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- 1. International Journal on Recent and Innovation Trends in Computing and Communication ISSN: 2321-8169 Volume: 4 Issue: 3 288 - 291 _______________________________________________________________________________________ 288 IJRITCC | March 2016, Available @ http://www.ijritcc.org _______________________________________________________________________________________ High Speed and Low Power Pseudo Noise(PN) Sequence Generator Kruttika Golwelker1 , Ritu Kumari2 School of Electronics Engineering VIT University Chennai, India Kruttika.golwelker2015@vit.ac.in1 Ritu.kumari2015@vit.ac.in2 Prof. T. Vigneswaran3 School of Electronics Engineering VIT University Chennai, India Vigneswaran.t@vit.ac.in3 Abstract—The Pseudo Noise (PN) sequence has become a significant component in digital communication. A pseudo random code are generated using two techniques namely, gold code and Kasami code. The generation of PN sequence involves the use of Linear Feedback Shift Register (LFSR) as its building block. When compared to other multiplexing methods,gold code and Kasami code techniques are better in terms of power utilization, noise flexibility and frequency efficiency. The generation of these codes involves the use of two maximum length sequence (M-sequence). The auto-correlation properties of gold and Kasami sequences are the basis for this research work. The software used to simulate these methods is NC Launchand the language used is Verilog Hardware Description Language(HDL). The results of the above two methods are compared in terms of power utilization and speed in the CADENCE environment. When comparing Gold code with Kasami code, Gold code consumes 42% less power than the Kasami code. In the modified Kasami code generator, the speed is increased by 8%, when compared to modified Gold code generator. Keywords—PN sequence, LFSR, Gold Codes, Kasami Codes. __________________________________________________*****_________________________________________________ I. INTRODUCTION The Pseudo Noise (PN) sequence is a stream of binary digits i.e. 0‟s and 1‟s. PN sequences are obtained from various methods such as Maximum length sequence (m- sequences), Gold codes, Kasami codes, Barker sequences, Walsh codes and Hadamard codes. This research work discusses in detail about the Gold code and the Kasami code.A PN sequence generator is based on the concept of a Linear Feedback Shift Register (LFSR), where the degree of the polynomial decides the size of the LFSR. A. Properties 1) Balance Property The number of 1s in a PN sequence is always more by one than the number of 0s in each period. 2) Run property In every period of a PN sequence, half the runs have a length of one, one-fourth have length of two, one-eight have a length of three and so on. 3) Correlation property The measure of similarity when comparing two sequences is termed as correlation. When the comparison is between two distinct sequences, it is called „cross-correlation‟ and when the sequences are a shifted version of the original sequences, it is called „auto-correlation‟ [1]. B. Requirements To obtain an improvised performance some of the requirements have to be fulfilled by the PN sequence [7]. 1) A sharp auto-correlation function must be achieved by the PN sequence and its cross-correlation value must be comparable to zero. 2) The period of the PN sequence should be long enough to ensure encryption and hence security. C. Polynomial Selection For generating PN sequences by methods such as gold codes and Kasami codes a set of preferred polynomials is considered. Both the polynomials are of degree n where, n indicates the size of the LFSR.Preferred polynomials can be expressed by different formats. 1) A vector listing the coefficients of the selected polynomial in the decreasing order of its powers. The first entry and the last entry have to be 1. The vector‟s length is always one more than the polynomial‟s degree. 2) A vector expressed in terms of the exponents of x for all the nonzero terms present in the polynomial. Consider the following example, the vectors [4 1 0] and [1 0 0 1 1] represent a polynomial𝑥4 + 𝑥 + 1. Table 1. Preferred Polynomials Sl.No. N Preferred Polynomial 1 Preferred Polynomial 2 1 4 [4 1 0] [4 3 0] 2 5 [5 2 0] [5 4 3 2 0] 3 6 [6 1 0] [6 5 2 1 0] The set of the preferred polynomials for a few values of n are listed in Table 1.
