Incoherent space-time modulation method based on parameterized Alamouti structure

Abstract

The invention provides an incoherent space-time modulation method based on a parameterized Alamouti structure, which comprises the following steps: firstly, aiming at any given transmission rate, constructing an incoherent space-time modulation constellation by fusing an Alamouti unitary matrix and a power distribution matrix, and parameterizing the incoherent space-time modulation constellation; secondly, analyzing the KL distance of the conditional probability density of the received signal, and establishing a constellation optimization problem based on a KL criterion; the problem is converted into a structured constellation joint design problem in a multi-dimensional parameter space; then, based on link signal-to-noise ratio dynamic adjustment, determining an optimal bit allocation scheme under different modulation orders by using a maximum and minimum criterion; and finally, decoding each parameter of the incoherent space-time modulation constellation by using a low-complexity incoherent maximum likelihood rapid detection algorithm. According to the invention, the constellation structure and the bit distribution are jointly optimized, so that the requirements of high reliability and low delay in short packet transmission of a large-scale MIMO (Multiple Input Multiple Output) system are met.

Description

Technical Field

[0001] The present invention relates to the field of wireless communication technologies, and in particular, to a short-packet transmission method for a large-scale multiple-input multiple-output system based on parametric non-coherent space-time modulation, which is particularly suitable for high-reliability transmission in a limited time slot in an ultra-reliable low-latency communication scenario. Background Art

[0002] Ultra Reliable Low Latency Communications (URLLC) is crucial for industrial Internet of Things and has been integrated into 5G and future 6G networks. URLLC plays a key role in applications such as autonomous driving, telemedicine, and industrial automation, where strict latency and reliability requirements are of utmost importance. To meet these demands, the 3rd Generation Partnership Project (3GPP) has set strict performance targets for URLLC in 5G, including 10 -5 to 10 -9The block error rate and latency of 1ms to 10ms are expected to be reduced by 2020. With the introduction of new applications, performance requirements continue to rise, and future 6G networks are expected to achieve more stringent goals. Short-Packet Communications (SPCs) are essential to achieve low transmission latency. However, traditional channel coding methods rely on long data packets and face the challenge of limited channel coding gain when transmitting short data packets, making it difficult to meet the reliability requirements of URLLC. How to develop other diversity resources besides time resources within a limited transmission period to improve system reliability has become a core challenge that needs to be solved in URLLC short packet transmission. Massive Multiple-Input Multiple-Output (MIMO) technology can significantly improve wireless link reliability without using additional time resources, making it a key enabler of URLLC. However, most existing research on massive MIMO systems relies on coherent communications, which requires accurate channel state information (CSI) and pilot signals. These pilot signals consume time and bandwidth, reducing efficiency. In contrast, non-coherent space-time modulation enables MIMO systems to improve reliability and spectral efficiency without the need for CSI, eliminating the overhead of pilot signals. This method is considered to be an effective strategy for implementing URLLC in massive MIMO systems. Existing research on incoherent space-time modulation constellations in massive MIMO systems mainly focuses on large-scale single-input multiple-output (SIMO) systems with single antennas, and most of them improve coding gain by increasing time resources. When time resources are limited, how to improve the coding gain of incoherent space-time modulation constellations by developing spatial resources in multi-antenna systems is still an issue that needs to be explored in depth.

[0003] In summary, existing technologies face the following challenges: (1) Pilot overhead bottleneck: Traditional coherent communications rely on CSI, which requires 20% to 30% of time-frequency resources for pilot transmission, seriously restricting the spectrum efficiency in short packet scenarios; (2) High-order modulation defects: Existing incoherent constellation designs focus on single-transmit multiple-receive (SIMO) systems, which have problems such as high structural complexity and significant detection error platform effect in dual-transmit multiple-receive (MIMO) scenarios; (3) Imbalanced resource utilization: Existing solutions improve performance by increasing time slots, but cannot fully utilize spatial diversity gain under strict delay constraints. Summary of the invention

[0004] To meet the requirements of high reliability and low latency in short-packet transmission for large-scale MIMO systems, the present invention proposes a non-coherent space-time modulation method based on a parameterized Alamouti structure, which fully utilizes the spatial diversity gain of the large-scale MIMO system and the time coding gain of the modulation signal to achieve ultra-reliable and low-latency transmission of short data packets.

