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**1 - 6**of**6**### Networks with Noise Variance Uncertainty

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All in-text references underlined in blue are linked to publications on ResearchGate, letting you access and read them immediately.

### Optimal Cooperative Sensing for Sensors Equipped with Multiple Antennas

"... Abstract—This paper considers multi-sensor multi-antenna spectrum sensing. First, it is assumed that all users are able to send their raw data to the fusion center. In this case the global optimial solution is the likelihood ratio test (LRT) using all the raw data. A simple closed-form expression fo ..."

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Abstract—This paper considers multi-sensor multi-antenna spectrum sensing. First, it is assumed that all users are able to send their raw data to the fusion center. In this case the global optimial solution is the likelihood ratio test (LRT) using all the raw data. A simple closed-form expression for the LRT is found. Although LRT is optimal, it is hardly useful in practice due to its reliance on the knowledge of primary user’s channels and noise powers of all users. Thus a method using the estimated channels and noise powers is proposed, which is called generalized LRT (GLRT). Secondly, the optimal fusion scheme (OFS) is found if each user computes its test statistic based on an eigenvalue based detection and sends the test statistic to the fusion center. Both GLRT and OFS need the SNR information of all users. To make the detections more practical, two totally blind detections, namely, approximated OFS and approximated GLRT, are proposed. Simulations are provided to support the results. I.

### Correspondence On the Eigenvalue-Based Spectrum Sensing and Secondary User Throughput

"... Abstract—In this paper, we study the tradeoff between sensing time and achievable throughput of the secondary user that employs robust eigenvalue-based spectrum sensing techniques in the presence of noise uncertainty. First, we study exact distributions of the test statistics for two types of robust ..."

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Abstract—In this paper, we study the tradeoff between sensing time and achievable throughput of the secondary user that employs robust eigenvalue-based spectrum sensing techniques in the presence of noise uncertainty. First, we study exact distributions of the test statistics for two types of robust eigenvalue-based sensing techniques, namely, the blind generalized likelihood ratio test (B-GLRT) detection and energy with minimum eigenvalue (EME) detection. The developed threshold setting is more accurate than benchmark methods in achieving a target constant false alarm rate (CFAR). Second, prior to the throughput analysis, the necessary asymptotic detection and false alarm probabilities under noise uncertainty are formulated for eigenvalue-based detectors such as max-imum eigenvalue detection (MED) and maximum–minimum eigenvalue (MME) detection. Finally, the throughput is maximized using eigenval-ue-based spectrum sensing techniques which are B-GLRT, EME, MME, and MED detectors. The results are compared with the commonly used energy detector (ED). An improved achievable throughput is obtained under low-signal-to-noise-ratio (SNR) regime by incorporating the robust eigenvalue-based techniques, which are insusceptible to noise uncertainty. Index Terms—Cognitive radio (CR), eigenvalue-based detection, sensing–throughput tradeoff, spectrum sensing. I.

### COOKED SUMMARY This cooked summary explains the main ideas of the paper ”Max-Min SNR Signal Energy based Spectrum Sensing Algorithms for Cognitive Radio Networks with Noise

"... Variance Uncertainty ” by referring the equation numbers in the paper. This cooked summary is very helpful for researchers in the field and who would like to know the novelty and key contribution of the paper without reading the whole text. Objective of the paper Given N samples, the objective is to ..."

