A method for generating bandwidth and duty cycle adjustable linear frequency modulation signal based on IFFT

Abstract

The application provides a method for generating a bandwidth and duty cycle adjustable linear frequency modulation signal based on IFFT. The IFFT operation on a discrete sequence with an amplitude of 1 and a quadratic phase growth can generate a periodic linear frequency modulation signal, and on this basis, the input sequence length and the quadratic phase coefficient of the input sequence are reasonably set to generate linear frequency modulation signals with different bandwidths and duty cycles, thereby realizing flexible adjustment of the periodic linear frequency modulation signal.

Description

Technical Field

[0001] This invention relates to the fields of communications and radar, and specifically to a method for generating a linear frequency modulated signal with adjustable bandwidth and duty cycle based on IFFT. Background Technology

[0002] Radar possesses excellent sensing capabilities, and with the continuous development of radar technology, it has been widely applied in military and civilian fields. The increasingly complex electromagnetic environment places higher demands on the detection range, resolution, and measurement accuracy of modern radar systems. Radar ranging accuracy and range resolution are mainly related to the frequency structure of the signal, while velocity accuracy and velocity resolution are related to the time structure of the signal. For a single-carrier-frequency pulse signal, its time-bandwidth product is approximately 1. There is a contradiction between the need for large bandwidth and large time width. To resolve this contradiction, radar systems need to use signals with a large time-bandwidth product. Linear Frequency Modulation (LFM), as a pulse compression signal with a large time-bandwidth product, is widely used in radar systems. At the same time, how to generate LFM signals with excellent detection performance has received increasing attention. Currently, methods for generating LFM signals in the electrical domain include analog and digital methods.

[0003] Analog methods are more traditional, including active and passive methods. Active methods, also known as direct synthesis, generate linear frequency modulated (LFM) signals by controlling a voltage-controlled oscillator (VCO) with a linear sawtooth wave voltage. Passive methods convert narrow pulses into LFM signals by utilizing the dispersion delay characteristics of a dispersion delay line (or a surface acoustic wave (SAW) device). However, both active and passive methods suffer from drawbacks in generating LFM signals through analog systems, including large size, poor flexibility, unstable signal generation, and complex debugging and maintenance. Digital methods mainly include two types: waveform storage direct reading and direct digital synthesis (DDS). Waveform storage direct reading involves sequentially writing the sampled values ​​of two orthogonal signals calculated using the LFM signal expression into a high-speed memory based on signal parameters such as sampling frequency, baseband bandwidth, and duration. These values ​​are then decoded, quadrature modulated, and multiplied to generate a LFM signal that meets the required bandwidth and frequency band. Direct Digital Synthesis (DDS) first obtains a quadratic phase change through a two-stage phase accumulation structure. Then, based on this quadratic phase change, it looks up the corresponding I-channel and Q-channel baseband linear frequency modulated (LFM) signals in a ROM table. After quadrature modulation and frequency multiplication, the desired LFM signal can be obtained. Both of these digital methods can generate more stable LFM signals than analog methods, but each method also has its own drawbacks. For the DDS method, generating LFM signals often requires a special DDS chip, and the generated signal form is relatively fixed with poor adjustability. For waveform storage and direct reading methods, the circuit design is usually more complex and the development is more difficult. With the rapid development of information technology and microelectronics, electronic information systems sometimes need both radar detection and wireless communication functions to meet different needs. Conventional DDS methods for generating signal waveforms often cannot combine these two functions simultaneously, forcing communication and radar functions to be implemented on their respective electronic systems on the same platform, resulting in redundancy in system equipment. Summary of the Invention

[0004] This invention proposes a method for generating a linear frequency modulated (LFM) signal with adjustable bandwidth and duty cycle based on IFFT. The LFM signal generated by this method has flexible adjustability and is compatible with OFDM-based signal generation technology, enabling the integration of radar systems and wireless communication systems.