[0005] To achieve the above object, the technical solution of the present invention is implemented as follows:

[0006] A non-coherent space-time modulation method based on a parameterized Alamouti structure, the steps of which are as follows:

[0007] S1: In a non-coherent MIMO system, for any given transmission rate, construct a non-coherent space-time modulation constellation by fusing the Alamouti unitary matrix and the power allocation matrix, and parameterize the non-coherent space-time modulation constellation;

[0008] S2: According to the parameterized non-coherent space-time modulation constellation, analyze the KL distance of the conditional probability density of the received signal, and establish a constellation optimization problem based on the KL criterion;

[0009] S3: Transform the constellation optimization problem based on the KL criterion into a structured constellation joint design problem in a multi-dimensional parameter space;

[0010] S4: Based on the link signal-to-noise ratio, decompose the structured constellation joint design problem in the multi-dimensional parameter space into two sub-problems, and use the max-min criterion to determine the optimal bit allocation scheme for different modulation orders;

[0011] S5: At the receiving end, use a low-complexity non-coherent maximum likelihood fast detection algorithm to decode each parameter of the non-coherent space-time modulation constellation.

[0012] Preferably, the non-coherent MIMO system includes a transmitting end and a receiving end. The transmitting end deploys two antennas, and the receiving end deploys M antennas, where M >> 2;

[0013] Based on the case of short data packet transmission, the relationship between the transmitted signal and the received signal is:

[0014] Y = SH + N, (1)

[0015] Where, is the wireless channel between the transmitting end and the receiving end, is the transmitted signal, and is the received signal, is the noise matrix, which follows a complex Gaussian distribution with a mean of 0 and a variance of That is, As can be seen from Equation (1), the received signal-to-noise ratio at each antenna at the receiving end is Therefore, the maximum likelihood probability density function of the received signal is established as:

[0016]

[0017] where the superscript H represents conjugate transpose, det represents determinant operation, and tr represents trace operation.

[0018] Preferably, the method of constructing an incoherent space-time modulation constellation by fusing the Alamouti unitary matrix and the power allocation matrix and parameterizing the incoherent space-time modulation constellation is as follows:

[0019] For an incoherent MIMO system, the optimal decoder is an incoherent ML decoder, that is, finding S to maximize f(Y|S); that is, equivalently solving Establish the maximum likelihood detector for this signal transmission:

[0020]

[0021] By satisfying U H U = UU H = I 2 of the Alamouti-structured unitary matrix U and satisfying of P = diag([p 1 , p 2 ), p 1 , p 2 ≥ 0 power allocation matrix P to construct matrix S; first, U can be parameterized as:

[0022]

[0023] where 0 ≤ φ 1 , φ 2 < 2π, In Equation (4), cos(θ) and sin(θ) represent the amplitude information of the transmitted symbols in U, and further U can be rewritten as:

[0024]

[0025] where φ = φ 2 - φ 1 , and 0 ≤ φ < 2π; then S can be written as:

[0026]

[0027] To ensure the unique identification of S with the receiving party, SS H must be uniquely identified; therefore, Let and S can be equivalently transformed into:

[0028]

[0029] where, under the power constraint, a≥0, b≥0;

[0030] Based on the above discussion, S is characterized by four parameters a, b, θ, φ in the continuous space. According to a certain mapping rule, a, b, θ, φ are respectively selected from the sub - constellations Ω a , Ω b , Ω θ , Ω φ respectively. Therefore, the proposed space - time constellation is parameterized as:

[0031]

[0032] where the value ranges of the four parameters are respectively a≥0, b≥0, and 0≤φ<2π. The modulation orders of the four sub - constellations respectively satisfy and k a , k b , k θ , k φ are all non - negative integers.

[0033] Preferably, the calculation method of the KL - distance of the conditional probability density of the received signal is:

[0034]

[0035] where S i and S k are any two distinct constellation points in the constellation .

[0036] Preferably, the constellation optimization problem based on the KL criterion is:

[0037]

[0038] where k s is 's modulation order.

