A high-order QAM blind equalization method based on cognitive communication system

Abstract

Embodiments of the present application relate to the technical field of channel blind equalization, and particularly to a high-order QAM blind equalization method based on a cognitive communication system, comprising: constructing a system model of the cognitive communication system, the cognitive communication system using high-order QAM modulation; constructing a cost function for the first phase of the cognitive communication system under a high-order QAM modulation channel and an iterative formula for blind equalization in the first phase, optimizing the blind equalizer to optimize and minimize the cost function of the first phase; determining a switching threshold, and switching to the second phase when the function value of the cost function of the first phase is less than or equal to the switching threshold; constructing a cost function for the second phase of the cognitive communication system under a high-order QAM modulation channel and an iterative formula for blind equalization in the second phase, optimizing the blind equalizer to optimize and minimize the cost function of the second phase. This method effectively improves the convergence stability, convergence speed, and equalization quality of high-order QAM blind equalization.

Description

Technical Field

[0001] The embodiments of the present application relate to the technical field of channel blind equalization, and in particular to a high-order QAM blind equalization method based on a cognitive communication system. Background Art

[0002] Cognitive communication is a major future development trend in communications technology. In cognitive communication systems, if the duration of a signal transmission is less than the temporal dispersion of multipath propagation, the received signal will be subject to inter-symbol interference (ISI). Channel equalizers can effectively reduce ISI. Traditional channel equalizers require the use of predetermined training sequences, which consumes valuable spectrum resources. Therefore, it is necessary to reduce the need for training sequences, especially in non-cooperative communications where suitable training sequences are unavailable.

[0003] Due to the aforementioned drawbacks of training-based methods, blind equalization (BE), which does not require a training sequence, has garnered considerable attention. Theoretically, in cooperative communications, BE can fully utilize channel bandwidth and improve transmission efficiency. In particular, since BE does not require any training sequences, it may be the only applicable method for overcoming ISI in non-cooperative communications. However, BE suffers from slow convergence, high computational complexity, and a tendency to fall into local minima, resulting in poor equalization.

[0004] High-order Quadrature Amplitude Modulation (QAM) signals are widely used in communication systems due to their high spectral efficiency. However, due to inherent issues with BE, applying classic BE to high-order QAM also suffers from slow convergence, high computational complexity, and low equalization accuracy. Therefore, designing efficient BE for high-order QAM systems is crucial.

[0005] In the BE problem, an exhaustive search method (ESM) is often used to find local optimal solutions, or even global optimal solutions. When ESM and BE use the same received samples, BE can theoretically achieve the same equalization accuracy as training-based methods. Unlike training-based methods that only use received samples from the training sequence, BE utilizes all received samples to achieve optimal equalization performance. However, due to its high computational complexity, ESM is not suitable for practical communication applications. Therefore, one of the core goals of improving BE is to combine an efficient and computationally efficient method to find local optimal solutions.

[0006] BE techniques based on attribute recovery methods can overcome the combinatorial explosion problem inherent in classic BE techniques. Commonly used algorithms include the Constant Modulus Algorithm (CMA), the Multiple Mode Adaptive (MMA), and the Soft Decision Directed Algorithm (SDDA). CMA and MMA have low complexity and good convergence, making them frequently used to solve the BE problem. These methods reduce the number of combinations by combining the discrete states of each transmitted symbol. In a 4-QAM signal, the modulus remains constant regardless of the signal state. If there are 1000 samples, there is only one possible modulus value for the transmitted signal. However, when CMA and MMA are applied to high-order constellation systems, their performance degrades significantly because they only utilize partial information about the constellation points, leading to misalignment. Furthermore, these adaptive methods use small step sizes, resulting in slow convergence. Compared to CMA and MMA, SDDA can significantly reduce steady-state misalignment and improve convergence speed to a certain extent. However, when SDDA is applied to high-order QAM systems, its cost function becomes highly nonconvex and contains too many local minima, resulting in poor convergence performance. Furthermore, its computational complexity increases with the order. To overcome these shortcomings, some studies have adopted two-stage algorithms (dual-model algorithms), such as the dual-mode generalized Zoto algorithm, the sinusoidal constellation matching error minimization algorithm, CMA, and the radius-directed hybrid algorithm. In the first stage, traditional CMA is used to reduce local minima and ensure stable convergence. When the error level in the first stage is low, a decision-directed algorithm is further utilized to improve equalization performance. The switching threshold is a key parameter in these two-stage algorithms. If the algorithm switches to the decision-directed algorithm too early, it may not converge. If it switches to the decision-directed algorithm too late, it will converge slowly and incur high computational costs. Currently proposed algorithms fail to provide a suitable switching threshold. Therefore, it is necessary to provide a reliable and achievable switching threshold for the two-stage BE algorithm. Summary of the Invention

[0007] To solve the above technical problems, the embodiments of the present application propose a high-order QAM blind equalization method based on a cognitive communication system, aiming to improve the convergence stability, convergence speed and equalization quality of high-order QAM blind equalization, reduce the computational complexity, and thus effectively improve the communication quality of the cognitive communication system.

[0008] In order to achieve the above-mentioned purpose, an embodiment of the present application proposes a high-order QAM blind equalization method based on a cognitive communication system, which is applicable to the cognitive communication system and is characterized in that the method includes the following steps: constructing a system model of the cognitive communication system, the cognitive communication system adopting high-order QAM modulation; constructing the cost function of the first stage under the high-order QAM modulation channel of the cognitive communication system according to the MMA-MLSM algorithm, constructing the iterative formula of the blind equalization of the first stage under the high-order QAM modulation channel according to the Newton method, optimizing the blind equalizer based on the iterative formula of the blind equalization of the first stage to make it optimal and minimize the cost function of the first stage; determining the switching threshold based on the blind equalization output, and switching to the second stage when the function value of the cost function of the first stage is less than or equal to the switching threshold; constructing the cost function of the second stage under the high-order QAM modulation channel of the cognitive communication system according to the ISDDA-MLSM algorithm, constructing the iterative formula of the blind equalization of the second stage under the high-order QAM modulation channel according to the Newton method, optimizing the blind equalizer based on the iterative formula of the blind equalization of the second stage to make it optimal and minimize the cost function of the second stage, thereby realizing high-order QAM blind equalization of the cognitive communication system.

