Williamson-Hadamard spreading sequences for DS-CDMA applications

Summary Orthogonal bipolar spreading sequences are used in direct sequence code division multiple access (DS-CDMA) systems for both spectrum spreading and channel separation. The most commonly used sequences are Walsh– Hadamard sequences of lengths being an integer power of 2. A construction based on Williamson’s arrays leading to sequences of lengths N:4 (mod 8) is presented in the paper. Aperiodic correlation characteristics, for example sequence sets of lengths 12–252 are presented. The correlation properties of the sequence sets are later improved using a diagonal modification technique. Copyright # 2003 John Wiley & Sons, Ltd.

[1]  D K Smith,et al.  Numerical Optimization , 2001, J. Oper. Res. Soc..

[2]  Albert Leon Whiteman An Infinite Family of Hadamard Matrices of Williamson Type , 1973, J. Comb. Theory, Ser. A.

[3]  Christos Koukouvinos,et al.  Hadamard matrices of the Williamson type of order 4·m, m=p·q an exhaustive search for m=33 , 1988, Discret. Math..

[4]  Ronald L. Wasserstein,et al.  Monte Carlo: Concepts, Algorithms, and Applications , 1997 .

[5]  L. D. Baumert Hadamard matrices of orders 116 and 232 , 1966 .

[6]  Ian Oppermann,et al.  Complex spreading sequences with a wide range of correlation properties , 1997, IEEE Trans. Commun..

[7]  Jennifer Seberry,et al.  A Search for Hadamard Matrices constructed from Williamson Matrices , 2002 .

[8]  Tadeusz A. Wysocki,et al.  Modified Walsh‐Hadamard sequences for DS CDMA wireless systems , 2002 .

[9]  Dragomir Z. Dokovic Williamson Matrices of Orders 4.29 and 4.31 , 1992, J. Comb. Theory, Ser. A.

[10]  Richard J. Turyn An Infinite Class of Williamson Matrices , 1972, J. Comb. Theory, Ser. A.

[11]  Albert Leon Whiteman Hadamard matrices of Williamson type , 1976 .

[12]  Ian Oppenmann Orthogonal complex-valued spreading sequences with a wide range of correlation properties , 1997, IEEE Trans. Commun..

[13]  Dragomir Z. Dokovic Williamson matrices of order 4n for n=33, 35, 39 , 1993, Discret. Math..

[14]  Lajos Hanzo,et al.  Introduction to Digital Cellular Radio , 1999 .

[15]  Henning F. Harmuth,et al.  Transmission of information by orthogonal functions , 1969 .

[16]  Lloyd R. Welch,et al.  Lower bounds on the maximum cross correlation of signals (Corresp.) , 1974, IEEE Trans. Inf. Theory.

[17]  Kazue Sawade Hadamard Matrices of Order 100 and 108 , 1977 .

[18]  Pingzhi Fan,et al.  SEQUENCE DESIGN FOR COMMUNICATIONS APPLICATIONS , 1996 .

[19]  J. Williamson Hadamard’s determinant theorem and the sum of four squares , 1944 .

[20]  Mieko Yamada,et al.  On the Williamson Type j Matrices of Orders 4.29, 4.41, and 4.37 , 1979, J. Comb. Theory, Ser. A.

[21]  M. Pursley,et al.  Performance Evaluation for Phase-Coded Spread-Spectrum Multiple-Access Communication - Part I: System Analysis , 1977, IEEE Transactions on Communications.

[22]  Vladimir I. Levenshtein New Lower Bounds on Aperiodic Crosscorrelation of Binary Codes , 1999, IEEE Trans. Inf. Theory.