[0039] Preferably, the method of transforming the constellation optimization problem based on the KL criterion into a joint design problem of structured constellations in the multi - dimensional parameter space is:

[0040] S31: Obtain the expressions of S i and S k according to Equation (7): and Substitute it into Equation (10) to simplify the objective function to:

[0041]

[0042] where f(a, b) > 0 when (a i , b i ) ≠ (a k , b k ), and f(θ, φ) > 0 when (θ i , φ i ) ≠ (θ k , φ k ); to maximize the minimum KL distance it should be ensured that (a i - b i )(a k - b k ) > 0; assume a i > b i , a k > b k , and jointly design the constellations of a and b;

[0043] Let where a i ∈ Ω a , b i ∈ Ω b , and satisfy According to Equation (11), the design of

[0044] S32: The optimization objective function in Equation (10) can be transformed into:

[0045]

[0046] where respectively represent the optimal Ω p , Ω θ , Ω φ constellations, respectively represent the optimal modulation orders of the Ω p , Ω θ , Ω φ constellations.

[0047] Preferably, the specific implementation method of step S4 is:

[0048] S41: For any given set of non - negative integers {k p , k θ , k φ}, determine the optimal structure of each sub - constellation in the continuous space, that is:

[0049]

[0050] Let By solving Equation (13), it can be known that for any given non - negative integer k p , k θ , k φ , is a phase - shift keying constellation; is an arithmetic sequence, that is and the constellation points in and are geometric sequences. If for i = 1,..., 2 kp and r a ≥r b > 1 there is and then there is and

[0051] S42: According to the minimum KL - distance maximization criterion, determine, by means of exhaustive search, the optimal modulation - order configuration of each sub - constellation under a fixed modulation order, that is:

[0052]

[0053] Preferably, the method for decoding each parameter of the non - coherent space - time modulation constellation using a low - complexity non - coherent maximum - likelihood fast detection algorithm is:

[0054] Express the received signal vector in matrix form Then Equation (3) can be transformed into:

[0055]

[0056] In Equation (15), the expression of Ξ(θ, φ) is:

[0057]

[0058] where

[0059]

[0060] Design a two - stage detection algorithm: Obtain the maximum - likelihood estimate of the parameter (θ, φ) according to Equation (16); First, decode the parameter φ from Equation (a) in Equation (16): Then use and Equation (b) in Equation (16) to decode the parameter θ, Decode the parameters (a, b) from equation (b) in equation (15) by an exhaustive search method.

[0061] Advantages of the present invention:

[0062] 1) Adopt an incoherent space-time modulation technology based on a parameterized Alamouti structure: For a large-scale MIMO system with two transmit antennas configured at the transmitter, within a transmission period consisting of two consecutive coherent time slots, construct an incoherent space-time modulation constellation by fusing the Alamouti unitary matrix and the power allocation matrix, parameterize the constellation into a four-dimensional parameter space, and realize high-order modulation design by decoupling the joint optimization of the power allocation set, angle set, and phase set. This method does not rely on channel state information (CSI) estimation, eliminates the pilot resource overhead in traditional coherent communication, significantly improves the spectral efficiency of short-packet transmission, and is applicable to the URLLC scenario of large-scale MIMO systems.

[0063] 2) Adopt a constellation optimization method based on maximizing the KL divergence to ensure an exponential decrease in the bit error rate under a large-scale antenna array, effectively overcoming the structural complexity and detection error floor effect of existing incoherent constellations.

[0064] 3) Dynamically adjust the bit allocation scheme based on the link signal-to-noise ratio (SNR), and optimize the modulation order configuration using the max-min criterion: In a low SNR scenario, preferentially allocate bits to power parameters to improve the noise resistance performance using the advantage of energy detection; in a high SNR scenario, increase the bit proportion of angle / phase parameters to improve the spectral efficiency through a multi-dimensional constellation space; pre-compute the optimal bit allocation combinations at different SNRs through offline exhaustive search to achieve real-time dynamic adaptation. This strategy balances the resource utilization in the power and phase / angle dimensions, ensuring the robustness of the system under time-varying channels.

