CN113938227A - Signal-to-noise ratio dynamic judgment method based on iterative decoding - Google Patents
Signal-to-noise ratio dynamic judgment method based on iterative decoding Download PDFInfo
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Abstract
The invention discloses a signal-to-noise ratio strength judging method based on iterative decoding, which utilizes decoded data to estimate the signal-to-noise ratio, firstly sets a fixed iteration number of decoding, carries out similarity calculation on output sequences of two adjacent iterative decoding to obtain a group of similarity sequences, carries out signal-to-noise ratio strength statistics after judging the sequence to be effective, and finally judges the signal-to-noise ratio strength according to the statistical proportion. The invention only relates to binary exclusive-or operation and ratio calculation, and has simple realization and less resource occupation; the decoded data is used for judging the signal to noise ratio, so that the reliability is high; and dynamic updating of the strength of the signal-to-noise ratio is realized by utilizing periodic statistics.
Description
Technical Field
The invention belongs to the technical field of communication, and relates to a signal-to-noise ratio strength dynamic judgment method based on iterative decoding, in particular to a signal-to-noise ratio strength dynamic judgment method under the condition of no check assistance.
Background
In a communication system, the signal-to-noise ratio can reflect the power of a useful signal, and directly determines the quality of communication. The application of the signal-to-noise ratio estimation technology in the receiving equipment can enable a user to grasp the current communication quality condition in real time, avoid communication under the condition of poor communication quality, ensure the success rate of communication, reduce the transmitting power in real time when the signal-to-noise ratio is too strong, and reduce the interference to other communication equipment of adjacent frequency bands. Therefore, the research and the application of the signal-to-noise ratio estimation technology have high practical value.
The currently applied signal-to-noise ratio estimation methods mainly include: the method comprises the steps of maximum likelihood estimation, second-order fourth-order moment estimation, high-order cumulant estimation, minimum mean square error estimation signal-to-noise ratio estimation algorithm and the like, wherein the methods are generally placed before decoding, and operation is performed by using multi-bit quantized soft information, so that on one hand, the operation amount is large, the calculation is complex, on the other hand, the signal-to-noise ratio estimation precision is greatly influenced by a synchronous error, and when the synchronous error is large, the signal-to-noise ratio estimation becomes unreliable.
Disclosure of Invention
Objects of the invention
The purpose of the invention is: the signal-to-noise ratio strength dynamic judgment method based on iterative decoding is provided, the operation amount is reduced, the calculation complexity is simplified, and the high-reliability signal-to-noise ratio is realized.
(II) technical scheme
In order to solve the technical problem, the invention provides a signal-to-noise ratio strength judgment method based on iterative decoding, which carries out signal-to-noise ratio estimation by using decoded data, firstly sets a fixed iteration number of decoding, carries out similarity calculation on output sequences of two adjacent iterative decoding to obtain a group of similarity sequences, carries out signal-to-noise ratio strength statistics after judging the sequence to be effective, and finally judges the signal-to-noise ratio strength according to a statistical proportion.
Defining L as the length of a decoding output sequence, N as iteration fixed termination times (obtained by simulation), and both L and N being positive integers greater than 0.
The signal-to-noise ratio strength judging method based on iterative decoding comprises the following execution steps:
the method comprises the following steps: similarity calculation for adjacent twice iterative decoding output sequence
The similarity calculation method comprises the following steps: and performing binary XOR on the output sequence of the two iterative decoding processes bit by bit and then summing to obtain a result which is the similarity value of the two iterative outputs, wherein the value range is more than or equal to 0 and less than or equal to L, and the smaller the value is, the higher the similarity is.
Step two: constructing a similarity sequence by using the similarity value obtained by calculation, and carrying out validity judgment
When a similarity sequence is constructed, the step one is repeatedly executed until the iteration number reaches N, and N-1 similarity values are obtained and recorded as an S array, wherein S is [ S1, S2...... multidot.SN-1 ].
