Method for suppressing phase noise by projection histogram in coherent light OFDM (Orthogonal Frequency Division Multiplexing) system

Abstract

The invention relates to a method for suppressing phase noise by a projection histogram in a coherent light OFDM (Orthogonal Frequency Division Multiplexing) system. According to the method, a cyclic prefix is linearly processed to reduce the power of inter-carrier interference (ICI), and phase noise is preliminarily suppressed; the method comprises the following steps of: firstly, obtaining rough estimation of phase noise by using a small amount of pilot frequency, further suppressing the phase noise by using pseudo pilot frequency assistance, and finally compensating the phase noise by using a projection histogram twice so as to improve time resolution and suppression precision. Simulation results show that under 16-order quadrature amplitude modulation (16QAM), when the laser line width is 100 kHz, the compensation effect of the algorithm is improved compared with that of a traditional projection histogram, and the frequency spectrum utilization rate is effectively improved.

Description

Technical Field

[0001] The present invention belongs to the technical field of phase noise suppression in a coherent optical orthogonal frequency division multiplexing (CO-OFDM) system, and is a method for suppressing phase noise by combining a cyclic prefix linear processing and pseudo-pilots-aidedProjection Histogram (L-PS-PH) algorithm. Background Art

[0002] The Coherent Optical Orthogonal Frequency-Division Multiplexing (CO-OFDM) system was proposed in 2006. It is based on the Orthogonal Frequency Division Multiplexing (OFDM) system and combines the optical communication system and coherent detection technology. Therefore, the CO-OFDM system has the advantages of "coherent detection" and "OFDM" modulation, high spectrum utilization, the photoelectric conversion at the receiving end is approximately linear transformation, and there is no beat noise at the receiving end. When the system transmission rate is high, the system performance will not deteriorate sharply. At the same time, the CO-OFDM system has high receiving sensitivity, good tolerance to chromatic dispersion (CD), and strong ability to resist polarization mode dispersion (PMD).

[0003] A major drawback of the CO-OFDM system is that it is very sensitive to the phase noise introduced by the local oscillator. The noise is mainly divided into two categories: one is the common phase error (CPE) caused by the zero-order spectral component of the phase noise, which will cause the signal constellation point to rotate; the other is the inter-carrier interference (ICI) caused by the non-zero-order spectral component, which will cause the cloud-like divergence of the signal constellation point. Both will lead to the degradation of CO-OFDM performance. In order to solve the problem caused by phase noise, it is necessary to use narrow linewidth lasers with a linewidth of hundreds of kHz or less at the CO-OFDM transmitter and receiver, but as the laser linewidth decreases, the system cost will increase significantly. In addition to using narrow linewidth lasers, the phase noise suppression method of digital signal processing has become an economical and efficient solution. Therefore, using a good phase noise suppression method in the CO-OFDM system can greatly reduce the requirements for the laser linewidth. Summary of the invention

[0004] In view of this, an object of the present invention is to provide a phase noise compensation algorithm combining cyclic prefix linear processing with pseudo pilot assisted projection histogram in a coherent optical OFDM system.

[0005] To achieve the above object, the present invention provides the following technical methods:

[0006] In the first stage, the characteristic that the cyclic prefix (CP) and the orthogonal frequency division multiplexing (OFDM) symbol part of the information are the same is utilized. According to the Nyquist criterion, the relationship between the length used by the CP in linear processing and the combination coefficient of the tail information of the OFDM symbol is obtained. Then, the optimal combination coefficient is equivalently calculated according to the optimal solution problem to reduce the power of inter-carrier interference (ICI).

[0007] In the second stage, the linearly processed signal is converted to the frequency domain through fast Fourier transform, and the signal is roughly compensated using three pilots. After the pseudo pilot is selected, a tentative decision operation is performed on the roughly compensated signal and the pseudo pilot, and the received symbol after phase noise suppression is calculated in combination with the least squares (LS) principle.

[0008] In the third stage, the received symbols assisted by the pseudo pilot are compensated for the phase noise using the projection histogram method. In this stage, the phase noise problem is converted into a problem of solving a certain tilt angle of the image. The test phases with the same interval are obtained in the phase range of -π / 4 to π / 4. All the constellation points in the constellation diagram of different test phases are projected onto the real axis to obtain the corresponding projection histograms, and the compensation effect is judged according to the number of corresponding constellation points in the range.

