WO2019213931A1

WO2019213931A1 - Iterative demodulation method for improving reliability of multi-carrier differential chaotic communication system

Info

Publication number: WO2019213931A1
Application number: PCT/CN2018/086463
Authority: WO
Inventors: 张琳; 陈炳均; 陈翔
Original assignee: 中山大学
Priority date: 2018-05-09
Filing date: 2018-05-11
Publication date: 2019-11-14

Abstract

Disclosed is an iterative demodulation method for improving reliability of a multi-carrier differential chaotic communication system, improving the bit error rate performance of the multi-carrier differential chaotic communication system without changing a sending end by optimizing a demodulation mode of a receiving end of the multi-carrier differential chaotic communication system and fully utilizing information received by the receiving end. In the multi-carrier differential chaotic communication system, generally, one sub-carrier is used for transmitting a reference signal, and the remaining sub-carriers are used for transmitting modulation signals using the reference signal as a carrier. The energy efficiency and the transmission efficiency are improved by sharing one reference signal by a plurality of signals, and moreover, the problem of requiring delay lines is solved by using multiple carriers. In the present invention, by designing a novel demodulation scheme on the receiving end, performing iterative demodulation on the modulation signals sharing the same reference signal, and improving the signal-to-noise ratio of the reference signal by using correlation between the signals, the demodulation accuracy is improved, and the bit error rate of the system is reduced.

Description

An Iterative Demodulation Method for Improving the Reliability of Multi-Carrier Differential Chaotic Communication System

Technical field

The invention relates to the technical field of wireless multi-carrier chaotic communication, and particularly relates to an iterative demodulation method for improving the reliability of a multi-carrier differential chaotic communication system.

Background technique

Because chaotic sequences have the characteristics of initial value sensitivity and aperiodicity, chaotic modulation can effectively improve the security of the physical layer and enhance the robustness under multipath fading channels. The digital chaotic modulation scheme can be divided into two types, coherent and non-coherent, depending on whether chaotic synchronization is required. However, in practical communication systems, the realization of chaos is more difficult. Therefore, since it is not necessary to use a complex chaotic synchronization circuit to recover the reference chaotic signal at the receiving end, the non-coherent chaotic modulation has stronger practicability.

In the existing non-coherent chaotic modulation technology, Differential Chaos Shift Keying (DCSK) has received extensive attention due to the removal of complex chaotic synchronization circuits and the ability to provide better bit error rate. In the literature "M. Sushchik, LSTsimring, and AR Volkovskii, "Performance analysis of correlation-based communication schemes utilizing chaos," IEEE Trans. Circuits Syst. I, Fundam. Theory Appl., vol. 47, no. 12, pp .1684–1691, 2000.” A detailed analysis was made. Similarly, it has two major drawbacks, in the literature "T.Huang, L. Wang, W. Xu, and G. Chen, "A Multi-Carrier M-Ary Differential Chaos Shift Keying System With Low PAPR," IEEE Access , vol. 5, pp. 18793–18803, 2017.” indicates that because of the need to transmit reference signals, only half of the time slots are used to transmit information, resulting in lower energy utilization and spectral efficiency. At the same time, the implementation of the demodulator is more complicated due to the need for a delay line at the receiving end.

In order to solve the two shortcomings of DCSK, multi-carrier transmission is applied to the DCSK system. The use of multiple carriers allows the separation of reference and information signals without the use of delay lines and the sharing of the same reference signal by multiple information signals to improve energy efficiency and spectral efficiency. In the literature "G. Kaddoum, F. Gagnon, and F.-D. Richardson, "Design of a secure multi-carrier DCSK system," in Proc. 2012 International Symposium on Wireless Communication Systems, pp. 964-968, IEEE, In 2012, multi-carriers were first applied to DCSK systems to improve the security of DCSK systems. Subsequently, multiple versions of the multi-carrier DCSK system were proposed, in which the document "S. Li, Y. Zhao, and Z. Wu, "Design and analysis of an OFDM-based differential chaos shift keying communication system," J. Commun. Vol. 10, no. 3, pp. 199-205, 2015. proposes that the OFDM-DCSK system implementing multi-carrier using OFDM simplifies the complexity of the multi-carrier DCSK system.