[0005] To achieve the above objectives, the technical solution of the present invention includes the following:

[0006] A method for generating a bandwidth- and duty-cycle-adjustable linear frequency modulated signal based on IFFT includes the following steps:

[0007] Step 1: Derive a mathematical model for generating periodic linear frequency modulated signals based on IFFT from continuous periodic linear frequency modulated signals.

[0008] An LFM signal with period T can be represented in the form of a Fourier series. The expression for the Fourier series is:

[0009]

[0010] The Fourier series coefficients are:

[0011]

[0012] In the formula, s(t) represents the LFM signal within one period, and erfi(x) and I(m) are respectively:

[0013]

[0014]

[0015] When the LFM signal bandwidth is B and the period is T, assuming BT = N1, the amplitude of I(m) is close to 1 and the phase is very small (close to π / 2) within the range of 0 to N1; outside the range of 0 to N1, the amplitude of I(m) is close to zero. Therefore, S(t) can be simplified to:

[0016]

[0017]

[0018]

[0019] S(t) can be viewed as containing a quadratic phase. The result is obtained by superimposing N1 equally spaced (Δf = 1 / T) carriers. Therefore, by introducing a quadratic phase shift on each subcarrier through quadratic phase modulation of different carriers, a periodic LFM signal can be generated; S(t) is sampled and discretized, with a sampling time interval of T. s The corresponding sampling frequency is f s =1 / T s T s =1 / B=1 / NΔf=T / N; that is:

[0020]

[0021] When f0 = 0, that is, when S(t) is a baseband signal, equation (8) and X are the same. m The results of performing the inverse discrete Fourier transform differ only in the constant coefficients. Therefore, theoretically, according to the theory of the inverse discrete Fourier transform, for X... m A periodic LFM signal can be generated by performing an IFFT operation; let the coefficient of the squared phase shift introduced on each subcarrier be δ = -π / kT. 2Therefore, a mathematical model for generating periodic linear frequency modulated signals based on IFFT can be obtained:

[0022]

[0023] Step 2: The result is obtained from cos(δm) 2 (m=0~N1-1) is the real part, sin(δm) 2 The input sequence X is a discrete complex sequence with an amplitude of 1 and a phase exhibiting quadratic growth, consisting of the imaginary part of (m = 0 to N1-1). m ,

[0024] Changing the quadratic phase coefficient δ of the input sequence can alter the duration of the generated linear frequency modulated signal, thereby controlling the duty cycle of the linear frequency modulated signal.

[0025] When S(t) is a baseband signal, equation (5) can be written as:

[0026]

[0027] This indicates that the linear frequency modulated signal is generated by superimposing time-domain offsets of carriers of different frequencies, let the time offset be:

[0028]

[0029] The sign of the time offset τ determines the left and right offset of different frequency carriers in the time domain, and thus determines the sign of the chirp rate of the generated linear frequency modulation signal. That is, by changing the sign of δ, chirp signals with different polarities can be generated; a negative δ generates a positive chirp signal, and a positive δ generates a negative chirp signal.

[0030] Equation (9) generates a linear frequency modulated signal. This process is equivalent to Equation (10). Since Equation (10) can be seen as the result of superimposing different frequency carriers and then time-domain offsetting them, and performing IFFT on a sequence with all values ​​of 1 and a length of N1 is equivalent to superimposing different frequency carriers, Equation (9) can be seen as performing IFFT on a sequence with all values ​​of 1 and a length of N1, and then time-offsetting different frequency carriers.

[0031] When performing an N1-point IFFT on a sequence of length N1 containing only 1 values, i.e.:

[0032]

[0033] If, when n is constant, there exists an integer t such that for any integer m within the range 0 to N(1-1), ...

[0034]

[0035] If the equation holds, N1 carriers with different frequencies cancel each other out and superpose at x(n), and the superposition result is zero. On the contrary, when n is fixed, there is no integer t that satisfies Equation (13) for any integer m within the range of 0 to N1-1, then N1 carriers with different frequencies constructively superpose at x(n), and the superposition result is non-zero.

