A method for optimizing layer width of MML demodulation and a high-performance low-complexity spatial modulation system demodulator

Abstract

The application discloses a layer width optimization method of MML demodulation and a high-performance low-complexity spatial modulation system demodulator. The application decomposes the symbol vector error rate (SVER) performance constraint of MML into layers, introduces hierarchical capability, selects the minimum width satisfying the hierarchical capability constraint at each layer, and realizes the optimization of MML width through iteration from the root layer to the leaf layer. The application studies the behavior of the proposed scheme under different antenna configurations and channel state information. Numerical results show that the combination of the MML algorithm and the layer width optimization method of the application exhibits SVER comparable to the optimal demodulation, while significantly reducing the computational complexity by more than 90%. In addition, compared with existing low-complexity optimization demodulation algorithms, the method proposed by the application has the lowest computational complexity.

Description

Technical Field

[0001] This invention relates to a demodulation technique for a spatial modulation MIMO system, belonging to the field of mobile communication technology. Background Technology

[0002] Large-scale spatially multiplexed multiple-input multiple-output (MIMO) systems significantly improve spectral efficiency by activating all transmit antennas. However, given the significant contribution of radio frequency (RF) modules to the total transmitter power consumption, their energy efficiency has become a concern. As an alternative, spatial modulation (SM) has attracted considerable attention in recent years. SM selectively activates a single antenna in each time slot, effectively mitigating inter-channel interference (ICI) and reducing power consumption. In SM, the input bitstream is modulated into spatial symbols and constellation symbols. This two-dimensional modulation scheme improves both spectral and energy efficiency.

[0003] The optimal demodulation method for spatial modulation (SM) is the maximum likelihood (ML) algorithm. However, the complexity of ML demodulation increases with the number of transmit and receive antennas and the size of the modulation constellation. Therefore, adapting SM to large-scale MIMO systems presents a critical and unavoidable challenge in designing low-complexity demodulation methods. Various low-complexity SM demodulation algorithms have been proposed, including ball demodulation (SD) and minimum distance with maximum length (mM) algorithms, while maintaining bit error rate performance approximately equal to that of ML algorithms. However, both SD and mM algorithms exhibit serial characteristics, leading to significant delays. M-algorithm toML (MML) demodulation was initially proposed in the literature and has been further improved since (see J. Zheng, X. Yang, and Z. Li, “Low-complexity detection method for spatial modulation based on M-algorithm”; Z. Tian, ​​Z. Li, M. Zhou, and X. Yang, “M-algorithm-based optimal detectors for spatial modulation”; X. Zhang, G. Zhao, Q. Liu, N. Zhao, and M. Jin, “Enhanced M-algorithm-based maximum likelihood detectors for spatial modulation”). The MML algorithm transforms the search space into a tree structure searched in a breadth-first manner. Furthermore, the width of each layer in the tree is fixed at a constant value. By choosing appropriate layer widths, the MML algorithm can approach the ML bound. The fixed complexity and parallelism of the MML algorithm make it a competitive choice for practical communication systems. A key aspect of the MML algorithm is determining the optimal combination of layer widths to minimize computational complexity while satisfying bit error rate performance constraints. However, to our knowledge, there are few references specifically addressing the optimization problem of layer widths. Summary of the Invention

[0004] Purpose of the invention: In view of the problems existing in the prior art, the purpose of this invention is to provide a layer width optimization method for MML demodulation to improve MML, and to realize high-performance, low-complexity spatial modulation system demodulation based on the improved MML (iMML) algorithm.

[0005] Technical solution: To achieve the above-mentioned objectives, the present invention adopts the following technical solution:

[0006] A layer width optimization method for MML demodulation decomposes the Sign Vector Error Rate (SVER) performance constraint of MML into layers, introducing layer capability. Select the level that meets the requirements at each level. The minimum width of the constraint is optimized by iterating from the root to the leaf layer.

[0007] Furthermore, the first The layer was determined as in It is a tolerance constant based on the SVER design.

[0008] Furthermore, the aforementioned Set as ,in It's SVER. It refers to the number of receiving antennas. .

