Spectrum Sensing Algorithms via Finite Random Matrices

In cognitive radio networks, cooperative spectrum sensing typically requires two essential phases: the phase of primary user's signal detection by cognitive users and the phase of initial detection result reporting from the cognitive users to a fusion center, which are referred to as detection and reporting phases, respectively. Common control channels (also called dedicated reporting channels) from the cognitive users to fusion center are assumed in previous research to avoid interfering with the primary user in the reporting phase. This, however, requires additional channel resources and increases implementation complexity due to the dedicated reporting channels management. In this paper, we propose an alternative cooperative spectrum sensing framework without dedicated reporting channels and present an interference analysis of its impact on primary users. We show that the interference caused by the proposed scheme is controllable and can be constrained to satisfy a given primary user's quality-of-service (QoS) requirement. By jointly considering the detection and reporting phases, we further examine the receiver operating characteristics (ROC) performance of the proposed cooperative spectrum sensing scheme in Rayleigh fading environment. Numerical results illustrate that, with a guaranteed detection probability constraint, a minimized false alarm probability can be achieved through an optimization of the time durations between the detection and reporting phases.

Standard condition number (SCN) detector is a promising detector that can work effectively in uncertain environments. In this paper, we consider a Cognitive Radio (CR) with large number of antennas (eg. Massive MIMO) and we provide an accurate and simple closed form approximation for the SCN distribution using the generalized extreme value (GEV) distribution. The approximation framework is based on the moment-matching method and the expressions of the moments are approximated using bi-variate Taylor expansion and results from random matrix theory. In addition, the performance probabilities and decision threshold are also considered as they have a direct relation to the distribution. Simulation results show that the derived approximation is tightly matched to the condition number distribution.

In this paper, we implement energy detection (ED) based spectrum sensing using NI USRP 2942R software defined radio platform. It is observed that in practical scenario ED scheme gives poor performance at low gain (G) values. To overcome the shortcomings of energy detection, we propose eigenvalue based detection of the primary user (PU) signal, where, the ratio of the maximum eigenvalue to the average eigenvalue is used to detect the PU signal. Further, the experimental studies show that proposed technique gives optimum probability of detection. It has been observed that the proposed technique outperforms the ED based detection even if the Tx-Rx separation increases.

In the 70’s, Robert May demonstrated that complexity creates instability in generic models of ecological networks having random interaction matrices A. Similar random matrix models have since been applied in many disciplines. Central to assessing stability is the “circular law” since it describes the eigenvalue distribution for an important class of random matrices A. However, despite widespread adoption, the “circular law” does not apply for ecological systems in which density-dependence operates (i.e., where a species growth is determined by its density). Instead one needs to study the far more complicated eigenvalue distribution of the community matrix S = DA, where D is a diagonal matrix of population equilibrium values. Here we obtain this eigenvalue distribution. We show that if the random matrix A is locally stable, the community matrix S = DA will also be locally stable, providing the system is feasible (i.e., all species have positive equilibria D > 0). This helps explain why, unusually, nearly all feasible systems studied here are locally stable. Large complex systems may thus be even more fragile than May predicted, given the difficulty of assembling a feasible system. It was also found that the degree of stability, or resilience of a system, depended on the minimum equilibrium population.

Based on random matrix theory (RMT), a blind target detection algorithm for bistatic MIMO radar is investigated under correlated noise. In relatively snapshot-starving scenarios in which the number of snapshots is comparable in magnitude to the number of the arrays, robust detection performance of the proposed algorithm can be guaranteed. Exploiting the standard condition number (SCN) detector, a novel decision threshold under correlated noise is derived by the use of Stieltjes transform and multiplicative free convolution. The proposed algorithm does not require any prior information of the noise variance and the target scattering matrix. Compared with the existing target detector using M-P law-based threshold, the proposed algorithm significantly improves the robustness of target detection in bistatic MIMO radar under correlated noise environment. Simulations are conducted to illustrate its effectiveness.

Cognitive radio (CR) is seen as a promising technology to make radio spectrum usage more effective by providing an opportunistic access for secondary users to the licensed spectrum areas. CR systems need to detect the presence of a primary user (PU) signal by continuously sensing the spectrum area of interest. Radiowave propagation effects like fading and shadowing often complicate sensing of spectrum holes because the PU signal can be weak in a particular area. Cooperative spectrum sensing is seen as a prospective solution to enhance the detection of PU signals. This paper studies distributed spectrum sensing in a cognitive radio context. We investigate distributed energy detection schemes without using any fusion center. We propose the usage of distributed, diffusion least mean square (LMS) type of power estimation algorithms. In this paper an Adapt and Combine (ATC) diffusion based power estimation scheme is proposed and the performance is compared with the Combine and Adapt (CTA) and ring-around schemes in a common framework. The PU signal is assumed to be slowly fading. We analyse the resulting energy detection performance and verify the theoretical findings through simulations.

The problem of full-duplex primary users (PUs) signal extraction is studied for cognitive radio networks, and the polarization Jones vector distance (PJVD) is used as the extraction metric. Based on the orientation and magnitude difference of the signal samples from different PUs, the PJVD based signal extraction (PJVD-SE) can efficiently detect each PU's signal polarization by calculating the PJVD between any two samples. Due to the Gaussian distributed noise, the resultant PJVD for primary samples is noncentral chi-squared distributed. Based on the distribution, the extraction error probability is investigated. Theoretical analysis shows that the proposed PJVD-SE technique outperforms the polarization similarity based technique in terms of both error probability and computation complexity. It is found that the performance gain is proportional to the SU's antenna number, PUs' polarization angle and PUs' signal amplitude difference. In addition, the presented analytical studies are verified through extensive simulation results and the performance of PJVD-SE is validated.