[0009] In order to achieve the above-mentioned purpose, an embodiment of the present application also proposes a high-order QAM blind equalization system based on a cognitive communication system, the system comprising: a model construction module, a first-stage optimization module, a switching module and a second-stage optimization module; the model construction module is used to construct a system model of the cognitive communication system, the cognitive communication system adopts high-order QAM modulation; the first-stage optimization module is used to construct a first-stage cost function of a high-order QAM modulation channel of the cognitive communication system according to the MMA-MLSM algorithm, construct an iterative formula of blind equalization of the first stage under the high-order QAM modulation channel according to the Newton method, and optimize the iterative formula of blind equalization based on the first stage The blind equalizer optimizes and minimizes the cost function of the first stage; the switching module is used to determine the switching threshold based on the blind equalization output, and switch to the second stage when the function value of the cost function of the first stage is less than or equal to the switching threshold; the second stage optimization module is used to construct the cost function of the second stage under the high-order QAM modulation channel of the cognitive communication system according to the ISDDA-MLSM algorithm, construct the iterative formula of the blind equalization of the second stage under the high-order QAM modulation channel according to the Newton method, and optimize the blind equalizer based on the iterative formula of the blind equalization of the second stage to optimize it and minimize the cost function of the second stage, thereby realizing high-order QAM blind equalization of the cognitive communication system.

[0010] In order to achieve the above-mentioned purpose, an embodiment of the present application also provides an electronic device, which includes: at least one processor; and a memory communicatively connected to the at least one processor; wherein the memory stores instructions that can be executed by the at least one processor, and the instructions are executed by the at least one processor so that the at least one processor can execute a high-order QAM blind equalization method based on a cognitive communication system as described above.

[0011] In order to achieve the above-mentioned purpose, an embodiment of the present application further provides a computer-readable storage medium storing a computer program. When the computer program is executed by a processor, it can implement the above-mentioned high-order QAM blind equalization method based on a cognitive communication system.

[0012] The embodiments of the present application propose a high-order QAM blind equalization method based on a cognitive communication system. First, a system model of the cognitive communication system is constructed. The cognitive communication system uses high-order QAM modulation. A cost function for the first stage of the cognitive communication system under a high-order QAM modulation channel is constructed based on the MMA-MLSM algorithm. An iterative formula for blind equalization in the first stage of the high-order QAM modulation channel is constructed based on the Newton method. Based on the iterative formula for blind equalization in the first stage, the blind equalizer is optimized to achieve optimality and minimize the cost function of the first stage. Because the single constant modulus used in MMA is not equal to the multimodal value of the output signal, even if the equalizer fully converges, the output error level in the steady state will be large, thereby affecting the performance of the equalizer. Therefore, the present application determines a switching threshold based on the blind equalization output and promptly switches to the second stage. In the second stage, a cost function for the second stage of the cognitive communication system under a high-order QAM modulation channel is constructed based on the ISDDA-MLSM algorithm. Based on the Newton method, an iterative formula for blind equalization in the second stage of the high-order QAM modulation channel is constructed. Based on the iterative formula for blind equalization in the second stage, the blind equalizer is optimized to achieve optimality and minimize the cost function of the second stage, thereby achieving high-order QAM blind equalization in the cognitive communication system. It effectively reduces the computational complexity, improves the convergence stability, convergence speed and equalization quality of high-order QAM blind equalization, and thus effectively improves the communication quality of the cognitive communication system.

[0013] Optionally, constructing a system model of a cognitive communication system includes: denoting a channel order as L, denoting a sequence a(n) as a QAM modulated signal obeying an independent and identical distribution, and sending a(n) through a linear system with an impulse response h(n);

[0014] The blind equalization input is expressed by the following formula:

[0015]

[0016] Where v(n) is complex additive Gaussian white noise with a mean of 0 and a variance of

[0017] Let the channel order be The impulse response of the linear blind equalizer is:

[0018]

[0019] The blind equalization output is expressed by the following formula:

[0020]

[0021] Optionally, constructing a first-stage cost function of a high-order QAM modulation channel of a cognitive communication system according to an MMA-MLSM algorithm, constructing an iterative formula for blind equalization of the first stage under the high-order QAM modulation channel according to a Newton method, and optimizing a blind equalizer based on the iterative formula for blind equalization of the first stage to achieve an optimal result and minimize the cost function of the first stage, including:

[0022] The cost function of the first stage is expressed as follows:

[0023]

[0024] Where R is a preset constant, N is the total number of available samples, Re(·) means taking the real part, Im(·) means taking the imaginary part, represents the cost function of the first stage;

[0025] make right Derivatively, we get the gradient of the cost function in the first stage. The gradient of the cost function in the first stage is expressed by the formula:

[0026]

[0027] Among them, sign(·) is the sign function, is the sample matrix;

[0028] By letting Approximately equal to 0, we get:

[0029]

[0030] Where k is the number of iterations;

[0031] The approximate least squares solution of BE is:

[0032]

[0033] The iterative formula for the first stage of blind equalization is obtained as follows:

[0034]

[0035] in,

[0036] Optionally, determining a switching threshold based on a blind equalization output includes:

[0037] The cost function of the first stage is converted into the error function of the blind equalization output. The error function of the blind equalization output is expressed by the formula: in, A function representing the error of the blind equalization output, obeys the normal distribution, The probability density function is N(0,σ 2 );

[0038] when becomes When , the BE process enters the decision-oriented mode, and the error is σ th , the cost function of the first stage is written as:

[0039] The corresponding decision error probability should satisfy: p{|C|>2}=α th , p{|C|>2} represents the probability of decision error, α th A threshold indicating the probability of decision error;

[0040] remember is a standard normal random variable, and its probability distribution function is When α th = -2 / α, p{|C|>2}=α th Based on this, the switching threshold is

[0041] Optionally, constructing a cost function of the second stage of the cognitive communication system under a high-order QAM modulation channel according to the ISDDA-MLSM algorithm, constructing an iterative formula for blind equalization of the second stage under the high-order QAM modulation channel according to the Newton method, and optimizing the blind equalizer based on the iterative formula for blind equalization of the second stage to make it optimal and minimize the cost function of the second stage, including:

[0042] For high-order QAM signals, soft decisions are made on the real and imaginary parts of the output of the blind equalizer to obtain the cost function of the second stage. The cost function of the second stage is expressed as follows:

[0043]