[0009] Furthermore, the hierarchical capabilities The results were obtained based on offline estimation using the Monte Carlo method, including simulation using the Monte Carlo method. The ML algorithm calculates the frequency of the correct path at each position in each level of the ML tree; the positions in each level of the ML tree are sorted in ascending order of metric values; the width is determined layer by layer starting from level 1, and the width of level k is... Through formula Confirmed, among which The correct path is located at the . Front The sum of the frequencies at each position, It is a tolerance constant based on the SVER design.

[0010] A high-performance, low-complexity spatial modulation system demodulation method is proposed, which utilizes an improved MML demodulation algorithm to solve the following problem:

[0011]

[0012] in It is a modulating constellation. It is the number of transmitting antennas. It is the receive vector. Is the receiving end to The estimate, This represents the estimation error vector. This refers to the number of receiving antennas. The MML demodulation algorithm utilizes a tree structure to construct the search space for the ML demodulation algorithm. The tree contains... Each branch originates from the root node, and these branches represent indices of the transmitting antennas. Each branch contains... There are sub-branches, each with a length of . The improved MML demodulation algorithm employs a breadth-first tree search algorithm based on a width-limited strategy, in the first... Within the layer, retain the previous values ​​in ascending order of metric values. The nodes, the The layer width is determined according to the layer width optimization method for MML demodulation.

[0013] Furthermore, the tree in the MML demodulation algorithm is layered by element. Rearrange branches in descending order of magnitude Each floor.

[0014] A high-performance, low-complexity spatial modulation system demodulator, comprising:

[0015] The MML demodulation module is used to solve the following problems using the MML demodulation algorithm:

[0016]

[0017] in It is a modulating constellation. It is the number of transmitting antennas. It is the receive vector. Is the receiving end to The estimate, This represents the estimation error vector. This refers to the number of receiving antennas. The MML demodulation algorithm utilizes a tree structure to construct the search space for the ML demodulation algorithm. The tree contains... Each branch originates from the root node, and these branches represent indices of the transmitting antennas. Each branch contains... There are sub-branches, each with a length of . The improved MML demodulation algorithm employs a breadth-first tree search algorithm based on a width-limited strategy, in the first... Within the layer, retain the previous values ​​in ascending order of metric values. One node;

[0018] Additionally, a layer width optimization module is used to decompose the Sign Vector Error Rate (SVER) performance constraint of MML into layers, introducing hierarchical capabilities. Select the level that meets the requirements at each level. The minimum width of the constraint is optimized by iterating from the root to the leaf layer.

[0019] A computer system includes a memory, a processor, and a computer program / instructions stored in the memory and executable on the processor, wherein the computer program / instructions, when executed by the processor, implement the steps of any of the methods described above.

[0020] A computer-readable storage medium storing a computer program that, when executed by a processor, implements the steps of any of the above methods.

[0021] A computer program product includes a computer program / instructions that, when executed by a processor, implement the steps of any of the methods described above.

[0022] Beneficial Effects: Compared with existing technologies, this invention has the following advantages: This invention provides an improved MML (iMML) algorithm that optimizes layer width without sacrificing any Symbol Vector Error Rate (SVER) performance. This invention provides a layer-by-layer width optimization framework that decomposes the SVER performance constraints of MML into layers, introducing the concept of layer-by-layer capability. At each layer, the minimum width satisfying the layer-by-layer capability constraint is selected, and MML width optimization is achieved through iterative use from the root to the leaf layers. This invention further provides a Monte Carlo-based algorithm for layer-by-layer capability estimation, seamlessly integrated with the width optimization framework. The entire width optimization process is performed offline, ensuring no additional complexity is introduced during demodulation. Simulations in various scenarios verify the robustness of the iMML algorithm, and comparative analysis with other demodulation algorithms is conducted. Compared with the ML algorithm, the iMML algorithm saves more than 90% of computational complexity. Attached Figure Description

[0023] Figure 1 4-PSK modulation Example diagram of MML demodulation tree in SM system, where .

[0024] Figure 2 This is a flowchart of a layer width optimization method for an improved version of MML demodulation based on the Monte Carlo method.

[0025] Figure 3 A comparison chart of SVER performance of different demodulators in an underdetermined MIMO-SM system.

