Communications and Network, 2013, 5, 280285 http://dx.doi.org/10.4236/cn.2013.53B2052 Published Online September 2013 (http://www.scirp.org/journal/cn) Study of LDPC Coded SFH System with PartialBand Interference Chao Gong2, Manxi Wang1, Daoxing Guo2, Xiaofei Pan2 1TheState Key Laboratory of Complex Electromagnetic Environmental Effects on Electronics&Information System, China 2College of communications engineering PLA University of Science &Technology, China Email: jllshh@163.com Received July, 2013 ABSTRACT The application of Low Density Parity Check (LDPC) code in the antiinterference systems has drawn an increasing attention, due to its admiring performance which is very close to the theory limit. This paper focuses on a LDPC en coded slow frequency hopping (SFH) communication system with partialband interference. Firstly, a modified soft decision algorithm based on the utilization of interference information is proposed, and its performance is compared with some other softdecision methods. Secondly, with numerical simulation, the influence of code rate, code length and the number of symbols per h ops on the p erformance of th e system with partial band noise interference is illu strated and examined in detail. Considering the great influence of hops per symbol on the performance, interleaver should be used and its influence on the performance is further examined by simulation. Finally, some constructive advises for the design of LDPC coded SFH system are given. Simulation results show that, with a reasonable design, the SFH system with LDPC code could achieve a desirable performance. Keywords: LDPC; SFH; Softdecision; Partialband Interference 1. Introduction Frequency hopping (FH) transmissions, whose carrier frequency hops under control of a pseudorandom pattern, is an attractive access method in wireless communication, due to its special ability to anti interference and provides continuous communication under a severe interference situation [1]. In the civil communication, FH is often used in the wireless communication system working in unlicensed industrial, scientific and medical (ISM) band, such as Bluetooth and ZigBee, to overcome the interfer ence coming from other electronic equipment working in the same frequency band. While in the military commu nication, FH, which is almost to be a characteristic of military communication system, is widely used in the shortwave, microwave and satellite communication to overcome intentional interference. For example, both of America’s domain tactical wireless networks (JTIDS) and the Milstar satellite communication system base on frequency hopping tr ansmission [3]. Apar t from that, FH is also used in the cognitive radios due to the available frequency changes from time to time [4]. So far, researchers all along pay attention to the en hancement of FH systems’ antiinterference perfo rmance, some useful methods, such as channel coded diversity, interleave, are widely used. As a excellent channel code method, LDPC, which is close to the theory limit, has drawn an increasingly attention of researchers from worldwide, especially its application in the FH commu nication. In [5], some diversity methods based on LDPCFH system were examined. And the paper [6] focused on the technology of interference erasure in the LDPCFH communication. The performance of LDPC encoded fast frequency hopping (FFH) system under partialband noise interferen ce was analyzed in paper [7], and the performance of LDPC encoded FFH system with partial band multitone interference was given by [8].In this paper, we are focused on the performance of LDPCSFH system under partialband noise interference. There are some theory methods for the analysis of the performance of LDPC, some of which is illustrated in [9], such as density evolution, Gaussian approximate, extrin sic information transfer (EXIT) charts. All of those methods pay attention to the performance of certain kind of LDPC, rather than that of certain type of LDPC. However, in practice, the choice of LDPC is limited to the feasibility of hardware, code length, code rate and code’s structure and so on, which causes the real per formance of LDPC has a large difference with the theory bound. In the interference environment, the channel is no longer to be an additive white Gaussian noise (AWGN) channel, which makes it even more difficult for the analysis of performance of LDPC. As the approximation C opyright © 2013 SciRes. CN
