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C0531519

IOSR Journal of Electronics and Communication Engineering(IOSR-JECE) is an open access international journal that provides rapid publication (within a month) of articles in all areas of electronics and communication engineering and its applications. The journal welcomes publications of high quality papers on theoretical developments and practical applications in electronics and communication engineering. Original research papers, state-of-the-art reviews, and high quality technical notes are invited for publications.

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C0531519

  1. 1. IOSR Journal of Electronics and Communication Engineering (IOSR-JECE)e-ISSN: 2278-2834,p- ISSN: 2278-8735. Volume 5, Issue 3 (Mar. - Apr. 2013), PP 15-19www.iosrjournals.org A New Class of Binary Zero Correlation Zone Sequence Sets B. Fassi1, A. Djebbari1, Taleb-Ahmed. A2 And I. Dayoub3 1 (Telecommunications and Digital Signal Processing Laboratory, Djillali Liabes University of Sidi Bel Abbes, Algeria) 2 (Laboratoire LAMIH UMR, C.N.R.S, UniversitΓ© de Valenciennes et du Hainaut Cambresis, le Mont Houy, France)3 (I.E.M.N. Dept. O.A.E, U.M.R, C.N.R.S,UniversitΓ© de Valenciennes et du Hainaut CAMBRESIS, le Mont Houy, France) Abstract: This paper proposes a new class of binary zero correlation zone (ZCZ) sequence sets, in which theperiodic correlation functions of the proposed sequence set is zero for the phase shifts within the zero-correlation zone. It is shown that the proposed zero correlation zone sequence set can reach the upper bound onthe ZCZ codes.Keywords- Sequence design, theoretical upper bound, zero correlation zone (ZCZ) sequences. I. IntroductionZero correlation zone (ZCZ) sequences can be used in spread spectrum systems and CDMA systems to reducethe multiple access interference and co-channel interference [1]. There are several intensive studies on theconstructing of ZCZ sequences set [1-8]. The ZCZ sequences set construction is limited by the correlation property and theory bounds [1-7].Generally, sets of ZCZ sequences are characterized by the period of sequences