[0026] Figure 4 This is a comparison chart of the SVER performance of different demodulators in a stationary MIMO-SM system.

[0027] Figure 5 A comparison chart of SVER performance of different demodulators in a stationary MIMO-SM system.

[0028] Figure 6 This is a graph showing the relationship between the reduction in computational complexity of each demodulator in an underdetermined MIMO-SM system and the signal-to-noise ratio.

[0029] Figure 7This is a graph showing the relationship between the reduction in computational complexity of each demodulator in a stationary MIMO-SM system and the signal-to-noise ratio.

[0030] Figure 8 This is a graph showing the relationship between the reduction in computational complexity of each demodulator and the signal-to-noise ratio in a stationary MIMO-SM system. Detailed Implementation

[0031] The technical solution of the present invention will now be clearly and completely described with reference to the accompanying drawings and specific embodiments. To clearly understand the method of the embodiments of the present invention, the relevant system model and existing MML algorithms will first be introduced.

[0032] Consider a having Transmitting antenna and An uplink MIMO system with a receiving antenna. In SM, the input binary stream is divided into segments of length... The blocks, in which This refers to the constellation size of the modulation scheme. In this letter, we adopt... Phase Shift Keying (PSK) -PSK) modulation, where the modulation constellation is Each block is divided into two groups: the first... The bits are mapped to the index of the active antenna, while the remaining bits are mapped to the index of the active antenna. The bits are mapped to a modulation symbol. In each time slot, only one antenna is activated to transmit information, while the rest ( ( ) antennas remain silent. Based on the above, the spectral efficiency of the SM system is... Bits per channel user (bpcu).

[0033] Assuming a flat Rayleigh fading channel, its channel matrix... Each entry is an independent and identically distributed complex Gaussian distribution with zero mean and unit variance. The received vector is...

[0034]

[0035] in , , express The List, It has zero mean and a covariance matrix of The additive white Gaussian noise (AWGN) vector. The maximum likelihood (ML) demodulation algorithm aims to solve for...

[0036]

[0037] in Is the receiving end to The estimate, This represents the estimation error vector, whose elements follow an independent and identically distributed complex Gaussian distribution with a mean of . The covariance matrix is Equation (2) shows that the ML solution corresponds to the solution in the lattice. Mid-range The nearest point, of which , Therefore, the ML demodulation algorithm needs to traverse... All points.

[0038] The MML algorithm solves equation (2) using graph theory, which utilizes a tree structure to construct the search space for the ML demodulation algorithm. This tree contains... Each branch emanates from the root node, and these branches represent indices of the transmitting antennas. Each branch contains... There are sub-branches, each with a length of . . No. The first branch Each sub-branch is represented as a branch. , representing grid points Branch The Layer nodes and metrics Related, among which

[0039]

[0040] in Equation (3) means that the metric of a node is the sum of the metric of its parent node and an increment.

[0041] MML employs a breadth-first tree search algorithm based on a width-constrained strategy. In the... In the layers, according to Preserve ascending order One node is pruned, while the rest are trimmed. Note We represent the width set as... On the last floor (the...) The node with the smallest metric in the layer is the solution of the MML algorithm, i.e.

[0042]

[0043] in It includes reserved branches. The candidate list, . Note that when In this case, the MML algorithm is equivalent to the ML algorithm. Figure 1 shows an example of an MML tree. The The element represents the first element. The number of nodes retained in the layer (drawn in black). Therefore, the number of nodes in this MML tree is... With Compared to an ML tree with a certain number of nodes, the number of nodes is reduced. .

[0044] The literature [X. Zhang, G. Zhao, Q. Liu, N. Zhao, and M. Jin, “Enhanced M-algorithm-based maximum likelihood detectors for spatial modulation,” AEU-Int. J. Electron. Commun., vol. 70, no. 9, pp. 1361–1366, 2016] proposes a reordering technique to improve the performance of the MML algorithm. Unlike traditional MML, where the tree layers are constructed in ascending order according to the index of the receiving antenna (see Equation (3)), the reordering technique is based on element-wise... Rearrange branches in descending order of magnitude Each layer. For branches Using vectors Record the detection order of this branch. For example, The measure in equation (3) is converted to

[0045]

[0046] This reordering technique is employed in the embodiments of the present invention.

