In this paper, we study some relationships between the detection and estimation theories for a bi... more In this paper, we study some relationships between the detection and estimation theories for a binary composite hypothesis test against and a related estimation problem. We start with a one-dimensional (1D) space for the unknown parameter space and one-sided hypothesis problems and then extend out results into more general cases. For one-sided tests, we show that the uniformly most powerful (UMP) test is achieved by comparing the minimum variance and unbiased estimator (MVUE) of the unknown parameter with a threshold. Thus for the case where the UMP test does not exist, the MVUE of the unknown parameter does not exist either. Therefore for such cases, a good estimator of the unknown parameter is deemed as a good decision statistic for the test. For a more general class of composite testing with multiple unknown parameters, we prove that the MVUE of a separating function (SF) can serve as the optimal decision statistic for the UMP unbiased test where the SF is continuous, differentiable, positive for all parameters under and is negative for the parameters under . We then prove that the UMP unbiased statistic is equal to the MVUE of an SF. In many problems with multiple unknown parameters, the UMP test does not exist. For such cases, we show that if one detector between two detectors has a better receiver operating characteristic (ROC) curve, 1 then using its decision statistic we can estimate the SF more -accurately, in probability. For example, the SF is the signal-to-noise ratio (SNR) in some problems. These results motivate us to introduce new suboptimal SF-estimator tests (SFETs) which are easy to derive for many problems. Finally, we provide some practical examples to study the relationship between the decision statistic of a test and the estimator of its corresponding SF.
EURASIP Journal on Wireless Communications and Networking, 2013
In the context of cognitive network architecture, an opportunistic cognitive receiver must identi... more In the context of cognitive network architecture, an opportunistic cognitive receiver must identify the present active networks. In this article, we propose an efficient algorithm for the identification of OFDM networks exploiting the pilot patterns used in these standards which are prescribed uniquely by their underlying standards. These pilots are inserted for the channel estimation and synchronization between the base stations and their users. The proposed generalized likelihood ratio test (GLRT) not only allows a cognitive observer to detect the active networks by analyzing the observed signals but also performs channel estimation, time-frequency synchronization as well as estimation of the noise variance. These informations are of a great interest for Quality of Service estimation in the purpose of an association with the base station. The proposed solution is applicable to the existing standards (e.g., LTE, WiMAX, WiFi), doesn't require any signaling overhead to be embedded on the pilot tones, is computationally inexpensive and only requires to know the pilot patterns. An other GLRT is proposed as a pre-detector which ignores the pilot information and allows to reduce the computational cost of the system for the cases where a large number of patterns/systems are to be tested.
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Papers by Saeed Gazor