Generation of “Optimal” PN Sequences for Use in Direct Sequence Spread Spectrum

Pseudorandom noise (PN) sequences are used to spread and recover data in direct-sequence spread spectrum (DSSS) transceivers. We consider the problem of designing multiple PN sequences that are to be used as pilot signals and spreading sequences for transceivers whose clocks are not synchronized.Because the transceivers are unsynchronized, there will be phase shifts between the receiver and the transmitter, and in order for such a system to work well, the PN sequences should have three properties. The pilot signal and the spreading signal that are used by each user should be (nearly) orthogonal to one another. The cyclic autocorrelation of each sequence should be as small as possible (for non-zero shifts). Finally, the cyclic cross-correlation between pilot and data sequences corresponding to different users should be as small as possible.We consider a moderately simplified version of the problem and show that drawing sequences at random can be used to produce many good sequences, and is, in this sense, better than using Gold sequences when designing such systems.