High-order QAM blind equalization method based on cognitive communication system

Abstract

The embodiment of the invention relates to the technical field of channel blind equalization, in particular to a high-order QAM (Quadrature Amplitude Modulation) blind equalization method based on a cognitive communication system, which comprises the following steps: constructing a system model of the cognitive communication system which adopts high-order QAM modulation; the method comprises the following steps: constructing a cost function of a first stage under a high-order QAM modulation channel of a cognitive communication system and a blind equalization iterative formula of the first stage, and optimizing a blind equalizer to enable the blind equalizer to be optimal and minimize the cost function of the first stage; determining a switching threshold, and switching to a second stage when the function value of the cost function of the first stage is smaller than or equal to the switching threshold; and constructing a cost function of a second stage under a high-order QAM modulation channel of the cognitive communication system and a blind equalization iterative formula of the second stage, and optimizing the blind equalizer to enable the blind equalizer to be optimal and minimize the cost function of the second stage. According to the method, the convergence stability, the convergence speed and the equalization quality of high-order QAM blind equalization are effectively improved.

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 development trend in the field of communication technology. In cognitive communication systems, if the duration of signal transmission is less than the time dispersion of multipath propagation, the received signal will be subject to inter-symbol interference (ISI), and the channel equalizer can effectively reduce ISI. Traditional channel equalizers require the use of predetermined training sequences, which will consume precious spectrum resources. Therefore, it is necessary to reduce the demand for training sequences, especially in non-cooperative communications where there is no suitable training sequence.

[0003] Due to the above-mentioned defects of the training-based method, the blind equalization (BE) technology that does not require the use of training sequences has received considerable attention. Theoretically, in cooperative communication, BE can make full use of the channel bandwidth to improve transmission efficiency. In particular, since BE does not require any training sequence, it may be the only applicable method to overcome ISI in non-cooperative communication. However, BE has the disadvantages of slow convergence speed and high computational complexity, and is prone to fall into local minima and 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 the problems of BE itself, applying classical BE to high-order QAM will also have problems such as slow convergence speed, high computational complexity, and low equalization accuracy. Therefore, it is very important to design an efficient BE for high-order QAM systems.

[0005] In the BE problem, an exhaustive search method (ESM) is usually used to find the local optimal solution or even the global optimal solution. When ESM and BE use the same received samples, BE can theoretically achieve the same equalization accuracy as the training-based method. Unlike the training-based method that only uses received samples from the training sequence, BE can use all received samples to achieve the best equalization performance. However, due to the huge amount of computation, ESM is not suitable for application in actual communications. Therefore, one of the core goals of improving BE is to combine an effective and computationally inefficient method to find the local optimal solution.

[0006] BE technology based on attribute recovery method can overcome the combinatorial explosion problem existing in classic BE technology. Common algorithms include constant modulus algorithm (CMA), multiple mode adaptive algorithm (MMA), and soft decision directed algorithm (SDDA). CMA and MMA have low complexity and good convergence, so they are often used to solve BE problems. These methods reduce the number of combinations by merging the discrete states of each transmitted codeword. In 4-QAM signals, no matter which state the signal is in, its modulus value is always constant. If there are 1000 samples, there is only one possible modulus value of the transmitted signal. However, when CMA and MMA are applied to high-order constellation systems, their algorithm performance will be severely degraded because they only use part of the information of the constellation points, resulting in misalignment problems. In addition, the two adaptive methods CMA and MMA use a small step size, which leads to a slow convergence speed. Compared with CMA and MMA, SDDA can significantly reduce steady-state misalignment and improve the convergence speed to a certain extent. However, when SDDA is applied to high-order QAM systems, its cost function becomes highly non-convex and contains too many local minima, resulting in poor convergence performance. In addition, 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 radius-directed hybrid algorithms. 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, the decision-oriented algorithm is further used to improve the equalization performance. Among them, the switching threshold is a key parameter of the two-stage algorithm. If the algorithm switches to the decision-oriented algorithm too early, it may not converge. If the algorithm switches to the decision-oriented algorithm too late, it will lead to a slow convergence of the algorithm and a high computational cost. None of the algorithms proposed so far can 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, an embodiment of the present application proposes 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 a cognitive communication system and is characterized in that the method includes the following steps: constructing a system model of a cognitive communication system, wherein the cognitive communication system adopts high-order QAM modulation; constructing a cost function of the first stage under a high-order QAM modulation channel of the cognitive communication system according to the MMA-MLSM algorithm, constructing an iterative formula of blind equalization of the first stage under a high-order QAM modulation channel according to the Newton method, optimizing the blind equalizer based on the iterative formula of blind equalization of the first stage to make it optimal and minimize the cost function of the first stage; determining a 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 a cost function of the second stage under a high-order QAM modulation channel of the cognitive communication system according to the ISDDA-MLSM algorithm, constructing an iterative formula of blind equalization of the second stage under a high-order QAM modulation channel according to the Newton method, optimizing the blind equalizer based on the iterative formula of 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 the high-order QAM modulation channel of the cognitive communication system according to the MMA-MLSM algorithm, construct an iterative formula for 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, optimize 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, and realize the 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 executable 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, which, when executed by a processor, can implement the above-mentioned high-order QAM blind equalization method based on a cognitive communication system.