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Variance Uncertainty ” by referring the equation numbers in the paper. This cooked summary is very helpful for researchers in the field and who would like to know the novelty and key contribution of the paper without reading the whole text. Objective of the paper Given N samples, the objective is to decide between H0 (the N samples contain noise only) and H1 (these N samples contain a transmitted signal + noise). Methodology • Express the baseband transmitted signal x(t) as in Equa-tion (1) of the paper. To do this we ASSUME that the transmitter pulse shaping filter is known to the cognitive receiver. • Introduce a linear combination scalars {αi}Li=1 and DE-FINE a new sample {ỹ[n]}Nn=1 as in Equation (3) (novel part). • Design {αi}Li=1 such that we can get two different signals from {ỹ[n]}Nn=1 such that the SNR of the first signal is different from the SNR of the second signal. This is possible by performing the following tasks: – Solve the optimization problem (6), substitute this optimal solution {αi}Li=1 in Equation (3) and set the resulting samples as {e[n]}Nn=1 (i.e., see Equation (14)) (novel part). – Solve the optimization problem (7), substitute this optimal solution {αi}Li=1 in Equation (3) and set the resulting samples as {z[n]}Nn=1 (i.e., see Equation (14)) (novel part). – Now it is clear that the SNR of z[n] is greater than (and is equal to) the SNR of e[n] under H1 (and H0) hypothesis, respectively. • Due to this mathematical outcome, we propose Equation (20) as our test statistics (novel part). • As we can see, Equation (20) will be closer to 0 and much greater than 0 under H0 and H1 hypothesis, respectively. • The Pf and Pd of this new test statistics is derived in (22) and (23). • All the explanation and analytical equations after Equa-tion (23) are to improve the test statistics (20) by taking into account the effect of synchronization between the transmitter and cognitive receiver, adjacent channel inter-ference, unknown pulse shaping filter and so on, which are very important for practical cognitive radio. ar X iv

### 1Wideband Sensing and Optimization for Cognitive Radio Networks with Noise Variance Uncertainty

"... IEEE Abstract—This paper considers wide-band spectrum sensing and optimization for cognitive radio (CR) networks with noise variance uncertainty. It is assumed that the considered wide-band contains one or more white sub-bands. Under this assumption, we consider throughput maximization of the CR net ..."

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IEEE Abstract—This paper considers wide-band spectrum sensing and optimization for cognitive radio (CR) networks with noise variance uncertainty. It is assumed that the considered wide-band contains one or more white sub-bands. Under this assumption, we consider throughput maximization of the CR network while appropriately protecting the primary network. We address this problem as follows. First, we propose novel ratio based test statistics for detecting the edges of each sub-band. Second, we employ simple energy comparison approach to choose one reference white sub-band. Third, we propose novel generalized energy detector (GED) for examining each of the remaining sub-bands by exploiting the noise information of the reference white sub-band. Finally, we optimize the sensing time (To) to maximize the CR network throughput using the detection and false alarm probabilities of the GED. The proposed GED does not suffer from signal to noise ratio (SNR) wall and outperforms the existing signal detectors. Moreover, the relationship between the proposed GED and conventional energy detector (CED) is quantified analytically. We show that the optimal To depends on the noise variance information. In particular, with 10TV bands, SNR=−20dB and 2s frame duration, we found that the optimal To is 28.5ms (50.6ms) with perfect (imperfect) noise variance scenario. Index Terms—Wideband cognitive radio, Spectrum sensing, Edge detection, SNR wall, Sensing Throughput tradeoff. I.

### 1Sensing Throughput Tradeoff for Cognitive Radio Networks with Noise Variance Uncertainty

"... Abstract—This paper proposes novel spectrum sensing al-gorithm, and examines the sensing throughput tradeoff for cognitive radio (CR) networks under noise variance uncertainty. It is assumed that there are one white sub-band, and one target sub-band which is either white or non-white. Under this ass ..."

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Abstract—This paper proposes novel spectrum sensing al-gorithm, and examines the sensing throughput tradeoff for cognitive radio (CR) networks under noise variance uncertainty. It is assumed that there are one white sub-band, and one target sub-band which is either white or non-white. Under this assumption, first we propose a novel generalized energy detector (GED) for examining the target sub-band by exploiting the noise information of the white sub-band, then, we study the tradeoff between the sensing time and achievable throughput of the CR network. To study this tradeoff, we consider the sensing time optimization for maximizing the throughput of the CR network while appropriately protecting the primary network. The sensing time is optimized by utilizing the derived detection and false alarm probabilities of the GED. The proposed GED does not suffer from signal to noise ratio (SNR) wall (i.e., robust against noise variance uncertainty) and outperforms the existing signal detectors. Moreover, the relationship between the proposed GED and conventional energy detector (CED) is quantified analytically. We show that the optimal sensing times with perfect and imperfect noise variances are not the same. In particular, when the frame duration is 2s, SNR = −20dB, and each of the bandwidths of the white and target sub-bands is 6MHz, the optimal sensing times are 28.5ms and 50.6ms with perfect and imperfect noise variances, respectively.