Estimating the number of sources in white Gaussian noise: simple eigenvalues based approaches

Estimating the number of sources is a key task in many array signal processing applications. Conventional algorithms such as Akaike's information criterion (AIC) and minimum description length (MDL) suffer from underestimation and overestimation errors. In this study, the authors propose four algorithms to estimate the number of sources in white Gaussian noise. The authors' proposed algorithms are categorised into two main categories; namely, sample correlation matrix (CorrM) based and correlation coefficient matrix (CoefM) based. Their proposed algorithms are applied on the CorrM and CoefM eigenvalues. They propose to use two decision statistics, which are the moving increment and the moving standard deviation of the estimated eigenvalues as metrics to estimate the number of sources. For their two CorrM based algorithms, the decision statistics are compared to thresholds to decide on the number of sources. They show that the conventional process to estimate the threshold is mathematically tedious with high computational complexity. Alternatively, they define two threshold formulas through linear regression fitting. For their two CoefM based algorithms, they re-define the problem as a simple maximum value search problem. Results show that the proposed algorithms perform on par or better than AIC and MDL as well as recently modified algorithms at medium and high signal-to-noise ratio (SNR) levels and better at low SNR levels and low number of samples, while using a lower complexity criterion function.