CN113726703A - Rotation guide blind phase retrieval algorithm facing high-order quadrature amplitude modulation signal - Google Patents
Rotation guide blind phase retrieval algorithm facing high-order quadrature amplitude modulation signal Download PDFInfo
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Abstract
The invention discloses a rotation guide blind phase retrieval algorithm facing a high-order quadrature amplitude modulation signal, which comprises the following steps: s1, dividing a plurality of primary test phases based on the high-order quadrature amplitude modulation signal, and taking the primary test phase with the minimum Euclidean distance as a rough phase; s2, dividing decision phases around the rough phase, and determining the phase rotation direction according to the Euclidean distance between the decision phases and the primary test phase; and S3, dividing a plurality of secondary test phases based on the rough phase, testing the secondary test phases in the determined phase rotation direction by taking the decision phase as a reference, and taking the secondary test phase or the decision phase with the minimum Euclidean distance as a fine phase. The rotation guide blind phase retrieval algorithm for the high-order quadrature amplitude modulation signal can effectively reduce the calculated amount and the error rate by judging the phase rotation direction.
Description
Technical Field
The invention relates to the technical field of phase retrieval, in particular to a rotation guide blind phase retrieval algorithm facing a high-order quadrature amplitude modulation signal.
Background
Multilevel quadrature amplitude modulation has been drawing attention in the field of high-rate optical transmission due to its advantage of high spectrum utilization. However, as the order of the modulation signal increases, the phase margin for the correct decision of the signal becomes less and less, resulting in the modulation signal becoming more and more sensitive to phase noise. Therefore, in order to correctly transmit a high-order modulated signal, a high-precision phase recovery algorithm is essential. With respect to the problem of phase recovery of high order modulated signals, numerous scholars have proposed a number of algorithms to solve. One type of algorithm is a feedback algorithm based on decision-directed, however, the algorithm has a large defect due to a large feedback delay in practical application. Among the feedforward phase recovery algorithms, the blind phase search algorithm (BPS) has high phase noise tolerance but is at the cost of a large amount of computation. In order to solve the problem of large calculation amount, a two-stage blind phase retrieval algorithm is proposed by scholars, and the algorithm can reduce the calculation amount to about one third of the original calculation amount. Later, learners have further reduced the complexity of the algorithm by combining blind phase retrieval with maximum likelihood (BPS/ML), but still have the problems of high bit error rate and large computational complexity.
Disclosure of Invention
The invention aims to provide a rotation guide blind phase retrieval algorithm facing high-order quadrature amplitude modulation signals, which can effectively reduce the calculated amount and the bit error rate.
In order to solve the above problem, the present invention provides a rotation-guided blind phase retrieval algorithm for high-order qam signals, which includes the following steps:
s1, dividing a plurality of primary test phases based on the high-order quadrature amplitude modulation signal, and taking the primary test phase with the minimum Euclidean distance as a rough phase;
s2, dividing decision phases around the rough phase, and determining the phase rotation direction according to the Euclidean distance between the decision phases and the primary test phase;
and S3, dividing a plurality of secondary test phases based on the rough phase, testing the secondary test phases in the determined phase rotation direction by taking the decision phase as a reference, and taking the secondary test phase or the decision phase with the minimum Euclidean distance as a fine phase.
As a further improvement of the present invention, step S1 includes:
s11, rotating the high-order quadrature amplitude modulation signal by a plurality of primary test phases distributed at equal intervals
Wherein the content of the first and second substances,
n is the number of one-time testing phases;
s12, using a decision circuit to search the constellation point closest to the rotated signal and calculating the Euclidean distance between the constellation point and the rotated signal;
and S13, taking the primary test phase with the minimum Euclidean distance as a rough phase.
As a further improvement of the present invention, step S12 further includes: and summing Euclidean distances between a plurality of continuous same test phase signals and the nearest constellation point thereof.
As a further refinement of the invention, the decision phase is in a clockwise or counterclockwise direction of the coarse phase.
As a further improvement of the present invention, when the decision phase is located clockwise of the coarse phase; if the Euclidean distance of the judged phase is larger than the Euclidean distance of the rough phase, determining the anticlockwise direction as a phase rotation direction; if the Euclidean distance of the judged phase is smaller than the Euclidean distance of the rough phase, determining the clockwise direction as the phase rotation direction;
when the decision phase is counterclockwise of the coarse phase; if the Euclidean distance of the judged phase is larger than the Euclidean distance of the rough phase, determining that the clockwise direction is the phase rotation direction; and if the Euclidean distance of the judged phase is smaller than the Euclidean distance of the rough phase, determining the anticlockwise direction as the phase rotation direction.