[0044] Among them, R p and I q are preset constants. represents the cost function of the second stage;

[0045] make right Derivatively, we get the gradient of the cost function in the second stage. The gradient of the cost function in the second stage is expressed by the formula:

[0046]

[0047] in, Represents the gradient of the cost function of the second stage;

[0048] make And 1 / 2σ 2 Ignore, you can Simplified to:

[0049] The iterative formula for the first stage of blind equalization is obtained as follows:

[0050]

[0051] Optionally, after optimizing the blind equalizer based on the iterative formula of the blind equalization in the second stage to make it optimal and minimize the cost function in the second stage, the method further includes:

[0052] The MSE between y(n) and a(n-τ) is used to evaluate the equalization quality of the high-order QAM blind equalization of the cognitive communication system. The formula for equalization quality evaluation is:

[0053] MSE=E{|Cy(n)-a(n-τ)| 2};

[0054] Where τ represents the delay, and MSE represents the equalization quality evaluation result.

[0055] Optionally, after optimizing the blind equalizer based on the iterative formula of the blind equalization in the second stage to make it optimal and minimize the cost function in the second stage, the method further includes:

[0056] The convergence speed of high-order QAM blind equalization in cognitive communication systems is evaluated by ISI. The formula for evaluating the convergence speed is:

[0057]

[0058] Wherein, ISI represents the convergence speed evaluation result. BRIEF DESCRIPTION OF THE DRAWINGS

[0059] In order to more clearly illustrate the embodiments of the present application or the technical solutions in the related technologies, the following is a brief introduction to the drawings required for use in the embodiments of the present application or the description of the related technologies. Obviously, the drawings described below are only some embodiments of the present application. For ordinary technicians in this field, other drawings can be obtained based on these drawings without any creative work.

[0060] Figure 1 This is a flowchart of a high-order QAM blind equalization method based on a cognitive communication system provided in one embodiment of the present application;

[0061] Figure 2 is a schematic diagram of a system model of a cognitive communication system provided in one embodiment of the present application;

[0062] Figure 3 is a schematic diagram of adaptive 4-neighbor selection provided in one embodiment of the present application;

[0063] Figure 4 In one embodiment of the present application, under the conditions that the signal-to-noise ratio is 12dB, 20dB, 28dB, 36dB, 44dB and the CIR is h1(n), TSBEA-MLSM is used for different thresholds σ th Comparison chart of the mean square error of the values;

[0064] Figure 5 An embodiment of the present application provides that, under the conditions of signal-to-noise ratio of 12dB, 20dB, 28dB, 36dB, 44dB and CIR of h1(n), TSBEA-MLSM is used at different thresholds σ th Comparison chart of symbol error rates under values;

[0065] Figure 6 This is a constellation diagram of SCMEMA provided by an embodiment of the present application, (a) is the equalizer output of the first stage of SCMEMA, (b) is the equalizer output of the second stage of SCMEMA, and (c) is the equalizer output at σ th = 0.7765, SNR is 20dB and CIR is h1(n), the equalizer output of the first stage of TSBEA-MLSM, (d) is the equalizer output under σ th =0.7765, SNR = 20dB, and CIR = h1(n).

[0066] Figure 7 This is a comparison chart of the MSE of TSBEA-MLSM, SCMEMA, D-MGSA and CMA under the condition that CIR is h1(n) provided by an embodiment of the present application;

[0067] Figure 8 This is a comparison chart of the SERs of TSBEA-MLSM, SCMEMA, D-MGSA, and CMA under the condition of CIR being h1(n) provided by an embodiment of the present application;

[0068] Figure 9 This is a comparison diagram of the ISI of TSBEA-MLSM, SCMEMA, and DMGSA under the conditions of SNR of 20 dB and CIR of h1(n) provided by an embodiment of the present application;

[0069] Figure 10 This is another constellation diagram of SCMEMA provided by an embodiment of the present application, (a) is the equalizer output of the first stage of SCMEMA, (b) is the equalizer output of the second stage of SCMEMA, and (c) is the equalizer output at σ th = 0.7765, SNR is 20dB and CIR is h2(n), the equalizer output of the first stage of TSBEA-MLSM, (d) is the equalizer output under σ th =0.7765, SNR = 20dB, and CIR = h2(n).

[0070] Figure 11 This is a comparison chart of the MSE of TSBEA-MLSM, SCMEMA, D-MGSA and CMA under the condition of CIR being h2(n) provided by an embodiment of the present application;

[0071] Figure 12 This is a comparison chart of the SERs of TSBEA-MLSM, SCMEMA, D-MGSA, and CMA under the condition of CIR being h2(n) provided by an embodiment of the present application;

[0072] Figure 13 This is a comparison diagram of the ISI of TSBEA-MLSM, SCMEMA, and DMGSA under the conditions of SNR of 20 dB and CIR of h2(n) provided by an embodiment of the present application;

[0073] Figure 14 is a structural diagram of a high-order QAM blind equalization system based on a cognitive communication system provided in another embodiment of the present application;

[0074] Figure 15 It is a structural diagram of an electronic device provided in another embodiment of the present application. DETAILED DESCRIPTION

[0075] In order to make the purpose, technical solutions and advantages of the embodiments of the present application clearer, each embodiment of the present application will be described in detail below with reference to the accompanying drawings. However, it will be understood by those skilled in the art that in each embodiment of the present application, many technical details are proposed to enable the reader to better understand the present application. However, even without these technical details and various changes and modifications based on the following embodiments, the technical solutions claimed in the present application can be implemented. The division of the following embodiments is for convenience of description and should not constitute any limitation on the specific implementation of the present application. The various embodiments can be combined and referenced with each other under the premise of no contradiction.

[0076] An embodiment of the present application proposes a high-order QAM blind equalization method based on a cognitive communication system, which is applied to an electronic device, wherein the electronic device can be a terminal or a server. This embodiment and the following embodiments are all described using the server as an example. The implementation details of the high-order QAM blind equalization method based on a cognitive communication system proposed in this embodiment are specifically described below. The following content is only the implementation details provided for easy understanding and is not necessary for implementing this solution.

[0077] The specific process of the high-order QAM blind equalization method based on the cognitive communication system proposed in this embodiment can be as follows: Figure 1 Shown, including:

[0078] Step 101: construct a system model of a cognitive communication system, where the cognitive communication system adopts high-order QAM modulation.

