Alternative Methods for Carrier Synchronization of Quadrature Phase Shift Keying (QPSK) Signals

Abstract

The present invention discloses an alternative method for QPSK signal carrier synchronization, which mainly solves the problems of poor real-time performance and complex implementation of existing carrier synchronization technologies. Its implementation scheme is: in response to the needs of QPSK signal carrier synchronization, a sine signal and a cosine signal of the phase difference are calculated in real time; the phase difference interval is determined based on the obtained sine signal and cosine signal, and four phase shifts are performed on the received signal to obtain four interval signals; according to the phase correspondence between the four interval signals and the baseband signal at different phase differences and the determined phase difference interval, a certain interval signal that is in phase with the baseband signal is selected for output, and the sign bit of each interval signal is taken to finally restore the baseband signal. Compared with the existing carrier synchronization method, the present invention has good real-time performance, low processing delay, simple implementation, small amount of calculation, low resource consumption, and strong adaptability to deviation changes. It can be used for fast demodulation of QPSK signals in high-dynamic large-deviation Doppler frequency shift scenarios.

Description

Technical Field

[0001] The invention belongs to the technical field of signal processing, and in particular relates to an alternative method for QPSK signal carrier synchronization, which can be used for digital communication and electronic navigation systems. Background Art

[0002] QPSK signal, or quadrature phase shift keying signal, is a four-phase digital phase modulation signal. Its phase has four possible states, each of which can represent two bits of binary information. It is widely used in the field of data communication technology.

[0003] During QPSK signal transmission, the received signal's frequency and phase offset from the local carrier occur due to factors such as Doppler shift and local oscillator frequency error. This frequency offset also causes phase offset. When the total phase offset exceeds the tolerance of ±0.25π, signal demodulation errors and data errors occur. Therefore, to mitigate the impact of phase differences on QPSK signal demodulation, carrier synchronization is necessary. Carrier synchronization enables stable tracking of the carrier frequency and phase, obtaining a local carrier with the same frequency and phase as the transmitted signal, thereby reducing the phase offset φ and ensuring correct demodulation. There are two main existing methods for carrier synchronization: closed-loop recovery methods based on feedback estimation, such as in-phase orthogonal Costas loops and multi-power-based polar loops; and open-loop recovery methods based on feedforward estimation, such as phase estimation based on fast Fourier transforms (FFTs) and Kalman filters, maximum likelihood estimation algorithms, and nonlinear transformations.

[0004] In 2018, Zhang Hongda et al. proposed a method in the journal Foreign Electronic Measurement Technology to reduce the design complexity of a digital Costas loop using an FPGA soft core. This method incorporates an inverse tangent phase detector into the Costas loop. The two baseband signals, filtered by a low-pass filter, are divided to obtain the tangent of the phase difference. The inverse tangent phase detector outputs the phase difference between the input signal and the carrier. The NCO then adjusts the phase of the carrier signal until the loop reaches a stable state. While the improved Costas loop designed by this method exhibits improved synchronization performance and effectively improves loop stability and synchronization performance, due to its negative feedback loop nature, carrier synchronization requires a certain amount of time to establish, hindering real-time performance.

[0005] In 2021, Mei Ruru et al. proposed the QPD algorithm in the journal Telecommunications Technology. This algorithm first performs a Q-power operation and phase rotation on the signal, then performs a power determination. The signal with the highest power after rotation is selected for polarity determination, and finally, the phase deviation is calculated. Compared to the Q-power-based polarity loop, this algorithm improves noise immunity, expands the frequency deviation capture range, and achieves high estimation accuracy. However, due to the complex processing steps and long processing time, its real-time performance is poor.

