A method, apparatus, and equipment for analog joint coding modulation based on amplitude probability shaping.

Abstract

This invention provides an analog joint coding modulation method, apparatus, and device based on amplitude probability shaping. By deeply coupling S-K mapping coding with multi-ring constellation modulation based on amplitude probability shaping, a modulation architecture combining geometric shaping and probability shaping is constructed. The radius of each ring in the constellation diagram is jointly determined by the amplitude scaling factor and the cumulative probability. A uniform phase offset is introduced between adjacent rings to optimize the geometric layout. Then, through joint iterative optimization of S-K mapping coding parameters and constellation amplitude and phase parameters, the signal distortion ratio is maximized. Thus, without increasing system complexity, a single modulation architecture can achieve collaborative adaptive optimization of coding and modulation, significantly improving the end-to-end transmission performance of the system.

Description

Technical Field

[0001] This invention relates to the field of wireless communication technology, and in particular to an analog joint coding modulation method, apparatus, and device based on amplitude probability shaping. Background Technology

[0002] In modern wireless communication systems, digital transmission architecture has long dominated. Its technological path relies on converting continuous analog signals into discrete digital signals through sampling, quantization, and encoding before processing and transmission. However, digital communication systems have limitations in practical applications: First, the system needs to perform analog-to-digital / digital-to-analog conversion, introducing unavoidable quantization errors; second, to achieve theoretically optimal performance, highly complex encoding and decoding algorithms are often required, leading to increased system latency; third, digital systems are sensitive to channel variations, and when channel conditions exceed design limits, they are prone to "flattening effects" or "cliff effects," affecting communication reliability. These shortcomings of digital systems are particularly prominent in scenarios such as the Internet of Things (IoT) and industrial control, where low power consumption and high real-time requirements are crucial.

[0003] Theoretical studies have shown that, without signal compression or bandwidth expansion, independent and identically distributed Gaussian sources can achieve theoretically optimal performance through direct transmission via an additive white Gaussian noise channel. This conclusion provides a theoretical basis for the development of Analog Joint Source-Channel Coding (AJSCC) technology. AJSCC directly maps analog source symbols to channel waveforms through nonlinear mapping, eliminating the need for quantization and complex encoding / decoding. It achieves smooth performance degradation, avoids the "cliff effect," and possesses advantages such as low complexity and low latency, making it an important research direction for next-generation wireless communication systems.

[0004] In AJSCC, we employ the Archimedes double helix coding function (SK mapping) for efficient encoding. Since the encoded output is a discrete-time continuous symbol, these continuous symbols need to be quantized into a finite number of constellation points, i.e., modulation. Modulation design is a key technical aspect of the AJSCC system. Current analog modulation schemes are often limited by insufficient geometric degrees of freedom. For example, while Quadrature Amplitude Modulation (QAM) achieves probabilistic shaping, its constellation points are confined to a rectangular grid structure. In terms of optimization methods, probabilistic shaping and geometric shaping are often designed separately, lacking an effective coordination mechanism. Furthermore, the modulation structure is mostly static and cannot be dynamically adjusted according to channel conditions. The implementation complexity is particularly prominent. For instance, Irregular Finite Constellations (IFCs) generate optimal constellation points through iterative methods. Although theoretically they can approach optimal performance, they have high computational complexity, significant system latency, and are difficult to deploy practically. These systemic defects restrict further improvements in the performance of the AJSCC system.

[0005] In view of the above, this application is hereby submitted. Summary of the Invention

[0006] This invention discloses an analog joint coding modulation method, apparatus, and device based on amplitude probability shaping, aiming to solve the problem that the geometric shaping and probability shaping are separated in the existing analog joint source-channel coding system, the modulation structure is fixed and cannot be adaptively adjusted according to channel conditions, resulting in limited end-to-end transmission performance of the system.

[0007] The first embodiment of the present invention provides an analog joint coding modulation method based on amplitude probability shaping, comprising:

[0008] Two independent and identically distributed Gaussian analog source signal sequences are generated. The Gaussian analog source signal sequences are then fed into an SK mapping encoder for joint source-channel coding. The coded symbols are output and then divided into two signals to form a complex signal.

[0009] Based on the signal characteristics of the complex signal, a modulation design combining geometric shaping and probabilistic shaping is performed. The complex signal is mapped to a preset shaping constellation diagram according to the minimum Euclidean distance criterion to generate a symbol sequence to be transmitted. The shaping constellation diagram adopts a multi-ring structure, and the radius of each ring is determined by the amplitude scaling factor and the cumulative probability of that ring. A uniform phase offset is introduced between adjacent rings.

[0010] The symbol sequence is sent into an additive white Gaussian noise channel for transmission to obtain the received symbols;

[0011] At the receiving end, the squared Euclidean distance from the received symbol to all candidate constellation points is calculated, and the constellation point corresponding to the minimum squared Euclidean distance is selected as the estimated symbol according to the maximum likelihood decision criterion.

[0012] The estimated symbols are fed into the SK mapping decoding module, and the source estimate is recovered through inverse mapping. The end-to-end mean square error is calculated, and the SK mapping parameters and constellation parameters are jointly iteratively optimized to maximize the signal distortion ratio and obtain the optimal end-to-end transmission performance.

