A review on spectrum sensing for cognitive radio: challenges and solutions <s> Practical Considerations and Future Developments <s> In a digital array, each receiver performs analog-to-digital-conversion (ADC), with the resulting digital data later combined via digital beamforming techniques. Since ADC is performed prior to beamforming, it is thus possible to enhance the dynamic range of each digital receiver through post-ADC array integration gain. Unfortunately, receiver correlation nonlinearities, such as spurious signals (spurs) or intermodulation distortion (intermods), across receivers can severely limit the achievable dynamic range enhancement. This paper proposes a methodology for mitigating the impact of receiver nonlinearities. In our approach the receiver input signals are carefully modified in a way that varies from channel to channel. The resulting signals are then processed by each digital receiver, introducing nonlinearities. Finally, the digital signals are corrected to restore the desired linear signal components. Examples are given of how this methodology can be applied to ADC, direct digital synthesizers (DDS), digital-to-analog converters (DAC), amplifiers, and mixers. In some cases, distortion is effectively reduced by a factor of N to N/sup 2/, where N is the number of receivers. <s> BIB001 </s> A review on spectrum sensing for cognitive radio: challenges and solutions <s> Practical Considerations and Future Developments <s> This paper considers the model problem of reconstructing an object from incomplete frequency samples. Consider a discrete-time signal f/spl isin/C/sup N/ and a randomly chosen set of frequencies /spl Omega/. Is it possible to reconstruct f from the partial knowledge of its Fourier coefficients on the set /spl Omega/? A typical result of this paper is as follows. Suppose that f is a superposition of |T| spikes f(t)=/spl sigma//sub /spl tau//spl isin/T/f(/spl tau/)/spl delta/(t-/spl tau/) obeying |T|/spl les/C/sub M//spl middot/(log N)/sup -1/ /spl middot/ |/spl Omega/| for some constant C/sub M/>0. We do not know the locations of the spikes nor their amplitudes. Then with probability at least 1-O(N/sup -M/), f can be reconstructed exactly as the solution to the /spl lscr//sub 1/ minimization problem. In short, exact recovery may be obtained by solving a convex optimization problem. We give numerical values for C/sub M/ which depend on the desired probability of success. Our result may be interpreted as a novel kind of nonlinear sampling theorem. In effect, it says that any signal made out of |T| spikes may be recovered by convex programming from almost every set of frequencies of size O(|T|/spl middot/logN). Moreover, this is nearly optimal in the sense that any method succeeding with probability 1-O(N/sup -M/) would in general require a number of frequency samples at least proportional to |T|/spl middot/logN. The methodology extends to a variety of other situations and higher dimensions. For example, we show how one can reconstruct a piecewise constant (one- or two-dimensional) object from incomplete frequency samples - provided that the number of jumps (discontinuities) obeys the condition above - by minimizing other convex functionals such as the total variation of f. <s> BIB002 </s> A review on spectrum sensing for cognitive radio: challenges and solutions <s> Practical Considerations and Future Developments <s> Suppose x is an unknown vector in Ropfm (a digital image or signal); we plan to measure n general linear functionals of x and then reconstruct. If x is known to be compressible by transform coding with a known transform, and we reconstruct via the nonlinear procedure defined here, the number of measurements n can be dramatically smaller than the size m. Thus, certain natural classes of images with m pixels need only n=O(m1/4log5/2(m)) nonadaptive nonpixel samples for faithful recovery, as opposed to the usual m pixel samples. More specifically, suppose x has a sparse representation in some orthonormal basis (e.g., wavelet, Fourier) or tight frame (e.g., curvelet, Gabor)-so the coefficients belong to an lscrp ball for 0<ples1. The N most important coefficients in that expansion allow reconstruction with lscr2 error O(N1/2-1p/). It is possible to design n=O(Nlog(m)) nonadaptive measurements allowing reconstruction with accuracy comparable to that attainable with direct knowledge of the N most important coefficients. Moreover, a good approximation to those N important coefficients is extracted from the n measurements by solving a linear program-Basis Pursuit in signal processing. The nonadaptive measurements have the character of "random" linear combinations of basis/frame elements. Our results use the notions of optimal recovery, of n-widths, and information-based complexity. We estimate the Gel'fand n-widths of lscrp balls in high-dimensional Euclidean space in the case 0<ples1, and give a criterion identifying near- optimal subspaces for Gel'fand n-widths. We show that "most" subspaces are near-optimal, and show that convex optimization (Basis Pursuit) is a near-optimal way to extract information derived from these near-optimal subspaces <s> BIB003 </s> A review on spectrum sensing for cognitive radio: challenges and solutions <s> Practical Considerations and Future Developments <s> In cognitive radio networks, the first cognitive task