[0006] In 2020, Ju Zhiyi et al. proposed an improved high-dynamic QPSK signal demodulation algorithm in the journal Information Technology. This algorithm uses the Quinn frequency estimation algorithm based on Zoom-FFT to estimate the carrier frequency offset. This frequency offset estimation is divided into two steps: coarse estimation and fine estimation. After compensating for the estimated frequency offset, the algorithm uses a Costas loop to achieve carrier synchronization. This algorithm offers a wider range of carrier frequency offset estimation, higher frequency offset estimation accuracy, and better bit error performance. However, since this algorithm still relies on Costas loops for carrier synchronization, it does not improve the real-time performance of carrier synchronization. Summary of the Invention

[0007] The purpose of the present invention is to address the deficiencies of the above-mentioned prior art and propose an alternative method for QPSK signal carrier synchronization to improve the real-time performance of carrier synchronization, simplify the complexity of carrier synchronization, reduce its calculation amount, and expand the tolerance range of phase difference.

[0008] To achieve the above objectives, the technical solutions of the present invention include the following:

[0009] (1) The received signal s'(t) = cos(2πf0t-θ-φ) at the receiving end is multiplied by the local carrier cos(2πf0t) and sin(2πf0t) respectively and low-pass filtered to obtain the in-phase signal a(t)' = cos(θ+φ) and the quadrature signal b(t)' = sin(θ+φ), where f0 is the carrier frequency, t is time, θ represents the phase modulation, and φ is the phase difference;

[0010] (2) performing four calculations of addition, subtraction, reverse addition, and reverse subtraction on the quadrature signal b(t)' and the in-phase signal a(t)' to obtain four interval signals;

[0011] (3) The quadrature frequency signal sin(4φ) with a phase difference φ is calculated based on the orthogonal signal b(t)' and the in-phase signal a(t)';

[0012] (4) performing digital frequency division on the quadruple frequency signal sin(4φ) of the phase difference φ to obtain the sine signal sinφ of the phase difference and the cosine signal cosφ of the phase difference;

[0013] (5) Establish a lookup table, and implement carrier synchronization replacement based on the mapping relationship between the four interval signals and the baseband signal at different phase differences in the lookup table to restore the baseband signal:

[0014] 5a) establishing a lookup table based on the polarity of the phase difference sine signal sinφ and the phase difference cosine signal cosφ and the corresponding relationship between the four interval signals and the baseband signal and their relative relationship;

[0015] 5b) Based on the current polarity of sinφ and cosφ, select from the lookup table one of the four interval signals that is in phase with the orthogonal baseband signal b(t) and output it, remove the sign bit of each interval signal, and recover the orthogonal baseband signal b(t). Simultaneously, select from the lookup table one of the four interval signals that is in phase with the in-phase baseband signal a(t) and output it, remove the sign bit of each interval signal, and recover the in-phase baseband signal a(t).

[0016] Compared with the prior art, the present invention has the following advantages:

[0017] 1) It simplifies the processing complexity, reduces the amount of calculation, and improves the real-time performance of the processing.

[0018] The closed-loop recovery method of the existing feedback estimation method includes a loop filter and a phase detector, which is a negative feedback loop and requires a certain amount of establishment time to achieve carrier synchronization; the open-loop recovery method of the existing feedforward estimation method includes operations such as logarithm calculation, derivative calculation, exponential calculation, division, and multiple multiplications. The algorithm formula is relatively complex, the processing steps are numerous, the calculation amount is large, and the processing time is long.

[0019] The present invention has no negative feedback loop and only involves simple low-latency calculation processing such as multiplication, addition and subtraction operations, judgment, and lookup tables. The processing delay is low, and the real-time performance of the processing is improved.

[0020] 2) The tolerance range of phase difference is expanded.

[0021] The tolerance range of the phase difference of the existing method is small, only ±0.25π. If the phase difference exceeds this range, the signal demodulation error occurs and a bit error occurs.

[0022] The present invention realizes four phase shifts through addition and subtraction calculations to obtain four interval signals. The phase interval of each interval signal is 0.5π. The four interval signals cover a period of phase difference 2π, which can extend the tolerance range of the QPSK signal phase difference to 2π, that is, there is no tolerance limit. BRIEF DESCRIPTION OF THE DRAWINGS

[0023] Figure 1 It is an implementation flow chart of the present invention.

