ 2 .

3. The large-scale SIMO system optimization method according to claim 2, characterized in that: The complex correlation coefficient satisfies \(0\leq|\rho|\lt1\).

4. The optimization method for the large-scale SIMO system according to claim 2, wherein: In the step S1, the zero-forcing ZF preprocessing matrix is where denotes the transpose of; Simplified to get The received signal after preprocessing is expressed as The noise after preprocessing is expressed as Since R is a real symmetric matrix and the mean of the preprocessed noise is zero, the covariance matrix is as follows: For the sake of simplicity of expression, define and The preprocessed received signal is expressed as: Among them, and 5. The large-scale SIMO system optimization method according to claim 4, characterized in that: In the step S2, the preprocessed received signal obeys the complex Gaussian distribution, that is where E i is the power of the i-th constellation point in the PAM constellation; The probability density function PDF is where is the conditional i probability density function given E ; Based on Bayesian decision theory, the optimal decision rule is to select the signal energy that maximizes the posterior probability: Using Bayes' formula, we have: Since the prior probability P(E i ) of each signal energy is the same, that is the objective function is simplified to: Substituting the expression of yields the equivalent objective function of the original ML detector as: The asymptotic ML detector is as follows: where The corresponding equivalent channel gain is The equivalent noise variance on all channels is σ 2 ; N represents the number of receiving antennas; E i is the power of the i-th constellation point; is the signal after detection and estimation decision; is the received signal is the modulus value of; The fast asymptotic ML detector is as follows: The analytical expression of the threshold is as follows: E i is the power of the constellation point, is the signal after detection, estimation, and decision; E i represents the transmitted constellation point; is the received signal and is the modulus value of 6. The large-scale SIMO system optimization method according to claim 5, characterized in that: In the step S3, when the transmission energy is E i , the error detection is E j with a probability of: The total error probability is the sum of the error probabilities between all adjacent signals Note that all constellations in the energy-based constellation are on a straight line, so the error probability mainly depends on the decision error probability between adjacent constellations; to simplify the analysis, the average PEP of the fast asymptotic ML detector between adjacent constellations is analyzed. where L is the modulation order of the PAM constellation and N is the number of receiving antennas; Using the cumulative distribution function (CDF) of the chi-square distribution: where Γ(a, x) is the incomplete gamma function; From E i The probability of error detected at E i+1 is: From E i The probability of error detected at E i-1 is: where T i is the analytical expression of the threshold, and the average pairwise error probability is 7. The optimization method for a large-scale SIMO system according to claim 6, characterized in that: In step S4, when minimizing the PEP and satisfying the average power constraint, minimizing the average PEP is transformed into a Lagrangian optimization problem: Among them, E i is the power of the constellation point, and P T is the average power; Construct the Lagrangian function where \(\lambda\) is the Lagrange multiplier; For Take the partial derivative and set it equal to zero, take the partial derivative with respect to the Lagrange multiplier and set it equal to zero, then Use the gradient descent method or the Newton method to solve the non-linear equations and iteratively solve for the optimal constellation {E i} and λ.

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