Incoherent SIMO short packet communication unitary constellation parameterization design and efficient detection method

Abstract

The invention provides an incoherent SIMO short packet communication unitary constellation parameterization design and efficient detection method which is used for meeting the requirements for high reliability and low delay in SIMO system short packet communication. The method comprises the following steps: firstly, constructing a unitary constellation containing L symbols for any given transmission rate, and parameterizing the unitary constellation; secondly, taking the minimum chord distance in the maximized unitary constellation as an objective function, and establishing a quantitative relation between the objective function and the pairing error probability by analyzing the chord distance between different sending signals; then constellation structure design and bit allocation are carried out in a combined manner, and an optimal bit allocation scheme under different modulation orders is determined by using a minimum distance maximization criterion; and finally, at a receiving end, realizing efficient decoding of each parameter by using a low-complexity recursive incoherent maximum likelihood rapid detection algorithm. According to the invention, the constellation structure and bit distribution are jointly optimized, so that the requirements of high reliability and low delay in short packet communication of the SIMO system are met.

Description

Technical Field

[0001] This invention relates to the field of wireless communication technology, and in particular to a high-gain noncoherent SIMO short packet communication unitary constellation parameterization design and efficient detection method, which is applicable to the need for high-reliability transmission within a finite symbol length in ultra-reliable low-latency communication scenarios. Background Technology

[0002] Ultra-Reliable Low-Latency Communication (URLLC), as a core technology of 5G and future 6G wireless communication, provides crucial support for critical business scenarios such as industrial automation and remote control. It requires a block error rate (BLER) as low as 10. -5 Up to 10 -9 The physical layer latency is strictly limited to between 1ms and 10ms. To meet the stringent latency requirements of URLLC, the physical layer often employs short-packet communication mechanisms, transmitting tens to hundreds of bytes of data in an extremely short time. However, traditional channel coding has limited performance under short packet lengths, thus necessitating the full utilization of diversity gains other than time within a finite number of symbols to improve transmission reliability. Among various diversity techniques, Single-Input Multiple-Output (SIMO) systems, through the configuration of multi-antenna receiver structures, can effectively improve link robustness and have become an important implementation scheme in short-packet communication. Most existing SIMO systems are based on coherent detection, and their performance heavily depends on accurate Channel State Information (CSI). In short-packet communication, the proportion of pilot symbols used for channel estimation increases significantly, leading to a decrease in system spectral efficiency. In contrast, incoherent communication does not rely on instantaneous CSI, providing a more efficient solution for SIMO short packet communication. Its advantages include: (1) achieving direct demodulation through technologies such as energy detection, differential detection, or Grassmannian signaling, improving resource utilization; (2) obtaining diversity gain through channel hardening or subspace consistency, enhancing link reliability; and (3) being suitable for high-dynamic scenarios where the channel changes rapidly and accurate CSI is difficult to obtain, such as industrial IoT and UAV communication. Therefore, incoherent SIMO technology is widely regarded as an effective way to realize URLLC short packet transmission. Most existing research on unitary constellations in SIMO systems adopts unstructured design, usually relying on exhaustive search, resulting in high design complexity. Therefore, how to design a structured unitary constellation for SIMO systems that combines low-complexity encoding and decoding with good performance remains an open question.

[0003] In summary, the existing technologies face the following challenges: (1) Pilot overhead bottleneck: Traditional coherent communication relies on CSI, which requires time and frequency resources for pilot transmission, severely limiting the spectral efficiency in short packet communication scenarios; (2) Lack of regular structure: Existing unitary constellation designs are mostly unstructured schemes, which have the problem of high design complexity. Summary of the Invention

[0004] To address the shortcomings of the aforementioned background technologies, this invention proposes a high-gain noncoherent SIMO short packet communication unitary constellation parameterization design and efficient detection method. By jointly optimizing the constellation structure and bit allocation, the high reliability and low latency requirements of short packet communication in SIMO systems are solved.

