A CFAR based model order selection criterion for complex sinusoids

The model order selection problem for complex sinusoidal signals has often been tackled using Akaike information criterion (AIC), minimum description length principle (MDL) or maximum a posterior criterion (MAP). As a finite-length noise sequence (discrete-time noise signal) can be expressed as a summation of sinusoidal signals, we propose signal-energy-to-noise-power-ratio (SENR) to be considered in the model order selection problem. In our proposal, a predefined SENR threshold is used to decide whether a signal exists or not and the signal order can then be obtained. Since this new criterion is just like the constant false alarm rate (CFAR) detector, we call the new criterion the CFAR criterion. In this paper, the performances of the AIC, MDL, MAP and CFAR criteria are compared. Simulation results testify the correctness of our analysis and the superior performance of the CFAR criterion.