preceding any form of dynamic spectrum management is the sensing and identification of spectrum holes in wireless environments. This paper develops a wavelet approach to efficient spectrum sensing of wideband channels. The signal spectrum over a wide frequency band is decomposed into elementary building blocks of subbands that are well characterized by local irregularities in frequency. As a powerful mathematical tool for analyzing singularities and edges, the wavelet transform is employed to detect and estimate the local spectral irregular structure, which carries important information on the frequency locations and power spectral densities of the subbands. Along this line, a couple of wideband spectrum sensing techniques are developed based on the local maxima of the wavelet transform modulus and the multi-scale wavelet products. The proposed sensing techniques provide an effective radio sensing architecture to identify and locate spectrum holes in the signal spectrum. <s> BIB004 </s> A review on spectrum sensing for cognitive radio: challenges and solutions <s> Practical Considerations and Future Developments <s> Measurements performed at several locations clearly show that frequency spectrum is under-utilized. Cognitive radio is a strong candidate to ensure better spectrum utilization by providing access in an opportunistic manner. Simulations performed on the algorithm that we proposed show promising results in sensing vacant channels in TV bands. Here we present the work, which implements the algorithm on a real-time prototype, and measure its sensing performance in actual environments. Results show that our algorithm is robust under realistic conditions. This confirmation will give much needed confidence in the capability of cognitive radio systems to detect the operation of primary users and protect their use of spectrum. <s> BIB005 </s> A review on spectrum sensing for cognitive radio: challenges and solutions <s> Practical Considerations and Future Developments <s> Conventional approaches to sampling signals or images follow Shannon's theorem: the sampling rate must be at least twice the maximum frequency present in the signal (Nyquist rate). In the field of data conversion, standard analog-to-digital converter (ADC) technology implements the usual quantized Shannon representation - the signal is uniformly sampled at or above the Nyquist rate. This article surveys the theory of compressive sampling, also known as compressed sensing or CS, a novel sensing/sampling paradigm that goes against the common wisdom in data acquisition. CS theory asserts that one can recover certain signals and images from far fewer samples or measurements than traditional methods use. <s> BIB006 </s> A review on spectrum sensing for cognitive radio: challenges and solutions <s> Practical Considerations and Future Developments <s> Prior study on the cognitive radio (CR) has mostly adopted the passive sensing protocol, where the CR keeps monitoring the spectrum of interest, and decides to transmit when the sensing result indicates that the primary radio (PR) is inactive. In this paper, we propose an alternative active sensing protocol where, prior to the sensing, the CR generates a temporary jamming signal to deliberately interfere with the PR. The jamming signal is aimed to trigger an interesting interaction between the CR and PR, named as the hidden power-feedback loop: If the PR is indeed active and reacts upon receiving the jamming signal by increasing its transmit power, the CR will receive a power-boosted PR signal that is more easily detectable. Moreover, this paper demonstrates the usefulness of exploiting the power-feedback loop for the CR to effectively estimate the channel from the CR to the PR. This is well-known as a crucial task to implement for the CR operating under the so-called interference temperature constraint, where the CR is allowed to transmit regardless of the PR's on/off status, provided that the resultant interference power level at the PR is kept below some predefined threshold. <s> BIB007 </s> A review on spectrum sensing for cognitive radio: challenges and solutions <s> Practical Considerations and Future Developments <s> Measurements performed at several locations clearly show that frequency spectrum is under-utilized. Cognitive radio (CR) is a strong candidate to ensure better spectrum utilization by providing access in an opportunistic manner, i.e., when the spectrum is temporary or spatially unutilized (a.k.a. white-space). The key enabling technology for realizing better frequency spectrum utilization in CR system is spectrum sensing. In particular, spectrum sensing in television (TV) bands is of great interest due to the potential availability of spectrum as a result of the planned migration of analog TV broadcasting to digital TV broadcasting. In this paper, we present the TV white-space prototype that we developed to detect vacant spectrum in TV bands. The prototype is implemented on a real-time platform and tested in practical environments. Results show that our prototype is able to detect vacant channels up to sensitivities from -116 to -120 dBm under realistic conditions. This confirmation will give the much needed confidence in the capability of CR systems to detect the operation of primary users and protect their use of spectrum. Copyright © 2008 John Wiley & Sons, Ltd. <s> BIB008 </s> A review on spectrum sensing for cognitive radio: challenges and solutions <s> Practical Considerations and Future Developments <s> Spectrum sensing is a fundamental component in a cognitive radio. In this paper, we propose new sensing methods based on the eigenvalues of the covariance matrix of signals received at the secondary users. In particular, two sensing algorithms are suggested, one is based on the ratio of the maximum eigenvalue to minimum eigenvalue; the other is based on the ratio of the average eigenvalue to minimum eigenvalue. Using some latest random matrix theories (RMT), we quantify the distributions of these ratios and derive the probabilities of false alarm and probabilities of detection for the proposed algorithms. We also find the thresholds of the methods for a given probability of false alarm. The proposed methods overcome the noise uncertainty problem, and can even perform better than the ideal energy detection when the signals to be detected are highly correlated. The methods can be used for various signal detection applications without requiring the knowledge of signal, channel and noise power. Simulations based on randomly generated signals, wireless microphone signals and captured ATSC DTV signals are presented to verify the effectiveness of the proposed methods. <s> BIB009 </s> A review on spectrum sensing for cognitive radio: challenges and solutions <s> Practical Considerations and Future Developments <s> Spectrum sensing is a fundamental problem in cognitive radio. As a result, it has been reborn as a very active research area in recent years despite its long history. Although various sensing methods have been proposed, their robustness at very low signal-to-noise ratio (SNR) and uncertain noise/interference environment is generally not satisfactory. In this paper, the concept of robust sensing is discussed first. Subsequently the cooperative covariance and eigenvalue based detections are proposed for robust spectrum sensing. It is proved mathematically that under some conditions the proposed methods are robust to uncertain and unpredictable noise and interference. The performances of the methods are also verified by simulations. <s> BIB010 </s> A review on spectrum sensing for cognitive radio: challenges and solutions <s> Practical Considerations and Future Developments <s> Powerline communication (PLC) is a preferred choice for smart home network. In this paper, a new system structure is proposed for PLC, which is based on distributed orthogonal frequency division multiple access (DOFDMA). Sub-carrier sensing, i.e., sensing every OFDM subcarrier to see if it is occupied or not, is proposed to replace the conventional carrier sensing multiple access (CSMA) for multi-user contention of a channel. This structure, borrowed from cognitive radio, allows multiple users to opportunistically share the same channel on different subcarriers and therefore increases the channel capacity. Two subcarrier sensing methods are proposed: one is based on information theory and the other is based on successive energy comparison. Simulations are provided to verify the methods. <s> BIB011 </s> A review on spectrum sensing for cognitive radio: challenges and solutions <s> Practical Considerations and Future Developments <s> In this paper, we consider a wideband cognitive radio network (CRN) which can simultaneously sense multiple narrowband channels and thus aggregate the perceived available channels for transmission. We study the problem of designing the optimal spectrum sensing time and power allocation schemes so as to maximize the average achievable throughput of the CRN subject to the constraints of probability of detection and the total transmit power. The optimal sensing time and power allocation strategies are developed under two different total power constraints, namely, instantaneous power constraint and average power constraint. Finally, numerical results show that, under both cases, for a CRN with three 6 MHz channels, if the frame duration is 100 ms and the target probability of detection is 90% for the worst case signal-to-noise ratio of primary users being -12 dB, -15 dB and -20 dB, respectively, the optimal sensing time is around 6 ms and it is almost insensitive to the total transmit power. <s> BIB012 </s> A review on spectrum sensing for cognitive radio: challenges and solutions <s> Practical Considerations and Future Developments <s> Most of existing works on spectrum sensing detect primary transmitters while the purpose of spectrum sensing is to avoid interfering with primary receivers (PRs). Therefore, it is more important to detect PRs. In this paper, we propose a proactive spectrum sensing method that detects whether a PR is within the coverage or the interference range of a CR transmitter by exploiting the close-loop power control policy in primary systems. With the proposed scheme, the CR user may still access the spectrum band even though a primary signal is present as long as its transmission does not interfere with the PR. Simulation results show the advantages of the proposed method. <s> BIB013
