Some Results On Impulse Radio Sequences With λ≥2

Impulse radio sequences were first introduced by Chu and Colboum in.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.In,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 relationship 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 studyed optical orthogonal codes,and the results of optical orthogonal codes.Giving 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.In this thesie,we use the relationship between impulse radio sequences and optical orthogonal codes,and the relationship between the optical orthogonal codes and cyclic packing to improve the upper bound for impulse radio sequences.Then,we will give the exact value ofφ(m,k,λ) withλ=k-1.There are four chapters in the thesis:The fist chapter introduce the background of impulse radio sequences,the definition and known results.We also give the relationship between impulse radio sequences and optical orthogonal codes.The upper bound for optical orthogonal codes was first introduced by Johnson in 1962.since impulse radio sequences is a class of optical orthogonal code,it satisfies the Johnson bound.However,if is not tight enough.A better upper bound for(m,k,1) impulse radio sequences was given by Gao and Chang.In the second chapter,we will present a upper bound for impulse radio sequences whenλ≥2.In this thesis we set up the relationship between impulse radio sequences and cyclic packing,then we will give a new upper bound for impulse radio sequences whenλ≥2.In the third chapter,we will present the exact value of impulse radio sequence whenλ=k-1.