A method for demodulating amplitude coded modulated linear frequency modulated signals

Abstract

The application provides a method for demodulating amplitude-coded modulated linear frequency modulation signals, which comprises the following steps: first, designing the amplitude-coded modulated linear frequency modulation signals; for a random communication sequence {a n}, the coded signal a(t) is a single-polarity non-return-to-zero signal of the coded sequence {a n}, the linear frequency modulation signal is denoted as s(t), the coded signal is used to modulate the linear frequency modulation signal, and the obtained modulated signal is x(t)=a(t)·s(t); second, designing the correlation reference signal; a code element width is T B , the linear frequency modulation signal is truncated with the width of T B , and a plurality of phase-coherent sub-linear frequency modulation signals are obtained; the nth sub-linear frequency modulation signal obtained by truncation is denoted as s n (t), and the correlation reference signal y(t) is the sum of all the sub-linear frequency modulation signals; third, performing correlation operation and sampling decision; the modulated signal x(t) is correlated with the preset correlation reference signal y(t), the correlation result is sampled at a specific time, and for a given threshold value, when the sampling value is greater than the threshold value, the result is determined as a "1" symbol, and otherwise, the result is determined as a "0" symbol.

Description

Technical field

[0001] The present invention relates to a method for demodulating an amplitude coded modulated linear frequency modulation signal, belongs to the field of radar communication integration, and specifically relates to a method for amplitude coded modulated linear frequency modulation signal and demodulating the modulated signal to recover communication information. [Background Technology]

[0002] With the rapid development of electronic information technology, radar sensing and wireless communication technologies have made significant progress in their respective specific tasks and application scenarios. Radar technology is primarily used for target detection, identification, and tracking, while wireless communication technology focuses on efficient information transmission. However, with spectrum resources becoming increasingly scarce, signal interference between radar and communication systems has become increasingly prominent. This not only limits the performance of both systems but also creates an urgent need for more efficient spectrum utilization.

[0003] To address these challenges, radar-communication integration has become a research hotspot in recent years. The core concept of radar-communication integration is to simultaneously meet the needs of radar sensing and wireless communication by sharing the same signal waveform, thereby improving spectrum utilization and reducing signal interference. Currently, research on integration focuses primarily on orthogonal frequency division multiplexing (OFDM) and linear frequency modulation (LFM) signal integration. However, both approaches inevitably face constraints and even conflicts between radar and communication functions, resulting in undesirable outcomes such as high bit error rates in the communication link or reduced radar target detection capabilities.

[0004] The present invention utilizes the coded signal in the communication system to perform amplitude modulation on the linear frequency modulation signal. The receiving end can effectively restore the original coded information by performing a correlation operation on the received modulated signal and a preset correlation reference signal, and making a judgment based on the result of the correlation operation, thereby reducing the bit error rate when the input signal-to-noise ratio is low. [Summary of the invention]

[0005] The technical problem addressed by this invention is that existing integrated signal processing systems suffer from defects such as high bit error rates due to the interplay between radar and communication functions. This invention modulates a coded signal onto a linear frequency modulation signal in amplitude form. At the receiving end, the modulated signal is correlated with a preset reference signal, and a decision is made based on the correlation result to ultimately recover the coded sequence.

[0006] The present invention relates to a method for demodulating an amplitude coded modulation linear frequency modulation signal, and the technical solution adopted is as follows:

[0007] The first step is to design the linear frequency modulation signal of amplitude coded modulation.

[0008] For a random communication sequence {a n}, let the coded signal a(t) be the coded sequence {a n} unipolar non-return-to-zero signal, with the symbols "0" and "1" corresponding to rectangular signals with amplitudes of 0 and +1, respectively. Assuming the linear frequency modulation signal is s(t), when the coded signal is used to amplitude modulate the linear frequency modulation signal, the resulting modulated signal is x(t) = a(t) · s(t). x(t) can be considered as consisting of multiple phase-coherent linear frequency modulation signals.

[0009] The second step is to design relevant reference signals.

[0010] Assume that the width of a code element (rectangular signal width) is T B , for linear frequency modulation signal, T B The width is truncated to obtain several phase-coherent sub-linear frequency modulation signals. Assume that the nth sub-linear frequency modulation signal obtained by truncation is s n (t), the related reference signal y(t) is the sum of all sub-linear frequency modulation signals.

