Novel Blind Recognition Algorithm of Frame Synchronization Words Based on Soft- Decision in Digital Communication Systems

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1 RESEARCH ARTICLE Novel Blind Recognition Algorithm of Frame Synchronization Words Based on Soft- Decision in Digital Commnication Systems Jiangyi Qin*, Zhiping Hang, Chnw Li, Shaojing S, Jing Zho College of Mechatronic Engineering and Atomation, National University of Defense Technology, Changsha , Hnan Province, P.R. China * qjyacmilan@163.com Abstract OPEN ACCESS Citation: Qin J, Hang Z, Li C, S S, Zho J (2015) Novel Blind Recognition Algorithm of Frame Synchronization Words Based on Soft-Decision in Digital Commnication Systems. PLoS ONE 10(7): e doi: /jornal.pone A novel blind recognition algorithm of frame synchronization words is proposed to recognize the frame synchronization words parameters in digital commnication systems. In this paper, a blind recognition method of frame synchronization words based on the hard-decision is dedced in detail. And the standards of parameter recognition are given. Comparing with the blind recognition based on the hard-decision, tilizing the soft-decision can improve the accracy of blind recognition. Therefore, combining with the characteristics of Qadratre Phase Shift Keying (QPSK) signal, an improved blind recognition algorithm based on the soft-decision is proposed. Meanwhile, the improved algorithm can be extended to other signal modlation forms. Then, the complete blind recognition steps of the hard-decision algorithm and the soft-decision algorithm are given in detail. Finally, the simlation reslts show that both the hard-decision algorithm and the soft-decision algorithm can recognize the parameters of frame synchronization words blindly. What s more, the improved algorithm can enhance the accracy of blind recognition obviosly. Editor: Zhaohong Deng, Jiangnan University, CHINA Received: March 6, 2015 Accepted: Jne 10, 2015 Pblished: Jly 8, 2015 Copyright: 2015 Qin et al. This is an open access article distribted nder the terms of the Creative Commons Attribtion License, which permits nrestricted se, distribtion, and reprodction in any medim, provided the original athor and sorce are credited. Data Availability Statement: All relevant data are within the paper. Fnding: The athors received no specific fnding for this work. Competing Interests: The athors have declared that no competing interests exist. Introdction In the digital commnication system, frame synchronization is the fondation for the followp signal processing, sch as forward error correction (FEC) and information access. Frame synchronization words can mark the place for mapping receiving binary stream and eliminating redndant information. However, the frame synchronization words parameters are different across the varios commnication systems. In backgrond of the non-cooperation commnication system, the blind recognition of frame synchronization words is necessary for obtaining the information contained in the nknown binary signal [1 4]. In this paper, a novel blind recognition algorithm of frame synchronization words is proposed. The algorithm exploits the soft-decision to enhance the accracy of blind recognition. Comparing with conventional hard-decision, soft-decision tilizes the confidence level of each receiving data to recognize parameters [5 9]. The QPSK signal is sed to verify the blind recognition algorithm and the simlations reslts show that soft-decision is better than the hard-decision. PLOS ONE DOI: /jornal.pone Jly 8, /8

2 Fig 1. Conventional frame form. doi: /jornal.pone g001 The rest of paper is organized as follow. In section 2, the basic frame synchronization words blind recognition method is described in detail. In section 3, the improved blind recognition algorithm of frame synchronization words is shown. In section 4, simlations reslt is shown to verify the algorithms performance. Finally, section 5 concldes this paper. Materials and Methods Signal is transmitted in the form of frames. The frame alignment is sed to realize the synchronization on the receiver and transmitter. The conventional frame form is shown in Fig 1. Each frame has two parts, one is synchronization words (SW), and the other is payload (P). On the transmitter, the payload is divided into grops. The length of each grop is L and the length of synchronization words is M. A payload grop and a synchronization words constitte a frame. On the receiver, the synchronization words are periodic emergence. However, the payload data is different between each frame. Therefore, the receiver can detect the place of synchronization words in the data stream to find the start point of each frame. Then, the receiver can obtain payload data from the data stream for other signal processing. Frame synchronization words blind recognition In backgrond of the non-cooperation commnication, the frame length (L), synchronization words form and synchronization words length (M) are nknown. In order to obtain the payload data for other signal processing, these parameters shold be recognized firstly [10]. According to frame synchronization words characteristic, the frame length can be recognized by detecting the periodic fragment in the data stream and confirming the period. Then, the frame synchronization words form and its length can be recognized by analyzing the periodic fragment. A l matrix X and a data stream vector Y are shown in Fig 2. Y means the receiving binary stream. Pt the data of Y into X sccessively. When the colmn nmber of X is eqal to the frame length, some colmns data are eqal and the other colmns data are random. The former are synchronization colmns and the latter are non-synchronization colmns. When the colmn Fig 2. The mapping relation between matrix X and vector Y. doi: /jornal.pone g002 PLOS ONE DOI: /jornal.pone Jly 8, /8