L, the family size, namely thenumber of sequences M, and the length of the zero-correlation zone ZCZ. A ZCZ (L, M, ZCZ) sequence set thatsatisfies the theoretical bound defined by the ratio 𝑀 𝑍 𝑐𝑧 + 1 /𝐿 = 1 is called an optimal zero-correlation zonesequence set [4]. Compared with earlier works on binary ZCZ sequence sets [1, 6], our proposed zero-correlation zone sequence set is, in all cases, an optimal or an approach optimal ZCZ sequence set. The paper is organized as follows. Section 2 introduces the notations required for the subsequentsections, the proposed scheme for sequence construction is explained in section 3. Examples of new ZCZsequence sets are presented in Section 4. The properties of the proposed sequence sets are shown in Section 5.Finally, we draw the concluding remarks. II. Notations2.1 Definition 1: Suppose 𝑋𝑗 =(π‘₯𝑗 ,0 , π‘₯𝑗 ,1 , … … . π‘₯𝑗 ,πΏβˆ’1 ) and, 𝑋 𝑣 =(π‘₯ 𝑣,0 , π‘₯ 𝑣,1 , … … . π‘₯ 𝑣,πΏβˆ’1 ) are two sequences ofperiod L. Sequence pair (𝑋𝑗 , 𝑋 𝑣 ) is called a binary sequence pair if π‘₯𝑗 ,𝑖 , π‘₯ 𝑣,𝑖 ∈ βˆ’1, +1 , 𝑖 = 0,1,2, … … … 𝐿 βˆ’ 1 [7].The Periodic Correlation Function (PCF) between 𝑋𝑗 and 𝑋 𝑣 at a shift 𝜏 is defined by [4]: πΏβˆ’1βˆ€πœ β‰₯ 0, πœƒ 𝑋 𝑗 ,𝑋 𝑣 𝜏 = 𝑖=0 π‘₯𝑗 ,𝑖 π‘₯ 𝑣, 𝑖+𝜏 π‘šπ‘œπ‘‘ (𝐿) (1)2.2 Definition 2: A set of M sequences 𝑋0 , 𝑋1 , 𝑋2 , … … , 𝑋 π‘€βˆ’1 is denoted by Xj 𝑗 π‘€βˆ’1 . =0A set of sequences Xj 𝑗 π‘€βˆ’1 =0 is called zero correlation zone sequence set, denoted by Z(L,M,ZCZ) if the periodiccorrelation functions satisfy [4] :βˆ€π‘—, 0 < 𝜏 ≀ 𝑍 𝑐𝑧 , πœƒ 𝑋 𝑗 ,𝑋 𝑗 𝜏 =0 (2)βˆ€π‘—, 𝑗 β‰  𝑣 , 𝜏 ≀ 𝑍 𝑐𝑧 , πœƒ 𝑋 𝑗 ,𝑋 𝑣 𝜏 =0 (3) III. Proposed Sequence ConstructionIn this section, a new method for constructing sets of binary ZCZ sequences is proposed.The construction is accomplished through three steps.3.1 Step 1: The 𝑗 π‘‘β„Ž row of the Hadamard matrix 𝐻 of order n is denoted byβ„Ž 𝑗 = β„Ž 𝑗 ,0 , β„Ž 𝑗 ,1 , … … … β„Ž 𝑗 ,𝑛 βˆ’1 . A set of 2𝑛 sequences 𝑑 𝑗 , each of length 2𝑛, is constructed as follows:For 0 ≀ 𝑗 < 𝑛, www.iosrjournals.org 15 | Page