[0047] This invention discloses a layer width optimization method for demodulation of a spatial modulation system (MML), which decomposes the symbol vector error rate (SVER) performance constraint of MML into layers and introduces layer capability. Select the level that meets the requirements at each level. The minimum width of the constraint is optimized through iterative processing from the root to the leaf layer. The following section details the width optimization framework involved in the improved MML algorithm and the hierarchical performance estimation method based on the Monte Carlo method.

[0048] Definition 1: Let the symbol vector correct demodulation rate (SVCR) of ML and MML be expressed as follows: and The symbol vector error rate (SVER) of ML and MML are expressed as follows: and .therefore and Furthermore, in ML and MML They are respectively represented as and .

[0049] The SVCR of MML / ML can be represented as

[0050]

[0051] in ,event Indicates the first One transmit antenna is activated to transmit modulation symbols. 。 "This is because of the circular symmetry of PSK modulation and the consistent channel characteristics of each antenna. In this embodiment, we will..." Record .

[0052] Lemma 1: In an MML tree, for and The following two events are equivalent:

[0053] 1) ;

[0054] 2) .

[0055] Proof: When From time to time Therefore, Lemma 1 can be obtained immediately.

[0056] Using the chain rule and Lemma 1 in probability theory, we can obtain

[0057]

[0058] For ML algorithms, ML search trees do not have pruning operations. Therefore, the formula... for Established. Using (7), we can represent SVCR in the ML algorithm as follows:

[0059]

[0060] because and If we combine equation (8), then equation (9) holds true.

[0061]

[0062] For the layer, This represents the ability of the current level of the MML tree to retain the correct path. Therefore, we call it hierarchical capability (HV). The layer width for improved MML performance was determined to be...

[0063]

[0064] in It is the tolerance constant based on the SVER design, and its value is determined according to Theorem 1.

[0065] Theorem 1: Determine the layer width based on equation (10) This allows the demodulation performance of the improved MML algorithm to meet the requirements. ,in and Set as .

[0066] Proof: Using equations (7)-(10), we have

[0067]

[0068] Furthermore, there are

[0069]

[0070] Q.E.D.

[0071] To ensure that the SVER performance of the improved MML algorithm is close to that of ML, users can set... Slightly greater than 1.

[0072] Monte Carlo simulation is an effective method for solving equation (10). Figure 8 The document presents layer width optimization algorithms. For example, in S210, the Monte Carlo simulation-based ML algorithm is executed. Times. In each simulation, the number of messages sent is... After the simulation, the frequency of the correct path at each position in each level of the ML tree is recorded and calculated. Here, the positions in each level of the ML tree are sorted in ascending order of the metric value. First, the value of δ needs to be determined according to Theorem 1. The algorithm determines the width layer by layer starting from level 1. For example, in S220, the width of the kth layer is expressed by the formula... Confirmed. Among them... (The correct path is located at the...) Front The sum of the frequencies at each position), this value has already been calculated in the previous layer. This is because when When it is large enough, it can Approximately and will The approximate correct path is located at the th Front The sum of the frequencies at each position, according to Bayes' theorem

[0073] .

[0074] After that, The correct path is located at the Front The sum of the frequencies at each position. This completes the calculation of the first... Layer operations. This algorithm is used to determine the layers sequentially. .

[0075] This invention discloses a high-performance, low-complexity spatial modulation system demodulation method based on the M-algorithm. Specifically, it uses the improved MML demodulation algorithm described above to solve the problem in equation (2), constructs the search space of the ML demodulation algorithm using a tree structure, and employs a breadth-first tree search algorithm based on a width-constrained strategy. Within the layer, retain the previous values ​​in ascending order of metric values. 1 node Determined according to the layer width optimization method.

[0076] This invention also discloses a high-performance, low-complexity spatial modulation system demodulator, comprising:

[0077] The MML demodulation module is used to solve the problem described in equation (2) using the MML demodulation algorithm. It constructs the search space for the ML demodulation algorithm using a tree structure and employs a breadth-first tree search algorithm based on a width-constrained strategy. Within the layer, retain the previous values ​​in ascending order of metric values. One node;

[0078] Additionally, a layer width optimization module is used to decompose the Sign Vector Error Rate (SVER) performance constraint of MML into layers, introducing hierarchical capabilities. Select the level that meets the requirements at each level. The minimum width of the constraint is optimized by iterating from the root to the leaf layer.