[0012] The embodiment of the present application 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 adopts high-order QAM modulation. The cost function of the first stage under the high-order QAM modulation channel of the cognitive communication system is constructed according to the MMA-MLSM algorithm. The iterative formula of blind equalization in the first stage under the high-order QAM modulation channel is constructed according to the Newton method. The blind equalizer is optimized based on the iterative formula of blind equalization in the first stage to make it optimal and minimize the cost function of the first stage. Since the single constant modulus used in MMA is not equal to the multi-mode value of the output signal, even if the equalizer is fully converged, the output error level in the steady state will be very large, thereby affecting the performance of the equalizer. Therefore, the present application determines the switching threshold based on the blind equalization output and switches to the second stage in time. In the second stage, the cost function of the second stage under the high-order QAM modulation channel of the cognitive communication system is constructed according to the ISDDA-MLSM algorithm. The iterative formula of blind equalization in the second stage under the high-order QAM modulation channel is constructed according to the Newton method. The blind equalizer is optimized based on the iterative formula of 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. 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 that obeys an independent and identical distribution, and a(n) is sent 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] The channel order is 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 cost function of the first stage under a high-order QAM modulation channel of a cognitive communication system according to an MMA-MLSM algorithm, constructing an iterative formula of blind equalization of the first stage under a high-order QAM modulation channel according to a Newton method, and optimizing a blind equalizer based on the iterative formula of blind equalization of the first stage to make it optimal and minimize the cost function of the first stage, including:

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

[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 Derived, 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 of the first stage 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, The function representing the error of the blind equalization output, It follows a 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 under a high-order QAM modulation channel of a cognitive communication system according to an ISDDA-MLSM algorithm, constructing an iterative formula of blind equalization of the second stage under a high-order QAM modulation channel according to a Newton method, and optimizing a blind equalizer based on the iterative formula of 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 by the formula:

[0043]

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

[0045] make right Derived, we get the gradient of the cost function of the second stage. The gradient of the cost function of 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 of the first stage 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 of 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 evaluating the equalization quality is:

[0053] MSE=E{|Cy(n)-a(n-τ)| 2};

[0054] Among them, 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 of the second stage, the method further includes:

[0056] The convergence speed of the high-order QAM blind equalization of the cognitive communication system 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 drawings required for use in the embodiments of the present application or the related technical descriptions will be briefly introduced below. 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 paying creative work.