  2. 2. A New Class of Binary Zero Correlation Zone Sequence Sets𝑑 𝑗 +0 = βˆ’β„Ž 𝑗 , β„Ž 𝑗 (4)𝑑 𝑗 +1 = β„Ž 𝑗 , β„Ž 𝑗 (5)3.2 Step 2: For a fixed integer value 𝑛, and for the first stage, 𝑝 = 0, we can generate, based on the scheme for 2π‘›βˆ’1sequence construction in [6], a series of sets 𝐡𝑗 𝑗 =0 of 2𝑛 sequences as follows: 2π‘›βˆ’1 2π‘›βˆ’1A sequence set 𝐡𝑗 𝑗 =0 is constructed from the sequences set 𝑑𝑗 𝑗 =0 . A pair of sequences 𝐡𝑗 +0 and 𝐡𝑗 +1 of 𝑝+2length (2 𝑛) are constructed by the process of interleaving a sequence pair 𝑑 𝑗 +0 and 𝑑 𝑗 +1 as follows:For 0 ≀ 𝑗 < 𝑛, 𝐡𝑗 +0 = 𝑑 𝑗 +0,0 , 𝑑 𝑗 +1,0 , 𝑑 𝑗 +0,1 , 𝑑 𝑗 +1,1 , … … . . , 𝑑 𝑗 +0,2π‘›βˆ’1 , 𝑑 𝑗 +1,2π‘›βˆ’1 (6)and, 𝐡𝑗 +1 = 𝑑 𝑗 +0,0 , βˆ’π‘‘ 𝑗 +1,0 , 𝑑 𝑗 +0,1 , βˆ’π‘‘ 𝑗 +1,1 , … … . . , 𝑑 𝑗 +0,2π‘›βˆ’1 , βˆ’π‘‘ 𝑗 +1,2π‘›βˆ’1 (7)The member size of the sequence set 𝐡𝑗 is 2𝑛. 2π‘›βˆ’13.3 Step 3: For 𝑝 > 0, we can recursively construct a new series of set, 𝐡𝑗 𝑗 =0 , by interleaving of actual 2π‘›βˆ’1 𝐡𝑗 𝑗 =0 . 2π‘›βˆ’1The 𝐡𝑗 𝑗 =0 is generated as follows:For 0 ≀ 𝑗 < 𝑛, 𝐡𝑗 +0 = 𝐡𝑗 +0,0 , 𝐡𝑗 +1,0 , 𝐡 𝑗 +0,1 , 𝐡𝑗 +1,1 , … … . . , 𝐡𝑗 +0,4π‘›βˆ’1 , 𝐡 𝑗 +1,4π‘›βˆ’1 (8)and, 𝐡𝑗 +1 = 𝐡𝑗 +0,0 , βˆ’π΅π‘— +1,0 , 𝐡 𝑗 +0,1 , βˆ’π΅π‘— +1,1 , … … . , 𝐡𝑗 +0,4π‘›βˆ’1 , βˆ’π΅ 𝑗 +1,4π‘›βˆ’1 (9)The length of both sequences 𝐡𝑗 +0 and 𝐡𝑗 +1 is equal to (2 𝑝+2 𝑛). IV. Example of Construction4.1 Step 1: Let 𝐻 be a Hadamard matrix of order n=2, given by: 1 1 β„Ž 𝐻= = 0 1 βˆ’1 β„Ž1A set of 2𝑛 = 4 sequences 𝑑 𝑗 , each of length 2𝑛 = 4, is constructed as follows:For 0 ≀ 𝑗 < 2, 𝑑0+0 = βˆ’β„Ž0 , β„Ž0 = βˆ’1, βˆ’1,1,1 𝑑1+0 = βˆ’β„Ž1 , β„Ž1 = βˆ’1,1,1, βˆ’1 𝑑0+1 = β„Ž0 , β„Ž0 = 1,1,1,1 𝑑1+1 = β„Ž1 , β„Ž1 = 1, βˆ’1,1, βˆ’14.2 Step 2: For the first iteration, 𝑝 = 0.A pair of sequences 𝐡𝑗 +0 and 𝐡𝑗 +1 of length 2 𝑝+2 𝑛 = 8 are constructed by interleaving a sequence pair 𝑑 𝑗 +0and 𝑑 𝑗 +1 as follows:For 0 ≀ 𝑗 < 2, 𝐡𝑗 +0 = 𝑑 𝑗 +0,0 , 𝑑 𝑗 +1,0 , 𝑑 𝑗 +0,1 , 𝑑 𝑗 +1,1 , … … . . , 𝑑 𝑗 +0,3 , 𝑑 𝑗 +1,3 𝐡0+0 = βˆ’1,1, βˆ’1,1,1,1,1,1 𝐡1+0 = βˆ’1,1,1, βˆ’1,1,1, βˆ’1, βˆ’1and, 𝐡𝑗 +1 = 𝑑 𝑗 +0,0 , βˆ’π‘‘ 𝑗 +1,0 , 𝑑 𝑗 +0,1 , βˆ’π‘‘ 𝑗 +1,1 , … … . . , 𝑑 𝑗 +0,3 , βˆ’π‘‘ 𝑗 +1,3 𝐡0+1 = βˆ’1, βˆ’1, βˆ’1, βˆ’1,1, βˆ’1,1, βˆ’1 𝐡1+1 = βˆ’1, βˆ’1,1,1,1, βˆ’1, βˆ’1,1 34.3 Step 3: For the next iteration 𝑝 = 1, The 𝐡𝑗 𝑗 =0 is generated as follows: 𝐡𝑗 +0 = 𝐡𝑗 +0,0 , 𝐡𝑗 +1,0 , 𝐡 𝑗 +0,1 , 𝐡𝑗 +1,1 , … … . . , 𝐡𝑗 +0,7 , 𝐡 𝑗 +1,7 𝐡0+0 = βˆ’1, βˆ’1, 1, βˆ’1, βˆ’1, βˆ’1, 1, βˆ’1,1, 1, 1, βˆ’1, 1, 1, 1, βˆ’1 , 𝐡1+0 = βˆ’1, βˆ’1, 1, βˆ’1, 1, 1, βˆ’1, 1,1, 1, 1, βˆ’1, βˆ’1, βˆ’1, βˆ’1, 1 ,and, 𝐡𝑗 +1 = 𝐡𝑗 +0,0 , βˆ’π΅π‘— +1,0 , 𝐡 𝑗 +0,1 , βˆ’π΅π‘— +1,1 , … … . , 𝐡𝑗 +0,7 , βˆ’π΅ 𝑗 +1,7 𝐡0+1 = βˆ’1, 1, 1, 1, βˆ’1, 1, 1, 1,1, βˆ’1, 1, 1, 1, βˆ’1, 1, 1 , 𝐡1+1 = βˆ’1, 1, 1, 1, 1, βˆ’1, βˆ’1, βˆ’1,1, βˆ’1, 1, 1, βˆ’1, 1, βˆ’1, βˆ’1 . www.iosrjournals.org 16 | Page
  3. 3. A New Class of Binary Zero Correlation Zone Sequence SetsThe length of both sequences 𝐡𝑗 +0 and 𝐡𝑗 +1 is equal to 2 𝑝+2 𝑛 = 16.The member size of the sequence set 𝐡𝑗 is 2𝑛 = 4. 3Iteratively for 𝑝 = 2, The 𝐡𝑗 𝑗 =0 is generated as follows: 𝐡0+0 = βˆ’1, βˆ’1, βˆ’1, 1, 1, 1, βˆ’1, 1, βˆ’1, βˆ’1, βˆ’1, 1, 1, 1, βˆ’1, 1, 1, 1, 1, βˆ’1,1, 1, βˆ’1, 1, 1, 1, 1, βˆ’1,1, 1, βˆ’1, 1 𝐡1+0 = βˆ’1, βˆ’1, βˆ’1, 1, 1, 1, βˆ’1, 1, 1, 1, 1, βˆ’1, βˆ’1, βˆ’1, 1, βˆ’1, 1, 1, 1, βˆ’1, 1, 1, βˆ’1, 1, βˆ’1, βˆ’1, βˆ’1, 1, βˆ’1, βˆ’1, 1, βˆ’1 𝐡0+1= βˆ’1, 1, βˆ’1, βˆ’1, 1, βˆ’1, βˆ’1, βˆ’1, βˆ’1, 1, βˆ’1, βˆ’1, 1, βˆ’1, βˆ’1, βˆ’1, 1, βˆ’1, 1, 1, 1, βˆ’1, βˆ’1, βˆ’1, 1, βˆ’1, 1, 1,1, βˆ’1, βˆ’1, βˆ’1 𝐡1+1= βˆ’1, 1, βˆ’1, βˆ’1, 1, βˆ’1, βˆ’1, βˆ’1, 1, βˆ’1, 1, 1, βˆ’1, 1, 1, 1, 1, βˆ’1, 1, 1, 1, βˆ’1, βˆ’1, βˆ’1, βˆ’1, 1, βˆ’1, βˆ’1 βˆ’ 1, 1, 1, 1 3 Also, we can find out that the zero correlation zone length of 𝐡𝑗 𝑗 =0 is 4. For example, for 𝜏 =0,1, … … … … 31, the periodic auto-correlation functions (PACF) (βˆ€π‘—, 𝑗 = 𝑣) given in 1 of 𝐡0+0 , 𝐡1+0 , 𝐡0+1and 𝐡1+1 are calculated as follows: πœƒ 𝐡0+0 ,𝐡0+0 𝜏 = 32, 0, 0, 0, 0, 4, 0, βˆ’4,16, βˆ’4, 0, 4, 0, 8, 0, βˆ’8, 0, βˆ’8, 0, 8, 0, 4, 0, βˆ’4,16, βˆ’4, 0, 4, 0, 0, 0, 0 πœƒ 𝐡1+0 ,𝐡1+0 𝜏 = 32, 0, 0, 0, 0, βˆ’4, 0, 4 , βˆ’16, 4, 0, βˆ’4, 0, 8, 0, βˆ’8, 0, βˆ’8, 0, 8, 0, βˆ’4, 0, 4, βˆ’16, 4, 0, βˆ’4, 0, 0, 0, 0 πœƒ 𝐡0+1 ,𝐡0+1 𝜏 = 32, 0, 0, 0, 0, βˆ’4, 0, 4,16, 4, 0, βˆ’4, 0, βˆ’8, 0, 8, 0, 8, 0, βˆ’8, 0, βˆ’4, 0, 4,16, 4, 0, βˆ’4, 0, 0, 0, 0 πœƒ 𝐡1+1 ,𝐡1+1 𝜏 = 32, 0, 0, 0, 0, 4, 0, βˆ’4, βˆ’16, βˆ’4, 0, 4, 0, βˆ’8, 0, 8, 0, 8, 0, βˆ’8, 0, 4, 0, βˆ’4, βˆ’16, βˆ’4, 0, 4, 0, 0, 0, 0 The periodic