Federico Penna

Cooperative spectrum sensing based on the limiting eigenvalue ratio distribution in wishart matrices

Recent advances in random matrix theory have spurred the adoption of eigenvalue-based detection techniques for cooperative spectrum sensing in cognitive radio. These techniques use the ratio between the largest and the smallest eigenvalues of the received signal covariance matrix to infer the presence or absence of the primary signal. The results derived so far are based on asymptotical assumptions, due to the difficulties in characterizing the exact eigenvalues ratio distribution. By exploiting a recent result on the limiting distribution of the smallest eigenvalue in complex Wishart matrices, in this paper we derive an expression for the limiting eigenvalue ratio distribution, which turns out to be much more accurate than the previous approximations also in the non-asymptotical region. This result is then applied to calculate the decision sensing threshold as a function of a target probability of false alarm. Numerical simulations show that the proposed detection rule provides a substantial improvement compared to the other eigenvalue-based algorithms.

Performance of Eigenvalue-Based Signal Detectors with Known and Unknown Noise Level

In this paper we consider signal detection in cognitive radio networks, under a non-parametric, multi-sensor detection scenario, and compare the cases of known and unknown noise level. The analysis is focused on two eigenvalue-based methods, namely Roys largest root test, which requires knowledge of the noise variance, and the generalized likelihood ratio test, which can be interpreted as a test of the largest eigenvalue vs. a maximum-likelihood estimate of the noise variance. The detection performance of the two considered methods is expressed by closed-form analytical formulas, shown to be accurate even for small number of sensors and samples. We then derive an expression of the gap between the two detectors in terms of the signal-to-noise ratio of the signal to be detected, and we identify critical settings where this gap is significant (e.g., low number of sensors and signal strength). Our results thus provide a measure of the impact of noise level knowledge and highlight the importance of accurate noise estimation.

Hybrid Cooperative Positioning Based on Distributed Belief Propagation

We propose a novel cooperative positioning algorithm that fuses information from satellites and terrestrial wireless systems, suitable for GPS-challenged scenarios. The algorithm is fully distributed over an unstructured network, does not require a fusion center, does not rely on fixed terrestrial infrastructure, and is thus suitable for ad-hoc deployment. The proposed message passing algorithm, named hybrid sum-product algorithm over a wireless network (H-SPAWN), is described and analyzed. A novel parametric message representation is introduced, to reduce computational and communication overhead. Through simulation, we show that H-SPAWN improves positioning availability and accuracy, and outperforms hybrid positioning algorithms based on conventional estimation techniques.

Exact non-asymptotic threshold for eigenvalue-based spectrum sensing

Eigenvalue-based detection is one of the most promising techniques proposed for spectrum sensing in cognitive radio as it is insensitive to the noise uncertainty problem. However, the eigenvalue-based detection schemes presented so far rely on asymptotic assumptions that are not suitable for many realistic scenarios, thus determining a substantial degradation of detection performance. In this paper, starting from the analytical distribution of the ordered eigenvalues of finite-dimension Wishart matrices, we derive an exact expression for the decision threshold as a function of the probability of false alarm. Since it is not based on asymptotical assumptions, the novel decision rule is valid for any, even small, number of samples and cooperating receivers. In addition to the exact expression, an alternative (approximated) formula is then derived to reduce the computational complexity. Simulation results show that the proposed detector, both with the exact and the approximated formula, outperforms the other existing eigenvalue-based techniques, especially when the receiver operates under non-asymptotical conditions.

Uniformly Reweighted Belief Propagation for Estimation and Detection in Wireless Networks

In this paper, we propose a new inference algorithm, suitable for distributed processing over wireless networks. The algorithm, called uniformly reweighted belief propagation (URW-BP), combines the local nature of belief propagation with the improved performance of tree-reweighted belief propagation (TRW-BP) in graphs with cycles. It reduces the degrees of freedom in the latter algorithm to a single scalar variable, the uniform edge appearance probability ρ. We provide a variational interpretation of URW-BP, give insights into good choices of ρ, develop an extension to higher-order potentials, and complement our work with numerical performance results on three inference problems in wireless communication systems: spectrum sensing in cognitive radio, cooperative positioning, and decoding of a low-density parity-check (LDPC) code.