When the validity of the S array is judged, if any one of the first condition and the second condition is met, adding 1 to the valid times, and recording the value of N-P:
the first condition is as follows: the presence of a positive integer P, 1 < P < N-1, holds true for S1 > S2. > SP-1. > SP + 1. >, SN-1;
and a second condition: a positive integer P, P1, SP +1, SN-1 holds.
Step three: signal-to-noise ratio strength statistics
And obtaining the high signal-to-noise ratio statistical times, the low signal-to-noise ratio statistical times and the medium signal-to-noise ratio statistical times according to the preset signal-to-noise ratio threshold value, and respectively calculating to obtain the high signal-to-noise ratio statistical proportion, the low signal-to-noise ratio statistical proportion and the medium signal-to-noise ratio statistical proportion.
The obtaining process of the high signal-to-noise ratio statistical times, the low signal-to-noise ratio statistical times and the medium signal-to-noise ratio statistical times is as follows:
two thresholds are set: the signal-to-noise ratio is high threshold TH and low threshold TL, both TH and TL are positive integers and satisfy N > TH > TL > 0. Comparing N-P to TH and TL:
if N-P is larger than or equal to TH and represents that the signal-to-noise ratio of the received signal is strong, adding 1 to the number KH of the high signal-to-noise ratio statistics;
if N-P is less than TL, representing that the signal-to-noise ratio of the received signal is weak, adding 1 to the low signal-to-noise ratio statistical frequency KL;
if TL is less than or equal to N-P and less than TH, the signal to noise ratio of the received signal is medium, and the statistical times KM of the medium signal to noise ratio is added by 1.
The process of calculating the high signal-to-noise ratio, the low signal-to-noise ratio and the medium signal-to-noise ratio is as follows: and repeating the first step and the second step until the effective times are accumulated to a preset value and recorded as K, wherein K is KH + KM + KL, and calculating the high signal-to-noise ratio KH/K, the low signal-to-noise ratio KL/K and the medium signal-to-noise ratio KM/K respectively.
Step four: judging the strength of the signal-to-noise ratio according to the statistical proportion
Comparing the sizes of the three values of KH/K, KL/K, KM/K, and if KH/K is the maximum, outputting a high signal-to-noise ratio indication; if the KL/K is maximum, outputting a low signal-to-noise ratio indication; and if the KM/K is maximum, outputting a medium signal-to-noise ratio indication.
Step five: and periodically and repeatedly executing the first step to the fourth step to realize dynamic updating of the signal-to-noise ratio strength indication.
(III) advantageous effects
The signal-to-noise ratio strength dynamic judgment method based on iterative decoding only relates to binary exclusive-or operation and ratio calculation, and is simple to realize and small in resource occupation; the decoded data is used for judging the signal to noise ratio, so that the reliability is high; and dynamic updating of the strength of the signal-to-noise ratio is realized by utilizing periodic statistics.
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Fig. 1 is a schematic diagram of a signal-to-noise ratio strength dynamic determination method based on iterative decoding.
Detailed Description
In order to make the objects, contents and advantages of the present invention clearer, the following detailed description of the embodiments of the present invention will be made in conjunction with the accompanying drawings and examples.
The signal-to-noise ratio strength judging method based on iterative decoding utilizes decoded data to estimate the signal-to-noise ratio, firstly sets a fixed iteration number of decoding, carries out similarity calculation on output sequences of two adjacent iterative decoding to obtain a group of similarity sequences, carries out signal-to-noise ratio strength statistics after judging the sequence to be effective, and finally judges the strength of the signal-to-noise ratio according to a statistical proportion.
Defining L as the length of a decoding output sequence, N as iteration fixed termination times (obtained by simulation), and both L and N being positive integers greater than 0.
Referring to fig. 1, the method for determining the strength of the signal-to-noise ratio based on iterative decoding according to the present invention includes the following steps:
the method comprises the following steps: similarity calculation for adjacent twice iterative decoding output sequence
The similarity calculation method comprises the following steps: and performing binary XOR on the output sequence of the two iterative decoding processes bit by bit and then summing to obtain a result which is the similarity value of the two iterative outputs, wherein the value range is more than or equal to 0 and less than or equal to L, and the smaller the value is, the higher the similarity is.