[0009] The beneficial effects of the present invention are:

[0010] The present invention relates to a phase noise compensation algorithm that combines cyclic prefix linear processing with pseudo pilot assisted projection histogram. The invented method eliminates the influence of CPE and ICI in the CO-OFDM system, improves the problem of low tolerance of the system to phase noise, and improves the spectrum utilization. Simulation results show that the method has a certain degree of improvement in bit error rate performance compared with the pilot assisted algorithm in the document [1] "HONG XZ, HONG XJ, HE S. Linearly interpolated sub-symbol optical phase noise suppression in CO-OFDM system [J]. Optics Express, 2015, 23 (4): 4691-4702." and the CPE phase noise compensation algorithm based on projection histogram in the document [2] "LI ZX, LI Y, MA JJ, et al. Projection Histogram-Assisted Estimation of Common Phase Error in Coherent Optical OFDM Systems [J]. IEEE Photonics Journal, 2019, 11 (3): 1-9." In summary, the algorithm proposed in the present invention has a relatively obvious suppression of phase noise and greatly improves the spectrum utilization rate. Therefore, in practical applications, the method of the present invention has a high utilization value and practical significance for suppressing the phase noise of the CO-OFDM system. BRIEF DESCRIPTION OF THE DRAWINGS

[0011] In order to make the purpose, technical method and beneficial effects of the present invention clearer, the present invention provides the following drawings for illustration:

[0012] Figure 1 A technical roadmap for the method of the present invention;

[0013] Figure 2 The constellation diagram and projection histogram of the method proposed in this paper under different conditions;

[0014] Figure 3 The signal-to-noise ratio-bit error rate comparison chart of each method under 16QAM and laser line width of 100kHz;

[0015] Figure 4 The bit error rate of each method varies with the laser line width under 16QAM; DETAILED DESCRIPTION

[0016] The preferred embodiments of the present invention will be described in detail below with reference to the accompanying drawings.

[0017] Step 1: Taking advantage of the fact that the back-end information in the OFDM symbol is the same as the CP part information, the OFDM symbol and CP are linearly processed in the time domain of the receiving end to reduce the ICI power. After processing, the OFDM symbol information is as shown in formula (1):

[0018]

[0019] In the formula, y m,n and y′ m,n They represent the symbol information of length n in the mth OFDM symbol before and after linear processing; N is the OFDM symbol length, g is the length used for calculation in the cyclic prefix; p n and q n are the combination coefficients of the CP length Ncp and the OFDM symbol tail information in linear processing; according to the Nyquist criterion, the relationship between the two satisfies equation (2):

[0020] p n =1-q n ,Ng≤n≤N-1 (2)

[0021] The linearly processed signal y′ m,n Convert to frequency domain, the converted frequency domain signal Y m ' is expressed as formula (3):

[0022] Y m ′=F(y′ m,n )=I m,n (0)HS m,n +I m,n +W m,n (3)

[0023] In the formula, I m,n (0) represents the common phase error (CPE) of the zero-order component of phase noise after linear processing and fast Fourier transformation (FFT); H is the channel impulse response after FFT; S m,n is the frequency domain signal at the transmitting end; I m,nis the non-zero-order component ICI of phase noise; W m,n is Additive White Gaussian Noise (AWGN);

[0024] To reduce the impact of ICI, it is necessary to make I m,n As small as possible, so the combination coefficient p selected during CP linear processing n and q n It becomes the key to reduce ICI power; the optimal solution problem is equivalent to formula (4):

[0025]

[0026] The constraint condition is formula (2), and the optimal combination coefficient is finally obtained as shown in formula (5):

[0027]

[0028] α and β are expressed as in formula (6):

[0029]

[0030] In formula (6), Δf is the laser line width; T s is the OFDM symbol period;

[0031] Step 2: In the CO-OFDM system, the OFDM symbol Y received in the frequency domain after linear processing of the CP is m ' is expressed as formula (7):

[0032] Y m ′=Fφ m F H HA m +W m (7)

[0033] definition W m is the residual caused by AWGN; A m is the mth OFDM symbol in the frequency domain of the transmitter;

[0034] The phase noise Expand from the basis to:

[0035]

[0036] B is the basis of the basis expansion, Γ m is the corresponding weight factor;

[0037] At the receiving end, the signal A after channel estimation mIt is expressed as formula (9):

[0038] A m =H -1 diag(Y m ′)B * Γ m * +ε m (9)

[0039] Where ε m represents the residual caused by AWGN;

[0040] After the time domain CP is linearly processed and Fourier transformed, three pilot signals are inserted into the frequency domain signal to perform a rough CPE estimation to obtain the phase. The received signal after channel equalization and compensation As shown in formula (10):

[0041]