3 nmber of X is not eqal to the frame length, each colmns data are random. The synchronization colmns will not appear. Therefore, calclate the sm of each colmn and se the sm to represent the nmber of 1. If the nmber of 1 in a colmn is closed to 0 or, this colmn can be recognized as the frame synchronization words colmn. Based on above methods, traverse the L vale. Then, the frame length and frame synchronization words can be recognized. In order to distingish the non-synchronization colmns and synchronization colmns, reasonable thresholds shold be designed [11 12]. And the colmn nmber of X is important to improve falt-tolerant ability and redce calclation. The colmns can be expressed as follow. X j ¼ðx 1;j ; x 2;j ;...; x ;j ; Þ T ð1 j lþ ð1þ When the colmn is non-synchronization colmn, each data in it is random. Therefore, the probability of 0 and the probability of 1 are eqal to 0.5 approximately. Z j is the sm of the j colmn. Therefore, Z j obeys the binomial distribtion and its mathematical expectation and variance can be expressed as follow. ( EðZ j Þ¼P r ¼ 1Þ ¼=2 ð2þ DðZ j Þ¼P r ¼ 1ÞP r ¼ 0Þ ¼=4 When it is synchronization colmn and there is no bit error in the colmn, every data in the colmn is 0, or everyone is 1. Sppose the channel conversion probability is τ and channel noise is existed. The bit flipping probability can be expressed as follow. ( P r ¼ sþ ¼1 t ; ð1 i ; 1 j lþ P r ¼ 1 sþ ¼t ð3þ Where s (s = 1 or 0) is transmission bit. In this case, Z j means the sm of j colmn. Z j obeys the binomial distribtion and its mathematical expectation and variance can be expressed as follow. ( EðZ Þ¼P ðx j r i;j ¼ 1Þ ¼ðt 2st þ sþ DðZ jþ¼p r ¼ 1ÞP r ¼ 0Þ ¼tð1 tþ ð4þ In order to balance the false alarm probability and false dismissal probability, according to the six times standard deviation principle, the average of non-synchronization and synchronization colmns six times standard deviation bondary vale is sed as the decision threshold. The decision threshold decides which colmn is synchronization colmn and which is not. And, there are two kinds of synchronization colmn. One is made p of 0 and the other is made p of 1. Therefore, there shold be two kinds of threshold, and they can be expressed as follow. 8 >< d p ¼ >: d down ¼ 2 þ rffiffiffi h p þ ð1 tþ 6 ffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi i tð1 tþ 4 2 rffiffiffi h p þ t 6 ffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi i tð1 tþ 4 When the vale of Z j is between the δ p and δ down, the j colmn is decided to be non-synchronization colmn. Otherwise, it wold be decided to be synchronization colmn. According 2 ð5þ PLOS ONE DOI: /jornal.pone Jly 8, /8