As a further refinement of the invention, the decision phase is one of two quadratic test phases adjacent to the coarse phase.
As a further improvement of the present invention, the decision phase is:
wherein the content of the first and second substances,
and B is the number of secondary test phases divided in the range of positive and negative of the coarse phase, and N is the number of primary test phases.
As a further improvement of the present invention, step S3 includes:
s31, dividing a plurality of secondary test phases in the positive and negative ranges of the rough phase
Wherein the content of the first and second substances,
b is the number of secondary test phases divided in the range of the positive phase and the negative phase of the rough phase;
and S32, testing the secondary test phase in the determined phase rotation direction by taking the decision phase as a reference, and taking the secondary test phase or the decision phase with the minimum Euclidean distance as a fine phase.
As a further improvement of the present invention, B ═ 2.
As a further improvement of the present invention, step S1 is preceded by: the number of primary test phases and secondary test phases is set.
The invention has the beneficial effects that:
the rotation guide blind phase retrieval algorithm for the high-order quadrature amplitude modulation signal can effectively reduce the calculated amount and the error rate by judging the phase rotation direction.
The foregoing description is only an overview of the technical solutions of the present invention, and in order to make the technical means of the present invention more clearly understood, the present invention may be implemented in accordance with the content of the description, and in order to make the above and other objects, features, and advantages of the present invention more clearly understood, the following preferred embodiments are described in detail with reference to the accompanying drawings.
Drawings
FIG. 1 is a block diagram of a high order quadrature amplitude modulation signal oriented rotation-directed blind phase retrieval algorithm in a preferred embodiment of the present invention;
FIG. 2 is a conceptual diagram of a high order QAM oriented rotation-guided blind phase retrieval algorithm in a preferred embodiment of the present invention;
fig. 3 is a graph of bit error rate as a function of the number of test phases in a preferred embodiment of the invention.
Detailed Description
The present invention is further described below in conjunction with the following figures and specific examples so that those skilled in the art may better understand the present invention and practice it, but the examples are not intended to limit the present invention.
As shown in fig. 1-2, the rotation-guided blind phase retrieval algorithm (RD-BPS) oriented to high-order quadrature amplitude modulation signals in the preferred embodiment of the present invention comprises the following steps:
s1, modulating signal Y based on high-order quadrature amplitudekDividing a plurality of primary test phases, and taking the primary test phase with the minimum Euclidean distance as a rough phase;
s2, dividing decision phases around the rough phase, and determining the phase rotation direction according to the Euclidean distance between the decision phases and the primary test phase;
and S3, dividing a plurality of secondary test phases based on the rough phase, testing the secondary test phases in the determined phase rotation direction by taking the decision phase as a reference, and taking the secondary test phase or the decision phase with the minimum Euclidean distance as a fine phase.
Specifically, step S1 includes:
s11, rotating the high-order quadrature amplitude modulation signal by a plurality of primary test phases distributed at equal intervals
Wherein the content of the first and second substances,
n is the number of one-time testing phases;
s12, using a decision circuit to search the constellation point closest to the rotated signal and calculating the Euclidean distance between the constellation point and the rotated signal;
and S13, taking the primary test phase with the minimum Euclidean distance as a rough phase.
Further, in order to reduce the interference due to the additive noise, step S11 further includes: and summing Euclidean distances between a plurality of continuous same test phase signals and the nearest constellation point thereof.
Optionally, the decision phase is in a clockwise direction or a counterclockwise direction of the coarse phase.
Specifically, when the decision phase is located clockwise of the coarse phase; if the Euclidean distance of the judged phase is larger than the Euclidean distance of the rough phase, determining the anticlockwise direction as a phase rotation direction; if the Euclidean distance of the judged phase is smaller than the Euclidean distance of the rough phase, determining the clockwise direction as the phase rotation direction;
when the decision phase is counterclockwise of the coarse phase; if the Euclidean distance of the judged phase is larger than the Euclidean distance of the rough phase, determining that the clockwise direction is the phase rotation direction; and if the Euclidean distance of the judged phase is smaller than the Euclidean distance of the rough phase, determining the anticlockwise direction as the phase rotation direction.
Optionally, the decision phase is one of two quadratic test phases adjacent to the coarse phase to reduce the amount of computation.
