Chintha Tellambura

Energy Detection Based Cooperative Spectrum Sensing in Cognitive Radio Networks

Detection performance of an energy detector used for cooperative spectrum sensing in a cognitive radio network is investigated over channels with both multipath fading and shadowing. The analysis focuses on two fusion strategies: data fusion and decision fusion. Under data fusion, upper bounds for average detection probabilities are derived for four scenarios: 1) single cognitive relay; 2) multiple cognitive relays; 3) multiple cognitive relays with direct link; and 4) multi-hop cognitive relays. Under decision fusion, the exact detection and false alarm probabilities are derived under the generalized k-out-of-n fusion rule at the fusion center with consideration of errors in the reporting channel due to fading. The results are extended to a multi-hop network as well. Our analysis is validated by numerical and simulation results. Although this research focuses on Rayleigh multipath fading and lognormal shadowing, the analytical framework can be extended to channels with Nakagami-m multipath fading and lognormal shadowing as well.

Performance of an Energy Detector over Channels with Both Multipath Fading and Shadowing

This paper analyzes the performance of an energy detector over wireless channels with composite multipath fading and shadowing effects. These effects are modeled by using the K and K_G channel models. Closed-form average detection probabilities are derived for both K and K_G channel models for the no-diversity reception case. A simple approximation is also derived for large values of energy threshold in the energy detector. The analysis is then extended to cases with diversity receptions including maximal ratio combining (MRC) and selection combining (SC). Analytical results are verified by Monte Carlo simulation and by numerical methods. Receiver operating characteristic (ROC) curves are presented for different degrees of multipath fading and shadowing. Finally, the Rayleigh-lognormal distribution and the K distribution are numerically compared, and the validity of the K channel model for representing the impact of shadowing on the performance of energy detection is affirmed.

Analysis of area under the ROC curve of energy detection

A simple figure of merit to describe the performance of an energy detector is desirable. The area under the receiver operating characteristic (ROC) curve, denoted (AUC), is such a measure, which varies between 1/2 and 1. If the detectors performance is no better than flipping a coin, then the AUC is 1/2 , and it increases to one as the detector performance improves. However, in the wireless literature, the AUC measure has gone unnoticed. In this paper, to address this gap, we comprehensively analyze the AUC of an energy detector with no-diversity reception and with several popular diversity schemes. The channel model is assumed to be Nakagami-m fading. First, the average AUC is derived for the case of no-diversity reception. Second, the average AUC is derived for diversity reception cases including maximal ratio combining (MRC), square-law combining (SLC) and selection combining (SC). Further, for Rayleigh fading channels, the impacts of channel estimation errors and fading correlations are analyzed. High SNR (signal-to-noise ratio) approximations and the detection diversity gain are also derived. The analytical results are verified by numerical computations and by Monte-Carlo simulations.

Optimal Bandwidth and Power Allocation for Sum Ergodic Capacity Under Fading Channels in Cognitive Radio Networks

This paper studies optimal bandwidth and power allocation in a cognitive radio network where multiple secondary users (SUs) share the licensed spectrum of a primary user (PU) under fading channels using the frequency division multiple access scheme. The sum ergodic capacity of all the SUs is taken as the performance metric of the network. Besides the peak/average transmit power constraints at the SUs and the peak/average interference power constraint imposed by the PU, total bandwidth constraint of the licensed spectrum is also taken into account. Optimal bandwidth allocation is derived in closed-form for any given power allocation. The structures of optimal power allocations are also derived under all possible combinations of the aforementioned power constraints. These structures indicate the possible numbers of users that transmit at nonzero power but below their corresponding peak powers, and show that other users do not transmit or transmit at their corresponding peak powers. Based on these structures, efficient algorithms are developed for finding the optimal power allocations.

Outage Probability of Decode-and-Forward Cognitive Relay in Presence of Primary User's Interference

In the presence of the primary users interference, the outage probability of a dual-hop decode-and-forward (DF) cognitive relay network (CRN) over Rayleigh fading channels is investigated. We first derive the exact expression for the outage probability, using which the impact of different system parameters on the outage performance is presented in the asymptotic regimes. In addition, the asymptotic outage probability is also derived in the high signal-to-noise ratio (SNR) regime.