[0024] Figure 2 This is a simulation result diagram of using the method of the present invention to perform carrier synchronization replacement on the receiving end receiving signal s'(t) when there is no Doppler frequency shift to recover the baseband signal.

[0025] Figure 3 This is a simulation result diagram of using the method of the present invention to perform carrier synchronization replacement on the receiving end received signal s'(t) when the Doppler frequency shift is 100 kHz to recover the baseband signal.

[0026] Figure 4This is a simulation result diagram of using the method of the present invention to perform carrier synchronization replacement on the receiving end received signal s'(t) when the Doppler frequency shift is 500kHz to recover the baseband signal. DETAILED DESCRIPTION

[0027] The embodiments and effects of the present invention are described in further detail below with reference to the accompanying drawings.

[0028] Reference Figure 1 The alternative method for QPSK signal carrier synchronization of the present invention comprises the following steps:

[0029] Step 1: The receiving end receives the transmission signal sent by the sending end.

[0030] During data transmission, the transmitter first sends a signal to the receiver: s(t) = cos(2πf0t-θ).

[0031] Due to the influence of Doppler frequency shift, local oscillator frequency error, etc., the signal received by the receiver is:

[0032] s'(t)=cos(2πf0t-θ-φ)

[0033] Where: f0 is the carrier frequency, t is time, θ represents the phase modulation, φ is the phase difference between the receiving and transmitting signals, The value of φ can be positive or negative. is the initial phase difference, f Δ is the frequency deviation between the receiving and transmitting signals; 2πf Δ t is the phase deviation, which is mainly caused by the frequency deviation f caused by Doppler shift Δ caused by.

[0034] Step 2: Orthogonally transform the received signal s'(t) to generate a pair of signals.

[0035] 2.1) The receiving end multiplies the received signal s'(t) by the local carrier cos(2πf0t) to obtain the product signal y1(t) = 0.5(cos(4πf0-θ-φ)+cos(θ+φ)). The product signal y1(t) is then low-pass filtered to obtain the in-phase signal a(t)' = cos(θ+φ).

[0036] 2.2) While executing step 2.1), the received signal s'(t) is multiplied by the local carrier sin(2πf0t) to obtain the product signal y2(t)=0.5(sin(4πf0-θ-φ)+sin(θ+φ)). The product signal y2(t) is then low-pass filtered to obtain the orthogonal signal b(t)'=sin(θ+φ).

[0037] Step 3: Perform four calculations of addition, subtraction, reverse addition, and reverse subtraction on the quadrature signal b(t)' and the in-phase signal a(t)' to obtain four interval signals.

[0038] 3.1) Perform addition calculation to obtain the first interval signal K1:

[0039] It is identified as the first interval signal K1, which is phase-shifted by 0.25π relative to sin(θ+φ);

[0040] 3.2) Perform subtraction calculation to obtain the second interval signal K2:

[0041] Identified as the second interval signal K2, K2 is phase-shifted by -0.25π relative to sin(θ+φ);

[0042] 3.3) Perform inverse addition calculation to obtain the third interval signal K3:

[0043] It is identified as the third interval signal K3, and the phase of K3 is shifted by -0.75π relative to sin(θ+φ);

[0044] 3.4) Perform inverse subtraction calculation to obtain the fourth interval signal K4:

[0045] Identified as the fourth interval signal K4, K4 is phase-shifted by -1.25π relative to sin(θ+φ);

[0046] 3.5) Determine the phase difference between each interval signal and the in-phase signal a(t)' = cos(θ + φ):

[0047] Since cos(θ+φ)=sin(θ+φ+0.5π), that is, cos(θ+φ) is phase-shifted by 0.5π relative to sin(θ+φ), the phase difference between each interval signal and the in-phase signal a(t)'=cos(θ+φ) is determined as follows:

[0048] K1 is phase-shifted by -0.25π relative to cos(θ+φ),

[0049] K2 is phase-shifted by -0.75π relative to cos(θ+φ),

[0050] K3 is phase-shifted by -1.25π relative to cos(θ+φ),

[0051] K4 is phase-shifted by 0.25π relative to cos(θ+φ).