[0079] In the specific implementation, the server first needs to build a system model of the cognitive communication system, which adopts high-order QAM modulation.

[0080] In one example, the system model of a cognitive communication system can be as follows Figure 2 As shown, the channel order is L, the sequence a(n) is a QAM modulated signal that obeys independent and identical distribution, and a(n) is sent through a linear system with impulse response h(n);

[0081] Then the blind equalization input can be expressed by the following formula:

[0082]

[0083] Where v(n) is complex additive Gaussian white noise with a mean of 0 and a variance of

[0084] Let the channel order be The impulse response of the linear blind equalizer is:

[0085]

[0086] The blind equalization output can be expressed by the following formula:

[0087]

[0088] Step 102: construct a cost function for the first stage of the cognitive communication system under a high-order QAM modulation channel based on the MMA-MLSM algorithm, construct an iterative formula for blind equalization in the first stage under the high-order QAM modulation channel based on the Newton method, and optimize the blind equalizer based on the iterative formula for blind equalization in the first stage to make it optimal and minimize the cost function of the first stage.

[0089] In the specific implementation, after completing the construction of the system model of the cognitive communication system, the server can enter the first stage of blind equalization. According to the MMA-MLSM algorithm, the cost function of the first stage of the cognitive communication system under the high-order QAM modulation channel is constructed. According to the Newton method, the iterative formula of the first stage of blind equalization under the high-order QAM modulation channel is constructed. Based on the iterative formula of the first stage of blind equalization, the blind equalizer is optimized to make it optimal and minimize the cost function of the first stage.

[0090] In one example, the cost function of the first stage (MMA cost function) can be expressed as:

[0091]

[0092] Where R is a preset constant, N is the total number of available samples, Re(·) means taking the real part, Im(·) means taking the imaginary part, represents the cost function of the first stage.

[0093] The constant R is defined as:

[0094]

[0095] Where p is set to 2. To address the problem of slow convergence of gradient-based algorithms, this embodiment proposes an improved MLSM optimized blind equalizer. Regardless of the value of parameter p, the cost function cannot be zero. For high-order QAM signals, even if the equalizer fully converges, there will be no misalignment. Moreover, when p = 2, the computational complexity and its corresponding gradient will be slightly lower than when p = 1, and |Re<y(n)> |or|Im<y(n)> The size of | is respectively related to Re<y(n)> or Im<y(n)> similar, while |Re(y(n))| 2 or |Im(y(n))| 2 The size of Re<y(n)> or Im<y(n)> The sizes of are different, which indicates that p=2 is more reasonable than p=1.

[0096] In order to improve the equalization accuracy, it is necessary to use time averaging instead of ensemble averaging, and the MMA cost function becomes:

[0097]

[0098] make right Derivatively, we get the gradient of the cost function in the first stage. The gradient of the cost function in the first stage is expressed by the formula:

[0099]

[0100] Among them, sign(·) is the sign function, is the sample matrix, is a function of y, along with changes with the changes of .

[0101] The Newton optimization method makes the linear gradient of the objective function approximately equal to zero. Similarly, if quilt Instead, we get another gradient approximation.

[0102] By letting Approximately equal to 0, we get:

[0103]

[0104] Where k is the number of iterations.

[0105] The approximate least squares solution of BE is:

[0106] The above scheme is called MLSM, and the iterative formula of the first stage blind equalization is obtained as follows:

[0107]

[0108] in,

[0109] Step 103: Determine a switching threshold based on the blind equalization output, and switch to the second stage when the function value of the cost function of the first stage is less than or equal to the switching threshold.

[0110] In the specific implementation, the first stage should be switched to the second stage in time after completion. Therefore, the server needs to determine the switching threshold based on the blind equalization output. When the function value of the cost function of the first stage is less than or equal to the switching threshold, it switches to the second stage.

[0111] In one example, the server converts the cost function of the first stage into a function of the error of the blind equalization output. The function of the error of the blind equalization output is expressed by the formula: in, A function representing the error of the blind equalization output, Obey the normal distribution, The probability density function is N(0,σ 2 ).

[0112] When the equalizer converges to its optimal value, the corresponding equalizer output Approximately a(n-τ), at this time the MMA cost function reaches its minimum. In order to speed up the convergence and avoid steady-state imbalance, the algorithm is switched to the decision-oriented algorithm before the MMA cost function reaches its minimum. The equalizer output y(n) is distributed in the area centered at a(n-τ). The greater the distance between y(n) and a(n-τ), the smaller the probability density function. To simulate this phenomenon, it is assumed that the real (imaginary) part of the equalizer output error C = Re<y(n)> -Re<a(n-τ)> , where C and C′ have the same distribution, is a normal random variable, and its probability density function is N(0,σ 2 ), which is independent of the transmitted signal. Then the MMA cost function is

[0113]

[0114] Since C and C′ have the same distribution and E[Re(a(n-τ))]=0, the MMA cost function can be simplified to:

[0115]

[0116] Among them, Re<a(n)> is a discrete random variable with probability C is a normal random variable, and its probability density function N(0,σ 2 ). Re(a(n)) and C are statistically independent. Then Re<a(n)> The joint probability density function of C is

[0117]

[0118] Re<a(n)> Substituting the joint probability density function of and C into the MMA cost function yields

[0119]

[0120] Using the symmetry of the normal probability density function, the cost function of MMA can be simplified to

[0121]

[0122] set up Then the MMA cost function is rewritten as:

[0123]

[0124] in, The value is when the equalizer output error obeys N(0,σ 2 ). In general, the larger the error between the equalizer and its optimal value, the larger the value of σ. The equalizer error corresponds to the MMA cost function, so when the mean square error σ increases, The value of increases. Therefore, it can be concluded that if C is a normal random variable, its probability density function N(0,σ 2 ) is more reasonable. The first-order derivative mean As σ increases, it increases. Finally, it can be concluded that if C is a normal random variable, its probability density function obeys N(0,σ 2 ) is more reasonable.

[0125] when becomes When , the BE process enters the decision-oriented mode, and the error is σ th , the cost function of the first stage is written as:

[0126] The corresponding decision error probability should satisfy: p{|C|>2}=α th , p{|C|>2} represents the probability of decision error, α th A threshold indicating the probability of decision error;

[0127] remember is a standard normal random variable, and its probability distribution function is When α th = -2 / α, p{|C|>2}=α th Based on this, the switching threshold is obtained as

[0128] when In order to improve the equalization accuracy and convergence speed, it switches to ISDDA-MLSM, that is, switches to the second stage.