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

[0006] A parameterized design and efficient detection method for unitary constellations in noncoherent SIMO short packet communication, comprising the following steps:

[0007] S1: Construct a SIMO uplink communication system under a block Rayleigh fading channel. For any given transmission rate, construct a unitary constellation containing L symbols and parameterize the unitary constellation.

[0008] S2: Taking the maximization of the minimum chord distance in the unitary constellation as the objective function, a quantitative relationship between the objective function and the pairwise error probability is established by analyzing the chord distance between different transmitted signals;

[0009] S3: Joint constellation structure design and bit allocation: Transform the high-order constellation optimization problem into a structured constellation joint design problem in a multi-dimensional parameter space; Use the minimum distance maximization criterion to determine the optimal bit allocation scheme under different modulation orders;

[0010] S4: At the receiving end, a low-complexity recursive incoherent maximum likelihood fast detection algorithm is used to achieve efficient decoding of each parameter.

[0011] Preferably, the SIMO uplink communication system includes a transmitter and a receiver, with a single antenna deployed at the transmitter and M antennas deployed at the receiver. The wireless channel between the transmitter and the receiver is...

[0012] Preferably, in step S1, a class of recursive unitary constellations is constructed using a parameterized form:

[0013]

[0014] Where θ=(θ0,θ1,...,θ) L-2 Let φ be the angle parameter, and φ = (φ0, φ1, ..., φ2). L-2Let θ be the phase parameter, and 0 ≤ θ i ≤π / 2, 0≤φ i <2π, i=0,...,L-2;

[0015] By decoupling the parameter space, the higher-order unitary constellation is transformed into... Where Θ={Ω θ,0 ,...,Ω θ,L-2} represents the set of angular constellations, Φ = {Ω} φ,0 ,...,Ω φ,L-2} represents the set of phase constellations, whose modulation orders are R and R, respectively. Θ and R Φ Satisfying R Θ +R Φ =R, where R is the total modulation order; the angle modulation order is further expressed as a vector form R θ =(R θ,0 ,R θ,1 ,...,R θ,L-2 ),satisfy The phase modulation order is expressed in vector form R φ =(R φ,0 ,R φ,1 ,...,R φ,L-2 ),satisfy And R φ,0 ≥…≥R φ,L-2 .

[0016] Preferably, the specific implementation method of step S2 is as follows:

[0017] When using a maximum likelihood detector, two different transmitted signals x i With x j The upper bound of the pairwise error probability between them is: Where d(x) i ,x j The chordal distance between two signals is defined as:

[0018]

[0019] Where the superscript H denotes the conjugate transpose, σ n 2 Let N be the variance of the additive white Gaussian noise matrix.

[0020] Therefore, in order to optimize system reliability and maximize the reliability of the zodiac sign, The minimum chord distance in the equation is the objective function:

[0021]

[0022] Based on the above description, the minimum chord distance of the proposed constellation Uri can be rewritten as:

[0023]

[0024] According to equation (6), the objective function described by equation (5) can be transformed into:

[0025]

[0026] Preferably, the specific implementation method of step S3 is as follows:

[0027] S31: Transform the objective function expressed in equation (7) into two sub-objectives; specifically, firstly, for any fixed set of non-negative integers {R} θ ,R φ}, determine the optimal structure of each sub-constellation in the continuous space, that is:

[0028]

[0029] Let d(R) θ ,R φ ) = max Θ,Φ mind((θ i ,φ i ),(θ j ,φ j For any two distinct constellation points x i ≠x j , equivalent to (θ i ,φ i )≠(θ j ,φ j At this point, the minimum chord distance occurs in the following two cases: θ i ≠θ j or θ i =θ j :

[0030] When θ i ≠θ j At that time, there are two cases: φ i ≠φ j and φ i =φ j ;because Therefore, the minimum chord distance is determined by θ. i ≠θ j ,φ i =φ j Decision; based on the minimum distance maximization criterion, the angle parameters θ i It should form an arithmetic sequence;