[0079] This invention also discloses a computer system, including a memory, a processor, and a computer program / instructions stored in the memory and executable on the processor, wherein the computer program / instructions, when executed by the processor, implement the steps of the layer width optimization method or demodulation method.

[0080] This invention also discloses a computer-readable storage medium storing a computer program that, when executed by a processor, implements the steps of the layer width optimization method or demodulation method.

[0081] To verify the effectiveness and advantages of the embodiments of the present invention, we compared the symbol vector error rate (SVER) performance and computational complexity of the proposed improved MML (iMML) algorithm with the ML algorithm. Furthermore, we considered two other algorithms that can achieve optimal SVER performance: Sphere decoding (SD) and the minimum-distance of maximum-length (mM) algorithm. The threshold of SD has been optimized to guarantee optimal SVER performance. The comparison was conducted under three MIMO systems (underdetermined, steady-state, and oversteady-state) and two spectral efficiency conditions (…). and The experiment was conducted under different channel state information (CSI) conditions. The receive and transmit antenna ratios for underdetermined, steady-state, and over-steady-state MIMO-SM systems were 3:4, 4:4, and 5:4, respectively. In this experiment, the modulation order was... Set as Therefore, for and The number of transmitting antennas are respectively and In the case of imperfect CSI, Assumed to be .also, That is, the upper limit of the SVER ratio of iMML and ML is set to This is to ensure that the proposed iMML algorithm achieves SVER performance comparable to ML.

[0082] We compared the SVER performance of the SD, SD, mM algorithms and the proposed iMML algorithm. Figures 2 to 4 The SVER performance of the three algorithms is presented in underdetermined, steady-state, and oversteady-state MIMO-SM systems, considering perfect and imperfect CSI conditions. It can be observed that under the same scenarios, the SVER performance of all algorithms is almost identical, indicating that the proposed iMML algorithm achieves SVER performance comparable to ML. Furthermore, Figures 2 to 4 The comparison of SVER under different scenarios demonstrates the strong robustness of the proposed iMML algorithm.

[0083] We compared the computational complexity of the ML, SD, mM, and iMML algorithms. We expressed the computational complexity of the algorithms as... ,in Computational complexity is measured by the number of real-valued multiplications. Note that complex-valued multiplication requires 4 real-valued multiplications, while calculating the square of the modulus of a complex number requires 2 real-valued multiplications.

[0084] The computational complexity of the iMML algorithm can be expressed as: ,in Yes The number of real-valued multiplications required to reorder the elements, where calculating the square of the modulus of all elements of the estimated channel vector consumes [amount missing]. A real number multiplication. Therefore . This is the number of real-valued multiplications required for the tree search. For each node, the expression must be calculated. This requires 6 real-valued multiplications. According to... Figure 1 The number of nodes in the iMML tree is .therefore, .

[0085] Table 1 Computational complexity of different demodulation algorithms

[0086]

[0087] Reference [1] is [I. Al-Nahhal, E. Basar, OA Dobre, and S. Ikki, “Optimum low complexity decoder for spatial modulation,” IEEE J. Sel. AreasCommun., vol. 37, no. 9, pp. 2001–2013, 2019].

[0088] The computational complexity of different demodulation algorithms is shown in Table 1. This is a dynamic value defined in the literature [A. Younis, S. Sinanovic, M. Di Renzo, R. Mesleh, and H. Haas, “Generalised sphere decoding for spatial modulation,” IEEE Trans. Commun., vol. 61, no. 7, pp. 2805–2815, 2013]. It is worth noting that the computational complexity of ML and iMML is constant. In contrast, the computational complexity of the SD and mM algorithms is a random variable. This random complexity poses a significant obstacle to the practical implementation of SD and mM in communication systems.