cross-correlation functions (PCCF) (βˆ€π‘—, 𝑗 β‰  𝑣) given in (1) are calculated as follows: πœƒ 𝐡0+0 ,𝐡1+0 𝜏 = 0, 0, 0, 0, 0, βˆ’4, 0, 4,16, 4, 0, βˆ’4, 0, 0, 0, 0, 0, 0, 0, 0, 0, 4, 0, βˆ’4 , βˆ’16, βˆ’4, 0, 4, 0, 0, 0, 0 πœƒ 𝐡0+0 ,𝐡0+1 𝜏 = 0, 0, 0, 0, 0, βˆ’4, βˆ’8, βˆ’4, 0, 4, βˆ’8, 4, 0, βˆ’8, βˆ’16, βˆ’8, 0, 8, βˆ’16, 8, 0, βˆ’4, βˆ’8, βˆ’4, 0, 4, βˆ’8, 4, 0, 0, 0, 0 πœƒ 𝐡0+0 ,𝐡1+1 𝜏 = 0, 0, 0, 0, 0, 4, 8, 4, 0, βˆ’4, 8, βˆ’4, 0, 0, 0, 0, 0, 0, 0, 0, 0, βˆ’4, βˆ’8, βˆ’4, 0, 4, βˆ’8, 4, 0, 0, 0, 0 πœƒ 𝐡1+0 ,𝐡0+1 𝜏 = 0, 0, 0, 0, 0, βˆ’4, βˆ’8, βˆ’4, 0, 4, βˆ’8, 4, 0, 0, 0, 0, 0, 0, 0, 0, 0, 4, 8, 4, 0, βˆ’4, 8, βˆ’4, 0, 0, 0, 0 πœƒ 𝐡1+0 ,𝐡1+1 𝜏 = 0, 0, 0, 0, 0, 4, 8, 4, 0, βˆ’4, 8, βˆ’4, 0, βˆ’8 , βˆ’16, βˆ’8, 0, 8, βˆ’16, 8, 0, 4, 8, 4, 0, βˆ’4, 8, βˆ’4, 0, 0, 0, 0πœƒ 𝐡0+1 ,𝐡1+1 𝜏 = 0, 0, 0, 0, 0, 4, 0, βˆ’4,16, βˆ’4, 0, 4, 0, 0, 0, 0, 0, 0, 0, 0, 0, βˆ’4, 0, 4, βˆ’16, 4, 0, βˆ’4, 0, 0, 0, 0 3We notice that the zero correlation zone length of 𝐡𝑗 𝑗 =0 is 4.The PACF and PCCF confirm that 𝐡𝑗 is a ZCZ (32,4,4) sequence set. V. The Properties of the Proposed Sequence The proposed zero-correlation zone sequence set can be generated from an arbitrary Hadamard matrixof order n.The length of Bj in equations (6) and (7), equal to (2p+2 n), is twice that of Bj in equations (8) and (9).The proposed ZCZ sequence set can satisfy the ideal autocorrelation and cross-correlation properties in thezero-correlation zone.The generated sequence set satisfies the following properties:βˆ€π‘—, βˆ€πœ β‰  0, 𝜏 ≀ 2 𝑝 πœƒ 𝐡 𝑗 ,𝐡 𝑗 𝜏 =0(10)and,βˆ€π‘— β‰  𝑣, βˆ€πœ, 𝜏 ≀ 2 𝑝 πœƒ 𝐡 𝑗 ,𝐡 𝑣 𝜏 =0.(11)The 𝐡𝑗 is a ZCZ sequence set having parameters (L,M, ZCZ)=(2 𝑝+2 𝑛, 2𝑛, 2 𝑝 ), its parameters perfectly satisfythe theory bound of ZCZ sequences set [4, 7]: www.iosrjournals.org 17 | Page
  4. 4. A New Class of Binary Zero Correlation Zone Sequence Sets 𝑀(𝑍 𝐢𝑍 + 1) ≀ 𝐿 (12) 𝑀(𝑍 𝐢𝑍 +1)Let πœ‡ = , if πœ‡ = 1 , it indicates that the ZCZ sequence set is optimal [1, 6]. 