[0031] (b) when θ i =θ j Sometimes, At this point, the minimum chord spacing depends on a series of forms such as The expression, where 0 < a, b < 1 and a + b = 1, increases as the phase difference Δφ i increases; therefore, each phase parameter φ i should be the uniformly distributed PSK constellation points;

[0032] Therefore, for any set of non - negative integers {R θ , R φ}, each sub - constellation Ω in Φ φ,i is a uniform PSK constellation containing points; each sub - constellation Ω in the angular constellation Θ θ,i is an arithmetic sequence, that is where<00002​​​​​​​​​​​​​​​​​​​​​​​​​​​​​​​​​​​​​​​​​​​​​​​​​​​​​​​​​​​​​​​​​

[0043]

[0044] By jointly considering equations (9) and (11), the following constellation parameter optimization problem can be established:

[0045]

[0046] S33: Based on the minimum distance maximization criterion, the optimal modulation order configuration for each sub-constellation under a fixed modulation order is determined through an exhaustive search method, i.e.:

[0047]

[0048] Preferably, the low-complexity recursive incoherent maximum likelihood fast detection algorithm is as follows:

[0049] Consider the received signal matrix in To receive the signal in the first time slot, The signal will be received in the next L-1 time slots;

[0050] For a transmitted signal of length L The detection of parameters (θ, φ) can be divided into two steps: first, based on... Detect x(L-1); then combine y0 with the preprocessed... Detection parameters (φ) L-2 ,θ L-2 ).

[0051] The beneficial effects of this invention are:

[0052] 1) Parametric Recursive Unitary Constellation Structure Design: For short packet transmission scenarios in SIMO systems, a unitary constellation with a clear mathematical structure is constructed recursively, decomposing the high-order constellation design problem into a joint optimization problem of angle parameter sets and phase parameter sets. This method eliminates the need for CSI estimation, avoids pilot overhead in traditional coherent communication, significantly improves the spectral efficiency of short packet transmission, and is suitable for high-reliability, low-latency communication requirements in URLLC scenarios.

[0053] 2) Constellation optimization criterion based on maximizing minimum chord spacing: By analyzing the chord spacing between transmitted signals, a quantitative relationship between it and the pairwise error probability is established. Constellation optimization is carried out with the goal of maximizing the minimum chord spacing, which effectively improves system reliability and ensures better bit error rate performance within a finite symbol length.

[0054] 3) Joint constellation structure and bit allocation optimization: The high-order constellation design is transformed into a structured joint design problem in a multi-dimensional parameter space. By using the minimum distance maximization criterion, the number of bits for angle and phase parameters is dynamically allocated according to different modulation orders to achieve efficient resource utilization and improve the system's adaptability under time-varying channels.

[0055] 4) Low-complexity recursive incoherent maximum likelihood detection algorithm: A recursive fast detection algorithm is designed to decompose the multidimensional detection problem into multiple serial subproblems, which significantly reduces the detection complexity and meets the strict requirements of millisecond-level latency in URLLC scenarios.

[0056] 5) Synergistic innovation of structured constellations and efficient coding: By organically combining parametric design, chord spacing optimization, dynamic bit allocation and recursive detection algorithms, the core problems of high complexity of unitary constellation design and low detection efficiency in incoherent SIMO systems are solved, providing a scalable and high-performance solution for short packet communication in 6G networks. Attached Figure Description

[0057] To more clearly illustrate the technical solutions in the embodiments of the present invention or the prior art, the drawings used in the description of the embodiments or the prior art will be briefly introduced below. Obviously, the drawings described below are only some embodiments of the present invention. For those skilled in the art, other drawings can be obtained based on these drawings without creative effort.

[0058] Figure 1 This is a flowchart of the present invention.

[0059] Figure 2 The diagram shows the minimum chord spacing of this invention compared to a typical unitary constellation and a pilot-based PSK constellation when L=3 and L=4.

