Non-Periodic Binary Sequences for Spread Spectrum Applications

Abstract

For a multiple access communication system it is desirable to have a set of sequences such that (a) each sequence has as peaky an auto-correlation as possible and (b) each pair of sequence has as negligible a cross-correlation as possible. Peakiness of the auto-correlation of a sequence is measured in terms of its discrimination, which is to be maximized. The negligibility of a cross-correlation is judged on the basis of the energy in the cross-correlation which is to be minimized. The satisfaction of the criterion (a) is achievable by maximizing the discrimination of the sequence having its minimum value in the set. The performance along the criterion (b) is improved by seeking to minimize the maximum value of the energy of the cross correlation among all pairs of sequences. These are two established optimization problems, first of a maxmin type and the second of a minimax type. In this work they are combined into a single optimization problem by Simonization, a procedure introduced earlier for simpler situations. Sets of four binary sequences of lengths up to 1000 have been obtained by combinatorial search based on non-local optimization techniques such as Hamming scan, Backtracking, and Sidetracking, introduced earlier in simpler contexts.

Indexing terms:

• Auto-correlation
• Cross-correlation
• Backtracking
• Simonization
• Hamming scan
• Sidetracking
• Segmented Hamming scan

Additional information

Notes on contributors

N Rajaiah

N Rajaiah obtained diploma in Electronics and Communication Engineering in the year 1976. He started his career as Lab Assistant in the Department of ECE, Engineering College, Osmania University, Hyderabad. He obtained his BTech degree in Electronics and Communication from Jawaharlal Nehru Technological University, Hyderabad (AP) in 1983 and ME (Systems and Control) from Osmania University in 1985. Presently working as Assistant Professor in the Department of Electronics and Communication Engineering, College of Engineering, Osmania University, Hyderabad and working for his PhD. His area of research interest is Signal Design for Spread Spectrum applications.

K Subba Rao

Kakarla Subba Rao graduated from Government Engineering College, Anantapur in 1974. He obtained the post graduation and PhD degrees from Osmania University, Hyderabad 1977 and 1998 respectively. He joined the Osmania University in 1981 as a Lecturer and presently he is working as Associate Professor. He has about 14 Research Publications/presentations in various Journals & Conferences. His research fields include Signal processing, Signal Design and Bio-Medical Signal Processing.