[0065] 4) Adopt a low-complexity incoherent maximum likelihood fast detection algorithm, decompose the multi-dimensional search problem into serial sub-problems, with the complexity reduced by an order of magnitude compared to traditional ML detection, meeting the millisecond-level delay requirements of the URLLC scenario.

[0066] 5) Adopt joint optimization of space-time multi-dimensional diversity gain: Utilize the space diversity of the large-scale antenna array at the receiver in the space dimension to improve the signal anti-fading ability; in the time dimension, realize the superposition of equivalent diversity gains through the time-domain orthogonality of the Alamouti coding matrix.

[0067] 6) Through the collaborative innovation of parametric constellation design, KL optimization criterion, dynamic bit allocation, and efficient detection algorithm, the present invention solves the core problems in URLLC short-packet transmission, such as high pilot overhead, low resource utilization rate, and high detection complexity. At high-order modulation orders, the present invention improves the system error performance and provides a scalable technical path for high-reliability and low-latency communication in 6G networks. BRIEF DESCRIPTION OF THE DRAWINGS

[0068] In order 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 be obtained based on these drawings.

[0069] Figure 1 It is a flowchart of the present invention.

[0070] Figure 2 It is a schematic diagram of the KL distance between the present invention and a single-antenna SIMO system when the modulation order is from 6 to 11.

[0071] Figure 3 It is a graph showing the change in the error performance of the present invention at the receiving end when the modulation order is 6 and the number of receiving antennas changes.

[0072] Figure 4 It is a graph showing the change in the error performance of the present invention at the receiving end when the modulation order is 8 and the number of receiving antennas changes.

[0073] Figure 5 It is a graph showing the change in the error performance of the present invention at the receiving end when the modulation order is 10 and the number of receiving antennas changes.

[0074] Figure 6 It is a graph showing the change in the error performance of the present invention at the receiving end when the modulation order is 11 and the number of receiving antennas changes. DETAILED DESCRIPTION OF THE EMBODIMENTS

[0075] The following will clearly and completely describe the technical solutions in the embodiments of the present invention with reference to the drawings in the embodiments of the present invention. Obviously, the described embodiments are only some embodiments of the present invention, rather than all embodiments. Based on the embodiments of the present invention, all other embodiments obtained by those of ordinary skill in the art without creative efforts belong to the scope of protection of the present invention.

[0076] Such as Figure 1As shown in the figure, an embodiment of the present invention provides a non - coherent space - time modulation method based on a parameterized Alamouti structure, which solves the high - reliability and low - latency requirements in short - packet transmission of a large - scale MIMO system by jointly optimizing the constellation structure and bit allocation. The specific steps are as follows:

[0077] S1: In a non - coherent MIMO system, for any given transmission rate, construct a non - coherent space - time modulation constellation by fusing the Alamouti unitary matrix and the power allocation matrix, and parameterize the non - coherent space - time modulation constellation; use the parameter form of a 2×2 code matrix with Alamouti structure to construct a class of non - unitary signal constellations, where (a, b) are power allocation parameters, θ∈[0, π / 2] is an angle parameter, and φ∈[0, 2π) is a phase parameter. By decoupling the parameter space, transform the high - order constellation design into a joint optimization problem of the power allocation set Ω p , the angle set Ω θ , and the phase set Ω φ , satisfying the total number of bits k s =k p +k θ +k φ and the power constraint

[0078] Specifically, this embodiment studies a large - scale MIMO uplink system in a Rayleigh - fading channel. Deploy two antennas at the transmitter and M antennas at the receiver, where M>>2. The wireless channel between the transmitter and the receiver is where the elements in H are independent of each other and follow a complex Gaussian distribution with a mean of 0 and a variance of 1, that is Assume that the channel H is unknown to both the transmitter and the receiver; to achieve short - data - packet transmission, the present invention assumes that the signal transmission period is two coherent time slots. During these two consecutive time intervals, the transmitted signal obeys the power constraint at the transmitter At the receiver, the received signal in two consecutive time slots can be expressed as:

[0079] Y = SH+N, (1)

[0080] where, is the noise matrix, and the elements in N are independent of each other and follow a complex Gaussian distribution with a mean of 0 and a variance of , that is From equation (1), it can be seen that the received signal - to - noise ratio at each antenna at the receiver is Therefore, establish the maximum - likelihood probability density function of the received signal:

[0081]

[0082] Among them, the superscript H represents conjugate transpose, det represents determinant operation, and tr represents trace operation.