[0060] Figure 1 is a flow chart 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, when 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 mean square error of 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 at different thresholds σ th Comparison chart of symbol error rate under values;

[0065] Figure 6 : 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 of the first stage of SCMEMA 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 of the first stage of TSBEA-MLSM under the condition of σ th =0.7765, SNR = 20dB and CIR = h1(n), the equalizer output of the second stage of TSBEA-MLSM;

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

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

[0068] Fig. 9 An embodiment of the present application provides a comparison diagram of ISI of TSBEA-MLSM, SCMEMA and DMGSA under the conditions of SNR of 20 dB and CIR of h1(n);

[0069] Fig.10 : 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 of the first stage of SCMEMA 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), the equalizer output of the second stage of TSBEA-MLSM;

[0070] Fig.11 An embodiment of the present application provides a comparison chart of the MSE of TSBEA-MLSM, SCMEMA, D-MGSA and CMA under the condition that CIR is h2(n);

[0071] Fig.12 An embodiment of the present application provides a comparison chart of the SERs of TSBEA-MLSM, SCMEMA, D-MGSA and CMA under the condition that CIR is h2(n);

[0072] Fig.13 An embodiment of the present application provides a comparison diagram of ISI of TSBEA-MLSM, SCMEMA and DMGSA under the conditions of SNR of 20 dB and CIR of h2(n);

[0073] Fig.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] Fig.15 It is a structural schematic diagram of an electronic device provided in another embodiment of the present application. DETAILED DESCRIPTION

[0075] To make the purpose, technical scheme and advantages of the embodiments of the present application clearer, the embodiments of the present application will be described in detail below in conjunction with the accompanying drawings. However, it will be appreciated by those skilled in the art that in the present application, many technical details are proposed in order 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 scheme claimed in the present application can also be implemented. The division of the following embodiments is for the convenience of description, and the specific implementation of the present application should not be construed as any limitation, and 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 ease of understanding and is not necessary for the implementation of 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 As 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] The channel order is The impulse response of the linear blind equalizer is:

[0085]

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

[0087]

[0088] Step 102, 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, and 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.

[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, and construct the cost function of the first stage of the cognitive communication system under the high-order QAM modulation channel according to the MMA-MLSM algorithm. The iterative formula of the first stage of blind equalization under the high-order QAM modulation channel is constructed according to the Newton method. Based on the iterative formula of the blind equalization of the first stage, 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 the gradient algorithm, 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 is fully converged, there is no possibility of misalignment. Moreover, when p = 2, the computational complexity and its corresponding gradient will be slightly lower than 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 average instead of ensemble average, and the MMA cost function becomes:

[0097]

[0098] make right Derived, 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, and the function of the error of the blind equalization output is expressed by the formula: in, The function representing the error of the blind equalization output, It follows a 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 which point the MMA cost function reaches its minimum. In order to speed up convergence and avoid steady-state imbalance, the algorithm is switched to a decision-oriented algorithm before the MMA cost function reaches its minimum. The equalizer output y(n) is distributed in a region 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, assume 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 and are normal random variables, and their 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 and C is

[0117]

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

[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 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 assuming 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

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

[0129] Step 104, 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 second stage blind equalization under the high-order QAM modulation channel according to the Newton method, optimizing the blind equalizer based on the iterative formula of the second stage blind equalization 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 according to the ISDDA-MLSM algorithm, and constructs the iterative formula of the second stage blind equalization under the high-order QAM modulation channel according to 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 the high-order QAM blind equalization of the cognitive communication system.

[0131] Since the single constant modulus used in MMA is not equal to the multi-modal value of the output signal, even if the equalizer is fully converged, the output error level in the steady state will be large, thus affecting the performance of the equalizer. Therefore, in the second stage, when the error level reaches the switching threshold, this embodiment uses an adaptive 4-neighbor selection scheme (A4NS) to make a hard decision. Then, the MLSM-based ISDDA is applied to the 4-neighbors, which reduces the computational complexity and improves the equalization performance and convergence speed.

[0132] Furthermore, A4NS is explained by taking 36-QAM signal as an example. A4NS of SDDA depends on all constellations. Figure 3 The display decision region method places y(n) as one of the four constellations within the red dashed rectangle. The decision region is not suitable for the equalizer output y(n). The optimal decision region is obtained according to the adaptive decision region selection scheme, where y(n) is located in the black solid rectangle, which is the nearest decision region determined based on the position of y(n). It can be concluded that in the adaptively selected decision region, the average distance from y(n) to the four constellations is smaller than that of 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. By 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 give 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 the robustness of decision making.

