A low-complexity noise-tolerant laser phase recovery method

Abstract

The application discloses a low-complexity noise-tolerant laser phase recovery method, and belongs to the technical field of signal processing.The application uses a two-stage structure to jointly estimate, realizes joint estimation of the frequency offset and phase of a signal carrier through phase estimation in a feedback stage and phase estimation in a feedforward stage, solves the problem of phase jump of a traditional Diff-4th algorithm at a low signal-to-noise ratio, and improves the carrier phase recovery performance.Based on a digital phase-locked loop and Viterbi-Viterbi phase estimation, compared with the traditional Diff-4th method, the application reduces the calculation complexity and the calculation resources.A phase detector, a loop filter and a digital controlled oscillator constitute a feedback loop, the carrier phase estimation is quickly adjusted in combination with a feedforward mechanism and a feedback mechanism, the Doppler shift caused by the relative motion of satellites is continuously tracked in real time, the constellation rotation caused by residual Doppler frequency offset and phase noise in an intersatellite coherent optical communication system can be eliminated, and compared with the traditional Diff-4th method, the stability and reliability of communication are improved.

Description

TECHNICAL FIELD

[0001] The application relates to a low-complexity noise-tolerant laser phase recovery method and belongs to the technical field of signal processing. BACKGROUND

[0002] Future space activities have increasingly higher requirements for data transmission rate and security. Satellite coherent optical communication has the characteristics of large communication capacity and high receiving sensitivity, and has high spectral efficiency under high-order modulation mode. However, the phase noise of a laser and the Doppler frequency offset caused by the relative motion of a satellite will lead to the decline of the transmission data recovery performance, and therefore the Doppler frequency offset and the phase noise need to be estimated and compensated.

[0003] Frequency offset estimation is divided into frequency domain estimation and time domain estimation. Frequency domain estimation is to obtain the frequency information of a signal through Fourier transform, so as to estimate the frequency offset, which is called fast Fourier transform-based frequency offset estimation (FFT-FOE). However, the calculation complexity in a high-speed communication scenario is too high, and the method is not suitable for a resource-limited satellite payload. Time domain estimation utilizes the phase difference information between adjacent symbols to estimate the frequency offset, which is called differential frequency offset estimation (Diff-FOE). Block estimation is used to smooth the differential phase to reduce the noise influence. Diff-FOE has a smaller calculation amount, but serious burst errors will occur under a lower signal-to-noise ratio.

[0004] Phase estimation methods mainly include blind estimation and data-aided estimation methods. The blind estimation method does not depend on pilot information, has the characteristics of high spectral efficiency and resource utilization rate, and has a smaller calculation complexity because it does not involve the probability calculation required by the data-aided method. The blind estimation method mainly includes Viterbi-Viterbi estimation algorithm (VV-PE) and blind phase search (BPS). BPS quantizes the phase space into a phase test set, searches for a phase with the minimum cost function by performing the same calculation for each test phase, and the phase estimation accuracy is proportional to the calculation amount. VV-PE estimates the carrier phase by eliminating the modulation signal, and has the advantages of simple implementation structure and small calculation amount.

[0005] At present, satellite laser communication mainly adopts binary phase shift keying (BPSK) and quadrature phase shift keying (QPSK) modulation modes. Due to the constraints of on-board resources, the traditional carrier recovery technology adopts Diff-FOE combined with VV-PE (Diff-4th) to estimate the carrier frequency offset and the phase. However, both of them are feedforward methods, and after cascading, the system performance is seriously lost at a lower signal-to-noise ratio. SUMMARY

[0006] To address the significant performance loss in systems with low signal-to-noise ratios, this invention aims to provide a low-complexity noise-tolerant laser phase retrieval method. This method eliminates constellation diagram rotation caused by residual Doppler frequency offset and phase noise in inter-satellite coherent optical communication systems, achieving low-complexity noise-tolerant laser phase retrieval. This invention also offers advantages such as low computational complexity, reduced hardware performance requirements, and reduced multiplier resources.

[0007] The objective of this invention is achieved through the following technical solutions.

[0008] This invention discloses a low-complexity noise-tolerant laser phase retrieval method, which achieves joint estimation of the frequency offset and phase of the signal carrier through feedback stage phase estimation and feedforward stage phase estimation, including the following steps:

[0009] Step 1: Analyze the laser signal Perform phase detection, phase Represented as:

[0010]

[0011] Step Two, Phase of Step One Phase detector gain K d Multiplication equals phase detection error K d θ in Second-order loop filter for K d θ in Noise reduction is performed to obtain a smooth signal θ. loop_0 ;

[0012] θ loop_0 The z-domain representation of Y(z) is:

[0013] Y(z)=H(z)X(z)

[0014] Where X(z) is K d θ in The z-domain representation; H(z) is the transfer function of the second-order loop filter, expressed as:

[0015]

[0016] Where K1 and K2 are the gain factors of the loop filter, which affect the loop's response speed and noise filtering capability.

