Elbow estimation -based source enumeration method for LPI/LPD signals

Spectrum awareness is important in multiple military and civilian applications, while various low probability of detection (LPD) waveforms have been developed to hide transmissions. In order to detect an LPD signal, one must be able to deal with very low signal-to-noise ratios (SNRs) and small numbers of temporal samples (snapshots). The reason for the limited availability of snapshots is that the carrier frequencies of LPD signals are usually unknown. Specifically, unknown carrier frequencies necessitate fast scans over wide frequency ranges, whereby only few snapshots per frequency bin are obtained. We have developed a new non-parametric source enumeration method, whose novelty lies in the fact that it uses elbow estimation to separate the signal and noise eigenvalues from each other. Accordingly, we call the developed method elbow-based source enumeration (EBSE). We compared the performance of EBSE against three state-of-the-art methods, namely Akaike’s information criterion (AIC), the minimum description length (MDL) and the accumulated ratio of eigenvalue gaps (AREG). The three simulations we used for performance comparisons had small numbers of snapshots, and the main advantage of EBSE was that it always had the smallest absolute error in the small-SNR regime.