[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] In the formula, ρ q for a q ∈{1+j,1-j,-1+j,-1-j}, For a q The variance of the correlation. Usually, The update according to the gradient descent method is 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 result in poor convergence. Therefore, when the MMA cost function When , SDDA is applied to the BE output based on the four constellations included in the decision region based on adaptive selection.

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

[0141]

[0142] Among them, R p (p=1,2) and I q (q = 1, 2) represent 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 follows an 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) follows an 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 good equalization performance of SDDA. However, they differ in mathematical calculations. The cost function of SDDA involves 4 complex multiplications, while the cost function of ISDDA requires 4 real multiplications, with the other calculations being the same. This shows that the computational complexity of ISDDA is low. In addition, ISDDA has the following advantages: First, ISDDA makes soft decisions on the real and imaginary parts separately, and then merges the results; second, ISDDA makes full use of the comprehensive information of the QAM constellation, resulting in low estimation errors.

[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, which is expressed by the formula:

[0146]

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

[0148] make right Derived, we get the gradient of the cost function of the second stage. The gradient of the cost function of 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 of the first stage 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 a 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 blind equalization in the second stage to make it optimal and minimize the cost function in 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] Among them, 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 blind equalization in the second stage to make it optimal and minimize the cost function in 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 adopts high-order QAM modulation. The cost function of the first stage under the high-order QAM modulation channel of the cognitive communication system is constructed according to the MMA-MLSM algorithm. The iterative formula of the blind equalization of the first stage under the high-order QAM modulation channel is constructed according to the Newton method. Then, the blind equalizer is optimized 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. Since the single constant modulus used in MMA is not equal to the multi-mode value of the output signal, even if the equalizer is fully converged, the output error level in the steady state will be very large, which will affect the performance of the equalizer. Therefore, this application determines the switching threshold based on the blind equalization output and switches to the second stage in time. In the second stage, the cost function of the second stage under the high-order QAM modulation channel of the cognitive communication system is constructed according to the ISDDA-MLSM algorithm. The iterative formula of the blind equalization of the second stage under the high-order QAM modulation channel is constructed according to the Newton method. The blind equalizer is optimized 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, so as to realize the high-order QAM blind equalization of 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 methods is only for clear description. When implemented, 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 to the algorithm or process or introducing insignificant designs 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, both SCMEMA and the proposed method avoid the local minimum points of the constellation matching function of SCMEMA and the ISDDA of TSBEA-MLSM through their first-stage equalization. In addition, when CIR is set to h1(n), the blind equalizer has good convergence performance.

[0167] like Figure 7As shown in Figure 2, when the SNR is large and the CIR is h1(n), the MSE of TSBEA-MLSM is almost equal to that of SCMEMA and DMGSA, and is significantly lower than that of CMA. The superior performance of the two-stage method is due to the constellation matching error method in the second stage, which avoids the misalignment 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 when CIR is h1(n). Figure 8 It can be seen that TSBEA-MLSM, SCMEMA and DMGSA have better equalization performance than CMA because the constellation matching error method eliminates the steady-state misalignment problem. In addition, the SER of TSBEA-MLSM is smaller than that of SCMEMA and DMGSA. This is due to the following two reasons. First, TSBEA-MLSM adopts a batch processing method to avoid the extreme error of the adaptive method. Second, the decision domain of adaptive selection improves the reliability of TSBEA-MLSM.

[0169] Fig. 9 The ISI of TSBEA-MLSM, SCMEMA, and DMGSA is shown when CIR is h1(n). The number of iterations required for TSBEA-MLSM to converge is less than 20, while SCMEMA is 4000, DMGSA is 12000, and CMA is 10000. TSBEA-MLSM has a faster convergence speed due to its quadratic termination feature.

[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 equalization accuracy.

[0171] like Fig. 9 As shown in Figure 1, the switching points of SCMEMA and TSBEA-MLSM are k = 3000 and k = 1, respectively. When k = 3000, the ISI of SCMEMA is about 0.04. In this case, the constellation matching error method can greatly speed up the convergence speed. In contrast, when k = 1, the ISI of TSBEA-MLSM is about 0.17, which shows that TSBEA-MLSM switches to the second stage earlier and ISDDA-MLSM has stronger fault tolerance.

