A GLRT approach for detecting correlated signals in white noise in two MIMO channels

In this work, we consider a second-order detection problem where rank-p signals are structured by an unknown, but common, p-dimensional random vector and then received through unknown M x p matrices at each of two M-element arrays. The noises in each channel are independent with identical variances. We derive generalized likelihood ratio (GLR) tests for this problem when the noise variance is either known or unknown. The resulting detection problems may be phrased as two-channel factor analysis problems.The work of I. Santamaría and J. Vía has been supported by the Ministerio de Economía, Industria y Competitividad (MINECO) of Spain, and AEI/FEDER funds of the E.U., under grants TEC2013-47141-C4-R (RACHEL), TEC2016-75067-C4-4-R (CARMEN), and TEC2016-81900- REDT (KERMES)

Two-Channel Passive Detection Exploiting Cyclostationarity

This paper addresses a two-channel passive detection problem exploiting cyclostationarity. Given a reference channel (RC) and a surveillance channel (SC), the goal is to detect a target echo present at the surveillance array transmitted by an illuminator of opportunity equipped with multiple antennas. Since common transmission signals are cyclostationary, we exploit this information at the detector. Specifically, we derive an asymptotic generalized likelihood ratio test (GLRT) to detect the presence of a cyclostationary signal at the SC given observations from RC and SC. This detector tests for different covariance structures. Simulation results show good performance of the proposed detector compared to competing techniques that do not exploit cyclostationarity

Analysis and Design of Multiple-Antenna Cognitive Radios with Multiple Primary User Signals

We consider multiple-antenna signal detection of primary user transmission signals by a secondary user receiver in cognitive radio networks. The optimal detector is analyzed for the scenario where the number of primary user signals is no less than the number of receive antennas at the secondary user. We first derive exact expressions for the moments of the generalized likelihood ratio test (GLRT) statistic, yielding approximations for the false alarm and detection probabilities. We then show that the normalized GLRT statistic converges in distribution to a Gaussian random variable when the number of antennas and observations grow large at the same rate. Further, using results from large random matrix theory, we derive expressions to compute the detection probability without explicit knowledge of the channel, and then particularize these expressions for two scenarios of practical interest: 1) a single primary user sending spatially multiplexed signals, and 2) multiple spatially distributed primary users. Our analytical results are finally used to obtain simple design rules for the signal detection threshold.Comment: Revised version (14 pages). Change in titl

Passive detection of rank-one signals with a multiantenna reference channel

In this work we consider a two-channel passive detection problem, in which there is a surveillance array where the presence/absence of a target signal is to be detected, and a reference array that provides a noise-contaminated version of the target signal. We assume that the transmitted signal is an unknown rank-one signal, and that the noises are uncorrelated between the two channels, but each one having an unknown and arbitrary spatial covariance matrix. We show that the generalized likelihood ratio test (GLRT) for this problem rejects the null hypothesis when the largest canonical correlation of the sample coherence matrix between the surveillance and the reference channels exceeds a threshold. Further, based on recent results from random matrix theory, we provide an approximation for the null distribution of the test statistic.The work of I. Santamaría was supported by the Spanish Government through grants PRX14/0028 (Estancias de Movilidad de Profesores, Ministerio de Educación) and by project RACHEL (TEC2013-47141-C4-3-R) funded by the Ministerio de Economía y Competitividad (MINECO). The work of L. Scharf and D. Cochran was supported in part by a sub-contract with Matrix Research for research sponsored by the Air Force Research Laboratory under contract FA8650-14-D-1722