4 to (5), another relation can be dedced as follow. 8 rffiffiffi 2 þ 6 h p < ð1 tþ 6 ffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi i >< tð1 tþ 4 rffiffiffi 2 6 h p < t 6 ffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi i >: tð1 tþ 4 Therefore, the shold be confirmed with the relation as follow. h > 36 1 þ 2 pffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffii tð1 tþ ð1 2tÞ 2 ð6þ ð7þ However, the τ is nknown in the blind recognition and the Z j probability distribtion is not dependent on τ. Therefore, δ p and δ down can be expressed as follow. 8 d p ¼ rffiffiffi 2 þ 6 ¼ ð þ 6 p >< ffiffiffi Þ d down ¼ rffiffiffi 2 6 ¼ 1 ð 6 ffiffiffi ð8þ p >: Þ 4 2 In order to ensre the validity of decision, the difference of δ p and δ down shold be small. d p d down < yð0 < y < 1Þ ð9þ Then, according to (8), can be expressed as follow. > 36 = y 2 ð10þ When θ is eqal to 0.5, the shold be larger than 144. The improve blind recognition algorithm In section 2, a basic frame synchronization words blind recognition method is proposed. The method is based on the hard-decision. In this section, an improved blind recognition algorithm based on the soft-decision will be proposed. QPSK signal will be sed to describe the improved algorithm. Sppose the QPSK signal transmitted throgh the Additive White Gassian Noise (AWGN) channel and the transmitted signal is random. The QPSK signal constellation diagrams on the transmitter and the receiver are shown in Fig 3. There are for types of transmission signals on the transmitter. They are s 1 =1+i, s 2 = 1+i, s 3 = 1 i and s 4 =1 i. The transmission signals in AWGN channel have been distorted. Therefore, these signals cannot be sed directly on the receiver. The constellation diagrams on the transmitter and receiver are shown in Fig 3. The data near the real axis and the imaginary axis will lead to misjdgment. Therefore, in each colmn of X, a certain nmber of nreliable receiving data shold be deleted. The confidence level of each receiving data can be expressed as follow. g j ¼ max fjr j s i jg i¼1;2;3;4 The data with a greater degree of confidence level will be reserved and the data with a lower degree of confidence level may be deleted. The complete steps of the improved blind recognition algorithm are shown as follow. ð11þ PLOS ONE DOI: /jornal.pone Jly 8, /8

5 Fig 3. (A) The constellation diagrams at the transmitter (B) The constellation diagrams at the receiver. doi: /jornal.pone g Set the frame length searching scope (l min and l max ), initialize l as l min. Calclate, δ p and δ down. 2. Pt the receiving data into the l matrix X. 3. Calclate the confidence level of each receiving data. The receiving data in the bottom fifth of confidence level will be deleted. The reserved data constitte the ' l matrix X'. The 'is eqal to b0.8 c. 4. Calclate the sm of each colmn in the, pt the reslt into the row vector U l and the vector length is l. 5. Search elements which are greater than δ p or less than δ down in U l. Record the sm of these elements as Q l, calclate the V l = Q l / l. 6. If l < l max, l = l + 1 and go to (2), otherwise, go to (7). 7. The vector V can be expressed as ½V l min ; V l min þ1;...; V l Š, record the maximm vale of V max as V max. 8. Search the elements which are larger than (2 / 3) V max, and the minimm sbscript of these elements will be the estimation of frame length, record as L^. 9. Make l eqal to L^, pt the reserved data into X' again and calclate the sm of each colmn in the matrix, pt the reslt into U^L. 10. Select the data which are greater than δ p or less than δ down from U^L. The data with consective sbscript will be the recognition of frame synchronization words. If the data is greater than δ p, the corresponding position bit of frame synchronization words is "1". Otherwise, it is "0". And the nmber of consective sbscript is the length of frame synchronization words. PLOS ONE DOI: /jornal.pone Jly 8, /8

6 Fig 4. The vale of Z ' when l 6¼ L. doi: /jornal.pone g004 Reslts and Discssion In this section, simlations are sed to verify the validity of the frame synchronization words blind recognition algorithms proposed in section 2 and section 3. Then a comparison will be made to test the performance between the algorithm based on hard-decision and the one based on soft-decision. The simlations se the QPSK signal commnication system and transmission channel is AWGN channel. Meanwhile, the assmptions proposed in section 2 and section 3 are tre. In Fig 5. (A) The vale of Z ' (B) The partial zoom of Z '. doi: /jornal.pone g005 PLOS ONE DOI: /jornal.pone Jly 8, /8

