To study, analysis and simulation of (Spread Spectrum) FH system based on Quadratic Prime Code

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1 To study, analysis and simulation of (Spread Spectrum) FH system based on Quadratic Prime Code using BPSK and FSK kapil Bhardwaj 1 ;Sandeep Agrawal 2 1 M.E student, digital communication,mahakal institute of technology ujjain,rgpv Bhopal 2 Associate Prof. mahakal institute of technology ujjain, RGPV Bhopal Abstract Performance of a FH communication system can be improved if QPC are used as a frequency generator instead of PN sequence. Quadratic prime codes are new types of frequency hopping (FH) sequences constructed by expanding the construct idea of prime codes to finite extension fields. The linear complexity and characteristics of frequency interval of quadratic prime codes are analyzed and compared with those of prime codes. Keywords: frequency hopping, spread spectrum, quadratic prime code, prime code, Galois field Introduction With excellent anti-jamming, anti multi-path fading and multiple access networking performance, frequency-hopping (FH) technique with Quadratic Prime codes has been widely used not only in military communication but also in civil mobile communication. FH sequences have decisive impact on the performance of FH communication systems, and how to seek and design FH sequences with ideal performance is one of the important topics in FH communication systems research. Quadratic Prime codes are FH sequences with ideal Hamming correlation properties, and the only FH sequences that achieve the five theoretical limits described. Quadratic prime codes are constructed by expanding the construct idea of prime codes to extension Galois fields GF (P²)[2]. Compared with prime codes, the sequence period of quadratic prime codes is increased from P to P², and sequence number increased from P-1 to P²-1with ideal Hamming autocorrelation property and crosscorrelation no greater than 2. After classification, the sequences in the same group maintain ideal Hamming auto and cross-correlation properties. More important, quadratic prime codes can provide P (P-1)/2 families of FH sequences rather than one family for prime codes, which is preferable to improve the security of communication systems. The linear complexity of FH sequences is an important index for the secrecy intensity of FH communication system. In order to obtain maximum security intensity, FH system requires that the FH sequences it uses have the largest possible linear complexity; therefore, how to design FH sequence with large linear complexity is a research focus [3]. In addition, FH communication is vulnerable to various kinds of jam, such as tracking jam, multipath jam, some frequency band jam, monophonic collimation jam, wideband jam, and so on. FH sequences with wide frequency interval could help improve the anti-jamming capability of FH communication [1]. This paper investigates the linear complexity and characteristics of wide frequency interval of quadratic prime codes, and new FH sequences with wide frequency interval are proposed based on the combination of prime codes and quadratic prime codes. Quadratic Prime Code Quadratic prime code is based on finite field GF (P^2) in the form of x² -y -1 ( y is the second non-surplus of prime number P),and it is the result of domain multiplication of mode of quadratic polynomial. Some good feathers of quadratic prime codes are : the maximum of QPM(Quadratic Prime Code) s autocorrelation side lobe is 0, the good Hamming cross-correlation distance feature, the uniformly frequency distribution characteristics. Therefore, quadratic prime code has become a new type frequency hopping sequences. According to finite field theory [6], we use a two dimensional vector in GF (P) to express the parameters of quadratic prime code. The polynomials are: L(x)=ix+j, m(x)=ax+b, k(x)=k 1 x+k 0 (1) i,j,a,b,k 1,k 0 Є GF(P) and (a,b) ( 0,0) According to the above agreements, using f(x)=x 2 -y (2) as irreducible polynomial using below formula to achieve the multiplication of GF(P²) domain: K[m(x),l(x)] =m(x)l(x) mod f(x) =(ax+b)(ix+j)mod(x 2 -y) = [aix 2 +(aj+bi)x +bj] mod (x 2 -y) =(aj bi)x +(bj yai) means mod P adder and (aj bi)x +(bj yai) corresponding frequency gap Each code group contains the number quadratic prime codes is P²-1, it means the quadratic prime sequence period P². The hamming autocorrelation side lobe of this quadratic rime code is 0, the maxim hamming cross correlation value ISSN: Page 3931