[0083] For a non - coherent MIMO system, the optimal decoder is the non - coherent ML decoder, that is, to find S to maximize f(Y|S); that is, equivalently solve Establish the maximum - likelihood detector under this signal transmission:

[0084]

[0085] By satisfying U H U = UU H = I 2 of the unitary matrix U with Alamouti structure and satisfying of P = diag([p 1 , p 2 ), p 1 , p 2 ≥ 0 power - allocation matrix P to construct the matrix S; first, U can be parameterized as:

[0086]

[0087] where 0 ≤ φ 1 , φ 2 < 2π, In formula (4), cos(θ) and sin(θ) represent the amplitude information of the transmitted symbols in U. Further, U can be rewritten as:

[0088]

[0089] where φ = φ 2 - φ 1 , and 0 ≤ φ < 2π; then S can be written as:

[0090]

[0091] To ensure the unique identification of S with the receiver, SS H must be uniquely identified. Therefore, Let and S can be equivalently transformed into:

[0092]

[0093] where, under the power constraint, a ≥ 0, b ≥ 0.

[0094] Based on the above discussion, S is characterized by four parameters a, b, θ, φ in the continuous space. According to a certain mapping rule, a, b, θ, φ are respectively from the sub - constellation Ωa , Ω b , Ω θ , Ω φ is selected from, so the proposed space-time constellation is parameterized as:

[0095]

[0096] where the value ranges of the four parameters are respectively \(a\geq0\), \(b\geq0\), and \(0\leq\varphi\lt2\pi\), and the modulation orders of the four sub-constellations respectively satisfy and \(k\) a , \(k\) b , \(k\) θ , \(k\) φ are all non-negative integers.

[0097] S2: According to the parameterized non-coherent space-time modulation constellation, analyze the KL distance of the conditional probability density of the received signal, and establish a constellation optimization problem based on the KL criterion; with the maximization of the minimum Kullback-Leibler (KL) divergence as the objective function, by analyzing the KL distance of the conditional probability density of the received signal, establish a quantitative relationship with the pairwise error probability (PEP) to ensure an exponential decrease in the error rate under a large-scale antenna array.

[0098] For the space-time modulation constellation, when the number of receiving antennas tends to infinity, use the KL distance as the constellation design criterion; and based on the maximization of the minimum distance, study the optimization problem of finite-size discrete constellations with the objective of maximizing the minimum KL distance between the conditional distributions of the received signals corresponding to different input signals.

[0099] S21: Calculate the KL distance of the maximum likelihood probability density function pairwise error probability.

[0100] Using the Chernoff-Stein criterion: when \(M\) tends to infinity, the pairwise error probability of this system will decrease exponentially, and the KL distance between constellation points determines the rate of decrease. Using the parameterized constellation defined by Equation (8), calculate the KL distance as:

[0101]

[0102] where \(S\) i and \(S\) k are any two distinct constellation points in the constellation .

[0103] S22: From Equation (9), a constellation optimization problem based on the KL criterion can be established:

[0104]

[0105] Among them, k s is the modulation order of

[0106] S3: Transform the constellation optimization problem based on the KL criterion into a joint design problem of structured constellations in a multi-dimensional parameter space;

[0107] S31: Obtain the expressions of S i and S k according to Equation (7): and Substitute them into Equation (10) to simplify the objective function to:

[0108]

[0109] Among them, when (a i , b i ) ≠ (a k , b k ), f(a, b) > 0, and when (θ i , φ i ) ≠ (θ k , φ k ), f(θ, φ) > 0; To maximize the minimum KL distance it should be ensured that (a i - b i )(a k - b k ) > 0. To be more adaptable to generality, assume a i > b i , a k > b k , and jointly design the constellations of a and b.