[0017] Step 3: The numerically controlled oscillator, based on the γ from Step 2... loop_0 The carrier phase estimate was calculated.

[0018] The z-domain representation of Y1(z) is:

[0019] Y1(z) = H1(z)Y(z)

[0020] where H1(z) is the transfer function of the numerically controlled oscillator, expressed as:

[0021]

[0022] Step four, the phase of step one Subtract the estimate output by step three Get the error value θ d , the phase detector gain K d and the error value θ d Multiply the phase error K d θ d ; the second-order loop filter reduces the noise of K d θ d , and gets the smooth signal θ loop ;

[0023] The z-domain representation of θ loop is Y'(z):

[0024] Y'(z) = H(z)X'(z)

[0025] where X'(z) is the z-domain representation of K d θ d ;

[0026] Step five, calculate the carrier phase estimate value loop according to θ

[0027] The z-domain representation of Y1'(z) is:

[0028] Y1'(z) = H1(z)Y'(z)

[0029] Step six, the phase detector, loop filter and numerically controlled oscillator form a feedback loop, repeat steps four and five, that is, replace in step four with the output of step five to update iteratively, output the carrier phase estimate value at each time; The iteration stops when there is no signal input to the phase detector;

[0030] Step seven, according to the phase error K d θ d of step four, calculate the feedforward phase estimate value

[0031]

[0032] Wherein, k represents signal sampling point serial number, N represents phase estimation window length;

[0033] Step eight, add the phase estimation value of the current iteration time in step six And the feedforward stage phase estimation value of the current time in step seven To obtain the carrier phase estimation value of the current time

[0034] Step nine, the carrier phase estimation value of the signal is calculated in real time by repeating steps six to eight iterations.

[0035] Further, the transfer function of the feedback loop in step six is represented as:

[0036]

[0037] Wherein K d , K1 and K2 are related to the characteristic frequency ω n Of the feedback loop, and the damping factor ξ parameter, when the product of the characteristic frequency and the symbol period T is much smaller than 1, that is, ω n T << 1, the relationship between the three variables K d , K1, K2 and ω n , ξ is represented as:

[0038]

[0039]

[0040] Wherein, the symbol period T is determined by system design, and the empirical value of ξ is The values of K1 and K2 depend on K d And the characteristic frequency ω n , ω n The empirical conditions are:

[0041]

[0042] Advantages:

[0043] 1. The low-complexity noise-tolerant laser phase recovery method disclosed in the application realizes joint estimation of the frequency deviation and phase of the signal carrier through feedback stage phase estimation and feedforward stage phase estimation, solves the problem of phase jump of the traditional Diff-4th algorithm at low signal-to-noise ratio, and improves the carrier phase recovery performance.

[0044] 2. The low-complexity noise-tolerant laser phase recovery method disclosed in the application is based on digital phase-locked loop and Viterbi-Viterbi phase estimation, reduces the burst error in the phase recovery process at low signal-to-noise ratio, reduces the calculation complexity and calculation resources compared with the traditional Diff-4th method.

[0045] 3. The application discloses a low-complexity noise-tolerant laser phase recovery method, a phase detector, a loop filter and a digital controlled oscillator form a feedback loop, combining a feedforward mechanism and a feedback mechanism, realizing fast adjustment of carrier phase estimation, continuously tracking a Doppler frequency shift caused by relative motion of satellites in real time, being capable of eliminating constellation rotation caused by residual Doppler frequency offset and phase noise in an intersatellite coherent optical communication system, and improving stability and reliability of communication compared with a traditional Diff-4th method. BRIEF DESCRIPTION OF DRAWINGS

[0046] Figure 1 is a schematic diagram of a laser communication receiving end composition structure and signal processing in the application;

[0047] Figure 2 is a flowchart of a low-complexity noise-tolerant laser phase recovery method in the application;

[0048] Figure 3 is a log square root error comparison diagram of phase estimation of a low-complexity noise-tolerant laser phase recovery method in the application and a traditional Diff-4th method;

[0049] Figure 4 is a BER comparison diagram of a low-complexity noise-tolerant laser phase recovery method in the application and a traditional Diff-4th method. DETAILED DESCRIPTION

[0050] The application content is further explained and described in detail in combination with the drawings and examples.