[0052] Step 4: Calculate the quadruple frequency signal sin(4φ) of the phase difference.

[0053] 4.1) Since the values ​​of θ are 0.25π, 0.75π, 1.25π, and 1.75π, the values ​​of 4θ are π, 3π, 5π, and 7π, respectively. Therefore, we can obtain: sin(4θ+4φ)=sin(π+4φ)=-sin(4φ);

[0054] 4.2) According to the equation in step 4.1), the quadruple frequency signal sin(4φ) for calculating the phase difference is derived as follows:

[0055]

[0056] formula:

[0057] 4.3) Substitute the quadrature signal b(t)' and the in-phase signal a(t)' into the formula in 4.2) to calculate the quadrature signal sin(4φ) with a phase difference of φ.

[0058] Step 5: Process the quadruple frequency signal sin(4φ) of the phase difference to obtain a sine signal sinφ of the phase difference and a cosine signal cosφ of the phase difference.

[0059] 5.1) Input the quadruple frequency signal sin(4φ) of the phase difference into a four-frequency divider and perform digital four-frequency division to obtain a sinusoidal signal sinφ of the phase difference;

[0060] 5.2) The sinusoidal signal sinφ is passed through a phase shifter to shift its phase left by 0.5π, yielding the cosine signal cosφ with the phase difference.

[0061] Step 6: Create a lookup table, remove the phase difference according to the mapping method, and restore the baseband signal.

[0062] 6.1) Determine the relative relationships between the phase difference sine signal sinφ, the phase difference cosine signal cosφ, and the four interval signals obtained in the above steps and the baseband signal as follows:

[0063] When the phase difference φ is in the range of 0 to 0.5π, sinφ and cosφ are both positive, then the first interval signal K1 is in phase with the orthogonal baseband signal b(t), and the fourth interval signal K4 is in phase with the in-phase baseband signal a(t);

[0064] When the phase difference φ is in the range of 0.5π to π, sinφ is positive and cosφ is negative, then the second interval signal K2 is in phase with the orthogonal baseband signal b(t), and the first interval signal K1 is in phase with the baseband signal a(t);

[0065] When the phase difference φ is in the range of π to 1.5π, sinφ and cosφ are both negative, then the third interval signal K3 is in phase with the orthogonal baseband signal b(t), and the fourth interval signal K2 is in phase with the in-phase baseband signal a(t);

[0066] When the phase difference φ is in the range of 1.5π to 2π, sinφ is negative and cosφ is positive, then the fourth interval signal K4 is in phase with the orthogonal baseband signal b(t), and the third interval signal K3 is in phase with the in-phase baseband signal a(t);

[0067] 6.2) From the four interval signals, select one interval signal that is in phase with the baseband signals a(t) and b(t) using the polarity of sinφ and cosφ according to the relative relationship determined in 6.1) and create a lookup table, as shown in Table 1:

[0068] Table 1. Lookup table

[0069]

[0070] 6.3) Recover the quadrature baseband signal b(t) according to the lookup table:

[0071] In the lookup table, based on the polarity of sinφ and cosφ, one of the four interval signals that is in phase with the orthogonal baseband signal b(t) is selected and output. The selected interval signal is then concatenated and the sign bit is taken to restore the orthogonal baseband signal b(t).

[0072] 6.4) Recover the in-phase baseband signal a(t) according to the lookup table:

[0073] In the lookup table, based on the polarity of sinφ and cosφ, one of the four interval signals that is in phase with the in-phase baseband signal a(t) is selected and output. The interval signals are then concatenated and the sign bit is taken to restore the in-phase baseband signal a(t).

[0074] The effects of the present invention can be further illustrated by the following simulation results:

[0075] 1. Simulation conditions

[0076] 1. Press in the simulation software MATLAB Figure 1 , build a circuit by implementing an alternative method of QPSK signal carrier synchronization, and use MATLAB to generate QPSK modulated signals;

[0077] 2. Set the carrier frequency f0 = 10Mhz, the code element 12 bits, the number of sampling points per code element 10000, and set different Doppler shift f Δ .