However, the multi-carrier DCSK system has the same disadvantages as the general DCSK system with a high peak-to-average power ratio (PAPR). In the literature "T.Huang, L. Wang, W. Xu, and G. Chen, "A Multi-Carrier M-Ary Differential Chaos Shift Keying System With Low PAPR," IEEE Access, vol. 5, pp. 18793 - 18803 , 2017" proposed a multi-carrier DCSK scheme of MM-DCSK to reduce PAPR.

In the various multi-carrier DCSK system schemes, most of the multi-carrier nature is utilized to remove the delay line and improve energy and spectrum utilization. There is no further consideration for using other methods to improve the reliability of the system. Moreover, the multi-carrier DCSK system is not sufficient for the received information, and its bit error rate performance is still somewhat different from the traditional BPSK system.

Summary of the invention

The object of the present invention is to solve the above-mentioned drawbacks in the prior art, further improve the reliability of the multi-carrier DCSK system, and provide an iterative demodulation method for improving the reliability of the multi-carrier differential chaotic communication system.

The object of the present invention can be achieved by adopting the following technical solutions:

An iterative demodulation method for improving the reliability of a multi-carrier differential chaotic communication system, the method comprising the following steps:

S1, chaotic sequence generation step, using chaotic signal generator to generate chaotic sequence. The vector form is expressed as C=[c ₁ c ₂ ... c _β ], where β is the spreading factor, which is the length of the chaotic sequence, and c _β is the βth chaotic signal in the chaotic sequence.

S2, multi-carrier modulation step of differential chaotic communication system, the differential chaotic system needs to use the chaotic sequence C as the reference signal, and the binary phase shift keying (BPSK) signal d generates the modulated signal as dC=[dc ₁ dc ₂ ... dc _β ], in the differential chaotic system, the reference signal C and the modulated signal dC need to be transmitted through the wireless signal. For the case of a multi-carrier differential chaotic system, the reference signal C is used to modulate m BPSK signals to generate d _n C=[d _n c ₁ d _n c ₂ ... d _n c _β ], 1≤n≤m, ie m BPSK The signal shares a set of reference signals C. Then, the reference chaotic signal C is separately transmitted by using one subcarrier, and the m subcarriers respectively transmit the modulated signal d _n C (1≤n≤m), and the total number of subcarriers is (m+1).

S3. The receiving and separating steps of the multi-carrier signal separate the received multi-carrier signals and store a total of m+1 sets of chaotic sequences.

S4. The demodulation step of the received signal. In the wireless communication channel, the signal is subjected to multiplicative fading and additive noise. At the receiving end of the multi-carrier chaotic communication, let h denote the channel fading factor of the flat slow fading channel, and N ₀ denotes A Gaussian white noise vector with a length of β, where each noise is an independently and equally distributed Gaussian white noise signal. And their variance is σ ² and the bilateral power spectral density is N ₀ /2. , the received reference signal is expressed as

R=hC+N ₀ (1)

Similarly, the received modulated signal is expressed as

R _n =hd _n C+N _n (2)

Where R _n represents the nth modulated signal (1 ≤ n ≤ m). N _n is a noise vector with a length of β, where each noise is an independently and equally distributed Gaussian white noise signal. And their variance is σ ² and the bilateral power spectral density is N ₀ /2. The initial demodulation of the nth modulated signal (1 ≤ n ≤ m) results in:

Where sgn[·] is a symbolic function that returns the positive and negative of the argument. [R·R _n ] is the inner product operation of the vector.

S5. The calibration step of the reference signal corrects the reference signal according to the demodulation result, and the correction mode is as shown in the formula (4).

In the formula,

For the first demodulation result obtained in step S4, corresponding to the demodulation result of the nth modulated signal (1≤n≤m), R _n is represented by the formula (2), R _n =hd _n C+N _n . C ¹ is the first corrected reference signal.

S6. Iterative demodulation step. The modulated signal is iteratively demodulated according to equations (3) and (4) in step S4 and step S5. The reference signal is first corrected by equation (4) for each iteration. For the ith correction, the result can be given by equation (5):

among them

The result of the i-1th demodulation of the nth modulated signal (1 ≤ n ≤ m), when i = 1,

As shown in equation (3), when i>1,

Given by equation (6):

Where C ^i-1 is the reference signal for the i-1th correction. The general formula (5) (6) can be obtained, and the iterative reference signal is:

S7, an iterative termination step, each of which can determine the corrected reference signal C ⁱ and the demodulation result

The termination condition of the selected iteration is terminated if it is satisfied, otherwise the iterative process in step S6 is repeated.

