Abstract
We propose a simple algorithm for improving the MDL (minimum description length) estimator of the number of sources of signals impinging on multiple sensors. The algorithm is based on the norms of vectors whose elements are the normalized and nonlinearly scaled eigenvalues of the received signal covariance matrix and the corresponding normalized indexes. Such norms are used to discriminate the largest eigenvalues from the remaining ones, thus allowing for the estimation of the number of sources. The MDL estimate is used as the input data of the algorithm. Numerical results unveil that the so-called norm-based improved MDL (iMDL) algorithm can achieve performances that are better than those achieved by the MDL estimator alone. Comparisons are also made with the well-known AIC (Akaike information criterion) estimator and with a recently-proposed estimator based on the random matrix theory (RMT). It is shown that our algorithm can also outperform the AIC and the RMT-based estimator in some situations.
Highlights
The estimation of the number of sources of signals impinging on multiple sensors is a fundamental problem in communications and signal processing
This paper proposed an empirical algorithm for improving the performance of the minimum description length (MDL) estimator of the number of sources of signals impinging on multiple sensors
As shown by the numerical results, the proposed improved MDL (iMDL) algorithm achieves performances that are better than or equal to those achieved by the MDL estimator alone
Summary
The estimation of the number of sources of signals impinging on multiple sensors is a fundamental problem in communications and signal processing This number is important in itself in a huge number of applications [1,2,3,4,5,6,7,8,9], e.g., to determine the approximate number of neurons responding to some stimulus in the brain [10], to estimate the number of active muscles during an action for identifying the action and determining pathologies [11], to find the number of chemical elements in a mixture [12], to determine the number of speakers in a room with background noise and reverberation [13] or, yet, in a cognitive radio network, to estimate the number of active radio transmitters in a given area [14] or to find the best spectrum opportunities [15]. In [2], an RMT-based sequential hypothesis test is proposed, claiming high detection performance at low SNR, similar to the AIC estimator, and near consistency at large sample sizes, similar to the MDL estimator.
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