[0042] At this time, select The pseudo pilot of , M represents the number of pseudo pilots; is an N×1 vector, where the kth i The first input is 1, and the rest are 0; the pseudo pilot after detection and judgment It is expressed as:

[0043]

[0044] Q represents a tentative decision operation, σ represents the power enhancement factor of the pseudo pilot at the transmitter;

[0045] The roughly estimated Compensation A m Then, define:

[0046]

[0047] Using pseudo pilot and the least squares (LS) principle, Γ is calculated. m * Estimates:

[0048]

[0049] Therefore, the received symbol after channel equalization and phase noise suppression is It is expressed as:

[0050]

[0051] Step 3: Perform constellation processing on the received symbols after the CP linear processing and the phase noise suppression after adding the pseudo pilot;

[0052] First, obtain M1 test phases with the same interval in the phase interval of -π / 4 to π / 4; the nth test phase of the mth OFDM symbol It is expressed as formula (15):

[0053]

[0054] Will As the receiving end symbol CPE compensation value, the nth signal after the test phase compensation It is expressed as formula (16):

[0055]

[0056] In each OFDM symbol, all constellation points in the constellation diagrams of M1 different test phases are projected onto the real axis to obtain the corresponding projection histograms. (x′, y′) and (x, y) represent the pixel coordinates of the constellation points before and after compensation, respectively. The projection values ​​are transformed by Radon into:

[0057]

[0058] The obtained projection values ​​are centered at -3, -1, 1, and 3, and the number of corresponding constellation points within the range w is counted respectively, denoted as s -3 ,s -1 ,s1,s3, then sum the total number of constellation points contained in the four projection centers within the range w As shown in formula (18):

[0059]

[0060] The larger the value of is, the better the effect of compensating CPE by the test phase value is. As the number of test phases in the range of -π / 4 to π / 4 increases, the phase division becomes more refined, which improves the compensation accuracy of the algorithm, but at the same time also leads to an increase in the complexity of the algorithm.

[0061] The best test phase compensation value is recorded as Compensate the signal, the compensated signal r m,n Formula (19):

[0062]

[0063] Then the test phase is divided for the second time to obtain M2 test phases, and the test phase is updated to As shown in formula (20):

[0064]

[0065] r∈{-M2 / 2,-M2 / 2+1,···,M2 / 2}, by dividing the test phase into two stages, the M1+M2 test phases are used to achieve the compensation effect of the M1×M2 test phase; the number of test phases used is reduced, thereby reducing the algorithm complexity; the signal r after the second stage compensation m ' ,n As shown in formula (21):

[0066]

[0067] 2. Combine with attachment Figure 2 , Figure 3 and Figure 4 To further illustrate that the method of the present invention has a relatively significant improvement in the suppression performance of phase noise to a certain extent.

[0068] Table 1 Simulation parameter settings

[0069]

[0070]

[0071] The parameters used in the experimental simulation are shown in Table 1.

[0072] Figure 2 The constellation diagram and projection histogram under different conditions when the laser line width is 100kHz under 16QAM and the signal-to-noise ratio is 15dB. Figure 2 (a) and Figure 2 (d) is the original signal constellation diagram without using any phase noise compensation algorithm and its projection histogram on the real axis; Figure 2 (b) and Figure 2 (e) are the signal constellation diagram without phase noise influence and its projection histogram on the real axis; Figure 2 (c) and Figure 2 (f) are the signal constellation diagram affected by phase noise after compensation by the algorithm proposed in this paper and its projection histogram on the real axis; Figure 2 (a) and Figure 2 (d) Since the system is affected by phase noise, the constellation diagram rotates violently to form a ring and the peak of the projection histogram near its projection center is not obvious; Figure 2 (b) and Figure 2 (e) The signal constellation diagram that is not affected by any phase noise is regularly arranged into sixteen constellation points, and a clear peak is formed at the projection center on the projection histogram; Figure 2 (e) and Figure 2 (f) The constellation clusters in the constellation diagram after compensation by the L-PS-PH algorithm are compared with Figure 2 (a) has been greatly improved, so its corresponding projection histogram shows an obvious peak at the projection center. It can be seen that the algorithm proposed by the method of the present invention has a good compensation effect on the phase noise in the CO-OFDM system.

