Abstract
When we make a sequence by sampling every s digit of an M-sequence, the properties of the obtained sequence are already known. But the properties of randomly sampled M-sequence are not yet known. This paper describes the properties of the randomly sampled M-sequence.
The random sampling method is as follows. First, successive k-tuple of an M-sequence is generated and then using uniform random number Xi(0≤Xi<1), ([k·Xi]+1)'th digit of the k-tuple is chosen.
Autocorrelation function of the original M-sequence has a sharp peak at delay N (N: period of M-sequence), while ensemble averaged autocorrelation functions of the randomly sampled sequences have small peaks at several delays other than N. Mean values of the autocorrelation functions of the sequences are obtained theoretically as a function of the period of M-sequence and tuple length.
Maximum values of the ensemble averaged crosscorrelation functions between the randomly sampled sequences are also obtained theoretically and it is shown that these values are less than the maximum values of crosscorrelation functions between the original M-sequences.