[0036] According to Equation (13), only the result of x(0) is a non-zero value, and the other N1-1 values are all zero. When an LFM signal is generated based on IFFT and the sampling theorem is satisfied, the length N1 of the input sequence needs to satisfy: 1<<N1≤N / 2. When performing N-point IFFT on a sequence with all values of 1 and length N1, it is necessary to extend the sequence length to N by zero-padding first. At this time, the bandwidth of the linear frequency modulation signal is B=N1×Δf=N1 / T, that is, BT=N1, and the linear frequency modulation signal is composed of BT carriers. A linear frequency modulation signal with positive chirp is formed by offsetting different frequency carriers at x(0) to the right, and a linear frequency modulation signal with negative chirp rate is formed by offsetting different frequency carriers at x(N) in the next period to the left.

[0037] The offset of the highest frequency carrier determines the time width of the generated linear frequency modulation signal. If the length of the input sequence is N1, when the sampling theorem is satisfied, the length N1 of the input sequence needs to satisfy: 1<<N1≤N / 2. When m=N1-1, the value of τ is the maximum, at this time τ max is the offset of the highest frequency carrier:

[0038]

[0039] Since the input sequence will be subjected to odd-even grouping processing during IFFT, the time width T of the finally generated LFM signal LFM =2τ max .

[0040] To ensure that the generated LFM signal does not overlap within one signal period, the quadratic phase coefficient δ of the input sequence needs to satisfy T LFM ≤T, that is:

[0041]

[0042] Since B=N1×Δf=N1×f s / N, when N1>>1, the chirp rate of the finally generated LFM signal is:

[0043]

[0044] Under the condition of a fixed bandwidth, changing the value of δ can change the time width of the generated LFM signal, that is, the duty cycle can be adjusted by changing the chirp rate of the LFM signal.

[0045] Furthermore, by changing the length N1 of the IFFT input sequence, the bandwidth and duty cycle of the linear frequency modulated signal can be altered.

[0046] Since B = N1 × Δf = N1 × f s / N, when f s When the value of N is constant, changing the length of the input sequence N1 will also change the bandwidth of the linear frequency modulated signal. The length of the input sequence N1 must satisfy: 1 ​​< <N1≤N / 2。

[0047] According to equation (16), when N1>>1, the chirp rate of the generated linear frequency modulation signal will not change with the value of N1. That is, when the chirp rate is constant, the duty cycle of the linear frequency modulation signal can be changed by changing the length N1 of the input sequence of the IFFT.

[0048] Step 3: For the input sequence X m The sequence is extended to length N by padding with zeros and then subjected to a serial-to-parallel transformation.

[0049] Step 4: Repeat the N-point IFFT continuously on the parallel data after serial-to-parallel transformation with a time period of T;

[0050] Step 5: Perform parallel-to-serial transformation on the parallel sequence output after IFFT in each cycle;

[0051] Step 6: Using sampling rate f s =N / T digital-to-analog converter (DAC) converts the parallel-to-serial conversion data into an analog signal, which is the generated periodic linear frequency modulated (LFM) signal. The bandwidth and duty cycle of the LFM signal are adjustable.

[0052] The method for generating adjustable bandwidth and duty cycle linear frequency modulated (LFM) signals based on IFFT proposed in this invention is simple in principle and highly adjustable. By changing the length of the input sequence and the quadratic phase coefficient δ, LFM signals with different bandwidths and duty cycles can be generated. Furthermore, since the generation of LFM signals is based on IFFT operations, and IFFT is also required in orthogonal frequency division multiplexing (OFDM) systems to achieve multi-carrier modulation, the LFM signal and OFDM signal can share a digital signal processing system, enabling the integration of radar and communication in the system and forming a radar-communication full-duplex system. Attached Figure Description

[0053] Figure 1 This is a block diagram illustrating the principle of a method for generating a linear frequency modulated signal with adjustable bandwidth and duty cycle based on IFFT, as proposed in this invention.

