The Inventors set forth a statistical framework, where a decision vector is obtained from a received sample vector through a non-linear transformation and a linear compression. The search is then performed by selecting an element of the vector through a decision rule. The system design is divided parts corresponding to the three sections of the scheme: (i) non-linear transformation; (ii) linear compression; and (iii) decision rule. The non-linear transformation improves the performance under different operating conditions. The linear compression is used to reduce the search computational complexity.
If the non-linear transformation is a monotonic function, the probability distribution functions of the variables at the output of the compression operation can be easily derived from the probability distribution functions of the variables at the input of the compression operation. The decision rule is designed by defining an objective function related to a performance metric, which can be written in terms of probability of selecting each element of the decision vector.