Analysis And Construction Of Time-frequency Two-dimensional Hamming Correlation For Frequency-hopping Sequences And Several Types Of Multiple Direct Sequences

With the rapid development of wireless communication technology,people have put forward higher and higher requirements for the quality and anti-interference ability of communication systems.Spread spectrum communication technology meets this demand because of its good anti-interference,easy to achieve multiple access,good confidentiality,and anti-fading.The frequency hopping system(referred to as frequency hopping system,FH-SS)and the direct sequence spread spectrum system(referred to as direct expansion system,DS-SS)are the two most widely used spread spectrum methods.Due to the existence of Doppler shift in high-speed motion communications such as satellite communications,navigation systems,ranging systems,etc.,the study of two-dimensional hopping sequence sets with time delay and frequency shift is particularly important.The polyphase sequence breaks through the limitation of the number of binary sequences with ideal correlation values,has good correlation characteristics and the number of sequences can better meet the needs of spread spectrum communication.Gaussian integer sequences have received much attention due to their ability to achieve high bandwidth efficiency and transmission speed.This thesis focuses on the theoretical bound of two-dimensional frequency hopping sequence sets and designs a frequency hopping sequence set with two-dimensional periodic Hamming correlation values at or near the theoretical bound.It will solve the key problem of frequency hopping sequence design by the combination of the finite field theory and the combination method.It will construct perfect or almost perfect Gaussian integer sequences,polyphase sequence set and polyphase quasi-complementary sequence set on the unit circle of the complex plane.Firstly,several theoretical bounds of periodic Hamming correlation values of frequency hopping sequence sets are researched,and the optimality of existing two-dimensional hopping sequence sets under the theoretical boundary is analyzed.Calculate the distribution of the two-dimensional periodic Hamming correlation values of the existing frequency hopping sequence sets designed by CAI and polynomial sequence frequency hopping sets,judge whether the two-dimensional periodic Hamming correlation of these two sequence sets reaches or approaches the theoretical boundary,and analyze the key problems that cannot be approached or reached the theoretical boundary.In this thesis,we improved the construction by CAI via set theory,and obtained the new optimal hopping sequence set of low hit zone.Secondly,the hopping sequence is constructed using m-sequence or its decimation.In this paper,we analyze the frequency-hopping sequence set constructed by the continuous state sequence of m-sequence and the specific mapping,and calculate its two-dimensional Hamming correlation value by means of mathematical solutions such as the solution of the equations on the finite field.Further expand the original construction method,choose the appropriate set,and use continuous or discontinuous state sequence of m-sequence to construct a new frequency hopping sequence set that reaches or approaches the theoretical boundary under the same limiting conditions.The 3-ary hopping sequence is constructed by Coulter-Matthews decimation of m-sequence,and its two-dimensional Hamming correlation value is calculated by algebraic method.The trace function is a special kind of difference balanced function.Based on the difference balanced function and the interleaving technique on the finite field?Firstly,select the appropriate difference balance function as the initial sequence,secondly choose any permutation on the finite field and add the initial sequence as the base sequence,and finally interleave the base sequence with a suitable shift sequence to establish the optimal frequency hopping sequence set in the low collision region.Then,a new set of hopping sequences is constructed based on a combination of polynomials and trace functions.Polynomial has flexible parameters,and the sequence set based on polynomial contains a larger number of hopping sequences,which can be applied to communication systems to accommodate more users.The theoretical bounds of two-dimensional Hamming correlation values of hopping sequence sets constructed by polynomial and trace functions are proposed.The hopping sequence sets are constructed based on binomial,modular function and trace function methods,there two-dimensional Hamming are analyzed by exponential sums.Finally,this thesis considers Gaussian integers taken from the residue class determined by the prime p and constructs a perfect or nearly perfect p-1-degree balanced Gaussian integer sequence and develops the specific steps to implement the sequence.The polyphase sequence set and the complementary polyphase sequence set on the unit circle of the complex plane are constructed by means of the addictive character and the multiplicative character.The constructed sequence set has new and more flexible parameters.