Further, in the chaotic sequence generation step, the chaotic signal generator adopts a Chebyshev map, and the map can be expressed as:

c _n+1 =cos(kcos ^-1 c _n )c _n ∈(-1,1) (8)

Where k is the order of the Chebyshev map, which is a positive integer, and c _n is the generated chaotic signal. When the spreading factor is β, β chaotic signals are continuously taken from the chaotic signal generator to form a chaotic sequence C=[c ₁ c ₂ ... c _β ]. Generally, k=2 is used, and the formula (8) can be rewritten as:

Further, in the multi-carrier modulation step of the differential chaotic communication system, the chaotic sequence is modulated onto the multi-carrier, and the orthogonal frequency division multiplexing (OFDMC) method is used, and the inverse discrete Fourier transform (IDFT) is performed. The representation of) is:

Where d ₀ =1, ₀ ≤ k ≤ m, signals can be obtained after multi-carrier modulation

The obtained Y _{i is} sequentially transmitted.

Further, in the step of receiving and separating the multi-carrier signal, the separation of the multi-carrier signal is performed by using a Discrete Fourier Transform (DFT) method, and the signal is extracted from the modulated multi-carrier, for receiving signal of

The form in which the signal is separated using DFT is:

Where 0 ≤ n ≤ m. Signals modulated to multiple carriers can be extracted using DFT.

Further, in the iterative termination step, the condition of the iterative termination is that the iteration no longer corrects the reference signal and does not change the demodulation result, that is, C ⁱ =C ^i-1 and

When it stops, iterates. Depending on the complexity of the operation, choose

Terminate the condition for iteration.

The present invention has the following advantages and effects over the prior art:

The invention combines the demodulated information with the corresponding received signal by performing conventional DCSK demodulation at the receiving end, and combines all the signals obtained by the multiplication with the reference signal to obtain a corrected reference signal. The signal is demodulated again. This loop iterates until the results of the two demodulations are identical, that is, after the iteration does not have any benefit, the final demodulation result is obtained. The signal-to-noise ratio of the reference signal used for demodulation is improved by continuously correcting the reference signal. The method fully utilizes the frequency diversity of the wireless channel, and by continuously combining the demodulated signals, the signal carrying the information is used to modify the reference signal, thereby fully utilizing the received information, thereby reducing the bit error rate of the demodulated information, thereby effectively Improve the reliability of multi-carrier DCSK systems. The invention improves the reliability of multi-carrier differential chaotic communication with low complexity.

DRAWINGS

Figure 1 is a schematic diagram of DCSK modulation;

2 is a schematic diagram of DCSK demodulation;

3 is a schematic diagram of an iterative demodulation method for improving the reliability of a multi-carrier differential chaotic communication system disclosed in the present invention;

4 is a comparison diagram of bit error rate performance between AWGN channel and conventional multi-carrier DCSK;

Figure 5 is a comparison of the performance of the Rayleigh channel and the conventional multi-carrier DCSK bit error rate;

Figure 6 is a graph comparing the bit error rate performance at different spreading factors (i.e., chaotic sequence length β).

detailed description

The technical solutions in the embodiments of the present invention will be clearly and completely described in conjunction with the drawings in the embodiments of the present invention. It is a partial embodiment of the invention, and not all of the embodiments. All other embodiments obtained by those skilled in the art based on the embodiments of the present invention without creative efforts are within the scope of the present invention.

Embodiment 1

This embodiment discloses an iterative demodulation method for improving the reliability of a multi-carrier differential chaotic communication system, which specifically includes:

S1, chaotic sequence generation step, using chaotic signal generator to generate chaotic sequence. The vector form is expressed as C=[c ₁ c ₂ ... c _β ], where β is the spreading factor, which is the length of the chaotic sequence, and c _β is the βth chaotic signal in the chaotic sequence. The chaotic signal generator uses a Chebyshev map, which can be expressed as

c _n+1 =cos(kcos ^-1 c _n )c _n ∈(-1,1) (8)

Where k is the order of the Chebyshev map, which is a positive integer, and c _n is the generated chaotic signal. When the spreading factor is β, β chaotic signals are continuously taken from the chaotic signal generator to form a chaotic sequence C=[c ₁ c ₂ ... c _β ].

