TY - GEN

T1 - On minimax robust detection of stationary Gaussian signals in white Gaussian noise

AU - Zhang, Wenyi

AU - Poor, H. Vincent

PY - 2010

Y1 - 2010

N2 - The problem of detecting a wide-sense stationary Gaussian signal process embedded in white Gaussian noise, where the power spectral density of the signal process exhibits uncertainty, is investigated. The performance of minimax robust detection is characterized by the exponential decay rate of the miss probability under a Neyman-Pearson criterion with a fixed false alarm probability, as the length of the observation interval grows without bound. A dominance condition is identified for the uncertainty set of spectral density functions, and it is established that, under the dominance condition, the resulting minimax problem possesses a saddle point, which is achievable by the likelihood ratio tests matched to a so-called dominated power spectral density in the uncertainty set. No convexity condition on the uncertainty set is required to establish this result.

AB - The problem of detecting a wide-sense stationary Gaussian signal process embedded in white Gaussian noise, where the power spectral density of the signal process exhibits uncertainty, is investigated. The performance of minimax robust detection is characterized by the exponential decay rate of the miss probability under a Neyman-Pearson criterion with a fixed false alarm probability, as the length of the observation interval grows without bound. A dominance condition is identified for the uncertainty set of spectral density functions, and it is established that, under the dominance condition, the resulting minimax problem possesses a saddle point, which is achievable by the likelihood ratio tests matched to a so-called dominated power spectral density in the uncertainty set. No convexity condition on the uncertainty set is required to establish this result.

UR - http://www.scopus.com/inward/record.url?scp=77955680266&partnerID=8YFLogxK

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U2 - 10.1109/ISIT.2010.5513375

DO - 10.1109/ISIT.2010.5513375

M3 - Conference contribution

AN - SCOPUS:77955680266

SN - 9781424469604

T3 - IEEE International Symposium on Information Theory - Proceedings

SP - 1628

EP - 1632

BT - 2010 IEEE International Symposium on Information Theory, ISIT 2010 - Proceedings

T2 - 2010 IEEE International Symposium on Information Theory, ISIT 2010

Y2 - 13 June 2010 through 18 June 2010

ER -