The spread spectrum signal detection problem is examined in colored noise with an unknown covariance matrix. When the receiver is equipped with a symmetrically spaced linear array, persymmetry exists in the received data. We exploit the persymmetric structures to design adaptive detectors according to the principles of generalized likelihood ratio test (GLRT), Wald test, and Rao test. It turns out that the proposed GLRT has the same form as the proposed Wald test, and the Rao test does not exist. We prove that the proposed detector exhibits a constant false alarm rate against the unknown noise covariance matrix. Numerical examples demonstrate that the proposed detector has better performance than its non-persymmetric counterpart.

Free space optical (FSO) communication systems provide high bandwidth in unregulated spectrum and act as a powerful line-of-sight wireless connectivity solution. The performance of FSO systems can be seriously impaired by fading as a result of atmospheric turbulence and/or pointing errors due to misalignment. In the context of FSO systems, relaying was proposed as an effective fading mitigation technique due to the fact that the variance is distance-dependent in turbulence channels. In this article, we present a unified performance analysis of multi-hop FSO systems over Double Generalized Gamma (DGG) turbulence channels with pointing error impairments. We assume amplify-and-forward relaying and consider both heterodyne detection and intensity modulation with direct detection. We derive tight closed-form expressions for the outage probability and bit error probability of both fixed-gain and channel state information (CSI)-assisted relaying in terms of the bivariate Fox-H functions and Fox-H functions, respectively. We further analyze asymptotic behavior of the outage probability in terms of simple elementary functions and obtain the achievable diversity orders. Diversity gain is found to be a function of atmospheric turbulence parameters, pointing error, detection type and the number of hops. Monte Carlo simulation results are further provided to verify the accuracy of the derived expressions.

In this paper, we investigate the performance analysis of multi-hop free space optical (FSO) systems over Double Generalized Gamma (DGG) turbulence fading with pointing error impairments assuming both heterodyne detection and intensity modulation with direct detection (IMlDD). We derive closed-form expressions for the outage probability in terms of the Fox-H function. We further analyze asymptotical signal-to-noise-ratio (SNR) behavior of the outage probability and obtain the achievable diversity orders. Monte-Carlo simulation results are provided to verify the accuracy of the derived expressions.

We investigate the spectrum sensing problem in a single-input-multiple-output cognitive radio system under in-phase and quadrature imbalance (IQI). To do this, the received signal model is obtained in the presence of IQI at the analog front-ends of both the primary and secondary users. We first use a preprocessing stage to mitigate the effect of receiver IQI (RX-IQI). It is found that the received matrix signal is composed of an unknown rank-2 matrix contaminated by the receiver noise matrix. Then, we apply the likelihood ratio test principle to develop three eigenvalue-based detectors. Analytical expressions for the false alarm probabilities of the proposed detectors are derived to adjust their detection thresholds, especially under noise variance uncertainty. Simulation results are provided to illustrate the spectrum sensing performance of the proposed detectors in comparison with existing detectors in the literature also to verify the analytical expressions derived for the false alarm probability. Our simulation results show that the proposed spectrum sensing algorithms are not susceptible to the RX-IQI effects. In addition, we analytically show that one of the proposed spectrum sensing algorithms has constant false alarm rate property with respect to the noise variance uncertainty.