Step two: constructing a similarity sequence by using the similarity value obtained by calculation, and carrying out validity judgment
When a similarity sequence is constructed, the step one is repeatedly executed until the iteration number reaches N, N-1 similarity values are obtained in total and are recorded as an S array, and S is [ S ]1，S2，......，SN-1]。
When the validity of the S array is judged, if any one of the first condition and the second condition is met, adding 1 to the valid times, and recording the value of N-P:
the first condition is as follows: the positive integer P, 1 < P < N-1, is present such that S1＞S2＞......＞SP-1＞SP＝SP+1＝......＝SN-1If true;
and a second condition: presence of a positive integer P, P being 1, such that SP＝SP+1＝......＝SN-1This is true.
Step three: signal-to-noise ratio strength statistics
And obtaining the high signal-to-noise ratio statistical times, the low signal-to-noise ratio statistical times and the medium signal-to-noise ratio statistical times according to the preset signal-to-noise ratio threshold value, and respectively calculating to obtain the high signal-to-noise ratio statistical proportion, the low signal-to-noise ratio statistical proportion and the medium signal-to-noise ratio statistical proportion.
The obtaining process of the high signal-to-noise ratio statistical times, the low signal-to-noise ratio statistical times and the medium signal-to-noise ratio statistical times is as follows:
two thresholds are set: signal to noise ratio high threshold THSum signal-to-noise ratio low threshold TL，THAnd TLAre all positive integers and satisfy N > TH＞TLIs greater than 0. Mixing N-P with THAnd TLAnd (3) comparison:
if N-P is not less than THIf the received signal has strong signal-to-noise ratio, counting the number of times K of the high signal-to-noise ratioHAdding 1;
if N-P < TLRepresenting the signal-to-noise of the received signalIf the signal is weak, counting the times K of the low signal-to-noise ratioLAdding 1;
if TL≤N-P＜THIf the received signal is of medium signal-to-noise ratio, counting the medium signal-to-noise ratio by a time KMAnd adding 1.
The process of calculating the high signal-to-noise ratio, the low signal-to-noise ratio and the medium signal-to-noise ratio is as follows: repeating the first step and the second step until the effective times are accumulated to a preset value, which is recorded as K, wherein K is equal to KH+KM+KLRespectively calculating the statistical ratio K of high signal-to-noise ratioHK, low signal-to-noise ratio statistical ratio KLK, medium signal-to-noise ratio statistic proportion KM/K。
Step four: judging the strength of the signal-to-noise ratio according to the statistical proportion
Comparison KH/K、KL/K、KMThe size of the three values of/K, if KHIf the/K is maximum, outputting a high signal-to-noise ratio indication; if KLIf the/K is maximum, outputting a low signal-to-noise ratio indication; if KMAnd when the/K is maximum, a medium signal-to-noise ratio indication is output.
Step five: and periodically and repeatedly executing the first step to the fourth step to realize dynamic updating of the signal-to-noise ratio strength indication.
The above description is only a preferred embodiment of the present invention, and it should be noted that, for those skilled in the art, several modifications and variations can be made without departing from the technical principle of the present invention, and these modifications and variations should also be regarded as the protection scope of the present invention.
Claims (10)
1. A signal-to-noise ratio strength judging method based on iterative decoding is characterized in that signal-to-noise ratio estimation is carried out by using decoded data, a decoding fixed iteration number is set at first, similarity calculation is carried out on output sequences of two adjacent iterative decoding to obtain a group of similarity sequences, signal-to-noise ratio strength statistics is carried out after the sequences are judged to be effective, and finally the signal-to-noise ratio strength is judged according to a statistical proportion.