[0060] Figure 3 This is a schematic diagram illustrating the change in block error rate at the receiving end of the present invention with the signal-to-noise ratio when the transmission rate is 3 bits / channel.

[0061] Figure 4 This is a schematic diagram illustrating the change in block error rate at the receiving end of the present invention with the signal-to-noise ratio when the transmission rate is 4 bits / channel.

[0062] Figure 5 This is a schematic diagram showing the change of block error rate at the receiver as a function of signal-to-noise ratio when L=4 and modulation order is 12, compared to existing solutions.

[0063] Figure 6 This is a schematic diagram showing the bit error rate at the receiver as a function of the signal-to-noise ratio when L=4 and the modulation order is 12, compared to existing solutions. Detailed Implementation

[0064] The technical solutions of the embodiments of the present invention will be clearly and completely described below with reference to the accompanying drawings. Obviously, the described embodiments are only some embodiments of the present invention, and not all embodiments. Based on the embodiments of the present invention, all other embodiments obtained by those skilled in the art without creative effort are within the scope of protection of the present invention.

[0065] like Figure 1 As shown, this invention provides a method for parameterized design and efficient detection of unitary constellations in noncoherent SIMO short packet communication. By jointly optimizing the constellation structure and bit allocation, it addresses the high reliability and low latency requirements of short packet communication in SIMO systems. The specific steps are as follows:

[0066] S1: Construct a SIMO uplink communication system under a block Rayleigh fading channel. For any given transmission rate, construct a unitary constellation containing L symbols and parameterize the unitary constellation. This allows the design problem of a higher-order constellation to be decomposed into a joint design problem of multiple sub-constellations.

[0067] A SIMO uplink communication system under a block Rayleigh fading channel. A single antenna is deployed at the transmitter, and M antennas are deployed at the receiver. The wireless channel between the transmitter and receiver is... The elements in h are independent and follow a complex circular symmetric Gaussian distribution with a mean of 0 and a variance of 1. Assume the channel h is unknown to both the transmitter and receiver; this system employs a block fading model, assuming the channel remains constant within a transport block of L symbols and varies independently between different blocks. Transmitted symbol sequence Taken from a power constraint ||x|| 2 =1 in the constellation of the Rooster Received signal It can be represented as:

[0068] Y = hx T +N, (1)

[0069] in The matrix is ​​an additive white Gaussian noise matrix, where each element is independent and identically distributed, and all elements follow the same distribution. The signal-to-noise ratio on each antenna at the receiver is defined as

[0070] Given a transmitted symbol sequence x, the probability density function of the received signal Y is:

[0071]

[0072] The maximum likelihood detector can be expressed as: Given that all constellation points satisfy the Unitary constraint The above problem can be simplified to:

[0073] For a transmitted signal of length L, x = (x1, x2, ..., x...) L ) T Each symbol x l It can be represented as Where |x l |≥0,0≤φ l <2π. According to the power constraint ||x|| 2 =1, there is It can be written as equivalent to Therefore, this constraint can be parameterized as Where 0≤θ L-2 ≤π / 2. Similarly, This can be further parameterized recursively. The phase of the first symbol can be absorbed in the channel, and its distribution is unaffected by this phase; therefore, the first symbol can be set as a real signal. Based on this, the transmitted signal can be recursively parameterized as follows:

[0074]

[0075] Where x(1) = 1. The parameter set includes the angle parameter θ = (θ0, θ1, ..., θ...). L-2 ) and phase parameters φ=(φ0,φ1,...,φ L-2 ), satisfying 0≤θ i ≤π / 2, 0≤φ i <2π, i=0,...,L-2.