S2, multi-carrier modulation step of differential chaotic system, the differential chaotic system needs to use the chaotic sequence C as the reference signal, and the Binary Phase Shift Keying (BPSK) signal d generates the modulated signal as dC=[dc ₁ Dc ₂ ... dc _β ], in the differential chaotic system, the reference signal C and the modulated signal dC need to be transmitted through the wireless signal. For the case of a multi-carrier differential chaotic system, the reference signal C is used to modulate m BPSK signals to generate d _n C=[d _n c ₁ d _n c ₂ ... d _n c _β ], 1≤n≤m, ie m BPSK The signal shares a set of reference signals C. Then, the reference chaotic signal C is separately transmitted by using one subcarrier, and the m subcarriers respectively transmit the modulated signal d _n C (1≤n≤m), and the total number of subcarriers is (m+1). The chaotic sequence is modulated onto multiple carriers and obtained by orthogonal frequency division multiplexing.

The obtained Y _{i is} sequentially transmitted.

S3. The receiving and separating steps of the multi-carrier signal, using the discrete Fourier transform to separate the received multi-carrier signals and storing a total of m+1 sets of chaotic sequences. For received signals

It uses DFT to separate the signal as

Where 0 ≤ n ≤ m.

S4. The demodulation step of the received signal. In the wireless communication channel, the signal is subjected to multiplicative fading and additive noise. At the receiving end of the multi-carrier chaotic communication, let h denote the channel fading factor of the flat slow fading channel, and N ₀ denotes A Gaussian white noise vector with a length of β, where each noise is an independently and equally distributed Gaussian white noise signal. And their variance is σ ² and the bilateral power spectral density is N ₀ /2. , the received reference signal is R=hC+N ₀ , and the received modulated signal is represented as R _n =hd _n C+N _n , where R _n represents the nth modulated signal (1≤n≤m ). N _n is a noise vector with a length of β, where each noise is an independently and equally distributed Gaussian white noise signal. And their variance is σ ² and the bilateral power spectral density is N ₀ /2. The initial demodulation of the nth modulated signal (1 ≤ n ≤ m) results in

In the formula,

among them

As shown in equation (3), when i>1,

Given by equation (6):

The termination condition for the selected iteration. Further, in the iterative termination step, the condition of the iterative termination is that the iteration no longer corrects the reference signal and does not change the demodulation result, that is, C ⁱ =C ^i-1 and

When it stops, iterates. Depending on the complexity of the operation, choose

Terminate the condition for iteration. If it is satisfied, it is terminated, otherwise the iterative process in step S6 is repeated.

Embodiment 2

S1, chaotic sequence generation step, using chaotic signal generator to generate chaotic sequence. The chaotic signal generator uses a second-order Chebyshev map, which can be expressed as

The spreading factor is chosen to be β=128, m=128. The number of subcarriers is m+1=129. The vector form is expressed as C = [c ₁ c ₂ ... c ₁₂₈ ].

S2. The multi-carrier modulation step of the differential chaotic communication system uses the reference signal C to modulate m=128 BPSK signals to generate d _n C=[d _n c ₁ d _n c ₂ ... d _n c ₁₂₈ ], 1≤n≤128. The reference chaotic signal C is then separately transmitted using one subcarrier, and the remaining 128 subcarriers respectively transmit the modulated signal d _n C (1 ≤ _n ≤ m).

The obtained Y _{i is} sequentially transmitted.

S3. The receiving and separating steps of the multi-carrier signal, using the discrete Fourier transform to separate the received multi-carrier signals and storing a total of 129 sets of chaotic sequences. For received signals

It uses DFT to separate the signal as

Where 0 ≤ n ≤ 128.