C. GONG ET AL. 281 and simplification have to be used for theory analysis, the result will be imprecise. In the practical system de sign, numerical simulation with certain type available code is a feasible and effective way for analysis. Based on above considerations, numerical simulation is ex ploited in this paper for analysis of application of LDPC on the SFH system, and some key points of designing antiinterference communication are analyzed further. 2. System Model The system model in this paper is shown as Figure 1. The transmitter consists of encoder, interleaver, and modulator and up frequency converter. By the number of ‘1’ in every row and column of check matrix, LDPC can be divided into kinds: regular LDPC and irregular LDPC. Generally, performance of irregular LDPC is better than regular LDPC, which is at the cost of more complex re alization of hardware. With a tradeoff between perform ance and complexity degree of hardware realization, this paper chooses quasicyclic regular binary LDPC [10] as channel code. In the SFH system, number of symbols per hop (SPH) is more than one, when the signal is jammed, it will bring about burst symbol errors. If number of burst symbol errors in a coded packet is larger than threshold number of decoding, decoding error will occur. In order to alleviate the burst errors influence and reduce frame error rate In practice, the coded bit stream is interleaved in the transmitter, making burst errors decentralize into every packet equally. The following simulation will show that interleaving do improved the performance of system with short code length dramatically when the code length is short. While it comes to long code length, impact of interlacing is not obvious, so it can conclude that interleaver is unnecessary for the system, and it can be chosen depending on the length of code. In the SFH system, FSK, DPSK, PSK is widely used, PSK has a higher bandwidth efficiency, so BPSK is used in this paper. Under the control of FH pattern, the modulated signal is transmitted through the up frequency converter, as Figure 1 shows. As the control methods of FH pattern isn’t the content of this paper, we don’t introduce it here. The transmitting signal is given by (2 ),1,2, ii jfnT ij ij cei N (1) where 1 ij c is information sequence, i is carrier frequency, T is symbol interval, i is initial phase per hop, N is num ber of sy mbols per hop. The channel model that we employ is an example of a blockinterference channel, including additive white Gaussian noise (AWGN) and partialband interference, which has been used in several previous investigations of FH communication [11]. Model of partialband interfer ence is given by bandwidthlimited white Gaussian noise with a band rate, here is the partialband inter ference factor, and it is a constant but unknown number for both transmitter and receiver. We assume all the symbols in a FH time slot are jammed when the signal in certain moment of the slot is hit by the interference sig nal, and vice versa. The probability of FH signal jammed is , power spectral density (PSD) of interference sig nal in the current time slot is 1 N , and in other slot without interference, the PSD is 0. Power of the interfer ence signal is in direct proportion to N and irrelevant with . AWGN diffuse during the transmitting, and PSD is , rate of bit power to PSD of AWGN is given by 0b 0 N ENR10log10(/ N) , rate of bit power to PSD of interference signal is given by EIR 10log10(/) bI N . The receive signal is given by (2 ),1,2, ii jfnT ij ijijij cenw iN (2) where ij is wideband white Gaussian noise, and is partialband interference. nij w Figure 1. Model of LDPCSFH system. Copyright © 2013 SciRes. CN
C. GONG ET AL. 282 As Figure 1 shows, receiver consists of decoder, dein terleaver, demodulator and down frequency converter. With the same FH pattern, the receiver change the FH signal to lowpass or fixed band pass signal, and the de modulater estimate the carrier phase and symbol timing in order to realize carrier and symbol synchronization, and then the information sequence will be obtained by softdecision method. Signal after carrier and symbol synchronization is given by (3), ,1,2, ijij ijij ycnwi N (3) where ij , ij is wideband white Gaussian noise and partialband interference after carrier and symbol syn chronization respectively. In this paper, we don’t focus on carrier and symbol synchronization, so we assume carrier phase and symbol timing are estimated correctly in the following. Softdecision methods will be discussed in the following section detailedly. Deinterleaver reorder the receive sequence to make it same as the original se quence, and finally channel decoder decodes