De Bruijn sequences for DS/CDMA transmission: Efficient generation, statistical analysis and performance evaluation

Nowadays, Direct Sequence Code Division Multiple Access (DS/CDMA) still represents the core technology for the physical layer of several commercially-remunerative applications and standards, ranging from cellular networking, radiolocalization, satellite communications, automotive radar, etc. A very critical issue of Spread Spectrum and CDMA is still represented by the necessity of keeping the probability of intercept as lowest as possible, therefore, a secure information hiding must be guaranteed at the physical layer. The use of De Bruijn binary sequences may represent a valuable solution to the aforesaid issue. De Bruijn sequences are nonlinear shift register sequences, whose sets are characterized by a cardinality much larger than the sequence length. This paper aims at considering some significant aspects about the usage of De Bruijn sequences in DS/CDMA, not yet addressed by prior works: the performance of De Bruijn sequences in asynchronous DS/CDMA transmission is assessed by means of explicit computations of multi-user interference statistics (variance and kurtosis), and closed form Bit-Error-Probability (BEP) analytic expressions. Numerical results on the obtained BEP after Reed-Solomon coding evidence that, when randomly selected, De Bruijn sequences perform very close to Gold sequences having the same length. The performance provided by De Bruijn sequences get remarkably better than the Gold ones when a proper selection procedure, aimed at minimizing the pairwise aperiodic cross-correlation, is adopted. The selection procedure and the corresponding results are discussed in details within the paper.