On the Performance of Cognitive Underlay Multihop Networks with Imperfect Channel State Information

This paper proposes and analyzes cognitive multihop decode-and-forward networks in the presence of interference due to channel estimation errors. To reduce interference on the primary network, a simple yet effective back-off control power method is applied for secondary multihop networks. For a given threshold of interference probability at the primary network, we derive the maximum back-off control power coefficient, which provides the best performance for secondary multihop networks. Moreover, it is shown that the number of hops for secondary network is upper-bounded under the fixed settings of the primary network. For secondary multihop networks, new exact and asymptotic expressions for outage probability (OP), bit error rate (BER) and ergodic capacity over Rayleigh fading channels are derived. Based on the asymptotic OP and BEP, a pivotal conclusion is reached that the secondary multihop network offers the same diversity order as compared with the network without back off. Finally, we verify the performance analysis through various numerical examples which confirm the correctness of our analysis for many channel and system settings and provide new insight into the design and optimization of cognitive multihop networks.

Aggregate Interference Analysis for Underlay Cognitive Radio Networks

This paper investigates the aggregate interference on a primary user caused by a random number of cognitive radio transmitters distributed in a finite ring. A composite model involving path loss, Rayleigh fading, and shadowing is considered. The exact closed-form moment generating function and an accurate approximation are derived. The aggregate interference is shown to be accurately approximated by a Gamma distribution. The exact outage and an asymptotic approximation are derived.

MGF Based Analysis of Area under the ROC Curve in Energy Detection

The area under the receiver operating characteristic (ROC) curve (AUC), an important performance measure of the energy detector, is derived for Nakagami-m and η-μ fading channels. The analysis is based on the moment generating function (MGF) of the received signal-to-noise ratio (SNR). The derived closed-form expressions do not include special functions, thus reducing computational issues. The analytical framework can also be applied in cases with other fading channels, with diversity reception, or with cooperative spectrum sensing.

Unified Analysis of Low-SNR Energy Detection and Threshold Selection

For spectrum sensing in cognitive radio networks, the IEEE 802.22 standard requires the detection of primary signals with a signal-to-noise ratio (SNR) as low as -20 dB and receiver sensitivity as low as -116 dBm. Under such low-SNR levels, the performance of a conventional energy detector is analyzed in this paper. The analysis includes novel expressions for missed-detection probability and area under the receiver operating characteristic (ROC) curve. Thus, a unified framework covering fading channels, square-law diversity combining, and cooperative spectrum-sensing scenarios is developed. The detection threshold is optimized to minimize the total error rate subject to bounded false-alarm and missed-detection probabilities, which outperforms traditional detection threshold selection. Numerical results and Monte Carlo simulation results with the IEEE 802.22 sensing requirements are provided and discussed.

Performance of

Performance analysis of the p-norm detector to date has been limited to ad hoc approximations, nonfading channels, and Rayleigh fading. To overcome these limitations, we develop several analytical/numerical solutions for detection probability Pd and false alarm probability Pf, which are necessary to specify the receiver operating characteristic (ROC) curves of the p-norm detector. First, for nonfading channels (additive white Gaussian noise (AWGN) only), the moment-generating function (mgf) of the decision variable is derived in two forms: 1) closed form for even integer p and 2) series form for arbitrary p. To evaluate Pd and Pf, a numerical method utilizing the Talbot inversion is developed for case 1, and an infinite series expansion with convergence acceleration based on the e-algorithm is derived for case 2. As an alternative to mgf-based analysis, a Laguerre polynomial series is also used to derive new Pd and Pf approximations. Second, series-form mgf-based Pd expressions are derived for κ-μ and α-μ fading channels. Third, for antenna diversity reception, new p-law combining (pLC) and p-law selection (pLS) schemes are proposed. The performance of these combiners with the p-norm detector is derived for Nakagami-m fading and is compared with that of the classical maximal ratio combining (MRC) and selection combining (SC). Interestingly, both pLC and pLS perform similarly to SC at low signal-to-noise ratio (SNR) but outperform it at relatively high SNR, with pLC performing closer to the optimal MRC. Numerical results are presented to verify the derived results and to provide further insights.