[0110] Let where a i ∈Ω a , b i ∈Ω b , and satisfy According to Equation (11), the design of

[0111] S32: The optimization objective function in Equation (10) can be transformed into:

[0112]

[0113] Among them, respectively represent the optimal Ω p , Ω θ , Ω φConstellation respectively represent Ω p , Ω θ , Ω φ the optimal modulation order of the constellation.

[0114] Utilize the particularity of the parameterized constellation structure to determine the optimal constellation structure.

[0115] Power allocation set Ω p : Adopt a geometric sequence structure, let and constitute a geometric progression with a common ratio r a , r b , and determine the optimal (r a , r b ) by solving a constrained optimization problem;

[0116] Angle set Ω θ : Design an arithmetic sequence θ i = θ 0 + i△θ, where θ 0 is determined by the equation .

[0117] Phase set Ω φ : Adopt a standard constellation.

[0118] S4: Decompose the joint design problem of structured constellations in the multi-dimensional parameter space into two sub-problems based on the link signal-to-noise ratio, and use the max-min criterion to determine the optimal bit allocation scheme for different modulation orders;

[0119] S41: Problem (12) involves the joint optimization of mixed discrete integers and continuous parameters. Determine the solution of problem (12) by solving the following two sub-problems; specifically, first, for any given set of non-negative integers {k p , k θ , k φ}, determine the optimal structure of each sub-constellation in the continuous space, that is:

[0120]

[0121] Suppose By solving Equation (13), it can be known that: for any given non-negative integers k p , k θ , k φ , is a phase shift keying constellation; is an arithmetic sequence, that is and the constellation points in satisfy: and is a geometric sequence. If for and r a ≥r b > 1, there is and then there is and

[0122] S42: Determined according to the minimum KL - distance maximization criterion by means of exhaustive search, the optimal modulation - order configuration of each sub - constellation under a fixed S modulation order, that is:

[0123]

[0124] Dynamically adjust (k p , k θ , k φ ) based on the link signal - to - noise ratio:

[0125] (1) At low signal - to - noise ratio, preferentially allocate bits to the power parameter (k p increases), taking advantage of energy detection;

[0126] (2) At high signal - to - noise ratio, increase the angle / phase bits (k θ , k φ increases), improving the utilization rate of the constellation dimension.

[0127] (3) Determine the optimal allocation combination under different k s through offline exhaustive search.

[0128] According to the present invention, the optimal bit allocation and the optimal sub - constellation parameter configuration under a fixed constellation modulation order at different signal - to - noise ratios can be obtained, as shown in Table 1 and Table 2:

[0129] Table 1 (SNR = 5dB)

[0130]

[0131] Table 2 (SNR = 10dB)

[0132]

[0133]

[0134] Figure 2 The KL - distance comparison diagram between the constellation designed by the present invention and the single - antenna SIMO system when the modulation order is from 6 to 11 at is given. Figure 2 (a) is the signal - to - noise ratio of 5dB, Figure 2 (b) is the signal - to - noise ratio of 10dB. FromFigure 2 It can be seen that the minimum KL distance of the constellation designed by the present invention is larger than the minimum KL distance of the constellation designed for the SIMO system proposed in the literature [Li S, Dong Z, Chen H, et al. Constellation Design for Noncoherent Massive SIMO Systems in URLLC Applications [J]. IEEE Transactions on Communications, 2021(7):69.]. As the signal-to-noise ratio increases, the minimum KL distance shows a monotonically increasing trend.

