Some Results On Impulse Radio Sequences With λ_c=1

Impulse radio sequences were first introduced by Chu and Colbourn in [1]. This class of sequences were formulated to study sequence or signal design for ultra-wideband radio with unmodulated time-hopping. UWB systems for wireless communication have recently become an important area of research. For more information on UWB, the reader is referred to [2].In [1], the author gave the definition impulse radio sequences. Meanwhile, they gave the direct and recursive constructions of several given orders.An optical orthogonal codes is a family of (0,1) sequences with good auto-and cross-correlation properties. The impulse radio sequences has close relation-ship with optical orthogonal codes. The only difference between impulse radio sequences and optical orthogonal codes which we will discuss in this thesis, is that impulse radio sequences should satisfy another property called pulse position. Obviously, impulse radio sequences is a special class of optical orthogonal codes. Therefore, when we study the impulse radio sequences, we can use the method when we studied optical orthogonal codes, and the results of optical orthogonal codes.Given the upper bound and the exact codes of impulse radio sequences is a topic of combinatory design. Upper bound is the maximal possible number of sequences in an (m, k,λ)-IRS.There are four chapters in this thesis.In the first chapter, we will introduce the concept and background of impulse radio sequences. Then we will give some known results of it.In the second chapter, we will summarize the known results about conflict-avoiding codes and present the exact value of Φ(m,3,3,1) and construct an optimal (m,3,3,1)-IRS.In the third chapter, we will present the exact value of Φ(m,3,2,1) and construct an optimal (m,3,2,1)-IRS.In the fourth chapter, we will give a upper bound of Φ(m,4,4,1), but it is not tight enough.