[0051] Example 1

[0052] The signal is input into a digital signal processing process as shown in Figure 1 After two-way analog electrical signals I(t) and Q(t) are digitized through ADC, entering FPGA for matched filtering, clock recovery and channel equalization, entering the proposed carrier recovery method. For carrier phase recovery of signals under QPSK modulation, a satellite coherent optical communication process is simulated as shown in Figure 2 The low-complexity noise-tolerant laser phase recovery method disclosed in the embodiment forms loop calculation of input signal phase estimation value through feedback stage phase estimation and feedforward stage phase estimation, and the specific implementation steps are as follows:

[0053] Step one, the laser signal receiving module receives laser signals, the laser wavelength is 1550 nm, and the modulated signal received through an optical antenna is expressed as:

[0054]

[0055] wherein, E sis the symbol energy within the symbol interval T, the symbol rate is 2.5 Gsps, the symbol interval is 4 ns, a k is the amplitude of the kth sample point, K is the number of sample points contained in T, h(t - kT) represents the impulse response of the signal, f c is the carrier frequency, θ c (t) is the phase noise, n(t) represents a complex additive white noise with zero mean and variance N0 / 2. θ c (t) is modeled as a Wiener process, represented as:

[0056]

[0057] where G(x) is a Gaussian random variable with zero mean and variance δ v is the 3dB line width of the carrier 10 kHz. The received signal r(t) is mixed with a local oscillator (LO) signal f LO and θ LO represent the frequency and phase noise of the LO, respectively, the signal output by the optical mixer is converted into an analog electrical signal by a balanced detector, generating an in-phase (I) component and a quadrature (Q) component represented as:

[0058]

[0059] where Δf = f c -f LO is the residual Doppler frequency offset, n I (t) and n Q (t) are noise components, the input signal of the carrier recovery method is represented as:

[0060]

[0061] where θ is the carrier phase, represented as:

[0062]

[0063] where 2πΔfkT represents the phase introduced by the residual frequency offset, θ c (kT) - θ LO (kT) represents the phase noise related to δ v .

[0064] Step two, phase detection is performed on the laser signal , the phase is represented as:

[0065]

[0066] Step three, the phase of step two and the phase detector gain Kd K is the phase error d θ in , K is the phase error d = 4, the second order loop filter to 4θ in is denoised to get smooth signal θ loop_0 ;

[0067] θ loop_0 , Y(z) is the z-domain representation of:

[0068] Y(z) = H(z)X(z)

[0069] where X(z) is the z-domain representation of 4θ in ; H(z) is the transfer function of the second order loop filter, represented as:

[0070]

[0071] where K1, K2 are the gain factors of the loop filter, affecting the response speed of the loop and the ability to filter out noise;

[0072] Step four, the numerically controlled oscillator calculates the carrier phase estimation value according to θ loop_0 of step three

[0073] , the z-domain representation of Y1(z) is:

[0074] Y1(z) = H1(z)Y(z)

[0075] where H1(z) is the transfer function of the numerically controlled oscillator, represented as:

[0076]

[0077] Step five, the phase θ of step two is subtracted from the estimation output of step four to get the error value θ d ; the phase error 4θ d is multiplied by the phase detector gain 4 to get the phase error 4θ d ; the second order loop filter denoises 4θ d to get the smooth signal θ loop ;

[0078] θ loop , Y'(z) is the z-domain representation of:

[0079] Y'(z) = H(z)X'(z)

[0080] where X'(z) is the z-domain representation of 4θ d ;

[0081] Step six, θ according to step four loop The carrier phase estimation value is calculated

[0082] The z-domain representation Y1'(z) of Y1(z) is:

[0083] Y1'(z) = H1(z)Y'(z)

[0084] Step seven, the phase discriminator, loop filter and numerically controlled oscillator constitute a feedback loop, and steps five and six are repeated, i.e. the output of step six is used Step five is replaced by Iterative update is performed, and the carrier phase estimation value at each time is output The iteration stops when there is no signal input to the phase discriminator;

[0085] The transfer function of the feedback loop in step seven is represented as:

[0086]

[0087] where K1 and K2 are related to the characteristic frequency ω and the damping factor ξ parameters of the feedback loop, and when the product of the characteristic frequency and the symbol period T is much smaller than 1, i.e. ω n T << 1, the relationship between the two variables K1 and K2 and ω n , ξ is represented as:

[0088]

[0089] where the symbol period T is determined by system design, and the empirical value of ξ is The values of K1 and K2 depend on the characteristic frequency ω n , and the empirical conditions for ω n are:

[0090]

[0091] Step eight, the phase discriminator error 4θ d according to step five is used to calculate the feedforward stage phase estimation value at the current time by block estimation method

[0092]

[0093] where k represents the signal sampling point number, and N represents the phase estimation window length;

[0094] Step nine, the phase estimation value at the current iteration time of step seven and the feedforward stage phase estimation value at the current time of step eight The sum is the carrier phase estimation value of the current time

[0095] Step ten, the carrier phase estimation value of the signal is calculated in real time by repeating steps seven to nine.