S4. A demodulation step of the received signal. In the wireless communication channel, the signal is subjected to multiplicative fading and additive noise. At the receiving end of the multi-carrier chaotic communication, let h denote the channel fading of the flat slow fading channel (ie, the Rayleigh fading channel). The factor, N ₀ represents an additive white Gaussian noise vector with a length of β=128, wherein each noise is an independently and equally distributed Gaussian white noise signal. And their variance is σ ² and the bilateral power spectral density is N ₀ /2. , the received reference signal is R=hC+N ₀ , and the received modulated signal is represented as R _n =hd _n C+N _n , where R _n represents the nth modulated signal (1≤n≤m =128). N _n is a noise vector with a length of β, where each noise is an independently and equally distributed Gaussian white noise signal. And their variance is σ ² and the bilateral power spectral density is N ₀ /2. The initial demodulation of the nth modulated signal (1 ≤ n ≤ m = 128) results in

S5. The calibration step of the reference signal corrects the reference signal according to the demodulation result, and the calibration mode is as shown in the formula (4), and the correction is performed to obtain C ¹ .

S6. Iterative demodulation step. For the ith correction, the result can be given by equation (5):

among them

As shown in equation (3), when i>1,

Given by equation (6):

S7, iterative termination step, when

When it stops, iterates. If it is satisfied, it is terminated, otherwise the iterative process in step S6 is repeated.

When the channel fading factor h = 1 of the flat slow fading channel, the channel becomes an Additive White Gaussian Noise (AWGN) channel. As shown in FIG. 4, the comparison between the AWGN channel and the traditional multi-carrier DCSK bit error rate performance, wherein the spreading factor β=128, the number of subcarriers m+1=129. It can be observed from Fig. 4 that when only one iteration of demodulation is performed, a larger gain can be obtained, and the bit error rate is drastically reduced, and it can be seen that when multiple iterations are performed, it can be obtained better. The result, but much smaller than the gain obtained with the first time. At the same time, it can be found that after multiple iterations, it is easier to obtain further reduction in places where the bit error rate is relatively large.

When h≠1 and is a Rayleigh distribution variable, the variance σ ² =1, the spreading factor β=128, and the number of subcarriers m+1=129. It can be seen from Fig. 5 that in the Rayleigh fading channel, when an iterative demodulation is performed, a larger gain can be obtained, and the bit error rate is significantly reduced, and it can be seen that after performing multiple iterative demodulation, it can be obtained. Better results, but slightly smaller than the gain obtained with the first time. Overall, the gain obtained under the Rayleigh fading channel is relatively uniform.

Finally, the present embodiment considers different spreading factors β, that is, the perch information corresponding to the length of the chaotic sequence required for modulation, and the impact on the bit error performance of the improved demodulation scheme, wherein the channel fading factor h=1 the number of subcarriers m+ 1 = 129, signal to noise ratio SNR = 10 dB. It can be seen from Fig. 6 that in the case of each spreading factor, the improved demodulation scheme has different results for different spreading factors β, but it can be seen that better demodulation results can be obtained, and bit error reduction is achieved. The effect of the rate proves that its reliability is better than the traditional method.

According to Figure 4-6, the following conclusions can be drawn:

In the AWGN and Rayleigh fading channels, the improved demodulation scheme can effectively reduce the bit error rate of the multi-carrier DCSK system, and according to the comparison, the improved demodulation scheme under the AWGN channel can get better optimization effect. .

2. For different spreading factors β, the improved demodulation scheme can effectively reduce the bit error rate and improve the reliability of the system.

The above embodiments are preferred embodiments of the present invention, but the embodiments of the present invention are not limited to the above embodiments, and any other changes, modifications, substitutions, combinations, and combinations thereof may be made without departing from the spirit and scope of the invention. Simplifications should all be equivalent replacements and are included in the scope of the present invention.

Claims

An iterative demodulation method for improving the reliability of a multi-carrier differential chaotic communication system, characterized in that the method comprises the following steps:

S1, chaotic sequence generation step, chaotic sequence generator is used to generate chaotic sequence, chaotic sequence is represented by vector form as C=[c 1 c 2 ...c β ], where β is a spreading factor, which is the length of the chaotic sequence, c β is the βth chaotic signal in the chaotic sequence;

S2, a multi-carrier modulation step of the differential chaotic communication system, the differential chaotic communication system uses the chaotic sequence C as a reference signal, and the binary phase-shift keying signal d generates a modulated signal as dC=[dc 1 dc 2 ... dc β ], Then, the chaotic sequence C as the reference signal and the modulated signal dC are transmitted by the wireless signal. For the multi-carrier differential chaotic communication system, the chaotic sequence C is used to modulate the m BPSK signals d n to generate d n C=[d n c 1 d n c 2 ... d n c β ], 1 ≤ n ≤ m, that is, m BPSK signals share the chaotic sequence C as a reference signal, and then use a subcarrier to separately transmit a chaotic sequence C as a reference signal, m subcarriers respectively Transmitting the modulated signal d n C, the total number of subcarriers is (m+1);