[0135] Figure 3 、 Figure 4 、 Figure 5 and Figure 6 respectively give the constellations designed by the present invention at The figure shows the variation trend of the symbol error rate at the receiving end when the modulation order is 6, 8, 10, and 11 as the number of receiving antennas increases. It can be seen from the figure that the constellation designed in the present invention is superior to the constellation designed based on the KL distance in the SIMO system proposed in [Li S, Dong Z, Chen H, et al. Constellation Design for Noncoherent Massive SIMO Systems in URLLC Applications [J]. IEEE Transactions on Communications, 2021(7):69.], the constellation designed based on the Riemannian distance (RD) in the MIMO system proposed in [Li S, Sun X, Y.-H. X, et al. Noncoherent space-time coding for correlated massive MIMO channel with Riemannian distance [J]. Digital Signal Processing, 2023, 133(000):15. DOI: 10.1016 / j.dsp.2022.103876.], and the PAM constellation proposed in [Gao X C, Zhang J K, Chen H, et al. Energy-Efficient and Low-Latency Massive SIMO Using Noncoherent ML Detection for Industrial IoT Communications [J]. Internet of Things Journal, IEEE, 2019, 6(4):6247-6261. DOI: 10.1109 / JIOT.2018.2878716.]. It can be Figure 4 found that for signal-to-noise ratios of 5 dB, 10 dB, and 15 dB respectively, when the number of antennas exceeds 256, 128, and 32 respectively, the constellation designed in the present invention shows significant advantages, which indicates that the higher the signal-to-noise ratio, the fewer antennas are required to achieve better performance. At the same signal-to-noise ratio, the higher the modulation order, the more antennas are required for the constellation designed in the present invention to achieve better error performance.

[0136] S5: At the receiving end, a low-complexity noncoherent maximum likelihood fast detection algorithm is used to decode the parameters of the noncoherent space-time modulation constellation.

[0137] The received signal vector is expressed in matrix form Then Equation (3) can be converted to:

[0138]

[0139] In Equation (15), the expression of Ξ(θ, φ) is as follows:

[0140]

[0141] wherein,

[0142] Design a two-stage detection algorithm: Obtain the maximum likelihood estimate of the parameters (θ, φ) according to Equation (16); First, decode the parameter φ from Equation (a) in Equation (16): Then use and Equation (b) in Equation (16) to decode the parameter θ, Decode the parameters (a, b) from Equation (b) in Equation (15) by an exhaustive search method, The detailed algorithm process is shown in Table 3:

[0143] Table 3 Low-complexity maximum likelihood detection algorithm

[0144]

[0145]

[0146] The above are only the preferred embodiments of the present invention and are not intended to limit the present invention. Any modifications, equivalent replacements, improvements, etc. made within the spirit and principle of the present invention shall be included within the protection scope of the present invention.

Claims

1. A non-coherent space-time modulation method based on a parameterized Alamouti structure, characterized in that: The steps are as follows: S1: In a non-coherent MIMO system, for any given transmission rate, a non-coherent space-time modulation constellation is constructed by fusing the Alamouti unitary matrix with the power allocation matrix, and the non-coherent space-time modulation constellation is parameterized; S2: According to the parameterized incoherent space-time modulation constellation, the KL distance of the conditional probability density of the received signal is analyzed, and the constellation optimization problem based on the KL criterion is established; S3: Convert the constellation optimization problem based on the KL criterion into a structured constellation joint design problem in a multi-dimensional parameter space; S4: Based on the link signal-to-noise ratio, the structured constellation joint design problem in the multidimensional parameter space is decomposed into two sub-problems, and the maximum and minimum criteria are used to determine the optimal bit allocation scheme under different modulation orders; S5: At the receiving end, a low-complexity non-coherent maximum likelihood fast detection algorithm is used to decode the various parameters of the non-coherent space-time modulation constellation.

2. The incoherent space-time modulation method based on parameterized Alamouti structure according to claim 1, characterized in that: The non-coherent MIMO system includes a transmitting end and a receiving end, the transmitting end is deployed with two antennas, and the receiving end is deployed with M antennas, where M>>2; In the case of short data packet transmission, the relationship between the transmitted signal and the received signal is: Y=SH+N, (1) in, is the wireless channel between the transmitter and the receiver, is the transmitted signal, and To receive the signal, is a noise matrix with a mean of 0 and a variance of The complex Gaussian distribution of From formula (1), we can see that the received signal-to-noise ratio at each antenna of the receiving end is Therefore, the maximum likelihood probability density function of the received signal is established: Wherein, the superscript H represents conjugate transpose, det represents determinant operation, and tr represents trace operation.