[0013] Preferably, the SK mapping encoder encodes the source signal in the following manner:

[0014] Through nonlinear mapping function To achieve 2:1 bandwidth compression, the source signal is mapped to a one-dimensional real number symbol, specifically as follows:

[0015]

[0016] in, The polar coordinates of the symbol are angles. The distance between the two spiral arms on the double helix, the mapping which forms an Archimedean spiral structure on the complex plane, and These are the coordinate components of the coded symbol in the Cartesian coordinate system. Pi;

[0017] Perform a nonlinear transformation on the mapped output ,in, The angular components of the encoded symbol in polar coordinates. It is a distortion factor used to control the output distribution shape, making the output signal approximate the characteristics of a Gaussian probability distribution.

[0018] Preferably, the radius of the i-th ring of the formed constellation diagram The calculation method is as follows:

[0019]

[0020] Where d is the amplitude scaling factor, The cumulative probability up to the i-th ring, the cumulative probability The calculation method is as follows:

[0021]

[0022] in, Let N be the number of constellation points on ring q, N be the number of constellation points on ring i, B be the total number of bits in the constellation diagram, and q be the ring index.

[0023] Preferably, the channel model is represented as:

[0024]

[0025] in, The sequence of symbols to be sent. It is complex Gaussian noise, with its real and imaginary parts being independent and identically distributed, both obeying a mean of zero and a variance of 1. The Gaussian distribution.

[0026] Preferably, the end-to-end mean square error is calculated as follows:

[0027]

[0028] Wherein, the signal distortion ratio t is the discrete-time index. The original source sample value at time t, Let L be the source estimate obtained by the inverse mapping at time t, and L be the length of the source signal sequence.

[0029] Preferably, the joint iterative optimization includes:

[0030] For a given channel signal-to-noise ratio, performance is evaluated under four fixed-point structures: 4 points, 8 points, 16 points, and 32 points per revolution; the amplitude scaling factor is adjusted during the evaluation. And phase shift The radius of each ring is calculated according to the radius formula of the formed constellation diagram;

[0031] For each structure, the SK mapping parameters are jointly optimized to minimize the end-to-end mean square error. The minimum mean square error of the four structures under their respective optimal parameters is compared, and the structure with the lowest number of loops corresponding to the minimum mean square error is selected as the optimal configuration for that signal-to-noise ratio. ;

[0032] Based on the aforementioned optimal configuration, a joint optimization model is established, with the objective function being:

[0033]

[0034] in, and The encoding parameters for SK mapping, is the amplitude scaling factor, is the uniform phase offset between adjacent rings, and SNR is the ratio of signal power to noise power in the channel.

[0035] Preferably, the joint optimization model is solved through the following alternating iterative steps:

[0036] Step a: Initialize parameters, set , , , The initial value, where , Set a convergence threshold and maximum number of iterations Iteration count index ;

[0037] Step b: Fix the current constellation parameters , with SK mapping parameters To optimize the variables and find the optimal solution Its expression is:

[0038]

[0039] Step c: Fix SK mapping parameters and current phase offset parameters Using the amplitude scaling factor d as the optimization variable, the optimal solution is obtained. Its expression is:

[0040]

[0041] Step d: Fix SK mapping parameters and amplitude scaling factor Phase offset parameters As an optimization variable, the optimal solution is obtained. Its expression is:

[0042]

[0043] Step e: Calculate the mean square error after this round of iterations. ,like Or the maximum number of iterations has been reached. The iteration terminates, and the joint optimal solution is output. Otherwise, Return to step b and continue execution, where, Let be the current value of the amplitude scaling factor d in the k-th iteration. The phase offset parameter in the k-th iteration The current value, The optimized and updated SK mapping distortion factor in the (k+1)th iteration. The value, This represents the optimized and updated value of the SK mapping helical arm spacing Δ in the (k+1)th iteration. Let be the current value of the amplitude scaling factor d in the (k+1)th iteration. The phase offset parameter in the (k+1)th iteration The current value.

[0044] Preferably, the optimal configuration The value is a function of the channel signal-to-noise ratio (SNR). Different optimal constellation point configurations are provided for different SNR conditions, enabling the system to achieve coordinated optimization of geometric shaping and probabilistic shaping through a single modulation architecture across the entire SNR range.

[0045] A second embodiment of the present invention provides an analog joint coding modulation apparatus based on amplitude probability shaping, comprising:

[0046] The signal source generation unit is used to generate two independent and identically distributed Gaussian analog signal source sequences; the joint coding unit sends the Gaussian analog signal source sequence into the SK mapping encoder for joint source channel coding, outputs coded symbols, and divides the coded symbols into two signals to form a complex signal;

[0047] The modulation unit is used to perform a combined geometric shaping and probability shaping modulation design based on the signal characteristics of the complex signal, and to map the complex signal to a preset shaping constellation diagram according to the minimum Euclidean distance criterion to generate a symbol sequence to be transmitted. The shaping constellation diagram adopts a multi-ring structure, and the radius of each ring is determined by the amplitude scaling factor and the cumulative probability of the ring. A uniform phase offset is introduced between adjacent rings.