[0076] To simplify the design, it is assumed that the angle and phase parameters are independent and belong to different constellation sets. Furthermore, to implement Gray coding, it is assumed that the constellation number of each sub-constellation is a power of 2. Therefore, the proposed unitary constellation can be represented as: Where Θ={Ω θ,0 ,...,Ω θ,L-2} represents the set of angular constellations, Φ = {Ω} φ,0 ,...,Ω φ,L-2} represents the set of phase constellations, whose modulation orders are R and R, respectively. Θ and R Φ Satisfying R Θ +R Φ =R, where R is the total modulation order. The angle modulation order can be further expressed as a vector form R. θ =(R θ,0 ,R θ,1 ,...,R θ,L-2 ),satisfy Similarly, the phase modulation order can be expressed in vector form Rφ =(R φ,0 ,R φ,1 ,...,R φ,L-2 ),satisfy Without loss of generality, this embodiment assumes R φ,0 ≥…≥R φ,L-2 .

[0077] S2: Taking the maximization of the minimum chord distance in the genus constellation as the objective function, by analyzing the chord distance between different transmitted signals, a quantitative relationship between the objective function and the pairwise error probability is established to ensure an exponential decrease in the error rate.

[0078] For a unitary constellation, when using a maximum likelihood detector, the pairwise error probability increases as the chordal distance between two different transmitted signals decreases. Using maximizing the minimum chordal distance in the constellation as the design criterion, this study investigates the optimization problem of a discrete constellation of finite size. Specifically:

[0079] When using a maximum likelihood detector, two different transmitted signals x i With x j The upper bound of the pairwise error probability between them is: Where d(x) i ,x j The chordal distance between two signals is defined as:

[0080]

[0081] The superscript H indicates conjugate transpose. Let N be the variance of the additive white Gaussian noise matrix.

[0082] As can be seen from the upper bound of the pairwise error probability, the pairwise error probability increases as the chordal distance decreases. Therefore, to optimize system reliability and maximize the unitary constellation... The minimum chord distance in the equation is the objective function:

[0083]

[0084] Based on the above description, the minimum chord distance of the proposed constellation Uri can be rewritten as:

[0085]

[0086] According to equation (6), the objective function described by equation (5) can be transformed into:

[0087]

[0088] S3: Joint constellation structure design and bit allocation: Transform the high-order constellation optimization problem into a structured constellation joint design problem in a multi-dimensional parameter space; Use the minimum distance maximization criterion to determine the optimal bit allocation scheme under different modulation orders;

[0089] By leveraging the unique characteristics of parameterized constellation structures, the optimal constellation structure can be determined.

[0090] Angle of the constellation Omega θ,i Design arithmetic sequences in

[0091] Aspect of the sign Omega φ,i :Include A uniform phase-shift keying (PSK) constellation with 100 points.

[0092] Based on the maximum-minimum criterion, the optimal bit allocation under different modulation orders is determined by exhaustive search method.

[0093] The specific implementation method is as follows:

[0094] S31: Problem (7) is a joint optimization problem involving discrete integers and continuous parameters. The solution to problem (7) is determined by solving the following two subproblems; specifically, firstly, for any fixed set of non-negative integers {R} θ ,R φ}, determine the optimal structure of each sub-constellation in the continuous space, that is:

[0095]

[0096] Let d(R) θ ,R φ ) = max Θ,Φ mind((θ i ,φ i ),(θ j ,φ j For any two distinct constellation points x i ≠x j , equivalent to (θ i ,φ i )≠(θ j ,φ j At this point, the minimum chord distance occurs in the following two cases: θ i ≠θ j or θ i =θ j .

[0097] (a) when θ i ≠θ j At that time, there are two cases: φi ≠φ j and φ i =φ j . Since Therefore, the minimum chord distance is determined by θ i ≠θ j , φ i =φ j ; this distance is affected by △θ i (i = 0,..., L - 2), and increases as △θ i increases. Based on the minimum distance maximization criterion, the angle parameters θ i should form an arithmetic sequence.