3. The incoherent space-time modulation method based on parameterized Alamouti structure according to claim 2, characterized in that: The method of constructing a non-coherent space-time modulation constellation by fusing the Alamouti unitary matrix and the power allocation matrix and parameterizing the non-coherent space-time modulation constellation is: For the non-coherent MIMO system, the optimal decoder is the non-coherent ML decoder, that is, find S to maximize f(Y|S); that is, equivalent to solving Establish the maximum likelihood detector under this signal transmission: By meeting U H U=UU H =I2 of the unitary matrix U of the Alamouti structure and satisfies The power allocation matrix P with P = diag([p1, p2]), p1, p2 ≥ 0 constructs the matrix S; First, U can be parameterized as: Among them, 0≤φ1,φ2<2π, In formula (4), cos(θ) and sin(θ) represent the amplitude information of the transmitted symbol in U. U can be further rewritten as: Among them, φ=φ2-φ1, and 0≤φ<2π; then S can be written as: In order to ensure the unique identification of S and the receiver, SS H must be uniquely identified; therefore, you can ignore set up and S can be equivalently transformed into: Among them, Under power constraint, a≥0, b≥0; Based on the above discussion, S is represented by four parameters a, b, θ, φ in the continuous space. According to certain mapping rules, a, b, θ, φ are respectively derived from the sub-constellation Ω a ,Ω b ,Ω θ ,Ω φ Therefore, the proposed space-time constellation Parameterized as: Among them, the value ranges of the four parameters are a≥0, b≥0, and 0≤φ<2π, the modulation orders of the four sub-constellations satisfy And k a ,k b ,k θ ,k φ All are non-negative integers.

4. The incoherent space-time modulation method based on parameterized Alamouti structure according to claim 3, characterized in that: The calculation method of the KL distance of the received signal conditional probability density is: Among them, S i With S k For constellations Any two different constellation points in .

5. The incoherent space-time modulation method based on parameterized Alamouti structure according to claim 4, characterized in that: The constellation optimization problem based on the KL criterion is: Among them, k s yes The modulation order.

6. The incoherent space-time modulation method based on parameterized Alamouti structure according to claim 5, characterized in that: The method for converting the constellation optimization problem based on the KL criterion into a structured constellation joint design problem in a multi-dimensional parameter space is: S31: According to formula (7), S i With S k The expression is: and Substitute it into formula (10) and simplify the objective function to: Among them, (a i ,b i )≠(a k ,b k ) when f(a,b)>0, (θ i ,φ i )≠(θ k ,φ k ) when f(θ,φ)>0; to maximize the minimum KL distance Should ensure (a i -b i )(a k -b k )>0; Assume a i >b i ,a k >b k , jointly design the constellations of a and b; set up where a i ∈Ω a ,b i ∈Ω b , And meet According to formula (11), The design of is ultimately designed jointly by the constellation of vectors p, θ and φ; S32: The optimization objective function in formula (10) can be transformed into: in, Respectively represent the optimal Ω p ,Ω θ ,Ω φ constellation, Respectively represent Ω p ,Ω θ ,Ω φ The optimal modulation order of the constellation.

7. The incoherent space-time modulation method based on parameterized Alamouti structure according to claim 6, characterized in that: The specific implementation method of step S4 is: S41: For any given set of non-negative integers {k p ,k θ ,k φ }, determine the optimal structure of each sub-constellation in the continuous space, that is: set up By solving equation (13), we can know that: for any given non-negative integer k p ,k θ ,k φ , is the phase-shift keying constellation; is an arithmetic sequence, that is and The constellation points in satisfy: and is a geometric sequence, if and r a ≥r b >1 yes and Then there is and S42: According to the minimum KL distance maximization criterion, determine through exhaustive search method, fixed The optimal modulation order configuration of each sub-constellation under the modulation order is:

8. The incoherent space-time modulation method based on parameterized Alamouti structure according to claim 7, characterized in that: The method for decoding various parameters of the non-coherent space-time modulation constellation using a low-complexity non-coherent maximum likelihood fast detection algorithm is: Express the received signal vector in matrix form Then formula (3) can be converted into: In formula (15), the expression of Ξ(θ,φ) is: in, Design a two-stage detection algorithm: According to equation (16), the maximum likelihood estimate of the parameter (θ, φ) is obtained; first, the parameter φ is decoded by equation (a) in equation (16): Then use and the decoding parameter θ in equation (b) of equation (16), The parameters (a, b) are decoded by exhaustive search method using equation (b) in equation (15).

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