In one embodiment, the decision phase is located clockwise of the coarse phase, and the decision phase is:
wherein the content of the first and second substances,
and B is the number of secondary test phases divided in the range of positive and negative of the coarse phase, and N is the number of primary test phases.
Next, the phase will be tested twice
Corresponding Euclidean distance and coarse phase
Are compared. If calculated, the result is
The corresponding Euclidean distance is greater than
Then in the fine phase recovery of step S3, we only consider
In (b)<0, in the case of the first embodiment. Otherwise, if it is calculated
The corresponding Euclidean distance is less than
Then in the fine phase recovery of step S3, we only consider
In (b)>1. By this step of rotation guidance, the fine phase can be recovered
The number of required test phases was further reduced from 2B to B + 0.5.
Specifically, step S3 includes:
s31, dividing a plurality of secondary test phases in the positive and negative ranges of the rough phase,
wherein the content of the first and second substances,
b is the number of secondary test phases divided in the range of the positive phase and the negative phase of the rough phase;
and S32, testing the secondary test phase in the determined phase rotation direction by taking the decision phase as a reference, and taking the secondary test phase or the decision phase with the minimum Euclidean distance as a fine phase.
Wherein, step S1 is preceded by: the number of primary test phases and secondary test phases is set.
As shown in fig. 2, (a) is a QPSK signal affected by additive noise and phase noise; (b) the signal after the coarse phase recovery is obtained; (c) is the determined rotation direction; (d) is the signal after fine phase recovery. After the first coarse phase estimation is completed, the 2L +1 consecutive signals will be distributed around the centroid, which is marked with black dots. At this point, the phase recovery is inaccurate because the signals should be distributed around the constellation point in the middle of each decision interval. Finding the more accurate phase is the work to be done in the fine phase recovery phase. It is easy to find that after the coarse phase recovery, one can look for finer phases from two directions, clockwise rotation and counter-clockwise rotation respectively. Taking the signal shown in fig. 2 as an example, if the phase is found clockwise, more signals will be close to the edge of the decision interval, which means that the euclidean distance calculated for the corresponding test phase will increase. In contrast, if the phase is looked for counterclockwise, more signal will be away from the edge of the decision interval and the corresponding euclidean distance will decrease. By using this property, we add a step S2 of rotation direction decision after the coarse phase recovery in step S1 to guide step S3 to the direction that the fine phase recovery is looking for. The fine phase can eventually be recovered in the correct direction.
In one embodiment, the data is encoded by 64QAM and256QAM simulation experiments were performed to test the performance of the proposed RD-BPS algorithm. In the simulation, assuming clock recovery, channel equalization and frequency offset compensation are all completed. The phase noise model we build as random walk thetan＝θn-1+ Δ n, where Δ n is a gaussian random variable with a mean of zero and a variance of 2 π Δ fT. Where T is the symbol duration and af is the sum of the transmitter and local oscillator laser linewidths. In a simulation experiment of 64QAM, we set the product of the sum of laser linewidths and signal duration to 2X 10-5 and 6X 10-6 to simulate phase noise. For 256QAM, we set the product of the sum of laser linewidths and signal duration to 5 x 10-6 and 1 x 10-6 to model phase noise, since this signal is more sensitive to phase noise. The window length L of an ideal filter is affected by the signal-to-noise ratio of the signal, the laser linewidth and the code rate. In the simulation experiment, for convenience, L is uniformly set to 14, because under various conditions of the simulation, the setting can achieve near-optimal effect. To compare with RD-BPS, we also simulate BPS/ML the resulting bit error rate performance under various conditions. For BPS/ML, we set L to 14 as well. In addition, the scholars have pointed out that the amount of computation to perform one maximum likelihood is equivalent to testing two test phases in the BPS algorithm, so we set the value of B in the fine phase recovery of the RD-BPS algorithm to 2, so the amount of computation required for the RD-BPS in the fine phase recovery is equivalent to testing 2.5 test phases in the BPS algorithm. For coarse phase recovery with both, we set the number of test phases for BPS/ML to N +1 and the number of test phases for RD-BPS to N. The parameter setting is such that the calculation amount of RD-BPS is less than BPS/ML when the phase numbers N of the two algorithms are the same in the first stage.