- 2. International Journal on Recent and Innovation Trends in Computing and Communication ISSN: 2321-8169 Volume: 4 Issue: 3 288 - 291 _______________________________________________________________________________________ 289 IJRITCC | March 2016, Available @ http://www.ijritcc.org _______________________________________________________________________________________ D.Applications Spread spectrum techniques such as CDMA systems use PN sequences and preferably, Gold code and Kasami codes due to their correlation properties [6]. The key usage of security using cryptography is in random numbers generation [9]. Speech encryption can be performed using Kasami codes hence it is used in 3G wireless communication as it ensures security [8]. Gold codes and Kasami codes are highly desirable in Ultra-Wideband (UWB) communication as they can achieve high data rates [5]. PN sequences are used in Orthogonal Frequency Division Multiplexing (OFDM)[10]. II. BACKGROUND STUDY A. Gold Code Generator Gold codes are constructed using LFSRs and modulo-2 adders which are supported by preferred polynomials [2]. LFSR is a type of shift register in which output bit of one register is the input bit of the following register. The Gold code generates a PN sequence of length 2 𝑚 − 1, where m is the degree on the polynomial [3]. Fig.1 illustrates a Gold code generator with a set of polynomials as the preferred pair 𝑥4 + 𝑥 + 1 and𝑥4 + 𝑥3 + 1. Fig.1 Gold code generator The polynomial indicates the position of the modulo-2 adder in a Gold code generator. Each of the LFSRs generate a sequence of binary bits/digits. The output of the last register in the LFSR is fed back as the input to the first register. The output sequences of both the polynomials undergo modulo-2 addition to generate the gold code. B. Kasami Code Generator The Kasami code generator works similar to the Gold code generator. A PN sequence is generated using three LFSRs. A set of preferred pair polynomials is used for two LFSRs. The third polynomial is a decimated from of one of the two polynomials. Similar to Gold code, the Kasami code also generates a sequence of length 2 𝑘 − 1 , where k is the degree of the polynomial. The decimation factor is derived from the formula2 𝑘/2 + 1, k is the degree of the polynomial [4]. The final sequence is computed by the modulo-2 addition of preferred set of polynomials and the decimated polynomial . Fig.2 Kasami code generator Fig.2 illustrates the architecture for the Kasami code generator. The Kasami code is known for its capability of ensuring security as it has one level higher encryption when compared to the sequence generated by the Gold code method. III. PROPOSED WORK A. Modified Gold Code Generator A design consuming low power has become necessity in the present day scenario. This work proposes to reduce the power consumption. Also, the communication field demands high data rate and high speed. The conventional designing method contais a pair of LFSRs, with an XOR gate to perform the modulo-2 addition mentioned in the earlier part of this paper. This work proposes to replace the XOR gate by a 2:1 multiplexer at the output port to try and reduce the delay in order to increase the speed and preferably reduce the power consumption also. Fig.3 Modified Gold Code Generator Fig.3 illustrates the Gold code architecture by replacing the modulo-2 adder at the output side with a multiplexer. The multiplexer is expected to remove the unwanted switching and hence reduce the delay in the sequence generation.
- 3. International Journal on Recent and Innovation Trends in Computing and Communication ISSN: 2321-8169 Volume: 4 Issue: 3 288 - 291 _______________________________________________________________________________________ 290 IJRITCC | March 2016, Available @ http://www.ijritcc.org _______________________________________________________________________________________ B. Modified Kasami Code Generator The large set, modified Kasami code generator consists of LFSRs using three polynomials, each of degree n. The output of each of the LFSRs is fed into an XOR gate to obtain the final PN sequence in the conventional design. However, in the modified design of the Kasami code generator, the XOR gate at the output is replaced by two consecutive 2:1 multiplexers. One of the input is given to the select line of the multiplexer and the other input along with its complement is given as the inputs to the multiplexer. Similarly, the output of the third polynomial and its complement are fed as the inputs to the multiplexer, while the output of the preceding multiplexer is given as the select line to the multiplexer at the final stage of the PN sequence generator. Fig.4 Modified Kasami Code Generator Fig.4 demonstrates the Kasami code architecture with the help of the 2:1 multiplexer. IV. RESULTS AND DISCUSSION A.Simulation Tool This entire work is carried out in the CADENCE environment. The tool “NC Launch” is used for getting the output waveform and to display the PN sequence generated by the Gold and Kasami code. The waveform is generated for every positive edge of the clock. The power consumed, delay and the area utilized is obtained from the “RC Compiler”. Both, the conventional and the modified design of Gold and Kasami codes are compiled in using the CADENCE tools. B. Gold Code Fig.5 Gold Code