PERFORMANCE ANALYSIS OF SOME EIGEN-BASED HYPOTHESIS TESTS FOR COLLABORATIVE SENSING

Pascal Bianchi (1) , Jamal Najim (2) , Mylène Maïda (3) , Merouane Debbah (4)

1 Télécom ParisTech
2 LTCI - Laboratoire Traitement et Communication de l'Information
3 LM-Orsay - Laboratoire de Mathématiques d'Orsay
4 E3S - Supélec Sciences des Systèmes

In this contribution, we provide a theoretical study of two hypothesis tests allowing to detect the presence of an unknown transmitter using several sensors. Both tests are based on the analysis of the eigenvalues of the sampled covariance matrix of the received signal. The Generalized Likelihood Ratio Test (GLRT) derived in [1] is analyzed under the assumption that both the number K of sensors and the length N of the observation window tend to infinity at the same rate: K/N → c ∈ (0, 1). The GLRT is compared with a test based on the condition number used which is used in cognitive radio applications. Using results of random matrix theory for spiked models and tools of Large Deviations, we provide the error exponent curve associated with both test and prove that the GLRT outperforms the test based on the condition number.

Domains: Computer Science [cs]; Information Theory [cs.IT]; Mathematics [math]; Information Theory [math.IT]

Pascal Bianchi, Jamal Najim, Mylène Maïda, Merouane Debbah. PERFORMANCE ANALYSIS OF SOME EIGEN-BASED HYPOTHESIS TESTS FOR COLLABORATIVE SENSING. IEEE Workshop in Statistical Signal Processing (SSP-09), Aug 2009, United Kingdom. 4 p. ⟨hal-00447037⟩