The detection of an active primary user (PU) by a secondary base station (SBS) is essential for an interweave cognitive radio (CR). This work proposes a Bayesian method for model order selection to the detection problem in a multi-PU single-SBS CR network, where the PUs and the SBS are equipped with multiple antennas. Each PU transmits separate known beacon sequences when they are active but the multiple-input multiple-output (MIMO) channels from the PUs to SBS are not known. We select a Bayesian model among potential models of the received beacon sequences to decide the number of active PUs. It is accomplished by imposing Zellner’sg-prior on the unknown MIMO channels, obtaining the Bayes factor (BF) between an alternative hypothesis and the null hypothesis, and evaluating the posterior probability from the BFs as the test statistic. The resulting BF has an analytical form in terms of the hyperparametergfrom the prior. We develop three methods to address the unknowng. The first method assigns the inverse-gamma hyperprior togand uses the expectation of BF overginstead. The second estimatesglocally which is different for each data model and the third obtains thegestimate globally which is common to all candidate models. We conduct rigorous analysis for the proposed Bayesian selectors and determine the suitable ranges for the shape and scale parameters of theg-prior. In addition, analysis shows that they are consistent in fulfilling the information and model selection criteria. Numerical results reveal that the three proposed selectors have comparable performance and outperform the baselines Akaike information criterion (AIC), Bayesian information criterion (BIC), extended BIC (EBIC), and false discovery rate (FDR) at various settings of the signal-to-noise ratio (SNR), the length of beacon sequences, and the number of SBS antennas.

This paper proposes an objective Bayesian detector for the binary hypothesis testing problem in which the observation vectors are IID and follow multivariate Gaussian distribution under both the null and alternative hypotheses. The mean vector and covariance matrix under each hypothesis are not known, they also do not have special structure other than the covariance matrices are partially ordered in the positive definite cone with their difference positive semi-definite. An example of such a problem is the detection of Gaussian random signal in Gaussian noise. Non-informative priors are imposed on the unknown parameters for computing the marginals and evaluating the Bayes factor test statistic, where the prior for the covariance matrix is applied to the Cholesky factorization of the precision matrix. For the null hypothesis, we propose conjugate priors for the unknowns. For the alternative hypothesis, we propose uniform prior on the mean vector, and a class of objective priors that encompasses the Jeffreys, Independence Jeffreys, Geisser and Cornfield, Haar Measure and Reference priors for the precision matrix. The proposed priors enable closed-form expressions for the marginals and lead to an objective Bayes factor having the posteriors mainly governed by the data. The proposed detector is analyzed for justifying the priors used, deriving the theoretical moments, and approximating the false alarm and detection probability densities by the shifted Gamma distributions. The developed detector exhibits improvement in detection performance over the energy detector (ED) and the generalized likelihood ratio test (GLRT).

This paper develops an objective Bayesian detector for asserting the presence of primary user (PU) signal buried in additive noise/interference using a sequence of complex vector samples from a multi-antenna spectrum sensing system. The PU signal is zero mean Gaussian and the noise/interference is Gaussian with possibly non-zero mean and spatial correlation. No prior knowledge is available except the signal has non-zero power when present. For the noise only hypothesis, we propose a uniform prior for the mean, and a mix of the conjugate and uniform priors for the covariance matrix inverse in terms of the Cholesky factorization. For the signal presence hypothesis, we propose a class of objective priors that includes Jeffreys, independent Jeffreys, left-Haar measure and right-Haar measure priors. The test statistic is derived in closed-form and the setting of hyperparameter is devised to ensure the test is meaningful for the detection problem. Numerical results support the promising performance of the proposed detector over other state-of-the-art methods.

This paper proposes a Bayesian detector for spectrum sensing in a multi-antenna cognitive radio (CR) network in which no channel state information (CSI) is available. The Bayesian approach for detection necessitates a prior distribution of the CSI in terms of the spatial covariance matrix, and unfortunately it is often improper and cannot be applied directly. We shall introduce the use of the Fractional Bayes Factor (FBF) approach to handle improper prior, which in turn yields a well-defined Bayes factor as the test statistic for detection. A number of priors of the CSI are examined and a closed-form expression for the test statistics is derived. The developed Bayesian detector is compared with those by using the conjugate priors for both hypotheses and the generalized likelihood ratio test (GLRT), and it yields considerable improvement in detection performance.

This paper addresses the problem of optimizing the information rate of a multiple-input multiple-output (MIMO) secondary user (SU) in an underlay cognitive radio (CR) network when channel state information (CSI) from the SU to the primary user (PU) is inaccurate. Rather than applying the commonly used interference temperature metric, the proposed SU transmit precoder limits the interference leakage rate (LR) to maintain the quality of service (QoS) for the PU. We model the uncertainty in CSI as deterministic with the Schatten norm and apply the worst-case principle to derive a robust solution. Two solution methods are proposed to address the design with the LR metric. The first simplifies the LR metric that is valid under the low interference-to-noise ratio (INR) condition and the second uses an iterative linearization technique. We demonstrate the performance of the proposed solutions by numerical simulations.

This paper addresses the problem of precoder design that maximizes the throughput of a secondary user (SU) in an underlay multiple-input multiple-output cognitive radio network, where the channel state information (CSI) from the SU to the primary user (PU) is unavailable or inaccurate. The design maintains the quality of service for the PU through an interference amount measure in terms of the interference temperature or the leakage rate. For the case of unknown CSI, we propose an iterative adaptation algorithm by exploiting the side information in the primary communication network. For the case of imperfect CSI, we model the amount of uncertainty to be within a convex set defined by the Schatten norm and apply the maximin optimization to obtain the solution. To complete this paper, we derive the conditions on the CSI uncertainty radius under which the robust design with imperfect CSI would not perform better than the one with unknown CSI, when using the interference temperature metric. The proposed techniques are supported by numerical simulations.