Simulation Fig.5 contains the simulation waveform and the generated PN sequence for a Gold code generator.The power consumption, area occupied and the delay observed in this design is tabulated as shown in Table2. Table.2. Gold Code The number of cells utilized by this design is 12 and the area mentioned in Table.2 is calculated with respect to the number of cells. The area mentioned is the amount of area used by each cell. C. Kasami Code The output is generated at every positive edge of the clock. Fig.6 shows the simulation for the Kasami code with the input preferred polynomials 𝑥4 + 𝑥 + 1 and 𝑥4 + 𝑥3 + 1 along with the decimated polynomial𝑥4 + 𝑥2 + 1. Fig.6 Kasami Code Simulation The area, power consumed and the delay calculations are tabulated in Table.3. The area mentioned in Table.3 is in terms of the number of cells used during simulation. Table.3 Kasami Code It is observed that the area utilized by the Kasami code generator is more when compared to the Gold Code generator. D. Modified Gold Code Generator Fig.7 Modified Gold Code Simulation Area Power Delay Gold sequence 672 0.109mW 1734ps Area Power Delay Kasami sequence 978 0.1552mW 1871ps
- 4. International Journal on Recent and Innovation Trends in Computing and Communication ISSN: 2321-8169 Volume: 4 Issue: 3 288 - 291 _______________________________________________________________________________________ 291 IJRITCC | March 2016, Available @ http://www.ijritcc.org _______________________________________________________________________________________ The waveform and the PN sequence generated for the modified Gold code is shown in Fig.7. Table.4 Modified Gold Code Area Power Delay Modified Gold Code 978 0.155mW 17341ps Table.4 explains the power consumed, area occupied and the delay of the modified Gold code generator. E.Modified Kasami Code Generator The simulation waveform and the PN sequence generated for the modified Kasami Code generator is illustrated in Fig.8 Fig.8 Modified Kasami Code Simulation The results of the power consumption, area and delay for modified Kasami code are charted in Table.5. Table.5 Modified Kasami Code Area Power Time Modified Kasami Code 1254 0.216mW 1734ps The Gold code is better than Kasami code by 42% in terms of power consumption. When comparing modified Gold code with modified Kasami code, the speed of modified Kasami code is better by 8%.The power consumption is decreased in the modified Gold Code method whereas the delay is reduced in the modified Kasami method. V. CONCLUSION The conventional method of obtaining the Gold code requires minimum area when compared to Kasami code and modified Gold code. The power consumed by Gold code is less when compared to others. Also the delay is less in gold code. Comparing the conventional Gold and Kasami codes, the Gold code is more efficient. However, after modification, the power consumed by modified Gold code method is less and the speed of the modified Kasami code is better. But this achieved at the cost of increase in area. In order to improve these factors further, in future, all the XOR gates in the design can be replaced with multiplexers. The multiplexer removes the unwanted switching from the circuit which occurs due the XOR gates. This, therefore reduces the power consumed and the delay when compared to the conventional method. REFERENCES [1] Muhammad Baqer Mollah, Md. Rashidul Islam , “Comparative Analysis of Gold Codes with PN Codes Using Correlation Property in CDMA Technology”International Islamic University Chittagong, Chittagong, Bangladesh, International Confrerence on Computer Communication and Informatics, IEEE 2012 [2] Menahem Lowy, Krishna Anne, “A High Speed Low Power Spread Spectrum Code Generator”University of Texas at Arlington, IEEE1995 [3] T.M Nazmul Huda, Syed Foysol Islam, “Correlation Analysis of the Gold Codes and Wash codes in CDMA ” blekinge instituteof Technology, kralskrona ,swedwn, IEEE 2009. [4] Yuh-Ren Tsai, Member ,Ieee, and Xiu-Shengli, “Kasami Code –Shift-Keying Modulation for Ultra-wideband Communication syatems”IEEE transaction on communications Vol-55,june 2007. [5] Takuya Sakamoto, Member ,IEEE ,and Toru Sato, Member ,IEEE, “Code- Division Multiple transmission for High-Speed UWB Radar Imaging With an Antenna Array ”IEEE transaction on Geosciences and Remote sensing ,vol.47,April 2009. [6] Rodrigo Carvjal ,Kaushik mahata,and juan C. Aguero, “Low Complexity Wiener Filtering in CDMA systems using a class of pseudo-noise spreading codes”IEEE communication latter , vol.19, IEEE 2012. [7] Zhang Xinyu, “Analysis of M-Sequence and Gold- Sequrence in CDMA System” 2011 IEEE, International school ,Beijing University of posts and telecommunications. [8] Mau-Lin Wau, Kuei-Ann Wen,and- Wang Huang, “Efficient Pseudo noise Code Design for Spread Spectrum Wireless Communication Systems” IEEE transactions on Circuit and System, vol. 48,JUNE 2001. [9] Miroslav Perić, Predrag Milićević, Zoran Banjac, Vladimir Orlić, Saša Milićević, “High speed random number generator for section key generation in encryption devices ”, 21st Telecommunication forum, IEEE,2013 [10] Linglong Dai, Jian Fu,Jun Wang, and Jian Song “A Multi-user Uplink TDS-OFDM System Based on Dual PN Sequence Padding” ” IEEE Transactions on Consumer Electronics,Vol. 55, No. 3,AUGUST 20

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