[0129] Step 104: construct a cost function for the second stage of the cognitive communication system under a high-order QAM modulation channel based on the ISDDA-MLSM algorithm, construct an iterative formula for blind equalization in the second stage of the cognitive communication system under a high-order QAM modulation channel based on the Newton method, and optimize the blind equalizer based on the iterative formula for blind equalization in the second stage to make it optimal and minimize the cost function of the second stage, thereby realizing high-order QAM blind equalization of the cognitive communication system.

[0130] In the specific implementation, when the blind equalization switches to the second stage, the server constructs the cost function of the second stage under the high-order QAM modulation channel of the cognitive communication system based on the ISDDA-MLSM algorithm, and constructs the iterative formula of the blind equalization of the second stage under the high-order QAM modulation channel based on the Newton method. Based on the iterative formula of the blind equalization of the second stage, the blind equalizer is optimized to make it optimal and minimize the cost function of the second stage, thereby realizing high-order QAM blind equalization of the cognitive communication system.

[0131] Because the single constant modulus used in MMA is not equal to the multimodal value of the output signal, even if the equalizer fully converges, the output error level in steady state can be significant, thus affecting equalizer performance. Therefore, in the second phase, when the error level reaches the switching threshold, this embodiment uses an adaptive 4-nearest-neighbor selection scheme (A4NS) to make a hard decision. Then, applying MLSM-based ISDDA to the 4-nearest-neighbor scheme reduces computational complexity and improves equalization performance and convergence speed.

[0132] Furthermore, A4NS is explained using a 36-QAM signal as an example. The A4NS of SDDA depends on all constellations. Figure 3 The fixed decision region method shows that y(n) is located in the red dotted rectangle as one of the four constellations. The fixed decision region is not suitable for the equalizer output y(n). The optimal decision region is obtained based on the adaptive decision region selection scheme. y(n) is located in the black solid rectangle, which is the closest decision region determined based on the position of y(n). It can be concluded that in the adaptive decision region, the average distance from y(n) to the four constellations is smaller than that in the fixed decision region. More importantly, the basic function of the decision is to accurately judge the equalizer output, thereby accelerating the convergence speed and improving the equalization accuracy. Figure 3 It can be seen that if the distance between the real (imaginary) part of the equalizer output y(n) and the real (imaginary) part of the transmission signal a(n-τ) is less than 1, the decision region can make a correct decision.

[0133] In contrast, A4NS relaxes the distance for making a correct decision to 2. This shows that A4NS has the following advantages: first, if A4NS is adopted, BE can switch to the second stage earlier, thereby accelerating the convergence of BE; second, A4NS has greater fault tolerance and improves decision robustness.

[0134] For the 4-QAM system, SDDA obtains BE by adjusting the weight vector w to minimize the cost function. The cost function is as follows:

[0135]

[0136] Where, ρ q for a q ∈{1+j,1-j,-1+j,-1-j}, For a q The variance of the correlation. Typically, Update according to the gradient descent method as follows:

[0137]

[0138] Among them, μ is the step size and k is the iteration index.

[0139] For high-order QAM signals, directly using SDDA may lead to poor convergence. Therefore, when the MMA cost function When , SDDA is applied to the BE output based on the four constellations included in the adaptive selection decision region.

[0140] In order to reduce the amount of calculation, soft decisions are made on the real and imaginary parts of the equalizer output respectively. The improved cost function can be expressed as

[0141]

[0142] Among them, R p (p=1,2) and I q (q=1,2) represents the real and imaginary parts of the constellation points in the decision area. Similarly, in SDDA, the parameter ρ p and ρ q Re(a(n))=R p and Im(a(n))=I q The prior probability of . Since a(n) always obeys independent and identical distribution, ρ p =ρ q This holds true for all p and q. In addition, the variance Decided T p (I q ) corresponds to the width of the Gaussian function. When the variance is extremely large or extremely small, it will affect the equalization quality. In other cases, the variance has no effect on the equalization accuracy. Similarly, since a(n) obeys independent and identical distribution, we have Therefore, the constant and are equal and can be ignored. Then the ISDDA cost function can be described as:

[0143]

[0144] ISDDA maintains the excellent equalization performance of SDDA. However, they differ in their mathematical calculations. The cost function of SDDA involves four complex multiplications, while the cost function of ISDDA requires four real multiplications. The calculations are otherwise identical. This demonstrates the lower computational complexity of ISDDA. Furthermore, ISDDA offers the following advantages: First, ISDDA makes soft decisions on the real and imaginary parts separately and then combines the results; second, ISDDA fully utilizes the comprehensive information of the QAM constellation, resulting in low estimation error.

[0145] Furthermore, ignoring irrelevant constants, for high-order QAM signals, soft decisions are made on the real and imaginary parts of the output of the blind equalizer, respectively, to obtain the cost function of the second stage. The cost function of the second stage is expressed by the formula:

[0146]

[0147] Among them, R p and I q are all preset constants. represents the cost function of the second stage;

[0148] make right Derivatively, we get the gradient of the cost function in the second stage. The gradient of the cost function in the second stage is expressed by the formula:

[0149]

[0150] in, Represents the gradient of the cost function of the second stage;

[0151] make And 1 / 2σ 2 Ignore, you can Simplified to:

[0152] The iterative formula for the first stage of blind equalization is obtained as follows:

[0153]

[0154] In addition to the above advantages, ISDDA-MLSM also has stable convergence, from which we can draw the following conclusions: function It is also the Lyapunov function, the equalizer weight vector Converge to the invariant set It can be expressed by the formula:

[0155] In one example, after optimizing the blind equalizer based on the iterative formula of the second-stage blind equalization and minimizing the cost function of the second stage, the server can evaluate the equalization quality of the high-order QAM blind equalization of the cognitive communication system by the MSE between y(n) and a(n-τ). The formula for evaluating the equalization quality is:

[0156] MSE=E{|Cy(n)-a(n-τ)| 2};

[0157] Where τ represents the delay, and MSE represents the equalization quality evaluation result.