𝐿 𝑀(𝑍 +1) 2𝑛(2 𝑝 +1) (2 𝑝 +1)For the proposed 𝑍𝐢𝑍(2 𝑝 +2 𝑛, 2𝑛, 2 𝑝 ) sequence set, πœ‡ = 𝐢𝑍 = = 𝐿 2 𝑝 +2 𝑛 2 𝑝 +11) For 𝑝 = 0, πœ‡ = 1, the proposed ZCZ sequence set is optimal. lim2) For 𝑝 > 0, 1/2 ≀ πœ‡ < 1 and π‘β†’βˆž πœ‡ = 1/2.For a given family size M, we can construct different sets of sequences with different lengths L and zerocorrelation zone 𝑍 𝐢𝑍 . As an example, assuming that M=16, we can construct sets of ZCZ sequences withdifferent lengths L=32, 64, 128, 256, 512, 1024, 2048, 4096…., and different ZCZs, 𝑍 𝐢𝑍 =1, 2, 4, 8, 16, 32, 64,128,….and different parameters πœ‡=1, 0.75, 0.625, 0.5625, 0.53125, 0.515625, 0.5078125, 0.5039063,…….In step 1, other set of 2𝑛 sequences 𝑑 𝑗 , each of length 2𝑛, can be constructed as follows:1- For 0 ≀ 𝑗 < 𝑛, 𝑑 𝑗 +0 = β„Ž 𝑗 , βˆ’β„Ž 𝑗(13) 𝑑 𝑗 +1 = β„Ž 𝑗 , β„Ž 𝑗(14) 3In this case, the set of 𝐡𝑗 𝑗 =0 is generated as follows: 𝐡0+0= 1,1,1, βˆ’ 1, 1, 1, βˆ’1, 1,1,1,1, βˆ’ 1, 1, 1, βˆ’1, 1, βˆ’ 1, βˆ’ 1, βˆ’ 1,1,1, 1, βˆ’1, 1, βˆ’ 1, βˆ’ 1, βˆ’ 1,1,1, 1, βˆ’1, 1𝐡1+0 = 1,1,1, βˆ’ 1, 1, 1, βˆ’1, 1, βˆ’1, βˆ’1, βˆ’1, 1, βˆ’1, βˆ’1,1, βˆ’ 1, βˆ’ 1, βˆ’ 1, βˆ’ 1,1,1, 1, βˆ’1, 1,1,1,1, βˆ’1, βˆ’1, βˆ’1,1, βˆ’ 1 𝐡0+1= 1, βˆ’ 1,1,1, 1, βˆ’1, βˆ’1, βˆ’1,1, βˆ’ 1,1,1, 1, βˆ’1, βˆ’1, βˆ’1, βˆ’1,1, βˆ’ 1, βˆ’ 1, 1, βˆ’1, βˆ’1, βˆ’1, βˆ’ 1,1, βˆ’1, βˆ’ 1,1, βˆ’1, βˆ’1, βˆ’1 𝐡1+1 = 1, βˆ’ 1,1,1, 1, βˆ’1, βˆ’1, βˆ’1, βˆ’1, 1, βˆ’1, βˆ’1, βˆ’ 1,1,1,1, βˆ’1,1, βˆ’ 1, βˆ’ 1, 1, βˆ’1, βˆ’1, βˆ’1, 1, βˆ’1, 1,1, βˆ’1,1,1,12- For 0 ≀ 𝑗 < 𝑛, 𝑑 𝑗 +0 = β„Ž 𝑗 , β„Ž 𝑗(15) 𝑑 𝑗 +1 = βˆ’β„Ž 𝑗 , β„Ž 𝑗(16) 3The set of 𝐡𝑗 𝑗 =0 is generated as follows: 𝐡0+0 = 1,1,1, βˆ’ 1, βˆ’ 1, βˆ’ 1,1, βˆ’ 1,1,1,1, βˆ’1, βˆ’1, βˆ’ 1,1, βˆ’ 1, 1, 1, 1, βˆ’1,1, 1, βˆ’1, 1, 1, 1, 1, βˆ’1,1, 1, βˆ’1, 1 𝐡1+0 = 1,1,1, βˆ’ 1, βˆ’ 1, βˆ’ 1,1, βˆ’ 1, βˆ’1, βˆ’1, βˆ’1, 1, 1, 1, βˆ’1, 1, 1, 1, 1, βˆ’1,1, 1, βˆ’1, 1, βˆ’1, βˆ’ 1, βˆ’ 1,1, βˆ’1, βˆ’1,1, βˆ’ 1 𝐡0+1 = 1, βˆ’ 1,1,1, βˆ’ 1,1,1,1,1, βˆ’ 1,1,1, βˆ’ 1,1,1,1, 1, βˆ’1, 1, 1, 1, βˆ’1, βˆ’1, βˆ’1, 1, βˆ’1, 1, 11, βˆ’1, βˆ’1, βˆ’1 𝐡1+1 = 1, βˆ’ 1,1,1, βˆ’ 1,1,1,1, βˆ’1, 1, βˆ’1, βˆ’1, 1, βˆ’1, βˆ’1, βˆ’1, 1, βˆ’1, 1, 1, 1, βˆ’1, βˆ’1, βˆ’1, βˆ’ 1,1, βˆ’1, βˆ’1, βˆ’1,1,1,13- For 0 ≀ 𝑗 < 𝑛, 𝑑 𝑗 +0 = β„Ž 𝑗 , β„Ž 𝑗(17) 𝑑 𝑗 +1 = β„Ž 𝑗 , βˆ’β„Ž 𝑗(18) www.iosrjournals.org 18 | Page
