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## Wideband spectrum sensing from compressed measurements using spectral prior information (2013)

Venue: | IEEE Trans. Signal Process |

Citations: | 10 - 6 self |

### Citations

5089 |
Convergence of Probability Measures
- Billingsley
- 1999
(Show Context)
Citation Context ...his theorem assumes that is distributed according to a continuous non-degenerate probability distribution, in the sense that no set of zero Lebesgue measure can have a non-null probability6 (see e.g. =-=[27]-=-). In our case, this condition will hold provided that the covariance matrix is full rank. The reason for such an assumption is that we can take advantage of the fact that and are then linearly indepe... |

2135 |
An introduction to multivariate statistical analysis (2nd ed.).
- Anderson
- 1984
(Show Context)
Citation Context ...signal processing and statistics since it leads to tractable models and since many methods designed for Gaussian distributions also work even when there exist considerable departures from Gaussianity =-=[17]-=-. Using this assumption, we find that the algorithms for classical structured covariance estimation may be applied. However, the complexity of these algorithms limits their applicability to real-world... |

1542 |
Fundamentals of Statistical Signal Processing: Estimation Theory
- Kay
- 1993
(Show Context)
Citation Context ...onvergence for SSPICE follows from the arguments in [18]. In order to consider asymptotic statistical performance, let us assume, for simplicity, that . In that case and according to the arguments in =-=[19]-=-, the ML-based algorithms LIKES and IIA are expected to be asymptotically efficient and unbiased. Since the Cramér-Rao bound (CRB) is decreasing with the number of samples (See Section V for more info... |

933 |
Theory of Point Estimation
- Lehmann, Casella
- 1998
(Show Context)
Citation Context ...we are using the unbiased estimate, which may be more justified in the general case since then also represents the length of the -th block-diagonal of , i.e., the number of terms averaged. As we know =-=[24]-=-, the use of either one of these estimates will guarantee that is a consistent estimator for for a fixed as we take . Note that the simpler estimate lacks this property. In virtue of the interpretatio... |

840 |
Testing Statistical Hypotheses.
- Lehmann, Romano
- 2005
(Show Context)
Citation Context ...eyman-Pearson sense [20]. A sensible option arising from ML criteria is to make the decision based on the generalized likelihood ratio (GLR) statistic , which leads to the GLR test (GLRT) [17], [20], =-=[21]-=-: (4) Here, is some predefined threshold, set to satisfy certain probability of detection/false alarm requirements. The notation in (4) ROMERO AND LEUS: WIDEBAND SPECTRUM SENSING FROM COMPRESSED MEASU... |

662 |
Cognitive radio: making software radios more personal
- Mitola, Maguire
- 1999
(Show Context)
Citation Context ...rsions of one or more of the figures in this paper are available online at http://ieeexplore.ieee.org. Digital Object Identifier 10.1109/TSP.2013.2283473 (DSA) [2] (sometimes known as cognitive radio =-=[3]-=-).When several channels need to be scanned, a simple approach is to apply a conventional narrowband spectrum sensing procedure independently on a channel by channel basis. However, certain particulari... |

434 | A survey of dynamic spectrum access
- Zhao, Sadler
- 2007
(Show Context)
Citation Context ...e-mail: g.j.t.leus@tudelft.nl). Color versions of one or more of the figures in this paper are available online at http://ieeexplore.ieee.org. Digital Object Identifier 10.1109/TSP.2013.2283473 (DSA) =-=[2]-=- (sometimes known as cognitive radio [3]).When several channels need to be scanned, a simple approach is to apply a conventional narrowband spectrum sensing procedure independently on a channel by cha... |

197 |
Spectral analysis of signals
- Stoica, Moses
- 2005
(Show Context)
Citation Context ... may prefer to simply average along the actual diagonals, i.e., to take ... ... . . . ... (8) where and is a constant depending on . If , then is actually composed of the traditional biased estimates =-=[23]-=- of the autocorrelation/crosscorrelation of the processes . On the other hand, if we set , then we are using the unbiased estimate, which may be more justified in the general case since then also repr... |

161 |
SNR walls for signal detection
- Tandra, Sahai
- 2008
(Show Context)
Citation Context ...ut is maximized with an interference constraint on the primary network. The drawback though is that noise power knowledge is assumed, which makes the scheme sensitive to the noise uncertainty problem =-=[5]-=-. This problem is solved in [6], where this parameter is estimated using idle channels. However, in practice we may not guarantee the existence of such channels. This difficulty is overcome in [7] by ... |

122 | Toeplitz and Circulant Matrices: A Review.
- Gray
- 2006
(Show Context)
Citation Context ...which also suggests looking for an SCM of that particular form. The asymptotic theory of Toeplitz matrices will give us some clue about how to accomplish this search. 1) Averaging the SCM: As we know =-=[22]-=-, given a sequence of Toeplitz covariance matrices satisfying the assumption that the Fourier transform of the associated correlation sequences4 exists, it is possible to find a sequence of circulant ... |

