CN109547383B - Method for constructing low autocorrelation 16-QAM sequence - Google Patents
Method for constructing low autocorrelation 16-QAM sequence Download PDFInfo
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- H04—ELECTRIC COMMUNICATION TECHNIQUE
- H04L—TRANSMISSION OF DIGITAL INFORMATION, e.g. TELEGRAPHIC COMMUNICATION
- H04L27/00—Modulated-carrier systems
- H04L27/32—Carrier systems characterised by combinations of two or more of the types covered by groups H04L27/02, H04L27/10, H04L27/18 or H04L27/26
- H04L27/34—Amplitude- and phase-modulated carrier systems, e.g. quadrature-amplitude modulated carrier systems
- H04L27/3405—Modifications of the signal space to increase the efficiency of transmission, e.g. reduction of the bit error rate, bandwidth, or average power
- H04L27/3444—Modifications of the signal space to increase the efficiency of transmission, e.g. reduction of the bit error rate, bandwidth, or average power by applying a certain rotation to regular constellations
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- H—ELECTRICITY
- H04—ELECTRIC COMMUNICATION TECHNIQUE
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- H—ELECTRICITY
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Abstract
The invention discloses a method for constructing a low autocorrelation 16-QAM sequence, wherein the obtained sequence has an even period. The autocorrelation of the 16-QAM sequence generated by the method is ten times of the autocorrelation of the seed four-phase sequence, and the self-correlation has a better ratio of the autocorrelation auxiliary main peak. The invention can provide a synchronization sequence for synchronization of a communication system.
Description
Technical Field
The invention belongs to a communication sequence design and generation technology, and particularly relates to a method for realizing low autocorrelation 16-QAM sequence construction.
Background
One of the advantages of Quadrature Amplitude Modulation (QAM) signals is a high bit transmission rate, and table 1 describes the relationship between the order of QAM signals and the size of data transmission (m.and and p.v. kumar, Low-correlation sequence over the QAM constellation, ieee trans. on inf. theory, vol.54, No.2, pp.791-810, feb.2008).
TABLE 1 QAM constellation and data transmission rate
| Step (A) | QAM constellation | Bit transmission rate |
| 16 | 16-QAM | 4 |
| 64 | 64-QAM | 6 |
| 256 | 256-QAM | 8 |
| 42m | 42m-QAM | 2m |
Therefore, the QAM signal constellation is well suited for high transmission rate communication systems like the fifth generation mobile communication.
The 16-QAM constellation refers to the following symbol set:
Ω16-QAM＝{±1±j，±3±j，±1±3j，±3±3j}
wherein j is2＝-1。
From a signal implementation perspective, 16-QAM is the easiest to implement in all QAM constellations. Therefore, 16-QAM sequences have been intensively studied and developed. The 16-QAM sequences now known are: (1) a 16-QAM complementary sequence (c.v. chong, r.venkataramani, and v.tarokh, "a new constraint of 16-QAM Golay compensation sequences," IEEE trans. inf. theory, vol.49, No.11, pp.2953-2959, nov.2003); (2)16-QAM Low Correlation sequence (M.Anand and P.V.Kumar, "Low Correlation Sequences over The 16-QAM constellation," Proc.of The third National Conf.on Commun., Jan.26-28, 2007); (3) perfect 16-QAM sequences (f.x.zeng, x.p.zeng, z.y.zhang, and g.x.xuan, "Perfect 16-QAM sequences and arrays," ieee trans. fundamentals, vol.e95-a, No.10.oct.2012, pp.1740-1748), and the like.
In the communication system, the normal communication between the transmitter and the receiver is established on the basis of the synchronization between the transmitter and the receiver, and one of the methods for realizing the synchronization adopts a sequence with good autocorrelation characteristic as a synchronization signal to achieve the synchronization through a correlation detection technology. The out-phase autocorrelation value has great influence on the accuracy of correlation detection, the smaller the ratio of the autocorrelation auxiliary main peaks is, the higher the accuracy of synchronization is, and here, a sequenceuThe main autocorrelation peak refers to the periodic autocorrelation function Ru(τ) value R at time shift τ of 0u(0) The secondary peak refers to max { | Ru(τ) | τ ≠ 0 }. Thus, the ratio of its autocorrelation minor major peaks is made as small as possible when designing the synchronization sequence.
The invention provides a construction method of a 16-QAM sequence with small autocorrelation secondary main peak ratio.
Disclosure of Invention
The invention aims to provide a method for constructing a low autocorrelation 16-QAM sequence, which has simple structure, easy realization and small autocorrelation auxiliary main peak ratio.