[0011] The third step is related operations and sampling judgment.

[0012] According to the first and second steps, the modulated signal x(t) is correlated with the preset correlation reference signal y(t), and the correlation result is sampled at a specific time. For a given threshold value, when the sampled value is greater than the threshold value, it is judged as a "1" symbol, otherwise it is determined as a "0" symbol.

[0013] The beneficial effects of the present invention mainly include:

[0014] First, a demodulation method for amplitude-coded linear frequency modulation (LFM) signals is proposed. The coded signal is amplitude-modulated on the LFM signal, and correlation operations are used to recover the underlying communication information, reducing the bit error rate (BER) under low signal-to-noise ratio (SNR) conditions.

[0015] Second, a correlation reference signal model is designed. By segmenting the complete linear frequency modulation signal, several phase-coherent sub-linear frequency modulation signals are obtained. The correlation reference signal is synthesized by adding all the sub-linear frequency modulation signals.

[0016] Third, a bit error rate simulation experiment was completed, verifying that this demodulation method can reduce the bit error rate by adjusting the sampling rate and transmission rate.

Brief Description of the Drawings

[0017] Figure 1 It is the processing flow of the demodulation process.

[0018] FIG2(a) and FIG2(b) are waveform diagrams of the coded signal and the amplitude coded modulated linear frequency modulation signal, respectively.

[0019] FIG3(a) and FIG3(b) are waveform diagrams of the sub-linear frequency modulation signal and the related reference signal, respectively.

[0020] FIG4(a) and FIG4(b) are the correlation operation result and the coded signal after sampling and judgment, respectively.

[0021] Figure 5 It is a bit error rate curve at different sampling frequencies.

Specific implementation method

[0022] The present invention is further described below with reference to the accompanying drawings. The present invention relates to a method for demodulating an amplitude coded modulation linear frequency modulation signal, comprising the following steps:

[0023] The first step is to design the linear frequency modulation signal of amplitude coded modulation.

[0024] communication sequence {a n} is composed of random "0" and "1" symbols, and the corresponding coding signal a(t) is the coding sequence {a n} is a unipolar non-return-to-zero signal, recorded as:

[0025]

[0026] Among them, T B is the symbol width, rect(·) is a rectangular pulse with a height of 1 and a width of 1, which can be expressed as:

[0027]

[0028] The linear frequency modulation signal s(t) is:

[0029]

[0030] Where T is the signal pulse width, μ = B / T is the frequency modulation slope, B is the signal bandwidth, and j represents the imaginary unit.

[0031] The amplitude coded modulated linear frequency modulation signal x(t) can be expressed as:

[0032] x(t)=a(t)·s(t) (4)

[0033] The second step is to design relevant reference signals.

[0034] For the complete linear frequency modulation signal s(t), T B The width is segmented and truncated to obtain several phase-coherent sub-linear frequency modulation signals, and the nth sub-linear frequency modulation signal is recorded as s n (t) is:

[0035]

[0036] The relevant reference signal y(t) is the sum of all sub-linear frequency modulation signals and is expressed as:

[0037]

[0038] The third step is related operations and sampling judgment.

[0039] According to the first and second steps, the modulated signal x(t) is correlated with the reference signal y(t), and the correlation result R(τ) is:

[0040]

[0041] Where τ represents the time delay, m and n represent the subscript numbers, y*(t) represents the conjugate signal of y(t), R nm (τ) is s n (t) and s m The correlation function of (t). The correlation result can also be regarded as the matched filtering result of x(t) and y(t). k =kT B Time sampling, formula (7) is simplified to:

[0042]

[0043] where R kk (0) represents the value of the autocorrelation function of the kth sub-linear frequency modulation signal at time 0, and also represents the power of the kth sub-linear frequency modulation signal, R km (0) means that the cross-correlation function of the kth sub-linear frequency modulation signal and the mth sub-linear frequency modulation signal takes a value at time 0. When the kth code element is 1 (a k =1), the sampling value is composed of the autocorrelation function and the cross-correlation function; when the kth code element is 0 (a k =0), the sampled values ​​consist only of the cross-correlation function.