107 | Blind multiband signal reconstruction: Compressed sensing for analog signals
- Mishali, Eldar
- 2009
(Show Context)
Citation Context ... at the Nyquist rate, which drastically limits the maximum sensed bandwidth. The sampling rate clearly represents a bottleneck for WSS. This observation has led to the concept of compressive WSS (see =-=[8]-=- and the references therein), where the sensing is done based on samples taken below the Nyquist rate. However, most schemes employ lossless compression, i.e., they aim to exactly reconstruct the orig... |

93 | Theory and implementation of an analog-to-information converter using random demodulation
- Laska, Kirolos, et al.
- 2007
(Show Context)
Citation Context ...e sensing algorithm to tolerate moderate modeling errors in the PSD. In the considered model, a frequency band of large bandwidth is acquired by means of an analog to information converter (A2I) [14]–=-=[16]-=-, which provides linear measurements of the analog input signal at rates below the Nyquist rate. This signal is assumed to be the sum of a certain number of component signals whose second-order moment... |

90 |
Lower bounds for parametric estimation with constraints
- Gorman, Hero
- 1990
(Show Context)
Citation Context ...c. 3.8] for more details about how to accomplish this computation. Note that is constrained to satisfy , which means that the bound to be used is actually the constrained CRB. However, it is shown in =-=[37]-=- that this bound coincides with the unconstrained CRB at those points where . For simplicity, in this experiment we only consider points satisfying this condition. The MSE is measured by summing the s... |

81 |
Optimal multiband joint detection for spectrum sensing in dynamic spectrum access networks
- Quan, Cui, et al.
- 2009
(Show Context)
Citation Context ...certain particularities arise from considering multiple channels at the same time, these being the subject of study of the so-called wideband spectrum sensing (WSS). Previous wideband schemes include =-=[4]-=-, where the throughput is maximized with an interference constraint on the primary network. The drawback though is that noise power knowledge is assumed, which makes the scheme sensitive to the noise ... |

74 | Spectrum-sensing algorithms for cognitive radio based on statistical covariances
- Zeng, Liang
- 1815
(Show Context)
Citation Context ... blocks and for high , for example retaining only the blocks corresponding to lags not greater than , i.e., we only keep the blocks of the modified SCM in (8). This parameter was already used in [9], =-=[25]-=-, [26] where, like here, it is regarded as a design parameter. Observe that after applying this selection, the matrices and have dimension . For example, the averaged and cropped SCM is given by ... .... |

65 |
Estimation of structured covariance matrices
- Burge, Luenberger, et al.
- 1982
(Show Context)
Citation Context ... even for the simpler case where thematrices are Toeplitz, onemust resort to numerical computations [31]. An example of an algorithm to solve (16) is the inverse iteration algorithm (IIA) proposed in =-=[32]-=-, but, similarly to LIKES, the complexity is high, especially for large . Moreover, the numerical stability is low, and intense efforts must be made in order to stay in the positive definite region (r... |

64 | Spectrum sensing for cognitive radio: State-of-the-art and recent advances
- Axell, Leus, et al.
- 2012
(Show Context)
Citation Context ...lar performance at a much lower computational cost. Index Terms—Analog-to-information converters, compressed sensing, covariance matching, wideband spectrum sensing. I. INTRODUCTION S PECTRUM sensing =-=[1]-=- encompasses a collection of proce-dures intended to determine the occupancy state of a particular frequency band, and it is of critical importance in certain applications such as those employing dyna... |

44 | Nested arrays: A novel approach to array processing with enhanced degrees of freedom
- Pal, Vaidyanathan
- 2010
(Show Context)
Citation Context ...stics of the received signal are of interest, not the time-domain waveform itself [9], [10]. As a convenient byproduct, sparsity is typically not needed anymore. This standpoint is also used in [11], =-=[12]-=-, where the signal is acquired in the spatial domain to estimate the direction of arrival (DoA), and in [13], where a distributed scheme to estimate the power spectrum from lossy observations is propo... |

40 |
Covariance matching estimation techniques for array signal processing applications
- Ottersten, Stoica, et al.
- 1998
(Show Context)
Citation Context ...d cropped version . The first algorithm will be simply referred to as SPICE whereas the second one will be termed simplified SPICE (SSPICE). In [18], [33], the so-called extended invariance principle =-=[35]-=- is invoked to simplify the problem of structured covariance estimation, achieving an estimate that asymptotically matches 8It was shown by simulations that, in most cases, WLS works better than the p... |

31 |
Coprime sampling and the music algorithm
- Pal, Vaidyanathan
- 2011
(Show Context)
Citation Context ... statistics of the received signal are of interest, not the time-domain waveform itself [9], [10]. As a convenient byproduct, sparsity is typically not needed anymore. This standpoint is also used in =-=[11]-=-, [12], where the signal is acquired in the spatial domain to estimate the direction of arrival (DoA), and in [13], where a distributed scheme to estimate the power spectrum from lossy observations is... |