[0098] (b) When θ i =θ j , there is At this time, the minimum chord distance depends on a series of expressions in the form of , and 0 < a, b < 1, a + b = 1, and it increases as the phase difference △φ i increases. Therefore, each phase parameter φ i should be a uniformly distributed PSK constellation point.

[0099] Based on the above analysis, the constellation proposed in this invention has the following structural characteristics: for any set of non - negative integers {R θ , R φ}, each sub - constellation Ω φ,i in Φ is a uniform PSK constellation containing points; each sub - constellation Ω θ,i in the angle constellation Θ is an arithmetic sequence, that is where

[0100] S32: Taking L = 3 as an example, determine the parameter optimization under fixed bit allocation

[0101] Maximizing the minimum chord distance is equivalent to minimizing the cross - correlation function between the maximum different signals

[0102] When L = 3, let the transmitted signal At this time, the cross - correlation function can be written as:

[0103]

[0104] (a) When , there is:

[0105]

[0106] (b) When , there is:

[0107]

[0108] Define angle set in Similarly, define in {θ 0,0 ,θ0′ ,0 ,θ 1,0 ,θ1′ ,0} represents the parameters to be optimized.

[0109] To simplify the solution of equation (10), a function is defined. We can obtain: f(a, Δφ) = a 2 +(1-a) 2 +2a(1-a)cos△φ; This function has the following property: f(a,△φ) is symmetric, that is, f(a,△φ)=f(1-a,△φ). Moreover, when When f(a, Δφ) is monotonically decreasing with respect to a; when When f(a, Δφ) is monotonically increasing with respect to a. In particular, when When , f(a, Δφ) reaches its minimum value. When 'a' is fixed, f(a, Δφ) monotonically decreases with respect to Δφ.

[0110] Therefore, equation (10) can be further simplified to:

[0111]

[0112] By jointly considering equations (9) and (11), the following constellation parameter optimization problem can be established:

[0113]

[0114] S33: Based on the minimum distance maximization criterion, the optimal modulation order configuration for each sub-constellation under a fixed modulation order is determined through an exhaustive search method, i.e.:

[0115]

[0116] According to the present invention, the optimal bit allocation and optimal substellar parameter configuration for L=3 and L=4 can be obtained, as shown in Tables 1 and 2:

[0117] Table 1 (L=3)

[0118]

[0119] Table 2 (L=4)

[0120]

[0121] Figure 2 A comparison diagram of the minimum chord distance between the constellation designed in this invention and other Rosary constellations is provided. Figure 2 (a) is L = 3. Figure 2 (b) is L=4. As can be seen from the figure, the minimum chord pitch of the constellation designed in this invention is superior to that of the pilot-based PSK constellation, where the pilot-based scheme uses one pilot symbol and L-1 PSK symbols with the same amplitude and modulation order. Furthermore, the performance of the constellation designed in this invention is close to the minimum chord pitch of the unstructured general unitary constellation proposed by Hochwald et al. in their paper [Unitary Space-Time Modulation for Multiple-Antenna Communications in Rayleigh Flat Fading,”IEEE Transactions on Information Theory, Vol. 2, No. 46, pp. 543-564 (2000)].

[0122] Figure 3 and Figure 4 The graphs show the block error rate (BRR) as a function of signal-to-noise ratio (SNR) for the constellation designed in this invention at transmission rates of 3 bits / channel and 4 bits / channel, respectively. The graphs demonstrate that at the same transmission rate, a larger L value (i.e., a longer symbol block length) leads to better BRR performance, indicating that a longer block structure contributes to improved system reliability. Furthermore, the BRR performance of the constellation designed in this invention, combined with a recursive maximum likelihood detector, is close to that of a global search detection algorithm, verifying the effectiveness of the proposed low-complexity detection method.