[0048] The channel transmission unit is used to send the symbol sequence into the additive white Gaussian noise channel for transmission to obtain received symbols;

[0049] The decision unit is used at the receiving end to calculate the squared Euclidean distance from the received symbol to all candidate constellation points, and select the constellation point corresponding to the minimum squared Euclidean distance as the estimated symbol according to the maximum likelihood decision criterion.

[0050] The decoding optimization unit is used to send the estimated symbols into the SK mapping decoding module, recover the source estimate through inverse mapping, calculate the end-to-end mean square error, and perform joint iterative optimization of the SK mapping parameters and constellation parameters to maximize the signal distortion ratio and obtain the optimal end-to-end transmission performance.

[0051] The third embodiment of the present invention provides an analog joint coding modulation device based on amplitude probability shaping, characterized in that it includes a memory and a processor, wherein the memory stores a computer program, and the computer program can be executed by the processor to implement an analog joint coding modulation method based on amplitude probability shaping as described in any one of the above.

[0052] Based on the analog joint coding modulation method, apparatus, and device based on amplitude probability shaping provided by this invention, a modulation architecture combining geometric shaping and probability shaping is constructed by deeply coupling SK mapping coding with multi-ring constellation modulation based on amplitude probability shaping. The radius of each ring in the constellation diagram is jointly determined by the amplitude scaling factor and the cumulative probability. A uniform phase offset is introduced between adjacent rings to optimize the geometric layout. Then, by jointly iteratively optimizing the SK mapping coding parameters and the constellation amplitude and phase parameters, the signal distortion ratio is maximized. Thus, without increasing the system complexity, a single modulation architecture can achieve cooperative adaptive optimization of coding and modulation, significantly improving the end-to-end transmission performance of the system. Attached Figure Description

[0053] Figure 1 This is a flowchart illustrating an analog joint coding modulation method based on amplitude probability shaping provided in the first embodiment of the present invention;

[0054] Figure 2 This is a constellation diagram of 16 points obtained by using the scheme of this invention for the encoded signal points. ;

[0055] Figure 3 This is a system performance diagram of a 16-point constellation diagram with different numbers of concentric circles obtained by the solution provided in this invention;

[0056] Figure 4 This is a schematic diagram of a module of an analog joint coding modulation device based on amplitude probability shaping provided in the second embodiment of the present invention. Detailed Implementation

[0057] 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.

[0058] To better understand the technical solution of the present invention, the embodiments of the present invention will be described in detail below with reference to the accompanying drawings.

[0059] This invention discloses an analog joint coding modulation method, apparatus, and device based on amplitude probability shaping, aiming to solve the problem that the geometric shaping and probability shaping are separated in the existing analog joint source-channel coding system, the modulation structure is fixed and cannot be adaptively adjusted according to channel conditions, resulting in limited end-to-end transmission performance of the system.

[0060] Please see Figure 1The first embodiment of the present invention provides an analog joint coding modulation method based on amplitude probability shaping, comprising:

[0061] S101 generates two independent and identically distributed Gaussian analog source signal sequences.

[0062] The system first generates two independent and identically distributed Gaussian analog source signal sequences, denoted as source A and source B, respectively. Each source follows a sequence with a mean of 0 and a variance of 1. The standard Gaussian distribution is denoted as follows: and ,in Here, L is the discrete-time index, and L is the sequence length. In practice, two sets of random sequences of length L can be independently generated using a Gaussian random number generator, maintaining statistical independence between the two sources. and The two Gaussian source signal sequences are uncorrelated at any time t. These two sequences will serve as input to the subsequent SK mapping encoder, which will perform joint source-channel coding on them.

[0063] S102, the Gaussian analog source signal is sequentially fed into the SK mapping encoder for joint source-channel coding, outputting coded symbols, and the coded symbols are divided into two signals to form a complex signal;

[0064] The two source signals generated above and The signal is fed into the SK mapping encoder for joint source-channel coding. Specifically, the SK mapping encoder first uses a nonlinear mapping function... To achieve 2:1 bandwidth compression, two source signals are mapped to one-dimensional real-number symbols in the coded output. The calculation method is as follows: , , where θ is the signal from the source signal and The angle parameter obtained through polar coordinate transformation, Δ, represents the distance between the two spiral arms on the double helix. This mapping forms an Archimedean spiral structure in the complex plane, and θ ranges from negative infinity to positive infinity. Subsequently, a nonlinear companding transformation is performed on the mapping output to optimize the probability distribution of the encoded symbols, thus representing the angular components of the encoded symbols in polar coordinates. Transform into , where α∈(0,2] is the distortion factor. By adjusting the value of α, the output distribution shape can be controlled, so that the encoded output signal has a probability distribution characteristic that approximates Gaussian. This characteristic is beneficial for subsequent matching with the formed constellation diagram.