In order to detect the presence of the primary user signal with high probability, spectrum sensing is a fundamental requirement to achieve the goal of cognitive radio (CR). This ensures efficient utilization of the spectrum. Energy detection is one of the technique to detect the primary users that are receiving data within the communication range of a CR user. In this work, detection performance of the primary user (PU) signal on CR receiver is investigated. In particularly, the OFDM based CR receiver detect the primary user OFDM signal, where CR receiver is equipped with multiple antennas based energy detector. We observe significant improvement in primary user detection with SLC based energy detection at the MIMO CRs in comparison to single antenna CRs.

In this paper, we exploit cooperative spectrum sensing technique for applications in a relay based cognitive radio network. Relays are assigned in cognitive radio networks to transmit the primary user's signal to a cognitive coordinator. This research is focused on the detection of primary user in single or multiple cognitive relay scenarios. The performance of energy detector is analyzed for independent Rayleigh fading channels. False alarm and detection probabilities are derived theoretically with or without direct communication between the primary user and the cognitive coordinator. An upper bound is also given for detection probability. Our analysis is validated by numerical and simulation results.

Energy detection (ED) technique is a vastly used sensing technique in CRNs because of its operational simplicity. However at low SNR, the performance of ED is badly degraded. Matched Filter (MF) detection is an alternate sensing technique at low SNR, as it increases SNR of the received signal. MF detector gives far better performance when compared to ED at low SNR. But the problem with MF detector is that it must have priori knowledge about Primary User (PU) signal, therefore we need dedicated MF detector for each PU. Motivated by above drawback of ED and MF in this paper we proposed a new MF technique by which requirement of priori knowledge about PU signal can be eliminated as well as performance at low SNR is improved. At the MF detector front end, we perform blind estimation of PU signal parameters and accordingly update the coefficient of MF transfer function. Blind Estimation of signal parameters solves the problem of having priori information about PU signal for MF detector. Performance analysis and comparison of ED, conventional MF detector and proposed MF detector also have been done in this paper which show that the proposed MF detector perform better than ED and almost same as the conventional MF detector.

This paper considers a Fractional Sampling (FS) technique to enhance the Spectrum Sensing (SS) efficiency of a Cognitive Radio (CR) using a decision statistic based on asymptotic Random Matrix Theory (RMT). Firstly, the effect of noise correlation on eigenvalue based SS is studied analytically and by numerical evaluation. Secondly, new bounds for the Standard Condition Number (SCN) are proposed to enhance the SS efficiency in correlated noise scenarios. It is shown that proposed FS method can enhance SS efficiency up to certain FS rates at the expense of receiver complexity and no performance advantage is obtained if the FS rate is increased beyond this limit. As a result, a method for determining the operating point for the FS rate in terms of sensing performance and complexity is suggested.

Many cognitive radio (CR) networks adopt the collaborative sensing strategy that combines the sensing results of multiple CR stations, for getting the better primary user (PU) detection performance. In the practical CR networks with collaborative sensing, since a station reports the sensing result to a fusion center through a message, the reporting overhead is not negligible. In this paper, we design a sensing management scheme for CR networks, while taking this reporting overhead into account. First, we formulate an optimization problem that aims at finding the optimal number of sensing stations which collaborate to maximize the PU detection probability for given sensing/reporting time. Then, we propose a heuristic scheme to efficiently select the collaborative sensing stations, without a priori information for the locations of stations. Furthermore, we determine the optimal sensing interval for minimizing the PU detection delay while maintaining the CR channel utilization to a target value, by using a Markov analysis. The simulation results show that the proposed sensing management scheme significantly improves the PU detection performance.

The dimension boundary between finite random matrices and infinite random matrices is originally defined in this letter. The proposed boundary provides a theoretical approach to classify random matrices based on their dimensions. Two methods are proposed to determine the dimension boundary. One is based on the eigenvalue distribution and the other is based on the eigenvalue interval. In particular, a boundary-based threshold generation scheme in cognitive radio networks is studied. The theoretical analysis and numerical results verify the proposed dimension boundary and the corresponding boundary decision methods.

Cognitive radio systems are helpful to access the unused spectrum using the popular technique, referred to as spectrum sensing. Spectrum sensing involves the detection of primary user (PU) signal using dynamic spectrum access. Cooperative spectrum sensing takes advantage of the spatial diversity in multiple cognitive radio user networks to improve the sensing accuracy. Though the cooperative spectrum sensing schemes significantly improve the sensing accuracy, it requires the noise variance and channel state information which may lead to transmission overhead. To overcome the drawbacks in conventional cooperative spectrum sensing, this paper proposes a fuzzy system based cooperative spectrum sensing. Selection combining (SC) and maximum ratio combining (MRC) are used at fuzzy based fusion center to obtain the value of the sensing energy. These energy values are utilized in finding the presence of PU, results in improved sensing accuracy. In addition, an intelligent fuzzy fusion algorithm determines the PU presence without the channel state information based on multiple threshold values. Simulation results show that the proposed scheme outperforms the existing schemes in terms of sensing accuracy.

Random matrix theory and symmetric spaces