Generation of Antipodal Random Vectors With Prescribed Non-Stationary 2-nd Order Statistics

A Look-Up-Table-based method is proposed to generate random instances of an antipodal n-dimensional vector so that its 2-nd order statistics are as close as possible to a given specification. The method is based on linear optimization and exploits column-generation techniques to cope with the exponential complexity of the task. It yields a LUT whose storage requirements are only O(n(3)) and thus are compatible with hardware implementation for non-negligible n. Applications are shown in the fields of Compressive Sensing and of Ultra Wide Band systems based on Direct Sequence - Code Division Multiple Acces.