[0065] After the above encoding process, the SK mapping encoder outputs the encoded symbols. The encoded symbol is then split into two signals. and , forming complex signals This serves as the input for subsequent shaping and modulation design. In the actual parameter settings, Δ and α are key coding parameters for SK mapping, and their values ​​will be determined in conjunction with constellation parameters during subsequent joint iterative optimization to achieve the global optimum of system end-to-end performance.

[0066] S103, based on the signal characteristics of the complex signal, a modulation design combining geometric shaping and probability shaping is performed. The complex signal is mapped to a preset shaping constellation diagram according to the minimum Euclidean distance criterion to generate a symbol sequence to be transmitted. The shaping constellation diagram adopts a multi-ring structure, and the radius of each ring is determined by the amplitude scaling factor and the cumulative probability of the ring. A uniform phase offset is introduced between adjacent rings.

[0067] Based on the complex signal output above The signal characteristics are used for modulation design combining geometric shaping and probabilistic shaping. The shaped constellation diagram adopts a multi-ring structure, supporting various fixed point configurations per ring, including 4 points, 8 points, 16 points, and 32 points per ring, to adapt to the optimal modulation requirements under different channel conditions. The geometric structure and probability distribution of the constellation diagram are jointly designed as follows: the radius of the i-th ring... Where d is the amplitude scaling factor, Let be the cumulative probability up to the i-th ring, and the cumulative probability is calculated as follows: Where q is the ring index. Let N be the number of constellation points on ring q, N be the number of constellation points on ring i, and B be the total number of bits in the constellation diagram. This represents the total number of constellation points in the constellation map. The physical meaning of this radius formula is that the radius of each ring is determined by the inverse cumulative distribution function of the Rayleigh distribution, the amplitude scaling factor d uniformly controls the overall constellation scale, and the cumulative probability... This reflects the probability mass distribution from the inner ring to the outer ring, resulting in denser constellation points in the inner ring and sparser constellation points in the outer ring, thus achieving probability shaping. Simultaneously, to optimize the geometric layout, a uniform phase shift is introduced between adjacent rings. This causes the constellation points on adjacent rings to be staggered in the angular direction, increasing the minimum Euclidean distance between constellation points on different rings and further improving modulation performance. Please refer to... Figure 2 To illustrate with a specific example, when the total number of constellation points is 16 and a configuration of 4 points per ring is used, the constellation diagram has 4 rings, with 4 constellation points evenly distributed on each ring. The cumulative probability and baseline theoretical radius of each ring are as follows: The cumulative probability of ring 1... The cumulative probability of ring 2 The cumulative probability of ring 3 The cumulative probability of ring 4 With an initial amplitude scaling factor of d=1, the reference radius of each ring can be calculated. During modulation, the complex signal is calculated according to the minimum Euclidean distance criterion. The Euclidean distances to all constellation points in the formed constellation diagram are used to map the complex signal to the nearest constellation point, generating a symbol sequence to be transmitted. This serves as the input for subsequent channel transmission. It should be noted that the amplitude scaling factor d and the phase offset... The specific value will be determined in conjunction with the SK mapping coding parameters in subsequent joint iterative optimizations, and the optimal configuration of the number of points per round will also be selected in subsequent performance comparisons based on the channel signal-to-noise ratio conditions.

[0068] S104, the symbol sequence is sent into an additive white Gaussian noise channel for transmission to obtain the received symbol;

[0069] The generated symbol sequence to be sent It is transmitted through an additive white Gaussian noise channel. The channel model is represented as follows: ,in For symbolic sequence The k-th transmitted symbol in the sequence, For the corresponding received symbol, It is complex Gaussian noise, with its real and imaginary parts being independent and identically distributed, both obeying a mean of zero and a variance of 1. The channel model reflects the additive thermal noise interference experienced by the signal during transmission in a real wireless communication environment. The noise power is determined by the variance. Channel quality is determined by the signal-to-noise ratio (SNR), which is the ratio of the average power of transmitted symbols to the noise power. Under different SNR conditions, the degree of noise interference on transmitted symbols varies; a higher SNR results in less noise interference and better reception of received symbols. The closer to the original transmitted symbol Conversely, the greater the deviation of the received symbol from the transmitted symbol, the more it directly affects the accuracy of subsequent receiver decisions and source recovery. The received symbol obtained after channel transmission... It will be used as input for the decision processing.

[0070] S105, at the receiving end, calculate the squared Euclidean distance from the received symbol to all candidate constellation points, and select the constellation point corresponding to the minimum squared Euclidean distance as the estimated symbol according to the maximum likelihood decision criterion.