[0123] Figure 5 and Figure 6The paper presents the trend graphs of block error rate and bit error rate as a function of signal-to-noise ratio for the constellation designed in this invention at L=4 and R=12, comparing it with the unstructured general unitary constellation and pilot-based scheme in Hochwald et al.'s paper [Unitary Space-Time Modulation for Multiple-Antenna Communications in Rayleigh Flat Fading, IEEE Transactions on Information Theory, Vol. 46, pp. 543-564 (2000)]. In the pilot-based scheme, the system uses one pilot and L-1 PSK symbols or Quadrature Amplitude Modulation (QAM) symbols for transmission. The graphs show that the bit error rate performance of the constellation designed in this invention is superior to that of the pilot-based scheme. Specifically, it is about 1 dB better than the pilot-based QAM scheme and nearly 2 dB better than the pilot-based PSK scheme. Although the general unitary constellation using a maximum likelihood detector outperforms the designed constellation in terms of block error rate performance, from... Figure 6 The bit error rate curve shows that the performance gap between the designed constellation and a typical unitary constellation is smaller than the performance gap in block error rate.

[0124] S4: At the receiving end, a low-complexity recursive incoherent maximum likelihood fast detection algorithm is used to achieve efficient decoding of each parameter.

[0125] Consider the received signal matrix in To receive the signal in the first time slot, The signal is received in the next L-1 time slots.

[0126] For a transmitted signal of length L The detection of parameters (θ, φ) can be divided into two steps: first, based on... Detect x(L-1); then combine y0 with the preprocessed... Detection parameters (φ) L-2 ,θ L-2 The recursive process ultimately boils down to a two-symbol detection problem. The complete recursive detection process is shown in Table 3.

[0127] Table 3

[0128]

[0129] The above description is only a preferred embodiment of the present invention and is not intended to limit the present invention. Any modifications, equivalent substitutions, improvements, etc., made within the spirit and principles of the present invention should be included within the protection scope of the present invention.

Claims

1. A parameterized design and efficient detection method for unitary constellations in noncoherent SIMO short packet communication, characterized in that, The steps are as follows: S1: Construct a SIMO uplink communication system under a block Rayleigh fading channel. For any given transmission rate, construct a unitary constellation containing L symbols and parameterize the unitary constellation. S2: Taking the maximization of the minimum chord distance in the unitary constellation as the objective function, a quantitative relationship between the objective function and the pairwise error probability is established by analyzing the chord distance between different transmitted signals; S3: Joint constellation structure design and bit allocation: Transform the high-order constellation optimization problem into a structured constellation joint design problem in a multi-dimensional parameter space; Use the minimum distance maximization criterion to determine the optimal bit allocation scheme under different modulation orders; S4: At the receiving end, a low-complexity recursive incoherent maximum likelihood fast detection algorithm is used to achieve efficient decoding of each parameter.

2. The method for parameterized design and efficient detection of unitary constellations in noncoherent SIMO short packet communication according to claim 1, characterized in that, The SIMO uplink communication system includes a transmitter and a receiver. A single antenna is deployed at the transmitter, and M antennas are deployed at the receiver. The wireless channel between the transmitter and the receiver is...

3. The method for parameterized design and efficient detection of unitary constellations in noncoherent SIMO short packet communication according to claim 1, characterized in that, In step S1, a class of recursive unitary constellations is constructed using parameterized forms: Where θ=(θ0,θ1,...,θ) L-2 Let φ be the angle parameter, and φ = (φ0, φ1, ..., φ2). L-2 Let θ be the phase parameter, and 0 ≤ θ i ≤π / 2, 0≤φ i <2π, i=0,...,L-2; By decoupling the parameter space, the higher-order unitary constellation is transformed into... Where Θ={Ω θ,0 ,...,Ω θ,L-2 } represents the set of angular constellations, Φ = {Ω} φ,0 ,...,Ω φ,L-2 } represents the set of phase constellations, whose modulation orders are R and R, respectively. Θ and R Φ Satisfying R Θ +R Φ =R, where R is the total modulation order; the angle modulation order is further expressed as a vector form R θ =(R θ,0 ,R θ,1 ,...,R θ,L-2 ),satisfy The phase modulation order is expressed in vector form R φ =(R φ,0 ,R φ,1 ,...,R φ,L-2 ),satisfy And R φ,0 ≥…≥R φ,L-2 .