[0078] 2. Simulation Content and Results

[0079] Simulation 1. Under the above conditions, the method of the present invention is used to simulate f Δ= 0, that is, when there is no Doppler frequency shift, the receiving end receives the signal s'(t) = cos(2πf0t-θ-φ) and performs carrier synchronization replacement to restore the baseband signal. The results are as follows Figure 2 , where: waveform (a) is the baseband signal a(t) before and after the sign bit is taken; waveform (b) is the baseband signal b(t) before and after the sign bit is taken.

[0080] from Figure 2 It can be seen that the 2-bit binary baseband signals a(t) and b(t) recovered by the present invention are consistent with the 2-bit binary baseband signals at the transmitting end, indicating that the present invention can correctly demodulate the QPSK signal when the Doppler shift is 0.

[0081] Simulation 2. Under the above conditions, the method of the present invention is used to simulate f Δ =100khz, that is, when the Doppler frequency shift is 100kHz, the receiving end receives the signal s'(t)=cos(2πf0t-θ-φ) and performs carrier synchronization replacement to restore the baseband signal. The results are as follows Figure 3 , where: waveform (a) is the baseband signal a(t) before the sign bit is taken; waveform (b) is the baseband signal a(t) after the sign bit is taken;

[0082] Waveform (c) is the baseband signal b(t) before the sign bit is removed; waveform (d) is the baseband signal b(t) after the sign bit is removed.

[0083] from Figure 3 It can be seen that the 2-bit binary baseband signals a(t) and b(t) recovered by the present invention are consistent with the 2-bit binary baseband signals at the transmitting end, indicating that the present invention can correctly demodulate the QPSK signal when the Doppler frequency shift is 100 kHz.

[0084] Simulation 3. Under the above conditions, the method of the present invention is used to simulate f Δ =500khz, that is, when the Doppler frequency shift is 500kHz, the receiving end receives the signal s'(t)=cos(2πf0t-θ-φ) and performs carrier synchronization replacement to restore the baseband signal. The results are as follows Figure 4 , where: waveform (a) is the baseband signal a(t) before and after the sign bit is taken; waveform (b) is the baseband signal b(t) before and after the sign bit is taken.

[0085] from Figure 4 It can be seen that the 2-bit binary baseband signals a(t) and b(t) recovered by the present invention are consistent with the 2-bit binary baseband signals at the transmitting end, indicating that the present invention can correctly demodulate the QPSK signal when the Doppler frequency shift is 500kHz.

[0086] The above description is only a specific example of the present invention and does not constitute any limitation to the present invention. Obviously, for professionals in this field, after understanding the content and principles of the present invention, it is possible to make various modifications and changes in form and details without departing from the principles and structure of the present invention. However, these modifications and changes based on the ideas of the present invention are still within the scope of protection of the claims of the present invention.

[0087] It should be noted that the step numbers in the specification and claims of the present invention are only for the purpose of clearly describing the embodiments of the present invention and facilitating understanding, and the order of the step numbers is not limited.

Claims

1. An alternative method for QPSK signal carrier synchronization, characterized in that: include: (1) The received signal s'(t) = cos(2πf0t-θ-φ) at the receiving end is multiplied by the local carrier cos(2πf0t) and sin(2πf0t) respectively and low-pass filtered to obtain the in-phase signal a(t)' = cos(θ+φ) and the quadrature signal b(t)' = sin(θ+φ), where f0 is the carrier frequency, t is time, θ represents the phase modulation, and φ is the phase difference; (2) performing four calculations of addition, subtraction, reverse addition, and reverse subtraction on the quadrature signal b(t)' and the in-phase signal a(t)' to obtain four interval signals; (3) The quadrature frequency signal sin(4φ) with a phase difference φ is calculated based on the orthogonal signal b(t)' and the in-phase signal a(t)'; (4) performing digital frequency division on the quadruple frequency signal sin(4φ) of the phase difference φ to obtain the sine signal sinφ of the phase difference and the cosine signal cosφ of the phase difference; (5) Establish a lookup table, and implement carrier synchronization replacement based on the mapping relationship between the four interval signals and the baseband signal at different phase differences in the lookup table to restore the baseband signal: 5a) establishing a lookup table based on the polarity of the phase difference sine signal sinφ and the phase difference cosine signal cosφ and the corresponding relationship between the four interval signals and the baseband signal and their relative relationship; 5b) Based on the current polarity of sinφ and cosφ, select from the lookup table one of the four interval signals that is in phase with the orthogonal baseband signal b(t) and output it, remove the sign bit of each interval signal, and recover the orthogonal baseband signal b(t). Simultaneously, select from the lookup table one of the four interval signals that is in phase with the in-phase baseband signal a(t) and output it, remove the sign bit of each interval signal, and recover the in-phase baseband signal a(t).