[0158] In one example, after optimizing the blind equalizer based on the iterative formula of the second-stage blind equalization and minimizing the cost function of the second stage, the server can also evaluate the convergence speed of the high-order QAM blind equalization of the cognitive communication system through ISI. The formula for evaluating the convergence speed is:

[0159]

[0160] Wherein, ISI represents the convergence speed evaluation result.

[0161] This embodiment proposes a high-order QAM blind equalization method based on a cognitive communication system. First, a system model of the cognitive communication system is constructed. The cognitive communication system uses high-order QAM modulation. A cost function for the first stage of the cognitive communication system under a high-order QAM modulation channel is constructed based on the MMA-MLSM algorithm. An iterative formula for blind equalization in the first stage of the high-order QAM modulation channel is constructed based on the Newton method. The blind equalizer is then optimized based on the iterative formula for blind equalization in the first stage to achieve optimality and minimize the cost function of the first stage. Because the single constant modulus used in MMA is not equal to the multimodal value of the output signal, even if the equalizer fully converges, the output error level in the steady state will be large, thus affecting the equalizer's performance. Therefore, the present application determines a switching threshold based on the blind equalization output and promptly switches to the second stage. In the second stage, a cost function for the second stage of the cognitive communication system under a high-order QAM modulation channel is constructed based on the ISDDA-MLSM algorithm. An iterative formula for blind equalization in the second stage of the high-order QAM modulation channel is constructed based on the Newton method. The blind equalizer is then optimized based on the iterative formula for blind equalization in the second stage to achieve optimality and minimize the cost function of the second stage, thereby achieving high-order QAM blind equalization in the cognitive communication system. It effectively reduces the computational complexity, improves the convergence stability, convergence speed and equalization quality of high-order QAM blind equalization, and thus effectively improves the communication quality of the cognitive communication system.

[0162] The step division of the above various methods is only for the purpose of clear description. During implementation, they can be combined into one step or some steps can be split and decomposed into multiple steps. As long as they include the same logical relationship, they are all within the scope of protection of this application; adding insignificant modifications or introducing insignificant designs to the algorithm or process without changing the core design of the algorithm and process are all within the scope of protection of this application.

[0163] In one embodiment, the server studies the performance of TSBEA-MLSM through simulation experiments and compares it with the performance of CMA, DMGSA, and SCMEA in terms of equalization quality and convergence speed.

[0164] Consider a discrete 16-QAM system. The BE order is chosen to be 16, initialized to unity at the center and zero at all other locations. When , TSBEA-MLSM switches to ISDDA, and the number of iterations of SCMEMA is 3000. The number of samples N is set to 1000. The variance σ 2 Take 0.8. Set h(n) of CIR to h1(n) = [1.0, 0.5exp(-j3 / 4π)], h2(n) = [0.005-0.004j, 0.1+0.003j, -0.24-.0104j].

[0165] When CIR is h1(n), the threshold σ th =0.7765,0.8597,0.9216,0.9739,1.0204, corresponding decision error α th =1%, 2%, 3%, 4%, 5%. When SNR = 12dB, 20dB, 28dB, 36dB, 44dB, the MSE when TSBEA-MLSM converges is as follows: Figure 4 and Figure 5 As shown. We can observe that, th =0.7765 as the switching threshold, corresponding to the loss function value is the optimal value.

[0166] like Figure 6 As shown in Figure 2, both SCMEMA and the proposed method avoid the local minima of the constellation matching function of SCMEMA and the ISDDA of TSBEA-MLSM through their first-stage equalization. In addition, when the CIR is set to h1(n), the blind equalizer has good convergence performance.

[0167] like Figure 7As shown in the figure, when the signal-to-noise ratio is large and the CIR is h1(n), the MSE of TSBEA-MLSM is essentially equal to that of SCMEMA and DMGSA, and significantly lower than that of CMA. The superior performance of the two-stage approach is attributed to the constellation matching error method in the second stage, which avoids the detuning of CMA (MMA) when the equalizer is close to convergence.

[0168] Figure 8 The SER of the four algorithms under different signal-to-noise ratios is shown in Figure 1. Figure 8 As can be seen from the figure, TSBEA-MLSM, SCMEMA, and DMGSA achieve better equalization performance than CMA because their constellation matching error method eliminates the steady-state misalignment problem. Furthermore, TSBEA-MLSM achieves a lower SER than SCMEMA and DMGSA for two reasons. First, TSBEA-MLSM uses a batch processing approach, avoiding the extreme errors of adaptive methods. Second, the adaptively selected decision domain improves TSBEA-MLSM's reliability.

[0169] Figure 9 The ISIs of TSBEA-MLSM, SCMEMA, and DMGSA are shown when the CIR is h1(n). TSBEA-MLSM requires fewer than 20 iterations to converge, while SCMEMA requires 4000, DMGSA requires 12000, and CMA requires 10000. TSBEA-MLSM converges faster due to its quadratic termination property.

[0170] In addition, the steady-state ISI value of TSBEA-MLSM is 0.0005058, CMEMA is 0.003638, DMGSA is 0.003049, and CMA is 0.01593. This shows that TSBEA-MLSM adopts batch processing technology and adaptive selection of decision regions, which has the best balanced accuracy.

[0171] like Figure 9 As shown, the switching points for SCMEMA and TSBEA-MLSM are k = 3000 and k = 1, respectively. When k = 3000, SCMEMA's ISI is approximately 0.04. In this case, the constellation matching error method can significantly accelerate convergence. In contrast, when k = 1, TSBEA-MLSM's ISI is approximately 0.17, indicating that TSBEA-MLSM switches to the second stage earlier and ISDDA-MLSM has stronger fault tolerance.

[0172] Figure 10In (a), the transmitted signal profile exhibits phase rotation, indicating that the 3000 iterations of CMA provide a good initialization for SCMEMA. When the CIR is h2(n), SCMEMA fails. This is primarily because when the CIR is h1(n), the output of the SCMEMA's first-stage equalizer does not rotate as a whole, whereas a CIR of h2(n) causes the equalizer output signal to rotate in phase. SCMEMA is based on constellation coordinates, and the real (imaginary) parts of these rotated constellation points are not located at the minimum of the sine function. Therefore, the initialization is invalid, leading to equalization failure. In contrast, the algorithm has good convergence and equalization performance because the BE with MMA provides an unrotated output signal, and the coordinates of these output constellation points are close to the minimum of the improved soft decision cost function. Furthermore, since A4NS has a large error tolerance, its decisions are robust, so it does not require a good initialization. Figure 10 The constellation diagram shown in (c) shows that TSBEA-MLSM can enter the second stage earlier, achieve fast convergence, and avoid misalignment.