4. The method for parameterized design and efficient detection of unitary constellations in noncoherent SIMO short packet communication according to claim 3, characterized in that, The specific implementation method of step S2 is as follows: When using a maximum likelihood detector, two different transmitted signals x i With x j The upper bound of the pairwise error probability between them is: Where d(x) i ,x j The chordal distance between two signals is defined as: Wherein, the superscript H indicates conjugate transpose. Let N be the variance of the additive white Gaussian noise matrix. Therefore, in order to optimize system reliability and maximize the reliability of the zodiac sign, The minimum chord distance in the equation is the objective function: Based on the above description, the minimum chord distance of the proposed constellation Uri can be rewritten as: According to equation (6), the objective function described by equation (5) can be transformed into:

5. The method for parameterized design and efficient detection of unitary constellations in noncoherent SIMO short packet communication according to claim 1, characterized in that, The specific implementation method of step S3 is as follows: S31: Transform the objective function expressed in equation (7) into two sub-objectives; specifically, firstly, for any fixed set of non-negative integers {R} θ ,R φ }, determine the optimal structure of each sub-constellation in the continuous space, that is: Let d(R θ ,R φ ) = max Θ,Φ mind((θ i , φ i ), (θ j , φ j )); For any two different constellation points x i ≠ x j , which is equivalent to (θ i , φ i ) ≠ (θ j , φ j ); At this time, the minimum chord distance appears in the following two cases: θ i ≠ θ j or θ i = θ j : (a) When θ i ≠ θ j , there are two cases: φ i ≠ φ j and φ i = φ j ; Since Therefore, the minimum chord distance is determined by θ i ≠ θ j , φ i = φ j ; Based on the minimum distance maximization criterion, the angular parameters θ i should form an arithmetic sequence, i = 0,..., L - 2; (b) When θ i = θ j , there is At this time, the minimum chord distance depends on a series of expressions in the form of <00​​​ Therefore, each phase parameter φ i The PSK constellation points should be evenly distributed. Therefore, for any set of non-negative integers {R} θ ,R φ }, each sub-constellation Ω in Φ φ,i All include A uniform PSK constellation at each point; each sub-constellation Ω within the angular constellation Θ. θ,i All are arithmetic sequences, i.e. in S32: When L=3, determine the parameter optimization under fixed bit allocation. Maximizing the minimum chord interval is equivalent to minimizing the maximum cross-correlation function between different signals. When L=3, let the transmitted signal be... and At this point, the cross-correlation function It can be written as: (a) When At that time, there were: (b) when At that time, there were: Define angle set in Similarly, define in {θ 0,0 ,θ′ 0,0 ,θ 1,0 ,θ′ 1,0 } represents the parameters to be optimized; To simplify the solution of equation (10), a function is defined. We can obtain: f(a, Δφ) = a 2 +(1-a) 2 +2a(1-a)cos△φ; Therefore, equation (10) can be further simplified to: By jointly considering equations (9) and (11), the following constellation parameter optimization problem can be established: S33: Based on the minimum distance maximization criterion, the optimal modulation order configuration for each sub-constellation under a fixed modulation order is determined through an exhaustive search method, i.e.:

6. The method for parameterized design and efficient detection of unitary constellations in noncoherent SIMO short packet communication according to claim 5, characterized in that, The low-complexity recursive incoherent maximum likelihood fast detection algorithm is as follows: Consider the received signal matrix in To receive the signal in the first time slot, The signal will be received in the next L-1 time slots; For a transmitted signal of length L The detection of parameters (θ, φ) can be divided into two steps: first, based on... Detect x(L-1); then combine y0 with the preprocessed... Detection parameters (φ) L-2 ,θ L-2 ).

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