2. The method according to claim 1, wherein: In step (2), the quadrature signal b(t)' and the in-phase signal a(t)' are subjected to four calculations of addition, subtraction, reverse addition, and reverse subtraction to obtain four interval signals. The implementation steps include the following: 2.1) Perform addition calculation to obtain the first interval signal K1: Identified as interval signal K1 2.2) Perform subtraction calculation to obtain the second interval signal K2: Identified as interval signal K2 2.3) Perform inverse addition calculation to obtain the third interval signal K3: Identified as interval signal K3 2.4) Perform inverse subtraction calculation to obtain the fourth interval signal K4: It is identified as interval signal K4.

3. The method according to claim 1, wherein: In step (3), the quadrature frequency signal sin(4φ) with a phase difference φ is calculated based on the orthogonal signal b(t)' and the in-phase signal a(t)'. The calculation formula is as follows: sin(4φ)=-2(2×a(t)'×b(t)')×(2a 2 (t)'-1)。 4. The method according to claim 1, wherein: In step (4), the four-fold frequency signal sin(4φ) of the phase difference φ is digitally divided by four, and sin(4φ) is first digitally divided by four to obtain the sinusoidal signal sinφ of the phase difference; Then, sinφ is passed through a phase shifter to shift its phase to the left by 0.5π to obtain the cosine signal cosφ of the phase difference.

5. The method according to claim 1, wherein: In step 5a), a lookup table is established based on the polarity of the phase difference sine signal sinφ and the phase difference cosine signal cosφ, and the correspondence between the four interval signals and the baseband signal and their relative relationship. The implementation steps include the following: 5a1) Determine the interval in which the phase difference lies, the phase difference sine signal sinφ, the phase difference cosine signal cosφ, the relative relationship between the four interval signals and the baseband signal: When the phase difference φ is in the range of 0 to 0.5π, sinφ and cosφ are both positive, then the first interval signal K1 is in phase with the orthogonal baseband signal b(t), and the fourth interval signal K4 is in phase with the in-phase baseband signal a(t); When the phase difference φ is in the range of 0.5π to π, sinφ is positive and cosφ is negative, then the second interval signal K2 is in phase with the orthogonal baseband signal b(t), and the first interval signal K1 is in phase with the baseband signal a(t); When the phase difference φ is in the range of π to 1.5π, sinφ and cosφ are both negative, then the third interval signal K3 is in phase with the orthogonal baseband signal b(t), and the fourth interval signal K2 is in phase with the in-phase baseband signal a(t); When the phase difference φ is in the range of 1.5π to 2π, sinφ is negative and cosφ is positive, then the fourth interval signal K4 is in phase with the orthogonal baseband signal b(t), and the third interval signal K3 is in phase with the in-phase baseband signal a(t); 5a2) Select one of the four interval signals that is in phase with the baseband signals a(t) and b(t) according to the relative relationship determined in 5a1) and the polarity of sinφ and cosφ, and establish a lookup table.

6. The method according to claim 1, wherein: The quadrature baseband signal b(t) and the in-phase baseband signal a(t) recovered in step 5b) are expressed as follows: b(t) = sinθ; a(t)=cosθ.

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