[0089] Figures 5 to 7 It describes the ratio of computational complexity reduction relative to machine learning. The [signal-to-noise ratio] curves, which take into account both perfect and imperfect CSI, are compared to the [signal-to-noise ratio] curves. In all cases, the proposed iMML algorithm consistently exhibits the lowest computational complexity compared to SD and mM. In the low signal-to-noise ratio (SNR) region, the iMML algorithm shows a significant reduction in computational complexity, exceeding that of SD and mM. Compared to SD and mM, whose computational complexity reduction shows a clear upward trend with increasing SNR, iMML maintains a relatively stable reduction in computational complexity across all demonstrated SNR ranges. Figures 5 to 7 As shown, in In this case, the computational complexity reduction of the proposed iMML remains within the range of all signal-to-noise ratios. above.

Claims

1. A method for optimizing the layer width of MML demodulation, characterized in that, The Sign Vector Error Rate (SVER) performance constraint of MML is decomposed into layers, introducing hierarchical capabilities. Select the level that meets the requirements at each level. The minimum width of the constraint is optimized by iterating from the root to the leaf layer. The hierarchical capabilities The results were obtained based on offline estimation using the Monte Carlo method, including simulation using the Monte Carlo method. The ML algorithm calculates the frequency of the correct path at each position in each level of the ML tree; the positions in each level of the ML tree are sorted in ascending order of metric values; the width is determined layer by layer starting from level 1, and the width of level k is... Through formula Confirmed, among which The correct path is located at the . Front The sum of the frequencies at each position, It is a tolerance constant based on the SVER design. Set as ,in It's SVER. It refers to the number of receiving antennas. .

2. A demodulation method for a high-performance, low-complexity spatial modulation system, characterized in that, The following problem is solved using an improved MML demodulation algorithm: ， in It is a modulating constellation. It is the number of transmitting antennas. It is the receive vector. Is the receiving end to The estimate, This represents the estimation error vector. This refers to the number of receiving antennas. The MML demodulation algorithm utilizes a tree structure to construct the search space for the ML demodulation algorithm. The tree contains... There are 4 branches emanating from the root node, each representing an index of the transmitting antenna. There are sub-branches, each with a length of . The improved MML demodulation algorithm employs a breadth-first tree search algorithm based on a width-limited strategy, in the first... Within the layer, retain the previous values ​​in ascending order of metric values. The nodes, the The layer width optimization method for MML demodulation as described in claim 1 is used to determine this.

3. The demodulation method for a high-performance, low-complexity spatial modulation system according to claim 2, characterized in that, The tree in the MML demodulation algorithm is layered by element. Rearrange branches in descending order of magnitude Each floor.

4. A high-performance, low-complexity spatial modulation system demodulator, characterized in that, include: The MML demodulation module is used to solve the following problems using the MML demodulation algorithm: ， in It is a modulating constellation. It is the number of transmitting antennas. It is the receive vector. Is the receiving end to The estimate, This represents the estimation error vector. This refers to the number of receiving antennas. The MML demodulation algorithm utilizes a tree structure to construct the search space for the ML demodulation algorithm. The tree contains... There are 4 branches emanating from the root node, each representing an index of the transmitting antenna. There are sub-branches, each with a length of . The improved MML demodulation algorithm employs a breadth-first tree search algorithm based on a width-limited strategy, in the first... Within the layer, retain the previous values ​​in ascending order of metric values. Each node; The layer width optimization method for MML demodulation is determined according to claim 1; Additionally, a layer width optimization module is used to decompose the Sign Vector Error Rate (SVER) performance constraint of MML into layers, introducing hierarchical capabilities. Select the level that meets the requirements at each level. The minimum width of the constraint is optimized by iterating from the root to the leaf layer.

5. A computer system, comprising a memory, a processor, and computer programs / instructions stored in the memory and executable on the processor, characterized in that, When the computer program / instructions are executed by the processor, they implement the steps of the method according to any one of claims 1-3.

6. A computer-readable storage medium storing a computer program, characterized in that, When the computer program is executed by a processor, it implements the steps of the method according to any one of claims 1-3.

7. A computer program product comprising a computer program / instructions, characterized in that, When the computer program / instructions are executed by the processor, they implement the steps of the method according to any one of claims 1-3.

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