the se quence after softdecision. Decoding methods of LDPC is sorted into two kinds: harddecision and softdecision. Generally speaking, performance of softdecision meth ods is better than those of harddecision. Considering the complexity of hardware realization, modifyingmini mumsum softdecision method [12], which has low complexity for hardware realization and good perform ance close to the optimum method, is used in this paper. n w 3. Modifying Softdecision The probability of transmitting signal should be propor tional to the value of softdecision for modifyingmini mumsum softdecision method (MMSSD). Without in terference, ij maintain its probability statistic charac teristic, which could give probability of transmitting sig nal directly, so the sequence can be decoded with di rectdecision (DD). While there is interference with the received signal, the probability statistic characteristic of ij with and without interference will be different, so it will represent different probability of transmitting signal in the two conditions. In this case, probability of signal can’t archive from ij directly, which lead to drastic deterioration of performance is DD method is used. As Figure 2 shows, when y y y 1 , performance based on direct softdecision is very close to that the method with perfect channel side information (PCSI). However, with the decreasing of , the performance will deteriorate drastically. To solve above problem, we can estimate ENR of signal in every hop, and then modify the soft decision value accordingly. In [12], a simple square sig nal to noise ratio estimator is introduced, where the esti mator is given by (4) 2 1 0 2 11 2 00 1 11 1(1) N ij i iNN ij ij ii y N yy NNN (4) With the estimated value of ENR in ith FH time slot, we can modify value of softdecision with (5) ijij i zy (5) When the EIR is low, it is imprecise to estimate the EIR by above method, however, simulation suggests that the precision of the estimation can meet the need of LDPCSFH system, and comparing with DD, we have got admirable performance improvement. Figure 2 shows three softdecision methods’ performance, where the vertical axis is the required value of EIR to archiv e a packet error probability of 102. We found that the EIR increases no more than 0.2dB to reduce the packet error probability from 102 to 103. In general, most wireless networks, such as Ad hoc network, could work normally with a frame error rate of 102. The AWGN is consid ered in the following simulation, though PSD of partial band interf erence signal is fa r higher th an that of AWGN. In the simulation of this paper, we assume . is a exact known number and the methods of modifying the soft decision value are the same , when the interference signal is known. From the Figure 2 we can see that the per formance of modifying the value of softdecision based on estimating ENR with squareENR estimator is close to that of PCSI. 4. Performance of Antiinterference The following numerical simulation bases on the system model and MMSSD introduced in above sections, which 00.1 0.20.3 0.40.5 0.6 0.7 0.8 0.9 1 0.5 1 1.5 2 2.5 3 3.5 P art i al B and Int erference F actor, Signal to Interference Ratio ， E b /N I PCSI MD DD Figure 2. Performances of different softdecision methods. Copyright © 2013 SciRes. CN
C. GONG ET AL. 283 will give performance of LDPCSFH system with dif ferent code rate, code length, SPH and way of interleav ing. In the simulation, two cases are considered: the first is that, code length is fixed8064, value of code rate get ting from 1/2, 5/8 and 7/8; the second is code rate fixed3/4, and code rate varying with 8064, 4032, 2016 and 1008. Performance of above cases with AWGN channel is shown in Figure 3. In order to make a clear analysis, here, we introduce two basic conceptions: first is that the ˆ corresponding to the highest value of EIR is represented as worst partialband interference (WPBJ) factor, second is throughput, which is a key standard of a system, is given by ratio of number of available source sequences to that of encoded transmitting packet se quences. Besides, we also assume that it is a available packet only when the receiving sequences are all right, otherwise, the packet is un available. 