Although there have been quite a few methods proposed for spectrum sensing, their realization and performance in practical cognitive radio applications need to be tested  BIB005 BIB008 . To build a practical sensing device, many factors should be considered. Some of them are discussed as follows. (1) Narrowband noise. One or more narrowband filters may be used to extract the signal from a specific band. These filters can be analog or digital. Only if the filter is ideally designed and the signal is critically sampled (sampling rate is the same as the bandwidth of the filter), the discrete noise samples could be i.i.d. In a practical device, however, the noise samples are usually correlated. This will cause many sensing methods unworkable, because they usually assume that the noise samples are i.i.d. For some methods, a noise prewhitening process can be used to make the noise samples i.i.d. prior to the signal detection. For example, this method has been deployed in BIB009 to enable the eigenvalue-based detection methods. The similar method can be used for covariance-based detection methods, for example, the CAV. (2) Spurious signal and interference. The received signal may contain not only the desired signal and white noise but also some spurious signal and interference. The spurious signal may be generated by Analog-to-Digital Converters (ADC) due to its nonlinearity BIB001 or other intentional/unintentional transmitters. If the sensing antenna is near some electronic devices, the spurious signal generated by the devices can be strong in the received signal. For some sensing methods, such unwanted signals will be detected as signals rather than noise. This will increase the probability of false alarm. There are methods to mitigate the spurious signal at the device level BIB001 . Alternatively, signal processing techniques can be used to eliminate the impact of spurious signal/interference BIB010 . It is very difficult, if possible, to estimate the interference waveform or distribution because of its variation with time and location. Depending on situations, the interference power could be lower or higher than the noise power. If the interference power is much higher than the noise power, it is possible to estimate the interference first and subtract it from the received signal. However, since we usually intend to detect signal at very low SNR, the error of the interference estimation could be large enough (say, larger than the primary signal) such that the detection with the residue signal after the interference subtraction is still unreliable. If the interference power is low, it is hard to estimate it anyway. Hence, in general we cannot rely on the interference estimation and subtraction, especially for very low-power signal detection. (3) Fixed point realization. Many hardware realizations use fixed point rather than floating point computation. This will limit the accuracy of detection methods due to the signal truncation when it is saturated. A detection method should be robust to such unpredictable errors. (4) Wideband sensing. A cognitive radio device may need to monitor a very large contiguous or noncontiguous frequency range to find the best available band(s) for transmission. The aggregate bandwidth could be as large as several GHz. Such wideband sensing requires ultrawide band RF frontend and very fast signal processing devices. To sense a very large frequency range, typically a corresponding large sampling rate is required, which is very challenging for practical implementation. Fortunately, if a large part of the frequency range is vacant, that is, the signal is frequency-domain sparse, we can use the recently developed compressed sampling (also called compressed sensing) to reduce the sampling rate by a large margin BIB002 BIB006 BIB003 . Although there have been studies in wideband sensing algorithms BIB004  BIB011   BIB012 , more researches are needed especially when the center frequencies and bandwidths of the primary signals are unknown within the frequency range of interest. (5) Complexity. This is of course one of the major factors affecting the implementation of a sensing method. Simple but effective methods are always preferable. To detect a desired signal at very low SNR and in a harsh environment is by no means a simple task. In this paper, major attention is paid to the statistical detection methods. The major advantage of such methods is their little dependency on signal/channel knowledge as well as relative ease for realization. However, their disadvantage is also obvious: they are in general vulnerable to undesired interferences. How we can effectively combine the statistical detection with known signal features is not yet well understood. This might be a promising research direction. Furthermore, most exiting spectrum sensing methods are passive in the sense that they have neglected the interactions between the primary and secondary networks via their mutual interferences. If the reaction of the primary user (e.g., power control) upon receiving the secondary interference is exploited, some active spectrum sensing methods can be designed, which could significantly outperform the conventional passive sensing methods BIB007 BIB013 . At last, detecting the presence of signal is only the basic task of sensing. For a radio with high level of cognition, further information such as signal waveform and modulation schemes may be exploited. Therefore, signal identification turns to be an advanced task of sensing. If we could find an effective method for this advanced task, it in turn can help the basic sensing task.