[0172] Fig.10In (a), the transmission signal profile shows phase rotation, indicating that the 3000 iterations of CMA provide a good initial value for SCMEMA. When CIR is h2(n), SCMEMA fails. This is mainly because when CIR is h1(n), the first-stage equalizer output of SCMEMA does not rotate as a whole, while CIR h2(n) causes the phase rotation of the equalizer output signal. SCMEMA is based on constellation coordinates, and the real (imaginary) part of these rotated constellation points is not located at the minimum of the sine function. Therefore, the initialization is invalid, resulting in equalization failure. In contrast, the algorithm has good convergence and equalization because the BE with MMA provides an output signal that does not rotate, and the coordinates of these output constellation points are close to the minimum of the improved soft decision cost function. In addition, since A4NS has a large fault tolerance space, the decision of the algorithm is robust, so the algorithm does not require a good initial value. Fig.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 Fig.12 and Fig.13 As shown in Figure 2, when CIR is h2(n), TSBEA-MLSM has the best equalization performance in terms of MSE and SER. This is because the two-stage method avoids the misalignment of MMA, the batch processing technique eliminates the inaccuracy of the adaptive method, and the adaptive selection decision domain scheme improves the reliability of TSBEA-MLSM.

[0174] like Fig.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 CIR is h1(n), other methods show similar convergence performance. The algorithm has quadratic termination characteristics and optimal steady-state performance, with a faster convergence speed. When CIR is h2(n), switching to the second stage of TSBEA-MLSM, the convergence speed of TSBEA-MLSM is accelerated. Comparing the ISI when CIR is h1(n) and h2(n) 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 implementation details of the high-order QAM blind equalization system based on a cognitive communication system proposed in this embodiment are specifically described below. The following content is only for the convenience of understanding the implementation details provided, and is not necessary for implementing this example. Fig.14It 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, where the cognitive communication system adopts high-order QAM modulation.

[0177] The first-stage optimization module 202 is used to construct the first-stage cost function of the high-order QAM modulation channel of the cognitive communication system according to the MMA-MLSM algorithm, construct the iterative formula of the first-stage blind equalization under the high-order QAM modulation channel according to 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 used 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 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 second-stage blind equalization under the high-order QAM modulation channel according to 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 cost function of the second stage, so as to realize the 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 method embodiment, and this embodiment can be implemented in conjunction with the above method embodiment. The relevant technical details and technical effects mentioned in the above embodiments are still valid in this embodiment, and in order to reduce repetition, they are not repeated here. Accordingly, the relevant technical details mentioned in this embodiment can also be applied in the above embodiments.

[0181] It is worth mentioning that all modules involved in this embodiment are logic modules. In practical applications, a logic unit can be a physical unit, a part of a physical unit, or a combination of multiple physical units. In addition, in order to highlight the innovative part of this application, this embodiment does not introduce units that are not closely related to solving the technical problems proposed by this application, but this does not mean that there are no other units in this embodiment.

[0182] Another embodiment of the present application provides an electronic device, whose specific structure can be as follows: Fig.15As shown, it includes: at least one processor 301; and a memory 302 that is 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 so that the at least one processor 301 can execute a high-order QAM blind equalization method based on a cognitive communication system as described in the above-mentioned method embodiments.

[0183] Among them, the memory and the processor are connected in a bus manner, and the bus may include any number of interconnected buses and bridges, and the bus connects various circuits of one or more processors and memories together. The bus can also connect various other circuits such as peripheral devices, voltage regulators and power management circuits together, which are all well known in the art, so this article will not describe them further. The bus interface provides an interface between the bus and the transceiver. The transceiver can be one element or multiple elements, such as multiple receivers and transmitters, providing a unit for communicating with various other devices on a transmission medium. The data processed by the processor is transmitted on the wireless medium through the antenna, and further, the antenna also receives the data and transmits the data 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 can understand that all or part of the steps in the above-mentioned embodiment method can be completed by instructing the relevant hardware through a program, and the program is stored in a storage medium, including a number of instructions to enable a device (which can be a single-chip microcomputer, chip, etc.) or a processor to execute all or part of the steps of the method described in each embodiment of the present application. The aforementioned storage medium includes: U disk, mobile hard disk, ROM (Read-Only Memory), RAM (Random Access Memory), disk or optical disk and other media that can store program codes.