4.1. Influences of Code Rate Code rate is a vital factor of the performance, when code length is fixed, with decreasing of code rate , perform ance is improving, which don’t result in decreasing of system’s throughput, as Figure 4 shown, performance of system with 1/2, 5/8, 3/4 and 7/8 code rate and a fixed code length 8064 are given. When 1 , difference of InterferencetoSignal (JNS) threshold of four code rate is about 2dB, which will enlarge with decreasing of . When 0.5 , JNS threshold of LDPC with a 1/2 code rate is lower than 0dB; when 0.2 , JNS threshold of LDPC with a 7/8 code rate is larger than 7dB. Different code rate have different performance with the worst par tialband interference, and with increasing of code rate, ˆ is decreasing, and so is the threshold of . 00.5 11.5 22.5 33.5 4 10 4 10 3 10 2 10 1 10 0 S i gnal to Interference Rat i o ， Eb/N F rame Erro r Rat e Code Rate ： 1/2 ； Code Lengt h ： 8064 Code Rate ： 5/8 ； Code Lengt h ： 8064 Code Rate ： 3/4 ； Code Lengt h ： 8064 Code Rate ： 3/4 ； Code Lengt h ： 4032 Code Rate ： 3/4 ； Code Lengt h ： 2016 Code Rate ： 3/4 ； Code Lengt h ： 1008 Code Rate ： 7/8 ； Code Lengt h ： 8064 Figure 3. Performances of different code. In Figure 5, throughput of differ ent co de rate is sh own. We can see, low code rate has a stronger adaptability to drastic change of , and there is an inconspicuous change of throughput, with changing from 0 to 0.7, when LDPC code rate is 1/2. However, when is very small, the throughput of code with low rate is lower comparatively, which leads to low transmission effi ciency. Therefore, in practice, throughput could improve with a proper LDPC designed depending on , and code length of a system could be designed depending on throughput an d cost of hardware. 4.2. Influences of Code Length In Figure 6, performance of LDPC with a 3/4 code rate under 8064,4032,2016,1008 code length are shown, while number of symbols is 336(). When 336N1 , per formance of the four codes are very close, difference between maximum code length and minimum code length 00.1 0.20.3 0.40.5 0.6 0.7 0.8 0.91 0 1 2 3 4 5 6 7 P art i al B and Int erferenc e F ac tor, S i gnal to Interference Rat i o ， E b /N I Code Rate ： 1/ 2 Code Rate ： 5/ 8 Code Rate ： 3/ 4 Code Rate ： 7/ 8 Figure 4. Performances of different code rate with partial band interference. 00.1 0.20.3 0.40.5 0.6 0.70.8 0.91 0 1000 2000 3000 4000 5000 6000 7000 8000 Part i al B and Interference F ac tor, Throughput Code Rate：1/ 2 Code Rate：5/ 8 Code Rate：3/ 4 Code Rate：7/ 8 Figure 5. Throughput of different code r ate. Copyright © 2013 SciRes. CN
C. GONG ET AL. 284 is only 0.5 dB, however, which will enlarge with de creasing of . After JNS of code 8064 and 4032 reach to the highest, it will decreasing along with the decreas ing of , and then JNS of 2018 and 1008 is in direct proportion to . The main reason of that is , short code has a weak ability of antioutburstwrong, moreover, its performance also depend o n the value of . N 4.3. Influences of Symbols per Hop Influence of symbols per hop on the performance is shown from two aspects: on one hand, a increasing N will exaggerate the outburst wrong, and performance of system will also decrease, especially when is very small; on the other hand, amount of data processed by ENR estimator will also increase for N’s increasing, which lead to a more precise estimation and higher per formance. As Figure 7 shows, when code length is 1008, code rate is 3/4, and , performance keeps good with most value of 12N , and when 0.1 , EIR reaches to the highest. From Figure 7, we can conclude that number symbols is another factor which should be in a proper range during practical system design, and it is better design when value of is chosen depending on the change of N N . In practice, there is a simpler and available method of choosing , basing on interleaving, which makes outburst wrong sequence dispersing into all the transmitting packets, therefore, even with a large , performance still keeps a good leve l. N N 4.4. Influence of Interleaving The key parameter of interleaver is the deep degree of interleaving (), in the simulation, different values of , which is 4, 8, and 16, are considered, while code length is 1008 and code rate is 3/4. As Figure 8 shows, with increasing of , performance is also increasing. In D D D 00.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1 1 2 3 4 5 6 7 8 Part i al B and Interference Fact or, Signal to Interference Ratio，Eb/NI Code Length：8064 Code Length：4032 Code Length：2016 Code Length：1008 Figure 6. Performances of different code length with par tialband interference. 00.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.91 0 1 2 3 4 5 6 7 8 P artial Ba nd Interference Factor, Signal to Interference Ratio ， E b /N I N=12 N=64 N=16 8 N=33 6 Figure 7. Performances of different symbols per hop with partialband interference and code rate 3/4. 