[0173] like Figure 12 and Figure 13 As shown in Figure 2, when CIR is h2(n), TSBEA-MLSM achieves the best equalization performance in terms of MSE and SER. This is because the two-stage approach avoids the misalignment of MMA, the batch processing technique eliminates the inaccuracy of the adaptive approach, and the adaptive decision domain selection scheme improves the reliability of TSBEA-MLSM.

[0174] like Figure 13 As shown in the figure, SCMEMA diverges at the switching point due to the phase rotation of the equalizer output signal caused by CMA. When the CIR is h1(n), other methods show similar convergence performance. The proposed algorithm has quadratic termination characteristics and optimal steady-state performance, with a faster convergence speed. When the CIR is h2(n), switching to the second stage of TSBEA-MLSM, the convergence speed of TSBEA-MLSM is accelerated. Comparing the ISI when the CIR is h1(n) and h2(n), it shows that TSBEA-MLSM has convergence stability due to the good fault tolerance of ISDDA and the first-stage non-rotated output signal.

[0175] Another embodiment of the present application proposes a high-order QAM blind equalization system based on a cognitive communication system. The following is a detailed description of the implementation details of the high-order QAM blind equalization system based on a cognitive communication system proposed in this embodiment. The following content is only for the convenience of understanding the implementation details and is not necessary for implementing this example. Figure 14This is a structural diagram of a high-order QAM blind equalization system based on a cognitive communication system proposed in this embodiment, including: a model construction module 201, a first-stage optimization module 202, a switching module 203 and a second-stage optimization module 204.

[0176] The model building module 201 is used to build a system model of a cognitive communication system, which adopts high-order QAM modulation.

[0177] The first-stage optimization module 202 is used to construct the first-stage cost function of the cognitive communication system under the high-order QAM modulation channel based on the MMA-MLSM algorithm, construct the iterative formula of the first-stage blind equalization under the high-order QAM modulation channel based on the Newton method, and optimize the blind equalizer based on the iterative formula of the first-stage blind equalization to make it optimal and minimize the cost function of the first stage.

[0178] The switching module 203 is configured to determine a switching threshold based on the blind equalization output, and switch to the second stage when the function value of the cost function of the first stage is less than or equal to the switching threshold.

[0179] The second-stage optimization module 204 is used to construct the second-stage cost function of the cognitive communication system under the high-order QAM modulation channel based on the ISDDA-MLSM algorithm, construct the iterative formula of the second-stage blind equalization under the high-order QAM modulation channel based on the Newton method, optimize the blind equalizer based on the iterative formula of the second-stage blind equalization to make it optimal and minimize the second-stage cost function, thereby realizing high-order QAM blind equalization of the cognitive communication system.

[0180] It is not difficult to find that this embodiment is a system embodiment corresponding to the above-mentioned method embodiment, and this embodiment can be implemented in conjunction with the above-mentioned method embodiment. The relevant technical details and technical effects mentioned in the above-mentioned embodiments are still valid in this embodiment, and to reduce repetition, they are not repeated here. Accordingly, the relevant technical details mentioned in this embodiment can also be applied to the above-mentioned embodiments.

[0181] It is worth mentioning that all modules involved in this embodiment are logical modules. In actual applications, a logical unit can be a physical unit, a part of a physical unit, or a combination of multiple physical units. In addition, to highlight the innovation of this application, this embodiment does not include units that are not closely related to solving the technical problem proposed by this application. However, this does not mean that other units do not exist in this embodiment.

[0182] Another embodiment of the present application provides an electronic device, the specific structure of which can be as follows: Figure 15As shown, it includes: at least one processor 301; and a memory 302 communicatively connected to the at least one processor 301; wherein the memory 302 stores instructions that can be executed by the at least one processor 301, and the instructions are executed by the at least one processor 301 to enable the at least one processor 301 to execute a high-order QAM blind equalization method based on a cognitive communication system as described in the above-mentioned method embodiments.

[0183] The memory and processor are connected using a bus, which can include any number of interconnected buses and bridges. The bus connects various circuits of one or more processors and memories. The bus can also connect various other circuits such as peripheral devices, voltage regulators, and power management circuits. These are all well known in the art and therefore will not be described further in this article. The bus interface provides an interface between the bus and the transceiver. The transceiver can be a single component or multiple components, such as multiple receivers and transmitters, providing a unit for communicating with various other devices on a transmission medium. Data processed by the processor is transmitted on a wireless medium via an antenna. Furthermore, the antenna also receives data and transmits it to the processor.

[0184] The processor is responsible for managing the bus and general processing, and can also provide various functions, including timing, peripheral interfaces, voltage regulation, power management, and other control functions. Memory can be used to store data used by the processor when performing operations.

[0185] Another embodiment of the present application relates to a computer-readable storage medium storing a computer program. When the computer program is executed by a processor, it can implement a high-order QAM blind equalization method based on a cognitive communication system as described in the above method embodiments.

[0186] That is, those skilled in the art will understand that all or part of the steps in the above-mentioned embodiments can be implemented by instructing the relevant hardware through a program, which is stored in a storage medium and includes a number of instructions for causing a device (which may be a single-chip microcomputer, chip, etc.) or a processor to execute all or part of the steps of the methods described in each embodiment of the present application. The aforementioned storage medium includes: a USB flash drive, a mobile hard drive, a ROM (Read-Only Memory), a RAM (Random Access Memory), a magnetic disk, or an optical disk, etc., various media that can store program code.

[0187] Those skilled in the art will appreciate that the above embodiments are specific embodiments for implementing the present application, and that in actual applications, various changes may be made thereto in form and detail without departing from the spirit and scope of the present application.