[0071] Specifically, for each received symbol This requires traversing all candidate constellation points in the formed constellation diagram and calculating the squared Euclidean distance between the received symbol and each candidate constellation point. The calculation method is as follows: ,in The received symbol after transmission through the channel. For the i-th candidate constellation point in the formed constellation diagram, Indicates received symbol With the i-th candidate constellation point The squared Euclidean distance between the received symbol and all candidate constellation points. After calculating the squared Euclidean distances from the received symbol to all candidate constellation points, a hard decision is made according to the maximum likelihood criterion. Since the maximum likelihood decision is equivalent to the minimum Euclidean distance decision in an additive white Gaussian noise channel, the constellation point that minimizes the squared Euclidean distance is selected from all candidate constellation points as the estimate of the transmitted symbol. The decision expression is: That is, all candidate constellation points Search Engine The smallest constellation point is used as the estimation symbol. Output. This decision-making process essentially involves finding the closest legal constellation point in the observation space after the received symbol has been disturbed by noise, and determining it as the most likely transmitted symbol. In actual computation, for a total of constellation points... The formed constellation diagram requires calculation for each receiving symbol. By comparing the squared Euclidean distances, a ring-based search strategy can be used to reduce computational complexity when the number of constellation points is large. This involves first determining the probability ring neighborhood of the received symbol based on its amplitude, and then performing a fine-grained search on the constellation points within that neighborhood. This reduces computational load while ensuring decision accuracy. The estimated symbol output after decision processing... The signal will be sent to the SK mapping and decoding module in step S6 for inverse mapping to recover the original source signal.

[0072] S106, the estimated symbol is sent to the SK mapping decoding module, the source estimate is recovered through inverse mapping, the end-to-end mean square error is calculated, and the SK mapping parameters and constellation parameters are jointly iteratively optimized to maximize the signal distortion ratio in order to obtain the optimal end-to-end transmission performance.

[0073] The estimated sign of the output The data is fed into the SK mapping decoding module, where the inverse function of the SK mapping is used to recover the estimate of the original Gaussian source. and The end-to-end mean square error of the system is calculated by comparing the original source and the recovered source. The calculation method is as follows: Where L is the length of the source signal sequence, t is the discrete-time index, and S(t) is the original source sample value at time t. The source estimate is obtained by inverse mapping at time t. The signal distortion ratio is used as the source estimate. As an evaluation indicator of system performance, a larger SDR value indicates better end-to-end transmission performance.

[0074] Based on this, the SK mapping parameters and constellation parameters are jointly iteratively optimized to maximize SDR. This optimization process consists of two stages. The first stage is to determine the optimal configuration of constellation points per ring. For a given channel signal-to-noise ratio (SNR), where SNR represents the ratio of signal power to noise power in the channel, performance evaluation and parameter optimization are performed under four fixed ring point structures: 4 points per ring, 8 points per ring, 16 points per ring, and 32 points per ring. During the evaluation, the amplitude scaling factor d=1 and the phase offset φ=0, and the radius of each ring is based on the radius formula of the formed constellation diagram. The calculations were performed to jointly optimize the SK mapping coding parameters α and Δ for each loop structure, minimizing the end-to-end mean square error of the system. Finally, the minimum mean square error values ​​obtained by the four structures under their respective optimal SK mapping coding parameters were compared, and the loop structure with the minimum mean square error was selected as the optimal number of loops per loop configuration for that signal-to-noise ratio. This stage revealed a key principle: the optimal constellation structure is a function of the channel signal-to-noise ratio (SNR), with different optimal constellation point configurations per ring under different SNR conditions. This principle provides a structural foundation for subsequent deep joint optimization. Please refer to... Figure 3 To illustrate with a specific example, within a channel signal-to-noise ratio (SNR) range of 0 to 35 dB, three constellation diagram structures were set up: 4 points per cycle, 8 points per cycle, and 16 points per cycle. Using the theoretical radius formula and an initial state without phase offset, the SK mapping parameters α and Δ were jointly optimized to minimize end-to-end distortion. The minimum MSE values ​​of the three structures under their respective optimal coding parameters were compared. The results show that the configuration with 4 points per cycle has the best performance within this SNR range.

[0075] The second stage involves deep joint optimization based on the optimal constellation structure, using the optimal number of points per orbit determined in the first stage. A joint optimization model is established for SK coding parameters, constellation amplitude parameters, and phase parameters. The optimization objective is to achieve the global minimum of end-to-end distortion by coordinating the adjustment of all parameters under the conditions of optimal constellation structure and given average transmit power constraints. The objective function is: Here, α and Δ are the coding parameters of the SK mapping, d is the amplitude scaling factor, and φ is the uniform phase offset between adjacent rings. d and φ are the key optimization parameters for amplitude and phase. An alternating iterative algorithm is used to solve this joint optimization model. First, initialization is performed, setting the initial values ​​of the SK mapping coding parameters α and Δ, the initial value of the amplitude scaling factor d to 1, and the initial value of the phase offset φ to 0. A convergence threshold is also set. Given the maximum number of iterations Kmax, let the iteration index k=0. Then perform three alternating optimization steps: First, fix the magnitude scaling factor of the current k-th iteration. and phase shift The parameters remain unchanged, where the superscript (k) represents the parameter value corresponding to the k-th iteration. Using the SK mapping encoding parameters α and Δ as optimization variables, the optimal value that minimizes the end-to-end mean square error is found, i.e.:

[0076] The superscript (k+1) indicates the parameter value after this round of optimization and update; the second step is to fix the SK mapping parameters obtained in the first step. Phase offset parameters of the current round Keeping the amplitude scaling factor d constant, we solve for the optimal amplitude scaling factor, i.e.:

[0077] The third step is to fix the SK mapping parameters obtained in the first step. The amplitude scaling factor obtained in the second step Keeping the phase offset parameter φ constant, we solve for the optimal phase offset, i.e. After completing the above three optimization steps, calculate the overall mean square error of the system after this iteration. If the absolute value of the difference between the mean square errors of two adjacent rounds satisfies If the number of iterations has reached the maximum number of iterations Kmax, the iteration terminates, and the joint optimal solution under the current signal-to-noise ratio (SNR) and the optimal number of loop points is output. The superscript * indicates the optimal value after iterative convergence; otherwise, let k = k + 1 and return to continue executing the alternating optimization loop. Through the above joint iterative optimization, independent optimization is achieved at different signal-to-noise ratio points, realizing deep coupling between coding parameters and modulation parameters at the parameter level. This overcomes the defect of the separation between geometric shaping and probabilistic shaping in traditional schemes, enabling the system to achieve near-global optimal end-to-end transmission performance and adaptive capability across the entire signal-to-noise ratio range without increasing redundancy or architectural complexity, using only a single modulation architecture.

[0078] Please see Figure 4 The second embodiment of the present invention provides an analog joint coding modulation apparatus based on amplitude probability shaping, comprising:

[0079] The signal source generation unit 201 is used to generate two independent and identically distributed Gaussian analog signal source sequences;

[0080] The joint coding unit 202 sends the Gaussian analog source signal sequentially into the SK mapping encoder for joint source-channel coding, outputs coded symbols, and divides the coded symbols into two signals to form a complex signal;

[0081] The modulation unit 203 is used to perform a combined geometric shaping and probability shaping modulation design based on the signal characteristics of the complex signal, and to map the complex signal to a preset shaping constellation diagram according to the minimum Euclidean distance criterion to generate a symbol sequence to be transmitted. The shaping constellation diagram adopts a multi-ring structure, and the radius of each ring is determined by the amplitude scaling factor and the cumulative probability of the ring. A uniform phase offset is introduced between adjacent rings.

[0082] The channel transmission unit 204 is used to send the symbol sequence into the additive white Gaussian noise channel for transmission to obtain received symbols;

[0083] The decision unit 205 is used at the receiving end to calculate the squared Euclidean distance from the received symbol to all candidate constellation points, and select the constellation point corresponding to the minimum squared Euclidean distance as the estimated symbol according to the maximum likelihood decision criterion.

[0084] The decoding optimization unit 206 is used to send the estimated symbol into the SK mapping decoding module, recover the source estimate through inverse mapping, calculate the end-to-end mean square error, and perform joint iterative optimization of the SK mapping parameters and constellation parameters to maximize the signal distortion ratio and obtain the optimal end-to-end transmission performance.

[0085] The third embodiment of the present invention provides an analog joint coding modulation device based on amplitude probability shaping, characterized in that it includes a memory and a processor, wherein the memory stores a computer program, and the computer program can be executed by the processor to implement an analog joint coding modulation method based on amplitude probability shaping as described in any one of the above.

[0086] Based on the analog joint coding modulation method, apparatus, and device based on amplitude probability shaping provided by this invention, a modulation architecture combining geometric shaping and probability shaping is constructed by deeply coupling SK mapping coding with multi-ring constellation modulation based on amplitude probability shaping. The radius of each ring in the constellation diagram is jointly determined by the amplitude scaling factor and the cumulative probability. A uniform phase offset is introduced between adjacent rings to optimize the geometric layout. Then, by jointly iteratively optimizing the SK mapping coding parameters and the constellation amplitude and phase parameters, the signal distortion ratio is maximized. Thus, without increasing the system complexity, a single modulation architecture can achieve cooperative adaptive optimization of coding and modulation, significantly improving the end-to-end transmission performance of the system.

[0087] Exemplary examples show that the computer program described in the third and fourth embodiments of the present invention can be divided into one or more modules, which are stored in the memory and executed by the processor to complete the present invention. The one or more modules can be a series of computer program instruction segments capable of performing specific functions, which describe the execution process of the computer program in implementing an analog joint coding modulation device based on amplitude probability shaping. For example, the apparatus described in the second embodiment of the present invention.

[0088] The processor referred to can be a Central Processing Unit (CPU), or other general-purpose processors, digital signal processors (DSPs), application-specific integrated circuits (ASICs), field-programmable gate arrays (FPGAs), or other programmable logic devices, discrete gate or transistor logic devices, discrete hardware components, etc. The general-purpose processor can be a microprocessor or any conventional processor. This processor is the control center of the analog joint coding modulation method based on amplitude probability shaping, connecting various parts of the method through various interfaces and lines.

[0089] The memory can be used to store the computer program and / or modules. The processor implements various functions of an analog joint coding modulation method based on amplitude probability shaping by running or executing the computer program and / or modules stored in the memory and calling the data stored in the memory. The memory may mainly include a program storage area and a data storage area. The program storage area may store the operating system, at least one application program required for a function (such as sound playback function, text conversion function, etc.), etc.; the data storage area may store data created according to the use of the mobile phone (such as audio data, text message data, etc.). In addition, the memory may include high-speed random access memory, and may also include non-volatile memory, such as hard disk, memory, plug-in hard disk, smart media card (SMC), secure digital (SD) card, flash card, at least one disk storage device, flash memory device, or other volatile solid-state storage device.