[0044] When any two different sub-linear frequency modulation signals are uncorrelated, then

[0045]

[0046] Satisfaction When , formula (8) is further simplified to:

[0047]

[0048] In digital computing, assuming that N points are sampled within a pulse width T, there are M code elements, and when the amplitude of x(t) is A, If the average power of additive white Gaussian noise is 2σ 2 , the correlation function R between the noise n(t) and the related reference signal y(t)n (τ k ) obeys the normal distribution, and the variance has an upper limit:

[0049]

[0050] where s m [k] represents the discrete expression of the mth linear frequency modulation signal. In addition, The phase of is affected by multiple parameters (B, T, N, M, etc.). After taking the modulo 2π, we can approximately assume that the phase values ​​are independent. On the other hand, the number of sampling points N is generally large, so we can approximately assume that the phase is uniformly distributed on [0, 2π]. Therefore, according to the central limit theorem, Therefore, when Gaussian white noise exists, formula (10) can be rewritten as:

[0051]

[0052] Among them, R n (τ k ) has a mean of 0 and a variance of 2Nσ 2 If the real part is selected for judgment, Equation (12) can be regarded as a complex normal distribution with an amplitude of The noise intensity is Nσ 2 The coherent demodulation of the demodulation effect is equivalent to the input signal-to-noise ratio The effect of coherent demodulation, where r = A 2 / (2σ 2 ) is the actual input signal-to-noise ratio. Therefore, the decision threshold level is:

[0053]

[0054] Assume that the coding sequence {a n}, the probability of "0" and "1" code elements appearing is equal, the bandwidth of the linear frequency modulation signal s(t) is B = 10MHz, the pulse width is T = 10μs, and the code element width is T B =1μs, sampling frequency f s =10MHz, modulated signal amplitude A=1, actual input signal-to-noise ratio r=5dB.

[0055] according to Figure 1 The simulation is performed by the flowchart shown in FIG2(a). The coded signal is shown in FIG2(b). The coded signal modulates the amplitude of the linear frequency modulation signal, and the modulated signal is shown in FIG2(b). BThe width is truncated to obtain several sub-linear frequency modulation signals, among which the 1st, 2nd and 3rd sub-linear frequency modulation signals are shown in Figure 3(a). All sub-linear frequency modulation signals are summed to obtain the correlation reference signal shown in Figure 3(b). The modulated signal is correlated with the preset correlation reference signal, and the correlation result is shown in Figure 4(a). The correlation result is sampled regularly and compared with the decision threshold, and the recovered coding signal is shown in Figure 4(b). It is not difficult to see that the recovered coding signal is consistent with the original coding signal. The sampling frequency is adjusted to 10MHz, 20MHz and 50MHz respectively, the actual input signal-to-noise ratio is adjusted, and multiple simulations are performed to obtain the relationship curve between the bit error rate and the sampling frequency as shown in Figure 4(a). Figure 5 As shown in Figure 2, it can be seen that by increasing the sampling frequency, the bit error rate can be reduced, and low bit error rate demodulation can be achieved under low signal-to-noise ratio.

Claims

1. A method for demodulating an amplitude coded modulated linear frequency modulation signal, characterized in that: The steps are as follows: The first step is to design the linear frequency modulation signal of amplitude coded modulation; For a random communication sequence {a n }, let the coded signal a(t) be the communication sequence {a n } unipolar non-return-to-zero signal, "0" and "1" symbols correspond to rectangular signals with amplitudes of 0 and +1 respectively; let the linear frequency modulation signal be denoted as s(t), when the linear frequency modulation signal is amplitude modulated by the coded signal, the modulated signal obtained is x(t) = a(t) s(t); The second step is to design relevant reference signals; Assume a code element width is T B , for linear frequency modulation signal, T B The width is truncated to obtain several phase-coherent sub-linear frequency modulation signals; let the nth sub-linear frequency modulation signal obtained by truncation be s n (t), the related reference signal y(t) is the sum of all sub-linear frequency modulation signals; The third step is correlation operation and sampling judgment; According to the first and second steps, the modulated signal x(t) is correlated with the preset correlation reference signal y(t). The correlation result is sampled at a specific time. For a given threshold value, when the sampled value is greater than the threshold value, it is determined to be a "1" symbol, otherwise it is determined to be a "0" symbol.