7 Fig 6. The reslt of frame length recognition. doi: /jornal.pone g006 the simlations, the length of frame is 1024 signs, the frame synchronization words is 0xF628 and the is 150. The vale of l min is 970 signs and the vale of l max is 1070 signs. The Signal Noise Ratio (SNR) is 3dB, and the constellation diagrams on the transmitter and on the receiver are shown in Fig 3. To simplify calclation, the normalizing parameter Z ' j, δ ' p and δ ' dowm are sed to replace the Z j, δ p and δ down. According to the steps proposed in section 3, the simlation reslts of blind recognition algorithms based on soft-decision are shown in Fig 4 and Fig 5. The red lines in Fig 4 and Fig 5 mean the δ ' p and the δ ' dowm. The vale of δ ' p and the δ ' dowm can be calclated according to (8). When the l = 1023, there isn't any Z ' j greater than δ ' p or smaller than δ ' down in Fig 4. Therefore, the frame synchronization words cannot be recognized. When the l = 1024, there are several Z ' j greater than δ ' p or smaller than δ ' down in Fig 5. These colmns can be sed to recognize the frame synchronization words. The partial zoom Fig 7. (A) Hard-decision reslt of 32 bits frame synchronization words (B) Soft-decision reslt of 32 bits frame synchronization words (C) Harddecision reslt of 16 bits frame synchronization words (D) Soft-decision reslt of 16 bits frame synchronization words. doi: /jornal.pone g007 PLOS ONE DOI: /jornal.pone Jly 8, /8

8 figre is shown in Fig 5. From the partial zoom figre, the frame synchronization words can be recognized easily. To recognize the frame length, l shold be traversed from the l min to l max, the search reslts are shown in Fig 6. In Fig 6, only when l is eqal to 1024, there are several the Z ' j meet the reqirement. Therefore, according to the simlation reslts, the frame synchronization words are recognized as 0xF628 and the recognition reslt is correct. To compare the performance between the hard-decision and the soft-decision, the compare simlation reslts are shown in Fig 7. In the simlations, different AWGN is adding to the channel and recognize the frame synchronization words with different lengths. The 0xF628 and 0xF628F628 are sed respectively as the frame synchronization words in these simlations. Throgh 1000 simlations, the misjdgment rates of blind recognition are shown in Fig 7. The simlations crves mean that the soft-decision reslts are better than the hard-decision reslts. And the length of frame synchronization words will impact the misjdgment rate. Conclsions In this paper, a novel blind recognition algorithm of frame synchronization words is proposed. Comparing with the algorithm based on hard-decision, the one based on soft-decision is developed to improve the recognition performance. QPSK signal is sed to test the performance of these algorithms. The simlation reslts mean that these algorithms can recognize frame synchronization words and soft-decision is better than hard-decision. What is more, these algorithms can be sed in other signal modlation forms. Athor Contribtions Conceived and designed the experiments: JQ. Performed the experiments: CL. Analyzed the data: ZH. Contribted reagents/materials/analysis tools: JZ. Wrote the paper: SS. References 1. Cassaro T.M., Georghiades C.N., Frame synchronization for systems over AWGN channels, IEEE Trans. Commn. 52 (3) (2004) Massey J.L., Optimm frame synchronization, IEEE Trans. Commn. 20 (2) (1972) Li G.L., Tan H.H., Frame synchronization for Gassian channels, IEEE Trans. Commn. 35 (8) (1987) Mostofa M., Howlader K., Frame synchronization of convoltionally coded systems for packet transmission, IEEE Commn. Lett. 5 (7) (2001) S. Hocke, G. Sicot, Blind frame synchronization for block code, in: Porc. EUSIPCO2006, Florence, Italy, Imad R., Hocke S., Jego C., Blind frame synchronization for error correcting codes having a sparse parity check matrix, IEEE Trans. Commn. 57 (6) (2009) R. Imad, S. Hocke, C. Jego, Blind frame synchronization of prodct codes based on the adaptation of the parity check matrix, in: Proc. ICC2009, Dresden, Germany, R. Imad, C. Polliat, S. Hocke, Blind frame synchronization of Reed-Solomon codes: non-binary vs. binary approach, in: Proc. SPAWC2010, Marrakech, USA, Jing Zho, Zhiping Hang, Shaojing S, Blind frame synchronization of Reed-Solomon coded optical transmission systems, Optik 124 (2013) Clzea M., Finiasz M., Recognition of a Code s Length and Synchronization from a Noisy Intercepted Bitstream, Proc. ISIT2009, Seol, Korea, Imad R., Hocke S. Theoretical Analysis of a MAP Based Blind Frame Synchronizer, IEEE Trans. Wireless Commn., (11): Qi Y., Wang B., Rong M., Li T, Comments on Theoretical Analysis of a MAP Based Blind Frame Synchronizer. IEEE Trans. Wireless Commn., (10): PLOS ONE DOI: /jornal.pone Jly 8, /8