[0090] If the implemented module is implemented as a software functional unit and sold or used as an independent product, it can be stored in a computer-readable storage medium. Based on this understanding, all or part of the processes in the above embodiments of the present invention can also be implemented by a computer program instructing related hardware. The computer program can be stored in a computer-readable storage medium, and when executed by a processor, it can implement the steps of the various method embodiments described above. The computer program includes computer program code, which can be in the form of source code, object code, executable files, or certain intermediate forms. The computer-readable medium can include: any entity or device capable of carrying the computer program code, recording media, USB flash drives, portable hard drives, magnetic disks, optical disks, computer memory, read-only memory (ROM), random access memory (RAM), electrical carrier signals, telecommunication signals, and software distribution media, etc. It should be noted that the content included in the computer-readable medium can be appropriately added or removed according to the requirements of legislation and patent practice in the jurisdiction. For example, in some jurisdictions, according to legislation and patent practice, computer-readable media do not include electrical carrier signals and telecommunication signals.

[0091] It should be noted that the device embodiments described above are merely illustrative. The units described as separate components may or may not be physically separate, and the components shown as units may or may not be physical units; that is, they may be located in one place or distributed across multiple network units. Some or all of the modules can be selected to achieve the purpose of this embodiment according to actual needs. Furthermore, in the accompanying drawings of the device embodiments provided by this invention, the connection relationships between modules indicate that they have communication connections, which can be specifically implemented as one or more communication buses or signal lines. Those skilled in the art can understand and implement this without any creative effort.

[0092] The above description is merely a preferred embodiment of the present invention, but the scope of protection of the present invention is not limited thereto. Any variations or substitutions that can be easily conceived by those skilled in the art within the technical scope disclosed in the present invention should be included within the scope of protection of the present invention. Therefore, the scope of protection of the present invention should be determined by the scope of the claims.

Claims

1. An analog joint coding modulation method based on amplitude probability shaping, characterized in that, include: Generate two independent and identically distributed Gaussian analog source signal sequences; The Gaussian analog source signal sequence is fed into an SK mapping encoder for joint source-channel coding, outputting coded symbols. These coded symbols are then divided into two signals to form a complex signal. The SK mapping encoder encodes the source signal in the following manner: Through nonlinear mapping function To achieve 2:1 bandwidth compression, the two Gaussian analog source signal sequences are mapped to one-dimensional real-number symbols, specifically as follows: in, The polar coordinates of the symbol are angles. The distance between the two spiral arms on the double helix, the mapping which forms an Archimedean spiral structure on the complex plane, and These are the coordinate components of the coded symbol in the Cartesian coordinate system. Pi; Perform nonlinear transformation on the mapped output ,in, The angular components of the encoded symbol in polar coordinates. It is a distortion factor used to control the output distribution shape, making the output signal approximate the characteristics of a Gaussian probability distribution; Based on the signal characteristics of the complex signal, a modulation design combining geometric shaping and probabilistic shaping is performed. The complex signal is mapped to a preset shaping constellation diagram according to the minimum Euclidean distance criterion to generate a symbol sequence to be transmitted. The shaping constellation diagram adopts a multi-ring structure, and the radius of each ring is determined by the amplitude scaling factor and the cumulative probability of that ring. A uniform phase offset is introduced between adjacent rings. The symbol sequence is sent into an additive white Gaussian noise channel for transmission to obtain the received symbols; At the receiving end, the squared Euclidean distance from the received symbol to all candidate constellation points is calculated, and the constellation point corresponding to the minimum squared Euclidean distance is selected as the estimated symbol according to the maximum likelihood decision criterion. The estimated symbols are fed into the SK mapping decoding module, and the source estimate is recovered through inverse mapping. The end-to-end mean square error is calculated, and the SK mapping parameters and constellation parameters are jointly iteratively optimized to maximize the signal distortion ratio and obtain the optimal end-to-end transmission performance.

2. The analog joint coding modulation method based on amplitude probability shaping according to claim 1, characterized in that, The radius of the i-th ring of the formed constellation diagram The calculation method is as follows: Where d is the amplitude scaling factor, The cumulative probability up to the i-th ring, the cumulative probability The calculation method is as follows: in, Let N be the number of constellation points on ring q, N be the number of constellation points on ring i, B be the total number of bits in the constellation diagram, and q be the ring index.

3. The analog joint coding modulation method based on amplitude probability shaping according to claim 1, characterized in that, The received symbol Represented as: in, The sequence of symbols to be sent. It is complex Gaussian noise, with its real and imaginary parts being independent and identically distributed, both obeying a mean of zero and a variance of 1. The Gaussian distribution.

4. The analog joint coding modulation method based on amplitude probability shaping according to claim 1, characterized in that, The end-to-end mean square error is calculated as follows: Wherein, the signal distortion ratio t is the discrete-time index. The original source sample value at time t, Let L be the source estimate obtained by the inverse mapping at time t, and L be the length of the source signal sequence.

