1. A method for cognitive radio spectrum sensing of a signal, the method comprising: applying one or more pre-defined cyclostationary feature to a received signal having a wide spectrum to detect the presence of one or more modulated signals therein, wherein each of the one or more pre-defined cyclostationary feature is sparsely applied by randomly sampling over a pre-defined cyclic frequency domain of the received signal; and applying a reconstruction-less compressive sensing process comprising a matrix transform operation that structures nonlinear combination of low-rate samples of the modulation signals in the cyclic domain to generate a measurement matrix to classify the received signal based on the one or more applied pre-defined cyclostationary feature, wherein spectrums of the one or more modulation signals are sensed, via classification of patterns in the measurement matrix, without any reconstruction operation of the one or more modulation signals or signals associated therewith, including a L1 and/or L2 norm reconstruction operation.