[0096] In a preferred embodiment of the present application, the bit error rate curve is drawn according to the calculated carrier phase recovery bit error rate results at different signal-to-noise ratios, as shown in the figure Figure 4 The embodiment shows better estimation continuity when the bit signal-to-noise ratio is lower than 5.2 dB, and the effect is significantly better than the traditional algorithm when the bit signal-to-noise ratio is lower than 4.5 dB under QPSK modulation, and the bit error rate is 1 / 10 of the traditional algorithm.

[0097] As shown in Table 1, the low-complexity noise-tolerant laser phase recovery method disclosed in the embodiment can reduce 60% of the multiplier and 99% of the adder consumption compared with the traditional algorithm.

[0098] Table 1: Complexity comparison table

[0099]

[0100] In Table 1, N1 represents the first-stage frequency offset estimation window length, N2 represents the second-stage 4th power phase estimation window length, N represents the fine phase estimation window length in the low-complexity noise-tolerant laser phase recovery method, and K represents the data length.

[0101] The above specific description further details the purpose, technical solutions and beneficial effects of the present application. It should be understood that the above description is only a specific embodiment of the present application and is not used to limit the protection scope of the present application. Any modification, equivalent replacement, improvement, etc. made within the spirit and principles of the present application should be included in the protection scope of the present application.

Claims

1. A low-complexity noise-tolerant laser phase retrieval method, characterized in that: The joint estimation of the frequency offset and phase of the signal carrier is achieved through phase estimation in the feedback stage and phase estimation in the feedforward stage, including the following steps: Step 1: Analyze the laser signal Perform phase detection, phase Represented as: Step Two, Phase of Step One Phase detector gain K d Multiplication equals phase detection error K d θ in Second-order loop filter for K d θ in Noise reduction processing is performed to obtain a smooth signal θ loop_0 ; θ loop_0 The z-domain representation of Y(z) is: Y(z)=H(z)X(z) Where X(z) is K d θ in The z-domain representation; H(z) is the transfer function of the second-order loop filter, expressed as: Where K1 and K2 are the gain factors of the loop filter, which affect the loop's response speed and noise filtering capability. Step 3: The numerically controlled oscillator, based on θ from step 2... loop_0 The carrier phase estimate was calculated. The z-domain representation of Y1(z) is: Y1(z)=H1(z)Y(z) Where H1(z) is the transfer function of the numerically controlled oscillator, expressed as: Step 4, Phase of Step 1 Subtract the estimated output from step three Obtain the error value Phase detector gain K d and error value Multiplication is the phase detection error. Second-order loop filter Noise reduction processing is performed to obtain a smooth signal θ loop ; θ loop The z-domain representation of Y′(z) is: Y′(z)=H(z)X′(z) Where X′(z) is The z-domain representation; Step 5: Based on θ from Step 4 loop The carrier phase estimate was calculated. The z-domain representation of Y′1(z) is: Y′1(z)=H1(z)Y′(z) Step Six: The phase detector, loop filter, and digitally controlled oscillator form a feedback loop; repeat steps Four and Five, i.e., use the output from step Five. Replace step four Perform iterative updates and output the carrier phase estimate at each time step. Iteration stops when there is no signal input to the phase detector; Step 7: Based on the phase detection error in Step 4 The current feedforward stage phase estimate is calculated using the block estimation method. Where k represents the signal sampling point number, and N represents the phase estimation window length; Step 8: Take the phase estimate from Step 6 at the current iteration time. and the feedforward phase estimate at the current time step seven The carrier phase estimate at the current moment is obtained by adding them together. Step 9: Iterate through steps 6 to 8 to calculate the carrier phase estimate of the signal in real time.

2. The low-complexity noise-tolerant laser phase retrieval method as described in claim 1, characterized in that: The transfer function of the feedback loop described in step six is ​​expressed as follows: Where K d K1 and K2 and the characteristic frequency ω of the feedback loop n The damping factor ξ is related to the parameter. When the product of the characteristic frequency and the symbol period T is much less than 1, i.e., ω n T << 1, three variables K d K1, K2 and ω n The relationship between ξ is expressed as: The symbol period T is determined by the system design, and the empirical value of ξ is... The values ​​of K1 and K2 depend on K d and characteristic frequency ω n ω n The empirical conditions are:

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