2. The method as claimed in claim 1, wherein L is a length of a decoding output sequence, N is a fixed termination number of iterations, and both L and N are positive integers greater than 0.
3. The signal-to-noise ratio strength decision method based on iterative decoding as claimed in claim 2, wherein the decision method is executed by the steps of:
the method comprises the following steps: performing similarity calculation on the output sequences of the two adjacent iterative decoding;
step two: constructing a similarity sequence by using the similarity value obtained by calculation, and carrying out validity judgment;
step three: carrying out signal-to-noise ratio strength statistics;
step four: judging the strength of the signal-to-noise ratio according to the statistical proportion;
step five: and periodically and repeatedly executing the first step to the fourth step to realize dynamic updating of the signal-to-noise ratio strength indication.
4. The signal-to-noise ratio strength judgment method based on iterative decoding as claimed in claim 3, wherein in the step one, the similarity calculation method is as follows: and performing binary XOR on the output sequence of the two iterative decoding processes bit by bit and then summing to obtain a result which is the similarity value of the two iterative outputs, wherein the value range is more than or equal to 0 and less than or equal to L, and the smaller the value is, the higher the similarity is.
5. The method as claimed in claim 4, wherein in the second step, when the similarity sequence is constructed, the first step is repeated until the number of iterations reaches N, so as to obtain N-1 similarity values, which are denoted as S array, S ═ S1, S2.
6. The method according to claim 5, wherein in the second step, when the validity of the S array is determined, if any one of the first condition and the second condition is satisfied, the number of valid times is increased by 1, and the value of N-P is recorded:
the first condition is as follows: the presence of a positive integer P, 1 < P < N-1, holds true for S1 > S2. > SP-1. > SP + 1. >, SN-1;
and a second condition: a positive integer P, P1, SP +1, SN-1 holds.
7. The method as claimed in claim 6, wherein in the third step, the statistical times of high signal-to-noise ratio, the statistical times of low signal-to-noise ratio and the statistical times of medium signal-to-noise ratio are obtained according to the threshold value of signal-to-noise ratio, and the statistical proportions of high signal-to-noise ratio, low signal-to-noise ratio and medium signal-to-noise ratio are calculated respectively.
8. The method for determining snr strength based on iterative decoding as claimed in claim 7, wherein in step three, the obtaining procedure of the high snr statistical number, the low snr statistical number and the medium snr statistical number is:
two thresholds are set: the signal-to-noise ratio is high threshold TH and low threshold TL, both TH and TL are positive integers and satisfy N > TH > TL > 0. Comparing N-P to TH and TL:
if N-P is larger than or equal to TH and represents that the signal-to-noise ratio of the received signal is strong, adding 1 to the number KH of the high signal-to-noise ratio statistics;
if N-P is less than TL, representing that the signal-to-noise ratio of the received signal is weak, adding 1 to the low signal-to-noise ratio statistical frequency KL;
if TL is less than or equal to N-P and less than TH, the signal to noise ratio of the received signal is medium, and the statistical times KM of the medium signal to noise ratio is added by 1.
9. The method for signal-to-noise ratio strength decision based on iterative decoding as claimed in claim 8, wherein in step three, the process of calculating the high signal-to-noise ratio statistical proportion, the low signal-to-noise ratio statistical proportion and the medium signal-to-noise ratio statistical proportion is: and repeating the first step and the second step until the effective times are accumulated to a preset value and recorded as K, wherein K is KH + KM + KL, and calculating the high signal-to-noise ratio KH/K, the low signal-to-noise ratio KL/K and the medium signal-to-noise ratio KM/K respectively.
10. The iterative decoding-based snr robustness decision method of claim 9, wherein in step four, three values KH/K, KL/K, KM/K are compared, and if KH/K is the maximum, a high snr indication is output; if the KL/K is maximum, outputting a low signal-to-noise ratio indication; and if the KM/K is maximum, outputting a medium signal-to-noise ratio indication.