[0054] Figure 2 The amplitude spectrum of I(m) is given when T = 1.6384 μs and B = 2.5 GHz.

[0055] Figure 3 The phase spectrum of I(m) at T = 1.6384 μs and B = 2.5 GHz;

[0056] Figure 4 The time-domain waveform (2 cycles) of the positive chirped LFM signal generated when N1 = 4096, N = 8192, fs = 5 × (10^9) Hz, and δ = -0.000767;

[0057] Figure 5 The time-frequency diagram (2 cycles) of the positive chirped LFM signal generated when N1 = 4096, N = 8192, fs = 5 × (10^9) Hz, and δ = -0.000767;

[0058] Figure 6 The time-domain waveform (2 cycles) of the negative chirped LFM signal generated when N1 = 4096, N = 8192, fs = 5 × (10^9) Hz, and δ = 0.000767;

[0059] Figure 7 The time-frequency diagram (2 cycles) of the negative chirped LFM signal generated when N1 = 4096, N = 8192, fs = 5 × (10^9) Hz, and δ = 0.000767;

[0060] Figure 8 The graph shows the relationship between δ and the duty cycle of the LFM signal.

[0061] Figure 9 The graph shows the relationship between N1 and the bandwidth and duty cycle of the LFM signal. Detailed Implementation

[0062] To make the objectives, technical solutions, and advantages of the present invention clearer, the embodiments of the present invention will be described in detail below with reference to the accompanying drawings.

[0063] Figure 1 This is a block diagram illustrating the basic principle of the system in this embodiment. The present invention provides a method for generating linear frequency modulated (LFM) signals with adjustable bandwidth and duty cycle based on IFFT. By changing the quadratic phase coefficient δ of the input sequence and the length N1 of the input sequence, LFM signals with different bandwidths and duty cycles can be generated, thereby achieving flexible and adjustable LFM signals.

[0064] according to Figure 2 and Figure 3 The amplitude and phase of the Fourier series I(m) of the periodic linear frequency modulated signal shown are as follows: it can be seen that in the range of 0 to N1-1, the amplitude of I(m) is close to 1 and the phase is very small (close to π / 2); outside the range of 0 to N1-1, the amplitude of I(m) is close to zero.

[0065] The theory is verified through simulation: To generate a periodic LFM signal with a period of 1.6384 μs and a bandwidth of 2.5 GHz, N1 = 4096, and the quadratic phase coefficient δ must satisfy |δ| ≤ 0.000767. This is achieved by using cos(δm) 2 ) as the real part, sin(δm) 2 The discrete complex sequence X, with an imaginary part of amplitude 1 and a phase exhibiting quadratic growth, is extended by zero-padding to a sequence of length N = 8192, which serves as the input sequence X. m The parallel data is then subjected to serial-to-parallel conversion, and then the resulting parallel data is subjected to N=8192-point IFFT continuously at a time period of T. The parallel sequence output by IFFT is then converted from parallel to serial and then converted from digital to analog at a sampling rate of 5GHz to generate a periodic linear frequency modulated signal of BT=4096.

[0066] When f s When = 5GHz, δ = -0.000767, N1 = 4096, and N = 8192, τ can be obtained according to equation (14). max =0.819μs, which is the duration T of the LFM signal within one period. LFM =1.638μs, from B=N1×Δf=N1×f s / N yields a bandwidth B = 2.5GHz. The waveform of the generated positively chirped LFM signal over two cycles is shown below. Figure 4 As shown, the time-frequency graph is as follows: Figure 5 As shown, in Figure 5 The duration T of the LFM signal within one cycle can be seen in the image. LFM =1.638μs, bandwidth B =2.5GHz, consistent with the calculated results.

[0067] When the sampling rate f s With a fixed number of IFFT points N, different values ​​for the input sequence length N1 and the quadratic phase coefficient δ can generate LFM signals with different bandwidths and duty cycles. The simulation results are shown in the table below:

[0068]

[0069] Using the first row of simulation data as a reference, when the input sequence length, IFFT points, and sampling rate are constant, the chirp polarity of the generated LFM signal changes when the second phase coefficient δ is greater than zero. The waveforms of two cycles of the generated negatively chirped LFM signal are shown below. Figure 6 As shown, the time-frequency graph is as follows: Figure 7 As shown.