[0073] Figure 3 The figure is a SNR-BER comparison diagram of different phase noise suppression methods under 16QAM modulation and line width of 100kHz, where NPHN is the BER curve when there is no phase noise. It can be seen from the figure that the L-PS-PH algorithm proposed by the method of the present invention has a bit error rate of 10 -5 Compared with the LS algorithm proposed in the pilot-assisted algorithm in the literature [1] "HONG XZ, HONG XJ, HE S. Linearly interpolated sub-symbol optical phase noise suppression in CO-OFDM system [J]. Optics Express, 2015, 23 (4): 4691-4702.", the performance is improved by about 1 dB; compared with the PH algorithm proposed in the CPE phase noise compensation algorithm based on projection histogram in the literature [2] "LI ZX, LI Y, MA JJ, et al. Projection Histogram-Assisted Estimation of Common Phase Error in Coherent Optical OFDM Systems [J]. IEEE Photonics Journal, 2019, 11 (3): 1-9.", the performance is improved by about 0.6 dB. When the bit error rate is 10 -6 The L-PS-PH algorithm improves about 2.25dB compared with the LS algorithm, and improves the performance of the PH algorithm by 1.25dB. The LS algorithm improves compensation accuracy at the expense of spectrum utilization, but its ability to suppress CPE is limited at large signal-to-noise ratios. The PH algorithm uses the rotation and divergence of the constellation diagram to observe the phase noise compensation capability of CPE. However, since its algorithm relies on the rotation characteristics of the constellation diagram, it is susceptible to the impact of ICI. The L-PS-PH algorithm proposed in the method of the present invention reduces the power of ICI by linearly processing the CP, and then uses pseudo-pilots to improve the spectrum utilization of the system, reduces the divergence of the constellation points, increases the ability of the subsequent PH algorithm to suppress phase noise, and improves spectrum utilization.

[0074] Figure 4The BER curve is shown as the laser line width changes when the SNR is 15dB and 16QAM modulation is used. Figure 4 It can be seen that the performance of the L-PS-PH algorithm is always better than the LS algorithm in the literature [1] "HONG XZ, HONG XJ, HE S. Linearly interpolated sub-symbol optical phase noise suppression in CO-OFDM system [J]. Optics Express, 2015, 23 (4): 4691-4702." and the PH algorithm in the literature [2] "LI ZX, LI Y, MAJ J, et al. Projection Histogram-Assisted Estimation of Common Phase Error in Coherent Optical OFDM Systems [J]. IEEE Photonics Journal, 2019, 11 (3): 1-9." when the bit error rate is 10 -4 When the bit error rate is 10, the line width tolerance of the LS algorithm is 200kHz, and the line width tolerance of the PH algorithm is 250kHz. Compared with the LS algorithm and the PH algorithm, the line width tolerance is increased by 150kHz and 100kHz respectively. -3 When , the line width tolerance of the LS algorithm is 500kHz, and the line width tolerance of the PH algorithm is 550kHz. Compared with the line width tolerance of the LS algorithm and the PH algorithm, they are increased by 250kHz and 200kHz respectively. In general, the algorithm improves the spectrum utilization at the cost of a little time complexity under the condition of similar phase noise compensation effect, and its spectrum utilization increases with the increase of subcarriers.

[0075] Based on the above simulation verification, it can be seen that the present invention aims at the sensitivity of CO-OFDM system to phase noise, and proposes a method combining cyclic prefix linear processing with pseudo-pilot assisted projection histogram in coherent optical OFDM system to suppress the influence of phase noise on CO-OFDM system, thereby improving the performance and spectrum utilization of the system.

[0076] Finally, it should be noted that the above preferred embodiments are only used to illustrate the technical solutions of the present invention rather than to limit it. Although the present invention has been described in detail through the above preferred embodiments, those skilled in the art should understand that various changes can be made in form and details without departing from the scope defined by the claims of the present invention.

