A review on spectrum sensing for cognitive radio: challenges and solutions <s> Neyman-Pearson Theorem <s> The standard analysis of the radiometric detectability of a spread-spectrum signal assumes a background of stationary, white Gaussian noise whose power spectral density can be measured very accurately. This assumption yields a fairly high probability of interception, even for signals of short duration. By explicitly considering the effect of uncertain knowledge of the noise power density, it is demonstrated that detection of these signals by a wideband radiometer can be considerably more difficult in practice than is indicated by the standard result. Worst-case performance bounds are provided as a function of input signal-to-noise ratio (SNR), time-bandwidth (TW) product and peak-to-peak noise uncertainty. The results are illustrated graphically for a number of situations of interest. It is also shown that asymptotically, as the TW product becomes large, the SNR required for detection becomes a function of noise uncertainty only and is independent of the detection parameters and the observation interval. > <s> BIB001 </s> A review on spectrum sensing for cognitive radio: challenges and solutions <s> Neyman-Pearson Theorem <s> Preface I. Introduction II. Elements of Hypothesis Testing III. Signal Detection in Discrete Time IV. Elements of Parameter Estimation V. Elements of Signal Estimation VI. Signal Detection in Continuous Time VII. Signal Estimation in Continuous Time References Index <s> BIB002 </s> A review on spectrum sensing for cognitive radio: challenges and solutions <s> Neyman-Pearson Theorem <s> It has recently been shown that multiple-input multiple-output (MIMO) antenna systems have the potential to improve dramatically the performance of communication systems over single antenna systems. Unlike beamforming, which presumes a high correlation between signals either transmitted or received by an array, the MIMO concept exploits the independence between signals at the array elements. In conventional radar, target scintillations are regarded as a nuisance parameter that degrades radar performance. The novelty of MIMO radar is that it takes the opposite view; namely, it capitalizes on target scintillations to improve the radar's performance. We introduce the MIMO concept for radar. The MIMO radar system under consideration consists of a transmit array with widely-spaced elements such that each views a different aspect of the target. The array at the receiver is a conventional array used for direction finding (DF). The system performance analysis is carried out in terms of the Cramer-Rao bound of the mean-square error in estimating the target direction. It is shown that MIMO radar leads to significant performance improvement in DF accuracy. <s> BIB003 </s> A review on spectrum sensing for cognitive radio: challenges and solutions <s> Neyman-Pearson Theorem <s> In this letter, we consider cooperative spectrum sensing based on energy detection in cognitive radio networks. Soft combination of the observed energies from different cognitive radio users is investigated. Based on the Neyman-Pearson criterion, we obtain an optimal soft combination scheme that maximizes the detection probability for a given false alarm probability. Encouraged by the performance gain of soft combination, we further propose a new softened hard combination scheme with two-bit overhead for each user and achieve a good tradeoff between detection performance and complexity. <s> BIB004 </s> A review on spectrum sensing for cognitive radio: challenges and solutions <s> Neyman-Pearson Theorem <s> In this paper, we propose a soft decision based cooperative sensing method for cognitive radio (CR) in ad-hoc networks. A CR can sense a surrounding radio environment and adapt to the environment by the reconfigurability to achieve more effective frequency utilization. Observing the environment, CR should detect presence or absence of primary user and exploits this information to opportunistically provide communication among secondary users while performance of primary user should not be deteriorated by the secondary users. Because of multi- path fading or shadowing, the detection of primary users may be significantly difficult. For this problem, cooperative sensing (CS), where gathered observations obtained by multiple users is utilized to achieve higher performance of detection, has been investigated. We propose a soft decision based CS where test statistic used in traditional single user energy detection is treated as soft decision information. The detector is designed analytically, i.e., the statistic of the performance, detection probability and given false alarm, can be obtained analytically. By computer simulations, we have presented as follows; validity of analysis and that the CS has better performance compared to non-cooperative sensing. In addition, we have presented the detection performance of cooperative sensing when there are considerable differences regarding signal to noise ratio among users. <s> BIB005 </s> A review on spectrum sensing for cognitive radio: challenges and solutions <s> Neyman-Pearson Theorem <s> Superiority of multiple-input multiple-output (MIMO) radars over conventional phased array radars has been recently shown in many aspects. MIMO radars have better detection performance and can extract target information more precisely than phased array radars. In this paper, the problem of target detection using temporal coherent pulse terrain is considered for MIMO radars. We have introduced a structure that is suitable for coherent processing. Based on this structure, we have formulated this problem as a hypothesis test. One decision rule is developed for detection of target with unknown amplitude embedded in additive white gaussian noise (AWGN) with known power using the generalized likelihood ratio test (GLRT). Another adaptive scheme for the case of unknown power is presented. We have also proposed an ad-hoc constant false alarm rate (CFAR) detector against AWGN with unknown power. Performance of these detectors have been evaluated analytically. The results show the superiority of the MIMO radars with temporal coherent processing over the conventional phased arrays. <s> BIB006
The Neyman-Pearson (NP) theorem  BIB002  states that, for a given probability of false alarm, the test statistic that maximizes the probability of detection is the likelihood ratio test (LRT) defined as where p(·) denotes the probability density function (PDF), and x denotes the received signal vector that is the aggregation of x(n), n = 0, 1, . . . , N − 1. Such a likelihood ratio test decides H 1 when T LRT (x) exceeds a threshold γ, and H 0 otherwise. The major difficulty in using the LRT is its requirements on the exact distributions given in  . Obviously, the distribution of random vector x under H 1 is related to the source signal distribution, the wireless channels, and the noise distribution, while the distribution of x under H 0 is related to the noise distribution. In order to use the LRT, we need to obtain the knowledge of the channels as well as the signal and noise distributions, which is practically difficult to realize. If we assume that the channels are flat-fading, and the received source signal sample s i (n)'s are independent over n, the PDFs in LRT are decoupled as If we further assume that noise and signal samples are both Gaussian distributed, that is, η(n) ∼ N (0, σ 2 η I) and s(n) ∼ N (0, R s ), the LRT becomes the estimator-correlator (EC)  detector for which the test statistic is given by From (4), we see that R s (R s + 2σ 2 η I) −1 x(n) is actually the minimum-mean-squared-error (MMSE) estimation of the source signal s(n). Thus, T EC (x) in (7) can be seen as the correlation of the observed signal x(n) with the MMSE estimation of s(n). The EC detector needs to know the source signal covariance matrix R s and noise power σ 2 η . When the signal presence is unknown yet, it is unrealistic to require the source signal covariance matrix (related to unknown channels) for detection. Thus, if we further assume that R s = σ 2 s I, the EC detector in (7) reduces to the well-known energy detector (ED) BIB001  for which the test statistic is given as follows (by discarding irrelevant constant terms): Note that for the multi-antenna/receiver case, T ED is actually the summation of signals from all antennas, which is a straightforward cooperative sensing scheme BIB004 BIB005  . In general, the ED is not optimal if R s is non-diagonal. If we assume that noise is Gaussian distributed and source signal s(n) is deterministic and known to the receiver, which is the case for radar signal processing BIB003 BIB006  , it is easy to show that the LRT in this case becomes the matched filtering-based detector, for which the test statistic is