The invention discloses a method for constructing a low autocorrelation 16-QAM sequence, which comprises the following steps:
A) selecting seed four-phase sequence with even period N from known four-phase sequence library according to index required by userb＝(b0，b1，b2，…，bN-1)；
B) Storing seed four-phase sequences in a shift register of length N (a)0，a1，a2，…，aN-1) Seed four-phase sequence code element bi(i is more than or equal to 0 and less than or equal to N-1) is placed in a shift register ai(i is more than or equal to 0 and less than or equal to N-1);
C) shift register
The content in (1) is sent to a four-phase symbol converter 1 having a function that four-phase symbol 0 becomes 1, four-phase symbol 1 becomes j, four-phase symbol 2 becomes-1, and four-phase symbol 3 becomes-j, the output of the converter is multiplied by 2 with a multiplier, and the result is output;
D) will moveBit register a0The content in (1) is sent to a four-phase symbol converter 2 having a function of changing four-phase symbol 0 to j, changing four-phase symbol 1 to-1, changing four-phase symbol 2 to-j, and changing four-phase symbol 3 to 1, and the result is output;
E) adding the output results of the steps C) and D) by (1+ j) times to obtain the required 16-QAM sequenceA＝(A0，A1，A2，…，AN-1) A in (A)0；
F) Then, the shift register is circularly shifted by 1 bit to the left, and then C), D) and E) are executed to obtain the next code element of the 16-QAM sequence, and the steps are repeated until the shift register is shifted for N-1 times.
Obtained 16-QAM sequenceA＝(A0，A1，A2，…，AN-1) Is autocorrelation of RA(τ)＝10Rb(τ) ratio of minor major peaks
Wherein R isA(τ) is a sequenceAPeriodic autocorrelation function of (2), Rb(τ) is a sequencebIs a time-shift variable.
The present invention will be described in detail with reference to the accompanying drawings.
Drawings
FIG. 1 is a schematic diagram of a method of low autocorrelation 16-QAM sequence construction of the present invention;
FIG. 2 is a functional block diagram of the implementation of the "four-phase symbol converter 1" in FIG. 1 according to the present invention;
FIG. 3 is a functional block diagram of the implementation of the "four-phase symbol converter 2" of FIG. 1 according to the present invention;
Detailed Description
FIG. 1 shows a schematic block diagram of the method for constructing low autocorrelation 16-QAM sequence according to the present invention, which is composed of four-phase sequence database, N-length shift register (a)0，a1，a2，…，aN-1) Four-phase sign converter 1, four- phase sign converter 2, 1 multiplier and 1 adder. Let the 16-QAM sequence to be generated by the present invention beA＝(A0，A1，A2，…，AN-1) The working principle of the present invention is as follows.
First, initialization is performed. Disconnecting the switches in all the figures, then determining the even period N of the 16-QAM sequence required to be generated according to the index required by the user, and selecting a seed four-phase sequence with the even period N from the four-phase sequence databaseb＝(b0，b1，b2，…，bN-1)；
Second, switch 1 is turned on, the remaining switches remain off, and the selected seed is then placed in a four-phase sequence (b)0，b1，b2，…，bN-1) Shift register with serial input length N (a)0，a1，a2，…，aN-1) Middle, seed four-phase sequence code element bi(i is more than or equal to 0 and less than or equal to N-1) is placed in a shift register ai(i is more than or equal to 0 and less than or equal to N-1);
thirdly, setting 1 counter k, and initializing k to be 0;
fourthly, the switch 1 and the switch 2 are switched off, the switch 3 and the switch 4 are switched on, then the shift register works simultaneously in two paths, and one path is used for switching the shift register
The content in the shift register is sent to a four-phase symbol converter 1 for conversion, the four-phase symbol converter 1 (figure 2) realizes the functions that a four-phase code element 0 is changed into 1, a four-phase code element 1 is changed into j, a four-phase code element 2 is changed into-1, and a four-phase code element 3 is changed into-j, the converted result is multiplied by 2 through a multiplier, the result is output, and the other path is used for multiplying the content a in the shift register by the content a0Sending the data to a four-phase symbol converter 2, the four-phase symbol converter 2 (figure 3) realizes the function that the four-phase code element 0 becomes j, the four-phase code element 1 becomes-1, the four-phase code element 2 becomes-j, and the four-phase code element 3 becomes 1, outputting the result, and finally adding the two paths of results, wherein the sum of the two paths of results is (1+ j) times of the k code element A of the required 16-QAM sequencek；
Step five, k ← k +1, if k ═ N, go to step seven; otherwise, turning to the sixth step;
sixthly; disconnect switch 1, switch 3 and switch4, switch 2 is turned on, and then the shift register (a)0，a1，a2，…，aN-1) Shifting right circularly for 1 time, and then returning to execute the fourth step;
seventh step, the circuit stops working, the sequence of code elements output by the circuit (A)0，A1，A2，…，AN-1) Is the 16-QAM sequence to be generated by the present invention.
Modern research shows that there are abundant efforts to construct four-phase sequence databases ([1] y.s.kim, j.w.jang, s.h.kim, and j.s.no, "New constraint of quaternary sequence with ideal autocorrelation from the root sequences," proc.isit2009, Seoul, Korea, jun.29-jul.09, pp.282-285.[2] j.w.jang, y.s.kim, s.h.kim, and j.s.no, "New quaternary sequence with iterative reconstruction of linked family sequences with ideal autocorrelation, with iterative iteration" c.isit2009, koal, jun.29-29, jj.11, j.11, j.11.p.51.11, j.11, j.p.11, j.r.r.p.11, j.11, j.k.7.11, j.11.p.k.11, j.11, j.11.k.k.k.k.7.k.k.11, j.11, j.p.11, j.11, j.u.11, j.11, j.h.11, j.11, j.p.