Detecting and Counteracting Statistical Attacks in Cooperative Spectrum Sensing

In this paper we propose a novel Bayesian method to improve the robustness of cooperative spectrum sensing against misbehaving secondary users, which may send wrong sensing reports in order to artificially increase or reduce the throughput of a cognitive network. We adopt a statistical attack model in which every malicious node is characterized by a certain probability of attack. The key features of the proposed method are: (i) combined spectrum sensing, identification of malicious users, and estimation of their attack probabilities; (ii) use of belief propagation on factor graphs to efficiently solve the Bayesian estimation problem. Our analysis shows that the proposed joint estimation approach outperforms traditional cooperation schemes based on exclusion of the unreliable nodes from the spectrum sensing process, and that it nearly achieves the performance of an ideal maximum likelihood estimation if attack probabilities remain constant over a sufficient number of sensing time slots. Results illustrate that belief propagation applied to the considered problem is robust with respect to different network parameters (e.g., numbers of reliable and malicious nodes, attack probability values, sensing duration). Finally, spectrum sensing estimates obtained via belief propagation are proved to be consistent on average for arbitrary graph size.

Cramér-Rao Bound for Hybrid GNSS-Terrestrial Cooperative Positioning

In this contribution we derive an expression of the Cramér-Rao bound for hybrid cooperative positioning, where GNSS information is combined with terrestrial range measurements through exchange of peer-to-peer messages. These results provide a theoretical characterization of achievable performance of hybrid positioning schemes, as well as allow to identify critical network configurations and devise optimized node placement strategies.

Measurement-Based Analysis of Spectrum Sensing in Adaptive WSNs under Wi-Fi and Bluetooth Interference

As a consequence of the diffusion of wireless systems operating in the 2.4 GHz ISM band, harmful interference among heterogeneous networks is becoming a serious issue for their performance. This paper is focused on IEEE 802.15.4 WSNs undergoing the interference of co-located IEEE 802.11b/g WLANs or Bluetooth piconets. On the basis of energy measurements carried out using a standard-compliant testbed, the statistics of the interfering energy are characterized for an extensive set of traffic conditions. Then the impact of each interference pattern onto a practical WSN application is analyzed in terms of packet loss rate at the application layer. The last part of the paper introduces a channel selection algorithm based on the estimation of the information-theoretic capacity of the considered channels.

Uniformly reweighted belief propagation: A factor graph approach

Tree-reweighted belief propagation is a message passing method that has certain advantages compared to traditional belief propagation (BP). However, it fails to outperform BP in a consistent manner, does not lend itself well to distributed implementation, and has not been applied to distributions with higher-order interactions. We propose a method called uniformly-reweighted belief propagation that mitigates these drawbacks. After having shown in previous works that this method can sub-stantially outperform BP in distributed inference with pairwise interaction models, in this paper we extend it to higher-order interactions and apply it to LDPC decoding, leading performance gains over BP.

Probability of Missed Detection in Eigenvalue Ratio Spectrum Sensing

Eigenvalue-based detection is an efficient signal detection technique, recently introduced in the Cognitive Radio context to guarantee a reliable identification of primary users. In this paper we contribute to the theoretical analysis of this detection scheme by deriving a mathematical expression for the probability of missed detection as a function of the number of cooperating receivers, the number of samples and the signal-to-noise ratio of the primary user. The analysis is referred to a detector using as test statistic the ratio between the largest and the smallest eigenvalue of the covariance matrix. Along with previous results on the probability of false alarm, this contribution completes the performance evaluation of this type of detector.