As shown in FIG. 3, (a) is 64QAM signal under the condition that the signal-to-noise ratio is 22dB, the variation of the bit error rate with the tested phase number N. (b) For a 256QAM signal, the bit error rate varies with the number of test phases N at a signal-to-noise ratio of 28 dB. As can be seen, under the condition of larger phase noise, BPS/ML needs to test more phases than RD-BPS to obtain more ideal error rate result. In addition, when the computational resources are less, i.e., the number of test phases is less, the error rate performance of RD-BPS can be improved by about 10% compared to BPS/ML.
The above embodiments are merely preferred embodiments for fully illustrating the present invention, and the scope of the present invention is not limited thereto. The equivalent substitution or change made by the technical personnel in the technical field on the basis of the invention is all within the protection scope of the invention. The protection scope of the invention is subject to the claims.
Claims (10)
1. The rotation guide blind phase retrieval algorithm facing the high-order quadrature amplitude modulation signal is characterized by comprising the following steps of:
s1, dividing a plurality of primary test phases based on the high-order quadrature amplitude modulation signal, and taking the primary test phase with the minimum Euclidean distance as a rough phase;
s2, dividing decision phases around the rough phase, and determining the phase rotation direction according to the Euclidean distance between the decision phases and the primary test phase;
and S3, dividing a plurality of secondary test phases based on the rough phase, testing the secondary test phases in the determined phase rotation direction by taking the decision phase as a reference, and taking the secondary test phase or the decision phase with the minimum Euclidean distance as a fine phase.
2. The algorithm for rotary guided blind phase retrieval for higher order qam signals according to claim 1, wherein step S1 comprises:
s11, rotating the high-order quadrature amplitude modulation signal by a plurality of primary test phases distributed at equal intervals
Wherein the content of the first and second substances,
n is the number of one-time testing phases;
s12, using a decision circuit to search the constellation point closest to the rotated signal and calculating the Euclidean distance between the constellation point and the rotated signal;
and S13, taking the primary test phase with the minimum Euclidean distance as a rough phase.
3. The algorithm for rotary guided blind phase retrieval for higher order qam signals according to claim 2, wherein step S12 further comprises: and summing Euclidean distances between a plurality of continuous same test phase signals and the nearest constellation point thereof.
4. The algorithm for rotation-directed blind phase retrieval for higher order quadrature amplitude modulation signals of claim 1, wherein the decision phase is in a clockwise direction or a counter-clockwise direction of the coarse phase.
5. The higher order quadrature amplitude modulation signal oriented rotation-directed blind phase retrieval algorithm of claim 4, wherein when the decision phase is clockwise of the coarse phase; if the Euclidean distance of the judged phase is larger than the Euclidean distance of the rough phase, determining the anticlockwise direction as a phase rotation direction; if the Euclidean distance of the judged phase is smaller than the Euclidean distance of the rough phase, determining the clockwise direction as the phase rotation direction;
when the decision phase is counterclockwise of the coarse phase; if the Euclidean distance of the judged phase is larger than the Euclidean distance of the rough phase, determining that the clockwise direction is the phase rotation direction; and if the Euclidean distance of the judged phase is smaller than the Euclidean distance of the rough phase, determining the anticlockwise direction as the phase rotation direction.
6. The algorithm for rotation-guided blind phase retrieval for higher order quadrature amplitude modulated signals as claimed in claim 1, wherein said decision phase is one of two quadratic test phases adjacent to the coarse phase.
7. The algorithm for rotationally guided blind phase retrieval for higher order qam signals according to claim 6, wherein the decision phase is:
wherein the content of the first and second substances,
and B is the number of secondary test phases divided in the range of positive and negative of the coarse phase, and N is the number of primary test phases.
8. The algorithm for rotary guided blind phase retrieval for higher order qam signals according to claim 1, wherein step S3 comprises:
s31, dividing a plurality of secondary test phases in the positive and negative ranges of the rough phase
Wherein the content of the first and second substances,
b≠0；
b is the number of secondary test phases divided in the range of the positive phase and the negative phase of the rough phase; (ii) a
And S32, testing the secondary test phase in the determined phase rotation direction by taking the decision phase as a reference, and taking the secondary test phase or the decision phase with the minimum Euclidean distance as a fine phase.
9. The higher order quadrature amplitude modulation signal oriented rotation-guided blind phase retrieval algorithm of claim 8, wherein B-2.
10. The algorithm for rotary guided blind phase retrieval for higher order qam signals according to claim 1, wherein step S1 is preceded by: the number of primary test phases and secondary test phases is set.
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