[0187] Those skilled in the art will appreciate that the above embodiments are specific embodiments for implementing the present application, and 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 cognitive communication system, which uses high-order QAM modulation; The cost function of the first stage of the cognitive communication system under the high-order QAM modulation channel is constructed according to the MMA-MLSM algorithm. The iterative formula of the blind equalization of the first stage under the high-order QAM modulation channel is constructed according to the Newton method. The blind equalizer is optimized 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. 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 ISDDA-MLSM algorithm, the cost function of the second 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 second stage blind equalization under the 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, so as to realize the high-order QAM blind equalization of the cognitive communication system.

2. A high-order QAM blind equalization method based on a cognitive communication system according to claim 1, characterized in that: Construct a system model of cognitive communication system, including: Let the channel order be L, let the sequence a(n) be a QAM modulated signal that obeys independent and identical distribution, and a(n) is sent through a linear system with impulse response h(n); The blind equalization input is expressed by the following formula: Where v(n) is complex additive Gaussian white noise with a mean of 0 and a variance of The channel order is The impulse response of the linear blind equalizer is: The blind equalization output is expressed by the following formula:

3. A high-order QAM blind equalization method based on a cognitive communication system according to claim 2, characterized in that: The cost function of the first stage of the cognitive communication system under the high-order QAM modulation channel is constructed according to the MMA-MLSM algorithm. The iterative formula of the blind equalization of the first stage under the high-order QAM modulation channel is constructed according to the Newton method. The blind equalizer is optimized 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, including: The cost function of the first stage is expressed as: 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; make right Derived, 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: Among them, sign(·) is the sign function, is the sample matrix; By letting Approximately equal to 0, we get: Where k is the number of iterations; The approximate least squares solution of BE is: The iterative formula of the first stage blind equalization is obtained as follows: in, 4. The high-order QAM blind equalization method based on cognitive communication system according to claim 3, characterized in that: The switching threshold is determined based on the blind equalization output, including: 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, The function representing the error of the blind equalization output, It follows a normal distribution. The probability density function is N(0,σ 2 ); 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: 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; 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 5. A high-order QAM blind equalization method based on a cognitive communication system according to claim 4, characterized in that: According to the ISDDA-MLSM algorithm, the cost function of the second 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 blind equalization of the second stage under the high-order QAM modulation channel is constructed. 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, 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 by the formula: Among them, R p and I q are preset constants. represents the cost function of the second stage; make right Derived, we get the gradient of the cost function of the second stage. The gradient of the cost function of the second stage is expressed by the formula: in, Represents the gradient of the cost function of the second stage; make And 1 / 2σ 2 Ignore, you can Simplified to: The iterative formula of the first stage blind equalization is obtained as follows:

6. A high-order QAM blind equalization method based on a cognitive communication system according to any one of claims 2 to 5, 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 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 evaluating the equalization quality is: MSE=E{|Cy(n)-a(n-τ)| 2 }; Among them, τ represents the delay, and MSE represents the equalization quality evaluation result.

7. A high-order QAM blind equalization method based on a cognitive communication system according to any one of claims 2 to 5, 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 the high-order QAM blind equalization of the cognitive communication system is evaluated by ISI. The formula for evaluating the convergence speed is: Wherein, ISI represents the convergence speed evaluation result.

8. A high-order QAM blind equalization system based on a cognitive communication system, suitable for a cognitive communication system, characterized in that: The system comprises: A model building module for building a system model of a cognitive communication system using 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 according to the MMA-MLSM algorithm, construct the iterative formula of the first-stage blind equalization under the high-order QAM modulation channel according to 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; A switching module, used 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 cost function of the second stage under the high-order QAM modulation channel of the cognitive communication system 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 cost function of the second stage, and realize the high-order QAM blind equalization of the cognitive communication system.

9. 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 executable 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 in any one of claims 1 to 7.

10. 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 as described in any one of claims 1 to 7.

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