[0070] When the input sequence length, the number of IFFT points and the sampling rate are fixed, the duty cycle of the LFM signal generated decreases as the absolute value of δ decreases, and the duty cycle of the LFM signal generated increases as the absolute value of δ increases. In Figure 8 , it can also be seen that the absolute value of the quadratic phase coefficient δ is proportional to the duty cycle of the LFM signal, which indicates that when the bandwidth is fixed, keeping the polarity of the quadratic phase coefficient δ unchanged and only changing the magnitude of δ can adjust the time width of the generated linear frequency modulation signal, thereby realizing the regulation of the duty cycle of the linear frequency modulation signal;

[0071] When the number of IFFT points, the sampling rate and the value of δ are fixed, only changing the input sequence length N1 under the condition that 1<<N1≤N / 2 will not change the chirp rate of the generated LFM signal. The bandwidth and duty cycle of the generated LFM signal increase with the increase of N1 and decrease with the decrease of N1. In Figure 9 , it can be seen that the input sequence length N1 is proportional to both the bandwidth and the duty cycle of the LFM signal, which indicates that when the chirp rate is fixed, changing the input sequence length N1 of IFFT can realize the regulation of the bandwidth and duty cycle of the linear frequency modulation signal.

[0072] After analysis of simulation examples, the feasibility of the method for generating linear frequency modulation signals with adjustable bandwidth and duty cycle based on IFFT is finally verified.

[0073] The above description is only specific embodiments of the present invention. However, the protection scope of the present invention is not limited thereto. Any person skilled in the art can easily conceive of changes or substitutions within the technical scope disclosed by the present invention, which shall all be covered within the protection scope of the present invention. Therefore, the protection scope of the present invention shall be subject to the protection scope of the claims.

Claims

1. A method for generating a linear frequency modulated signal with adjustable bandwidth and duty cycle based on IFFT, characterized in that, The method includes the following steps: Step 1: The mathematical model for generating a periodic linear frequency modulated signal based on IFFT is derived from the continuous periodic linear frequency modulated signal. ； Step 2: The result is obtained from cos(δm) 2 sin(δm) is the real part. 2 The input sequence X is a discrete complex sequence with an amplitude of 1 and a quadratic phase growth, constructed as the imaginary part. m , Where m = 0 ~ N1−1, the baseband linear frequency modulated signal generated by IFFT can be expressed as: ； Step 3: For the input sequence X m The sequence is extended to length N by padding with zeros and then subjected to a serial-to-parallel transformation. Step 4: Repeat the N-point IFFT continuously on the parallel data after serial-to-parallel transformation with a time period of T; Step 5: Perform parallel-to-serial transformation on the parallel sequence output after IFFT in each cycle; Step 6: Using a sampling rate of f s The N / T digital-to-analog converter (DAC) converts the parallel-to-serial conversion data into an analog signal, which is the generated periodic linear frequency modulated (LFM) signal. The time width T of this LFM signal is... LFM The bandwidth B, duty cycle, and chirp rate k are adjustable. Specifically, By changing the length N1 of the input sequence of the IFFT, the duration, bandwidth, and duty cycle of the linear frequency modulated signal can be changed. By changing the secondary phase coefficient δ, the chirp rate of the generated linear frequency modulated signal can be adjusted, and the duration and duty cycle of the output linear frequency modulated signal with a certain bandwidth can be achieved.