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| Publication number | Priority date | Publication date | Assignee | Title |
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| CN114884778A (en) * | 2022-05-25 | 2022-08-09 | 中国电子科技集团公司第十研究所 | Multi-carrier combined signal-to-noise ratio estimation method, carrier combination method and communication system |
Citations (6)
| Publication number | Priority date | Publication date | Assignee | Title |
|---|---|---|---|---|
| KR20110004211A (en) * | 2009-07-07 | 2011-01-13 | 한양대학교 산학협력단 | Method for setting number of iterative decoding, apparatus and method for iterative decoding |
| WO2011091845A1 (en) * | 2010-01-27 | 2011-08-04 | Telefonaktiebolaget Lm Ericsson (Publ) | Error floor reduction in iteratively decoded fec codes |
| CN102882652A (en) * | 2012-10-09 | 2013-01-16 | 南京六九零二科技有限公司 | M-APSK (amplitude phase shift keying) signal to noise estimation method based on iterative decoding and decision feedback |
| CN104811991A (en) * | 2015-04-17 | 2015-07-29 | 合肥工业大学 | Wireless link quality predicting method based on dynamic time warping algorithm |
| CN107612560A (en) * | 2017-09-14 | 2018-01-19 | 山东科技大学 | Polarization code earlier iterations method of shutting down based on partial information bit log likelihood ratio |
| CN112217525A (en) * | 2020-10-15 | 2021-01-12 | 天津津航计算技术研究所 | Automatic updating method for iterative times of Turbo decoding |
-
2021
- 2021-10-08 CN CN202111172998.XA patent/CN113938227A/en active Pending
Patent Citations (6)
| Publication number | Priority date | Publication date | Assignee | Title |
|---|---|---|---|---|
| KR20110004211A (en) * | 2009-07-07 | 2011-01-13 | 한양대학교 산학협력단 | Method for setting number of iterative decoding, apparatus and method for iterative decoding |
| WO2011091845A1 (en) * | 2010-01-27 | 2011-08-04 | Telefonaktiebolaget Lm Ericsson (Publ) | Error floor reduction in iteratively decoded fec codes |
| CN102882652A (en) * | 2012-10-09 | 2013-01-16 | 南京六九零二科技有限公司 | M-APSK (amplitude phase shift keying) signal to noise estimation method based on iterative decoding and decision feedback |
| CN104811991A (en) * | 2015-04-17 | 2015-07-29 | 合肥工业大学 | Wireless link quality predicting method based on dynamic time warping algorithm |
| CN107612560A (en) * | 2017-09-14 | 2018-01-19 | 山东科技大学 | Polarization code earlier iterations method of shutting down based on partial information bit log likelihood ratio |
| CN112217525A (en) * | 2020-10-15 | 2021-01-12 | 天津津航计算技术研究所 | Automatic updating method for iterative times of Turbo decoding |
Non-Patent Citations (4)
| Title |
|---|
| C.R.SEETHAL，B YAMUNA: "A low complex turbo decoding algorithm with early iteration termination", 《2017 INTERNATIONAL CONFERENCE ON ADVANCES IN COMPUTING, COMMUNICATIONS AND INFORMATICS(ICACCI）》, 4 December 2017 (2017-12-04) * |
| 刘骏 等: "一种Turbo码随机交织器的迭代估计方法", 《通信学报》, vol. 36, no. 6, 15 June 2015 (2015-06-15) * |
| 台玉朋 等: "水声通信低复杂度最大似然联合均衡译码方法", 《声学学报》, no. 6, 30 November 2018 (2018-11-30) * |
| 杨祯琳: "基于深度学习的低复杂度LDPC译码器", 《电脑与电信》, no. 3, 10 March 2020 (2020-03-10) * |
Cited By (1)
| Publication number | Priority date | Publication date | Assignee | Title |
|---|---|---|---|---|
| CN114884778A (en) * | 2022-05-25 | 2022-08-09 | 中国电子科技集团公司第十研究所 | Multi-carrier combined signal-to-noise ratio estimation method, carrier combination method and communication system |
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