Claims

1. A method for suppressing phase noise by using a projection histogram in a coherent optical orthogonal frequency-division multiplexing (CO-OFDM) system; the method suppresses noise in three stages. In the first stage, the cyclic prefix (CP) is linearly processed by using the characteristic that the cyclic prefix and the orthogonal frequency division multiplexing (OFDM) symbol have the same information, so as to reduce the power of inter-carrier interference (ICI); in the second stage, the linearly processed signal is roughly compensated for the phase noise by using three pilots, and the phase noise of the OFDM symbol is finely compensated by selecting a suitable pseudo pilot; in the third stage, the projection histogram (PH) is used twice to suppress the residual noise; The specific steps are as follows: Step 1: Taking advantage of the fact that the back-end information in the OFDM symbol is the same as the CP part information, the OFDM symbol and CP are linearly processed in the time domain of the receiving end to reduce the ICI power. After processing, the OFDM symbol information is as shown in formula (1): In the formula, y m,n and y′ m,n They represent the symbol information of length n in the mth OFDM symbol before and after linear processing; N is the OFDM symbol length, g is the length used for calculation in the cyclic prefix; p n and q n The length N of CP in linear processing cp The combination coefficient of the OFDM symbol tail information; according to the Nyquist criterion, the relationship between the two satisfies equation (2): p n =1-q n ,N-g≤n≤N-1 (2) The linearly processed signal y′ m,n Convert to frequency domain, the converted frequency domain signal Y m ' is expressed as formula (3): Y m ′=F(y′ m,n )=I m,n (0)HS m,n +I m,n +W m,n (3) In the formula, I m,n (0) represents the common phase error (CPE) of the zero-order component of phase noise after linear processing and fast Fourier transformation (FFT); H is the channel impulse response after FFT; S m,n is the frequency domain signal at the transmitting end; I m,n is the non-zero-order component ICI of phase noise; W m,n is Additive White Gaussian Noise (AWGN); To reduce the impact of ICI, it is necessary to make I m,n As small as possible, so the combination coefficient p selected during CP linear processing n and q n It becomes the key to reduce ICI power; the optimal solution problem is equivalent to formula (4): The constraint condition is formula (2), and the optimal combination coefficient is finally obtained as shown in formula (5): α and β are expressed as in formula (6): In formula (6), Δf is the laser line width; T s is the OFDM symbol period; Step 2: In the CO-OFDM system, the OFDM symbol Y received in the frequency domain after linear processing of the CP is m ' is expressed as formula (7): Y m ′=Fφ m F H HA m +W m (7) definition W m is the residual caused by AWGN; A m is the mth OFDM symbol in the frequency domain of the transmitter; The phase noise Expand from the basis to: B is the basis of the basis expansion, Γ m is the corresponding weight factor; At the receiving end, the signal A after channel estimation m It is expressed as formula (9): A m =H -1 diag(Y m ′)B * C m * +e m (9) Where ε m represents the residual caused by AWGN; After the time domain CP is linearly processed and Fourier transformed, three pilot signals are inserted into the frequency domain signal to perform a rough CPE estimation to obtain the phase. The received signal after channel equalization and compensation As shown in formula (10): At this time, select The pseudo pilot of , M represents the number of pseudo pilots; is an N×1 vector, where the kth i The first input is 1, and the rest of the inputs are 0; the pseudo pilot after detection and judgment It is expressed as: Q represents a tentative decision operation, σ represents the power enhancement factor of the pseudo pilot at the transmitter; The roughly estimated Compensation A m Then, define: Using pseudo pilot and the least squares (LS) principle, Γ is calculated. m * Estimates: Therefore, the received symbol after channel equalization and phase noise suppression is It is expressed as: Step 3: Perform constellation processing on the received symbols after the CP linear processing and the phase noise suppression after adding the pseudo pilot; First, obtain M1 test phases with the same interval in the phase interval of -π / 4 to π / 4; the nth test phase of the mth OFDM symbol It is expressed as formula (15): Will As the receiving end symbol CPE compensation value, the nth signal after the test phase compensation It is expressed as formula (16): In each OFDM symbol, all constellation points in the constellation diagrams of M1 different test phases are projected onto the real axis to obtain the corresponding projection histograms. (x′, y′) and (x, y) represent the pixel coordinates of the constellation points before and after compensation, respectively. The projection values ​​are transformed by Radon into: The obtained projection values ​​are centered at -3, -1, 1, and 3, and the number of corresponding constellation points within the range w is counted respectively, denoted as s -3 ,s -1 ,s1,s3, then sum the total number of constellation points contained in the four projection centers within the range w As shown in formula (18): The larger the value of is, the better the effect of compensating CPE by the test phase value is. As the number of test phases in the range of -π / 4 to π / 4 increases, the phase division becomes more refined, which improves the compensation accuracy of the algorithm, but at the same time also leads to an increase in the complexity of the algorithm. The best test phase compensation value is recorded as Compensate the signal, the compensated signal r m,n Formula (19): Then the test phase is divided for the second time to obtain M2 test phases, and the test phase is updated to As shown in formula (20): r∈{-M2 / 2,-M2 / 2+1,···,M2 / 2}, by dividing the test phase into two stages, the M1+M2 test phases are used to achieve the compensation effect of the M1×M2 test phase; the number of test phases used is reduced, thereby reducing the algorithm complexity; The signal r after the second stage compensation m ' ,n As shown in formula (21): Finally, the signal after phase noise suppression by this method is expressed as r m ' ,n .

Images