2 is 2. The linear complexity of the quadratic prime code sequence of FH has direct impact on the anti-decipher ability and the ideal linear complexity of FH sequence is about half the length of code sequence. Assuming the length of quadratic prime code is N, then the linear complexity of the sequence is (N +1) / 2 Therefore, the quadratic prime code has ideal characteristics of linear complexity. Taking P=3 and y=3 as an example, 8 sequences with length of 9 are constructed and listed in Table I. Q 1 {0,1,2,3,4,5,6,7,8} Q 2 {0,2,1,6,8,7,3,5,4} Q 3 {0,3,6,2,5,8,1,4,7} Q 4 {0,4,8,5,6,1,7,2,3} Q 5 {0,5,7,8,1,3,4,6,2} Q 6 {0,6,3,1,7,4,2,8,5} Q 7 {0,7,5,4,2,6,8,3,1} Q 8 {0,8,4,7,3,2,5,1,6} Table I:Quadratic prime code for P=3 ISSN: Page 3932

3 OUTPUT DATA BPSK DE MODULA- TOR BPSK MODULATOR FH MOD- ULATOR CHANNEL FH DEMODULA- TOR RANDOM DATA FREQUENCY SYNTHESIZER FREQUENCY SYNTHESIZER QUADRATIC PRIME CODE QUADRATIC PRIME CODE FH SYNCHRONIZER ISSN: Page 3933

4 Results and Analysis Fig 2: waveform of BPSK,FSK using QPC and their bit error rate performance ISSN: Page 3934

5 In fig 2 various waveforms are shown. At top left waveform for BPSK system are shown, digital data is first randomly generated and it modulates the high frequency carrier signal using BPSK. BPSK is more immune to noise and interference.in FH system modulated signal is hopped at different frequencies so we have generated some frequency where the signal is hopped on periodic basis, that signal is called frequency hopped signal. That signal is transmitted through Gaussian channel and at the receiver the reverse operation is performed by using frequency synchronizer and demodulator.top right part displays the system using MFSK.Remaining part is same for this system. Bottom left displays the BER versus SNR for BPSK system Which shows better results than MFSK. Bottom right displays the BER versus SNR for MFSK system Acknowledgments I am very thankful to Prof Sandeep Agrawal of MITS ujjain for the support and guidance to develop this paper. Conclusion FH system using QPC with BPSK gives better performance than using MFSK. BPSK gives better bit error rate results than MFSK. Theoretical analysis and computation results show that, the proposed FH sequences have all advantages of prime codes and quadratic prime codes in that they not only have wide frequency interval and uniform frequency, but also have good Hamming correlation and ideal linear complexity. Quadratic prime codes have better confidentiality than prime codes. Moreover, two methods for constructing FH sequences with wide frequency interval are proposed with the combination of prime codes and quadratic prime codes. [5] Yang Yixian and Lin Xuduan, Coding cryptology. Beijing: Posts and Telecommunications Press, 1992, pp [6] Liu Qingge,Yang Dongkai, Zhang Qishan, Concatenated prime codes and quadratic prime codes, 11th IEEE Singapore International Conference on Communication Systems, Singapore, 2008, pp [7] Mei Wenhua and Yang Yixian, Families of Frequency Hopping Sequences with Given Minimum Gap, Journal of China Institute of Communications. China, vol.18(5), pp , 1997 Biographies KAPIL BHARDWAJ received the B.E. degree in Electronics Engineering from the RGPV University BHOPAL in 2004, And pursuing M.E. degree in Digital Communication from the RGPV University of BHOPAL respectively. Currently, He is an associate Professor of Electronics Engineering at MIT UJJAIN. His teaching and research areas include wireless communication, automation, and embedded system design. kapil bhardwaj may be reached at References [1] Mei Wenhua, Wang Shubo, Qiu Yonghong, and Du Xingmin, Frequency Hopping Communciations. Beijing: National Industry Press, 2005, pp [2] Qingge Liu, Dingrong Shao, Shujian Li., Quadratic prime codes, Proceedings of 2006 the IET International Conference on Wireless Mobile & Multimedia Networks. China, pp , 2006 [3] Mei Wenhua and Yang Yixian, Code Theory on FH Communication. Beijing: National Defence Industry Press, 1996, pp [4] J. L. MASSEY, Shift-register synthesis and BCH decoding, IEEE Transactions on Information Theory, 1969, vol. 15(1), pp ISSN: Page 3935