5. The analog joint coding modulation method based on amplitude probability shaping according to claim 2, characterized in that, The joint iterative optimization includes: For a given channel signal-to-noise ratio, performance is evaluated under four fixed-point structures: 4 points, 8 points, 16 points, and 32 points per revolution; the amplitude scaling factor is adjusted during the evaluation. And phase shift The radius of each ring is calculated according to the radius formula of the formed constellation diagram; For each structure, the SK mapping parameters are jointly optimized to minimize the end-to-end mean square error. The minimum mean square error of the four structures under their respective optimal parameters is compared, and the structure with the lowest number of loops corresponding to the minimum mean square error is selected as the optimal configuration for that signal-to-noise ratio. ; Based on the aforementioned optimal configuration, a joint optimization model is established, with the objective function being: in, SK mapping distortion factor, SK represents the pitch of the helical arms. is the amplitude scaling factor, is the uniform phase offset between adjacent rings, and SNR is the ratio of signal power to noise power in the channel.

6. The analog joint coding modulation method based on amplitude probability shaping according to claim 5, characterized in that, The joint optimization model is solved through the following alternating iterative steps: Step a: Initialize parameters, set , , , The initial value, where , Set a convergence threshold and maximum number of iterations Iteration count index ; Step b: Fix the current constellation parameters , with SK mapping parameters To optimize the variables and find the optimal solution Its expression is: Step c: Fix SK mapping parameters and current phase offset parameters Using the amplitude scaling factor d as the optimization variable, the optimal solution is obtained. Its expression is: Step d: Fix SK mapping parameters and amplitude scaling factor Phase offset parameters As an optimization variable, the optimal solution is obtained. Its expression is: Step e: Calculate the mean square error after this round of iterations. ,like Or the maximum number of iterations has been reached. The iteration terminates, and the joint optimal solution is output. Otherwise, Return to step b and continue execution, where, Let be the current value of the amplitude scaling factor d in the k-th iteration. The phase offset parameter in the k-th iteration The current value, The optimized and updated SK mapping distortion factor in the (k+1)th iteration. The value, This represents the optimized and updated value of the SK mapping helical arm spacing Δ in the (k+1)th iteration. Let be the current value of the amplitude scaling factor d in the (k+1)th iteration. The phase offset parameter in the (k+1)th iteration The current value.

7. The analog joint coding modulation method based on amplitude probability shaping according to claim 5, characterized in that, The optimal configuration The value is a function of the channel signal-to-noise ratio (SNR). Different optimal constellation point configurations are provided for different SNR conditions, enabling the system to achieve coordinated optimization of geometric shaping and probabilistic shaping through a single modulation architecture across the entire SNR range.

8. An analog joint coding modulation device based on amplitude probability shaping, characterized in that, include: The signal source generation unit is used to generate two independent and identically distributed Gaussian analog signal source sequences. The joint coding unit feeds the Gaussian analog source signal sequence into the SK mapping encoder for joint source-channel coding, outputs coded symbols, and divides the coded symbols into two signals to form a complex signal. The SK mapping encoder encodes the source signal in the following manner: Through nonlinear mapping function To achieve 2:1 bandwidth compression, the two Gaussian analog source signal sequences are mapped to one-dimensional real-number symbols, specifically as follows: in, The polar coordinates of the symbol are angles. The distance between the two spiral arms on the double helix, the mapping which forms an Archimedean spiral structure on the complex plane, and These are the coordinate components of the coded symbol in the Cartesian coordinate system. Pi; Perform nonlinear transformation on the mapped output ,in, The angular components of the encoded symbol in polar coordinates. It is a distortion factor used to control the output distribution shape, making the output signal approximate the characteristics of a Gaussian probability distribution; The modulation unit is used to perform a combined geometric shaping and probability shaping modulation design based on the signal characteristics of the complex signal, and to map the complex signal to a preset shaping constellation diagram according to the minimum Euclidean distance criterion to generate a symbol sequence to be transmitted. The shaping constellation diagram adopts a multi-ring structure, and the radius of each ring is determined by the amplitude scaling factor and the cumulative probability of the ring. A uniform phase offset is introduced between adjacent rings. The channel transmission unit is used to send the symbol sequence into the additive white Gaussian noise channel for transmission to obtain received symbols; The decision unit is used at the receiving end to calculate the squared Euclidean distance from the received symbol to all candidate constellation points, and select the constellation point corresponding to the minimum squared Euclidean distance as the estimated symbol according to the maximum likelihood decision criterion. The decoding optimization unit is used to send the estimated symbols into the SK mapping decoding module, recover the source estimate through inverse mapping, calculate the end-to-end mean square error, and perform joint iterative optimization of the SK mapping parameters and constellation parameters to maximize the signal distortion ratio and obtain the optimal end-to-end transmission performance.

9. An analog joint coding modulation device based on amplitude probability shaping, characterized in that, The system includes a memory and a processor, wherein the memory stores a computer program that can be executed by the processor to implement an analog joint coding modulation method based on amplitude probability shaping as described in any one of claims 1 to 7.

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