Examples of the present invention
For ease of understanding, an example is described below.
Example 1 a 4-phase periodic sequence with a period N-30 was selected
(0，1，0，3，0，1，2，3，0，3，0，3，2，3，2，1，0，1，2，1，0，3，2，1，2，1，2，3，2，3)，
Which autocorrelation is
(30，0，-2，0，-2，0，-2，0，-2，0，-2，0，-2，0，-2，0，-2，0，-2，0，-2，0，-2，0，-2，0，-2，0，-2，0)。
According to the method of the invention, a 16-QAM sequence with a period of 30 is generated;
A＝(-3+3j，1+j，-3+3j，-1-j，-3+3j，1+j，3-3j，-1-j，-3+3j，-1-j，-3+3j，-1-j，3-3j，-1-j，3-3j，1+j，-3+3j，1+j，3-3j，1+j，-3+3j，-1-j，3-3j，1+j，3-3j，1+j，3-3j，-1-j，3-3j，-1-j)
the autocorrelation function of the obtained 16-QAM sequence is:
(300，0，-20，0，-20，0，-20，0，-20，0，-20，0，-20，0，-20，0，-20，0，-20，0，-20，0，-20，0，-20，0，-20，0，-20，0)，
obtaining:
although the present invention has been described in detail hereinabove, the present invention is not limited thereto, and various modifications can be made by those skilled in the art in light of the principle of the present invention. Thus, modifications made in accordance with the principles of the present invention should be understood to fall within the scope of the present invention.
Claims (2)
1. A method of low autocorrelation 16-QAM sequence construction, comprising the steps of:
A) selecting seed four-phase sequence with even period N from known four-phase sequence library according to index required by userb＝(b0，b1，b2，…，bN-1)；
B) Storing seed four-phase sequences in a shift register of length N (a)0，a1，a2，…，aN-1) Seed four-phase sequence code element bi(i is more than or equal to 0 and less than or equal to N-1) is placed in a shift register ai(i is more than or equal to 0 and less than or equal to N-1);
C) after the placement, the shift register is put in
The content in (1) is sent to a four-phase symbol converter 1 having a function that four-phase symbol 0 becomes 1, four-phase symbol 1 becomes j, four-phase symbol 2 becomes-1, and four-phase symbol 3 becomes-j, the output of the converter is multiplied by 2 with a multiplier, and the result is output;
D) a shift register0Has four-phase symbol 0 changed to j, four-phase symbol 1 changed to-1, four-phase symbol 2 changed to-j, and four-phase symbol 3 changed toA four-phase symbol converter 2 with 1 function and outputs the result;
E) adding the output results of the steps C) and D) by (1+ j) times to obtain the required 16-QAM sequenceA＝(A0，A1，A2，…，AN-1) A in (A)0；
F) Then, the shift register is circularly shifted by 1 bit to the left, and then C), D) and E) are executed to obtain the next code element of the 16-QAM sequence, and the steps are repeated until the shift register is shifted for N-1 times.
2. The method of claim 1, wherein the autocorrelation of the generated 16-QAM sequence is RA(τ)＝10Rb(τ) ratio of minor major peaks
Wherein R isA(τ) is a sequenceAPeriodic autocorrelation function of (2), Rb(τ) is a sequencebIs a time-shift variable.
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Citations (3)
| Publication number | Priority date | Publication date | Assignee | Title |
|---|---|---|---|---|
| EP0735712A2 (en) * | 1995-03-27 | 1996-10-02 | Matsushita Electric Industrial Co., Ltd. | Multicarrier modulation receiver using remodulation |
| CN102291364A (en) * | 2010-06-17 | 2011-12-21 | 重庆无线绿洲通信技术有限公司 | Generation method and device of quasi perfect period 16 QAM sequence |
| CN102307176A (en) * | 2011-09-14 | 2012-01-04 | 重庆大学 | Method and device for generating perfect 16-QAM (quadrature amplitude modulation) sequence |
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| Publication number | Priority date | Publication date | Assignee | Title |
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| US5612651A (en) * | 1996-01-02 | 1997-03-18 | Loral Aerospace Corp. | Modulating array QAM transmitter |
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Patent Citations (3)
| Publication number | Priority date | Publication date | Assignee | Title |
|---|---|---|---|---|
| EP0735712A2 (en) * | 1995-03-27 | 1996-10-02 | Matsushita Electric Industrial Co., Ltd. | Multicarrier modulation receiver using remodulation |
| CN102291364A (en) * | 2010-06-17 | 2011-12-21 | 重庆无线绿洲通信技术有限公司 | Generation method and device of quasi perfect period 16 QAM sequence |
| CN102307176A (en) * | 2011-09-14 | 2012-01-04 | 重庆大学 | Method and device for generating perfect 16-QAM (quadrature amplitude modulation) sequence |
Non-Patent Citations (1)
| Title |
|---|
| Low Correlation Sequences over the QAM Constellation;M.Anand等;《IEEE》;20170128;全文 * |
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