S3. The receiving and separating steps of the multi-carrier signal, separating the received multi-carrier signals, and storing a total of m+1 sets of chaotic sequences;

S4. The demodulation step of the received signal, at the receiving end of the multi-carrier chaotic communication system, let h denote the channel fading factor of the flat slow fading channel, N 0 denotes an additive white Gaussian noise vector, and the length is β, wherein each noise is For independent and identically distributed Gaussian white noise signals, and their variance is σ 2 and the bilateral power spectral density is N 0 /2, the received reference signal is expressed as

R=hC+N 0 (1)

Similarly, the received modulated signal is expressed as

R n =hd n C+N n (2)

Where R n represents the nth modulated signal, where 1 ≤ n ≤ m, N n is a noise vector, and the length is β, wherein each noise is an independently and identically distributed Gaussian white noise signal, and their variance is σ 2. The bilateral power spectral density is N 0 /2, and the initial demodulation of the nth modulated signal results in:

Where sgn[·] is a symbolic function, returning the positive and negative of the parameter, and [R·R n ] is the inner product operation of the vector;

S5. The calibration step of the reference signal corrects the reference signal according to the demodulation result, and the correction mode is as shown in the formula (4):

In the formula,
For the first demodulation result obtained in step S4, corresponding to the demodulation result of the nth modulated signal, it is known from equation (2) that R n =hd n C+N n , and C 1 is the first corrected Reference signal

S6. Iterative demodulation step, iteratively demodulates the modulated signal, and corrects the reference signal by using equation (4) for each iteration. For the ith correction, the result is given by equation (5):

among them
The result of the i-1th demodulation of the nth modulated signal, when i=1,
As shown in equation (3), when i>1,
Given by equation (6):

Where C i-1 is the reference signal corrected by the i-1th time, and the reference signal obtained by the integrated equation (5) (6) is:

S7, an iterative termination step, each of which can determine the corrected reference signal C i and the demodulation result
The termination condition of the selected iteration is terminated if it is satisfied, otherwise the iterative process in step S6 is repeated.
An iterative demodulation method for improving the reliability of a multi-carrier differential chaotic communication system according to claim 1, wherein

In the chaotic sequence generation step, the chaotic signal generator adopts a Chebyshev map, and the map is expressed as:

c n+1 =cos(κcos -1 c n ),c n ∈(-1,1) (8)

Where κ is the order of Chebyshev map, which is a positive integer, c n is the generated nth chaotic signal. When the spreading factor is β, β chaotic signals are continuously taken from the chaotic signal generator to form a chaotic sequence C. =[c 1 c 2 ...c β ].
An iterative demodulation method for improving the reliability of a multi-carrier differential chaotic communication system according to claim 2, wherein the Chebyshev map has an order κ=2, and the equation (8) is rewritten as :
An iterative demodulation method for improving the reliability of a multi-carrier differential chaotic communication system according to claim 1, wherein

In the multi-carrier modulation step of the differential chaotic communication system, the chaotic sequence C is modulated onto the multi-carrier, and the orthogonal frequency division multiplexing method is adopted, and the representation of the inverse discrete Fourier transform is:

Where d 0 =1, 0 ≤ k ≤ m, c i represents the i-th chaotic signal. Signal obtained after multi-carrier modulation
1 ≤ i ≤ β, the differential chaotic communication system sequentially transmits the obtained Y i .
An iterative demodulation method for improving the reliability of a multi-carrier differential chaotic communication system according to claim 4, wherein

In the step of receiving and separating the multi-carrier signal, the separation of the multi-carrier signal is performed by using a discrete Fourier transform method to extract the signal from the modulated multi-carrier, for the received signal.
The form in which the signal is separated using DFT is:

Where 0 ≤ n ≤ m, the signal modulated to a plurality of carriers is extracted using DFT.
An iterative demodulation method for improving the reliability of a multi-carrier differential chaotic communication system according to claim 1, wherein

In the iterative termination step, the condition of the iterative termination is that the iteration no longer corrects the reference signal and no longer changes the demodulation result, ie, C i =C i-1 and
When it stops, iterates.