2. The method for demodulating an amplitude coded modulation linear frequency modulation signal according to claim 1, wherein: In the first step, the communication sequence {a n } is composed of random "0" and "1" symbols, and the corresponding coded signal a(t) is the communication sequence {a n } is a unipolar non-return-to-zero signal, recorded as: Among them, T B is the symbol width, rect(·) is a rectangular pulse with a height of 1 and a width of 1, which can be expressed as:

3. The method for demodulating an amplitude coded modulation linear frequency modulation signal according to claim 1 or 2, wherein: In the first step, the linear frequency modulation signal s(t) is: Where T is the signal pulse width, μ = B / T is the frequency modulation slope, and B is the signal bandwidth; The amplitude coded modulated linear frequency modulation signal x(t) is expressed as: x(t)=a(t)·s(t) (4).

4. The method for demodulating an amplitude coded modulation linear frequency modulation signal according to claim 1, wherein: In the second step, the complete linear frequency modulation signal s(t) is B The width is segmented and truncated to obtain several phase-coherent sub-linear frequency modulation signals, and the nth sub-linear frequency modulation signal is recorded as s n (t) is:

5. The method for demodulating an amplitude coded modulation linear frequency modulation signal according to claim 1 or 4, characterized in that: In the second step, the relevant reference signal y(t) is the sum of all sub-linear frequency modulation signals and is expressed as:

6. The method for demodulating an amplitude coded modulation linear frequency modulation signal according to claim 1, wherein: In the third step, the modulated signal x(t) is correlated with the reference signal y(t), and the correlation result R(τ) is: Where τ represents the time delay, m and n represent the subscript numbers, y*(t) represents the conjugate signal of y(t), R nm (τ) is s n (t) and s m (t), the correlation result can also be regarded as the matched filtering result of x(t) and y(t).

7. The method for demodulating an amplitude coded modulation linear frequency modulation signal according to claim 6, wherein: In the third step, the symbol starting time τ is selected k =kT B Time sampling, formula (7) is simplified to: Among them, R kk (0) represents the value of the autocorrelation function of the kth sub-linear frequency modulation signal at time 0, and also represents the power of the kth sub-linear frequency modulation signal, R km (0) means that the cross-correlation function of the kth sub-linear frequency modulation signal and the mth sub-linear frequency modulation signal takes a value at time 0; when the kth code element is 1, a k =1, when the kth code element is 0, a k =0.

8. The method for demodulating an amplitude coded modulation linear frequency modulation signal according to claim 7, wherein: In the third step, when any two different sub-linear frequency modulation signals are uncorrelated, then Satisfaction When , formula (8) is further simplified to: Wherein, μ=B / T is the frequency modulation slope.

9. The method for demodulating an amplitude coded modulation linear frequency modulation signal according to claim 8, wherein: In the third step, in digital calculation, assume that N points are sampled within the pulse width T, there are M code elements, and when the amplitude of x(t) is A, If the average power of additive white Gaussian noise is 2σ 2 , the correlation function R between the noise n(t) and the related reference signal y(t) n (τ k ) obeys the normal distribution, and the variance has an upper limit: Among them, s m [k] represents the discrete expression of the mth linear frequency modulation signal.

10. The method for demodulating an amplitude coded modulation linear frequency modulation signal according to claim 9, wherein: In the third step, The phase is affected by multiple parameters. After taking the modulo 2π, the phase values ​​are considered independent. The phase is considered to be uniformly distributed on [0,2π]. Therefore, according to the central limit theorem, Therefore, when Gaussian white noise exists, it is: Among them, R n (τ k ) has a mean of 0 and a variance of 2Nσ 2 If the real part is selected for judgment, formula (12) is regarded as a complex normal distribution with a magnitude of The noise intensity is Nσ 2 The coherent demodulation of the demodulation effect is equivalent to the input signal-to-noise ratio The effect of coherent demodulation, where r = A 2 / (2σ 2 ) is the actual input signal-to-noise ratio; therefore, the decision threshold level is:

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