Claims

1. A high-order QAM blind equalization method based on cognitive communication system, applicable to cognitive communication system, characterized in that: The method comprises: Construct a system model of a cognitive communication system that uses high-order QAM modulation; Based on the multi-mode and improved least squares algorithm MMA-MLSM algorithm, the cost function of the first stage of the cognitive communication system under the high-order QAM modulation channel is constructed. Based on the Newton method, the iterative formula of the first stage blind equalization under the high-order QAM modulation channel is constructed. Based on the iterative formula of the first stage blind equalization, the blind equalizer is optimized to make it optimal and minimize the cost function of the first stage. Determine a switching threshold based on the blind equalization output, and switch to the second stage when the function value of the cost function of the first stage is less than or equal to the switching threshold; Based on the improved soft decision guidance and improved least squares algorithm ISDDA-MLSM algorithm, the cost function of the second stage of cognitive communication system under high-order QAM modulation channel is constructed. Based on the Newton method, the iterative formula of the second stage blind equalization under high-order QAM modulation channel is constructed. Based on the iterative formula of the second stage blind equalization, the blind equalizer is optimized to make it optimal and minimize the cost function of the second stage, thus realizing high-order QAM blind equalization of cognitive communication system. Construct a system model of cognitive communication system, including: Let the channel order be , record sequence is a QAM modulated signal that obeys independent and identical distribution, By impulse response The linear system sends; The blind equalization input is expressed by the following formula: ； in, is a complex Gaussian white noise with a mean of 0 and a variance of ; Let the channel order be The impulse response of the linear blind equalizer is: ； The blind equalization output is expressed by the following formula: ； The cost function of the first stage of the cognitive communication system under the high-order QAM modulation channel is constructed based on the MMA-MLSM algorithm. The iterative formula of the blind equalization in the first stage under the high-order QAM modulation channel is constructed based on the Newton method. The blind equalizer is optimized based on the iterative formula of the first stage blind equalization to make it optimal and minimize the cost function of the first stage, including: The cost function of the first stage is expressed as follows: ； in, is a preset constant, is the total number of available samples, represents the real part, Indicates taking the imaginary part, represents the cost function of the first stage; make right Derivatively, we get the gradient of the cost function in the first stage. The gradient of the cost function in the first stage is expressed by the formula: ； ； ； in, is a symbolic function, is the sample matrix; By letting Approximately equal to 0, we get: ； in, is the number of iterations; The approximate least squares solution of blind equalization BE is: ； The iterative formula for the first stage of blind equalization is obtained as follows: ； in, ; Determining a switching threshold based on the blind equalization output includes: The cost function of the first stage is converted into the error function of the blind equalization output. The error function of the blind equalization output is expressed by the formula: ;in, A function representing the error of the blind equalization output, obeys the normal distribution, The probability density function of ; when becomes When , the BE process enters the decision-oriented mode, and the error is , the cost function of the first stage is written as: ; The corresponding decision error probability should satisfy: , represents the probability of decision error, represents the threshold value of the decision error probability, is a normal random variable; remember is a standard normal random variable, and its probability distribution function is , ,when hour, Based on this, the switching threshold is ; The cost function of the second stage of the cognitive communication system under the high-order QAM modulation channel is constructed based on the ISDDA-MLSM algorithm. The iterative formula of the blind equalization of the second stage under the high-order QAM modulation channel is constructed based on the Newton method. The blind equalizer is optimized based on the iterative formula of the second stage blind equalization to make it optimal and minimize the cost function of the second stage, including: For high-order QAM signals, soft decisions are made on the real and imaginary parts of the output of the blind equalizer to obtain the cost function of the second stage. The cost function of the second stage is expressed as follows: ； in, and are preset constants. represents the cost function of the second stage; make right Derivatively, we get the gradient of the cost function in the second stage. The gradient of the cost function in the second stage is expressed by the formula: ； ； ； ； ； in, Represents the gradient of the cost function of the second stage; make , , and Ignore, you can Simplified to: ; The iterative formula for the second stage of blind equalization is obtained as follows: 。 2. A high-order QAM blind equalization method based on a cognitive communication system according to claim 1, characterized in that: After optimizing the blind equalizer based on the iterative formula of the blind equalization in the second stage to make it optimal and minimize the cost function of the second stage, it also includes: pass and The mean square error (MSE) between the two is used to evaluate the equalization quality of the high-order QAM blind equalization of the cognitive communication system. The formula for equalization quality evaluation is: ； in, Indicates delay, Indicates the result of the equalization quality assessment.

3. The high-order QAM blind equalization method based on a cognitive communication system according to claim 1, characterized in that: After optimizing the blind equalizer based on the iterative formula of the blind equalization in the second stage to make it optimal and minimize the cost function of the second stage, it also includes: The convergence speed of high-order QAM blind equalization in cognitive communication systems is evaluated by the inter-symbol interference index ISI. The formula for evaluating the convergence speed is: ； ； ； in, Indicates the convergence speed evaluation result.

4. A high-order QAM blind equalization system based on a cognitive communication system, suitable for a cognitive communication system, characterized in that: A high-order QAM blind equalization method based on a cognitive communication system according to any one of claims 1 to 3 is implemented, the system comprising: A model building module is used to build a system model of a cognitive communication system that uses high-order QAM modulation; The first-stage optimization module is used to construct the first-stage cost function of the cognitive communication system under the high-order QAM modulation channel based on the MMA-MLSM algorithm, construct the iterative formula of the first-stage blind equalization under the high-order QAM modulation channel based on the Newton method, and optimize the blind equalizer based on the iterative formula of the first-stage blind equalization to make it optimal and minimize the first-stage cost function; A switching module, configured to determine a switching threshold based on the blind equalization output, and switch to the second stage when the function value of the cost function of the first stage is less than or equal to the switching threshold; The second-stage optimization module is used to construct the second-stage cost function of the cognitive communication system under the high-order QAM modulation channel based on the ISDDA-MLSM algorithm, construct the iterative formula of the second-stage blind equalization under the high-order QAM modulation channel based on the Newton method, and optimize the blind equalizer based on the iterative formula of the second-stage blind equalization to make it optimal and minimize the second-stage cost function, thereby realizing high-order QAM blind equalization of the cognitive communication system.

5. An electronic device, characterized in that: include: at least one processor; as well as, a memory communicatively connected to the at least one processor; wherein, The memory stores instructions that can be executed by the at least one processor, and the instructions are executed by the at least one processor so that the at least one processor can execute a high-order QAM blind equalization method based on a cognitive communication system according to any one of claims 1 to 3.

6. A computer-readable storage medium storing a computer program, characterized in that: When the computer program is executed by a processor, it can implement a high-order QAM blind equalization method based on a cognitive communication system according to any one of claims 1 to 3.

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