00.1 0.20.3 0.40.5 0.6 0.70.8 0.91 0 1 2 3 4 5 6 P artial Band Int erference F a ctor, S i gnal to I nterference Rat i o ， E b /N I D=4 D=8 D=16 Figure 8. Performances of different deep degree of inter leaving with partialband interference. general, a bigger makes random wrong sequences discrete further, which could improve the performance, however, a bigger will also means increasing of transmitting delay of the system. Therefore, both and transmitting delay should be taken into consideration. Meanwhile, a proper also depend on exact value of code length and methods of interleaving. D DD D 5. Advises for System Design When it comes to design a higher performance LDPC SFH communication system, code rate, code length, symbols per hop and deep degree of interleaving are key parameters. Different code rate will result in different performance, it is better for a low code rate when throughput of system is not considered in the design. But a higher code rate can benefit for the throughput when Copyright © 2013 SciRes. CN
C. GONG ET AL. Copyright © 2013 SciRes. CN 285 is small, it is advised the system’s code rate could adjust to the change of . As is analyzed in above sec tion, when is small, it will bring about a drastic dif ference of EIR with different code length, so a longer code will our best choice, however, which is only at cost of complexity of hardware. And of cause, considering the complexity of hardware, short will be better, when sym bols per hop is small and sequences is interleaved, per formance could also meet the need of design. 6. Conclusions This paper focuses on the design and performance analyses of LDPCSFH system in partialband interfer ence channel. A new softdecision method based on the estimation of EIR hop by hop is proposed, performance could be improved drastically as illustrated by simulation. The Influences of code rate, code length, symbols per hop and deep degree of interleaving are also analyzed with numerical simulation. Furthermore, some construc tive advises for practical system design are given based on the former work. The results of this paper will be benefit for the design of antijamming communication systems. REFERENCES [1] D. Torrieri, S. Cheng and M. C. Valenti, “Robust Fre quency Hopping for Interference and Fading Channels,” IEEE Transactions on Communications, Vol. 56, No. 8, August 2008, pp. 13431351 [2] P. Popovski, H. Yomo and R. Prasad, “Strategies for Adaptive Frequency Hopping in the Unlicensed Bands,” IEEE Wireless Communications, December 2006, pp. 6067 [3] K. L. B. Cook, “Current Wideband MILSATCOM Infra structure and the Future of Bandwidth Availability,” IEEE A&E Systems Magazine, December 2010, pp. 2328 [4] W. Hu, D. Willkomm, L. Chu, M. Abusubaih, J. Gross, G. Vlantis, M. Gerla and A. Wolisz, “Dynamic Frequency Hopping Communities for Efficient IEEE 802.22 Opera tion,” IEEE Commun. Mag., Special Issue: Cognitive Ra dios for Dynamic Spectrum Access, Vol. 45, No. 5, pp. 8087. [5] X. F. Wu, C. M. Zhao, X. H. You and S. Q. Li, “Robust DiversityCombing Receivers for LDPC Coded FFHSS with PartialBand Interference,” IEEE Communications Letters, Vol. 11, No. 7, July 2007, pp. 613615. [6] Y. H. Kim, K. S. Kim and J. Y. Ahn, “Erasure Decoding for LDPCcoded FHOFDMA System in Downlink Cel lular Environments,” Electronics Letters 28th, 2004, Vol. 40, No. 22. doi:10.1049/el:20046043 [7] L.D. Jeng, S.S. Lee, C.H. Wang and F.B. Ueng, “LowDensity ParityCheck Codes for FFH/BFSK Sys tems with PartialBand Noise Interference,” IWCMC’06, July 3–6, 2006, Vancouver, British Columbia, Canada, pp. 12131217 [8] L.D. Jeng, S.S. Lee, C.H. Wang and F. B. Ueng, “Per formance of LowDensity ParityCheck Coded FFH/BFSK Systems under Band Multitone Interference,” IWCMC’07, August 1216, 2007, Honolulu, Hawaii, USA, pp. 434438. [9] A. Ashikhmin, G. Kramer and S. ten Brink, “Extrinsic Information Transfer Functions: Model and Erasure Channel Properties,” IEEE Transactions Information Theory, Vol. 50, 2004, pp. 26572673. doi:10.1109/TIT.2004.836693 [10] G. Liva, W. E. Ryan and M. Chiani, “QuasiCyclic Gen eralized LDPC Codes with Low Error Floors,” IEEE Transactions on Communications, Vol. 56, No. 1, January, 2008, pp. 4957. [11] M. B. Pursley, Fellow, IEEE and J. S. Skinner, “Adaptive Coding for FrequencyHop Transmission in Mobile Ad Hoc Networks with PartialBand Interference,” IEEE Transactions on Communications, Vol. 57, No. 3, MARCH 2009, pp. 801811. [12] D. R. Pauluzzi and N. C. Beaulieu, “A Comparison of SNR Estimation Techniques for the AWGN Channel, IEEE Transactions On Communications, Vol. 48, No. 10, 2000, pp. 16811691.