  5. 5. A New Class of Binary Zero Correlation Zone Sequence SetsIt should be noted that in [9], the limits of the correlation function of binary zero-correlation zone sequences 3 𝐡𝑗 𝑗 =0 obtained from equation (17) and (18) are evaluated. VI. Conclusion In this paper, we have proposed a new method for constructing sets of binary ZCZ sequences .The structure ofthe proposed ZCZ sequences set is simple and thus it is easy to be generated. The PACF side lobes and PCCFof the proposed sequence set is zero for the phase shifts within the zero-correlation zone. The proposed ZCZsequence set with (2 𝑝+2 𝑛, 2𝑛, 2 𝑝 ) is optimal or asymptotically optimal ZCZ sequence set. This method isuseful for designing spreading sequences for multi-user CDMA system. References[1] P. Z. Fan, N. Suehiro, N. Kuroyanagi and X. M. Deng, Class of binary sequences with zero correlation zone, IEE Electronic Letters, 35(10), 1999, 777-779.[2] H. Torii, M. Nakamura, N. Suehiro, A new class of zero-correlation zone sequence, IEEE. Trans. Inf. Theory, 50(3), 2004, 559-565.[3] H. Torri, M. Nakamura, N. Suehiro, Enhancement of ZCZ sequence set construction procedure, Proc. IWSDA05, 2005, 67-72.[4] T. Hayashi, A class of zero-correlation zone sequence set using a perfect sequence, IEEE Signal ProcessingLetters, 16(4),2009, 331- 334.[5] Kai Liu, ChengqianXu Gang Li, Binary zero correlation zone sequence pair set constructed from difference set pairs, Proceedings of International Conference on Networks Security, Wireless Communications and Trusted Computing (NSWCTC’09),2, 2009, 543- 546.[6] T. Maeda, S. Kanemoto, T. Hayashi, A Novel Class of Binary Zero-Correlation Zone Sequence Sets, NΒ°978-1-4244-6890-Β©2010 IEEE, TENCON 2010.[7] S. Renghui, Z. Xiaoqun, Li. Lizhi, Research on Construction Method of ZCZ Sequence Pairs Set, Journal of Convergence Information Technology, 6(1). January 2011.[8] A. Rathinakumar and A.K. Chaturvedi, Mutually orthogonal sets of ZCZ sequences, ELECTRONICS LETTERS,40 (18),2004.[9] T. Hayashi, Limits of the Correlation Function of a Class of Binary Zero-correlation-zone Sequences, ftp://ftp.u-aizu.ac.jp/u- aizu/doc/Tech-Report/2002/2002-1-013.pdf, June 6, 2002. www.iosrjournals.org 19 | Page

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