2. The method for generating a linear frequency modulated signal with adjustable bandwidth and duty cycle based on IFFT according to claim 1, characterized in that, The mathematical model for generating a periodic linear frequency modulated signal based on IFFT in step 1 includes: An LFM signal with period T can be represented in the form of a Fourier series, the expression of which is: ，(1) Wherein, the Fourier series coefficients are ，(2) In the formula, s(t) represents the LFM signal within one period, and erfi(x) and I(m) are respectively ，(3) ；(4) When the LFM signal bandwidth is B and the period is T, assuming BT = N1, the amplitude of I(m) is close to 1 and the phase is close to π / 2 within the range of 0 to N1; outside the range of 0 to N1, the amplitude of I(m) is close to zero. Therefore, S(t) can be simplified to... ，(5) ，(6) ；(7) S(t) can be viewed as containing a quadratic phase φ m The result is obtained by superimposing N1 equally spaced carriers with a spacing Δf = 1 / T. Therefore, a periodic LFM signal can be generated by introducing a quadratic phase shift on each subcarrier through quadratic phase modulation of different carriers. S(t) is sampled and discretized with a sampling time interval of T. s The corresponding sampling frequency is f s =1 / T s T s =1 / B= 1 / NΔf=T / N, that is, ；(8) When f0=0, that is, when S(t) is a baseband signal, equation (8) and X are the same. m The results of performing the inverse discrete Fourier transform differ only in the constant coefficients; therefore, theoretically, we can use the theory of the inverse discrete Fourier transform to determine the relationship between X and X. m Perform IFFT operations to generate a periodic LFM signal; let the coefficient of the squared phase shift introduced on each subcarrier be... Thus, a mathematical model for generating periodic linear frequency modulated signals based on IFFT is obtained. 。(9) 3. The method for generating a linear frequency modulated signal with adjustable bandwidth and duty cycle based on IFFT as described in claim 2, characterized in that, Changing the quadratic phase coefficient δ of the input sequence can alter the duration of the generated linear frequency modulated (LFM) signal, thus controlling the duty cycle of the LFM signal. When S(t) is a baseband signal, equation (5) can be written as ，(10) Equation (10) indicates that the linear frequency modulated signal is generated by superimposing time-domain offsets of carriers of different frequencies, let the time offset be... ，(11) The sign of the time offset τ determines the left and right offset of different frequency carriers in the time domain, and thus determines the sign of the chirp rate of the generated linear frequency modulation signal. That is, by changing the sign of δ, chirp signals with different polarities can be generated; a negative δ generates a positive chirp signal, and a positive δ generates a negative chirp signal. The offset of the highest frequency carrier determines the duration of the generated linear frequency modulated signal. If the length of the input sequence is N1, under the condition of satisfying the sampling theorem, the length N1 of the input sequence must satisfy: 1 ​​< <N1≤N / 2; The value of τ is maximum when m = N1-1, at which point τ max The offset of the highest frequency carrier can be expressed as: ，(12) Because the input sequence is parity-grouped during IFFT, the final LFM signal has a time width T. LFM For 2τ max ; To ensure that the generated LFM signal does not aliased within one signal period, the quadratic phase coefficient δ of the input sequence must satisfy T LFM ≤T, that is ，(13) Since B = N1 × ∆f = N1 × f s When / N and N1>>1, the final generated LFM signal chirp rate is ； (14) Given a fixed bandwidth, changing the value of δ can alter the duration of the generated LFM signal, i.e., the duty cycle can be controlled by changing the chirp rate of the LFM signal.

4. The method for generating a linear frequency modulated signal with adjustable bandwidth and duty cycle based on IFFT according to claim 3, characterized in that, Changing the length N1 of the IFFT input sequence can change the bandwidth and duty cycle of the linear frequency modulated signal: Since B = N1 × ∆f = N1 × f s / N, when f s When the value of N is constant, changing the length of the input sequence N1 will also change the bandwidth of the linear frequency modulated signal. The length of the input sequence N1 must satisfy: 1 ​​< <N1≤N / 2; According to the formula for calculating k, when N1>>1, the chirp rate of the generated linear frequency modulation signal will not change with the value of N1. That is, when the chirp rate is constant, changing the length of the input sequence N1 of the IFFT can change the duty cycle of the linear frequency modulation signal.

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