30 |
Compressive wideband power spectrum estimation
- Ariananda, Leus
- 2012
(Show Context)
Citation Context ...red. An alternative view that implements lossy compression stems from the observation that only the second-order statistics of the received signal are of interest, not the time-domain waveform itself =-=[9]-=-, [10]. As a convenient byproduct, sparsity is typically not needed anymore. This standpoint is also used in [11], [12], where the signal is acquired in the spatial domain to estimate the direction of... |

23 |
SPICE: A sparse covariance-based estimation method for array processing
- Stoica, Babu, et al.
- 2011
(Show Context)
Citation Context ...ouple of algorithms are proposed for non-Gaussian signals. In this context, asymptotic considerations lead to an efficient algorithm that has been recently proposed in the context of array processing =-=[18]-=-. After discussing these algorithms for estimation in the time domain in Section III; we explore estimation in the frequency domain in Section IV. Finally, we asses the estimation and detection perfor... |

19 | A nonuniform sampler for wideband spectrally-sparse environments
- Wakin, Becker, et al.
- 2012
(Show Context)
Citation Context ...onable sensing algorithm to tolerate moderate modeling errors in the PSD. In the considered model, a frequency band of large bandwidth is acquired by means of an analog to information converter (A2I) =-=[14]-=-–[16], which provides linear measurements of the analog input signal at rates below the Nyquist rate. This signal is assumed to be the sum of a certain number of component signals whose second-order m... |

19 |
New method of sparse parameter estimation in separable models and its use for spectral analysis of irregularly sampled data
- Stoica, Babu, et al.
(Show Context)
Citation Context ... or a column vector and is a vector with the same dimension as . The program (23) is then solved as a second-order cone program (SOCP) or in an fixed-point fashion. It is derived in [18], [29], [30], =-=[33]-=-, [34] under different conditions, showing that the problem is convex since it can be reformulated as either a SOCP or a semi-definite program (SDP). Although, to the best of our knowledge, the core S... |

18 | Compressive power spectral density estimation - Lexa, Davies, et al. - 2011 |

18 |
Application of toeplitz covariance estimation to adaptive beamforming and detection
- Fuhrmann
- 1991
(Show Context)
Citation Context ...owledge, no analytical solution has been found yet for this non-linear system of equations. In fact, even for the simpler case where thematrices are Toeplitz, onemust resort to numerical computations =-=[31]-=-. An example of an algorithm to solve (16) is the inverse iteration algorithm (IIA) proposed in [32], but, similarly to LIKES, the complexity is high, especially for large . Moreover, the numerical st... |

14 | Sub-nyquist sampling: Bridging theory and practice,” submitted - Mishali, Eldar - 2010 |

11 | Frugal sensing: Wideband power spectrum sensing from few bits
- Mehanna, Sidiropoulos
- 2013
(Show Context)
Citation Context ... byproduct, sparsity is typically not needed anymore. This standpoint is also used in [11], [12], where the signal is acquired in the spatial domain to estimate the direction of arrival (DoA), and in =-=[13]-=-, where a distributed scheme to estimate the power spectrum from lossy observations is proposed. The scheme in [9] provides a general spectrum estimation method based on compressed measurements, where... |

10 | Compressive covariance sampling
- Romero, Leus
- 2013
(Show Context)
Citation Context ...r the A2I. This topic requires extensive analysis since it depends on the specific architecture of the acquisition system. For the case of periodic non-uniform sampling, this analysis can be found in =-=[28]-=-. Further results in this context will be the object of subsequent publications. 6In this case, it is usually said that the distribution of is absolutely continuous with respect to Lebesgue measure. I... |

9 |
and LIKES: Two hyperparameter-free methods for sparse-parameter estimation
- Stoica, Babu, et al.
- 2012
(Show Context)
Citation Context ...king into account the constraints . In order to minimize (11), one must resort to numerical methods such as LIKES (likelihood-based estimation of sparse parameters). LIKES is an algorithm proposed in =-=[29]-=- for rank-1 SCMs in the context of sparse-parameter estimation and subsequently extended to the full-rank case in [30]. In both cases the basis covariance matrices are assumed rank-1, but a simple ext... |

6 |
Wideband spectrum sensing in unknown white Gaussian noise
- Taherpour, Gazor, et al.
- 2008
(Show Context)
Citation Context ...rence constraint on the primary network. The drawback though is that noise power knowledge is assumed, which makes the scheme sensitive to the noise uncertainty problem [5]. This problem is solved in =-=[6]-=-, where this parameter is estimated using idle channels. However, in practice we may not guarantee the existence of such channels. This difficulty is overcome in [7] by assuming that the power spectra... |

6 |
Spectrum sensing exploiting guard bands and weak channels
- Vázquez-Vilar, López-Valcarce
- 2011
(Show Context)
Citation Context ...lem [5]. This problem is solved in [6], where this parameter is estimated using idle channels. However, in practice we may not guarantee the existence of such channels. This difficulty is overcome in =-=[7]-=- by assuming that the power spectral density (PSD) of the individual channels is known up to a scaling factor. Unfortunately, this scheme requires acquiring the wideband signal at the Nyquist rate, wh... |

3 |
Maximum-likelihood nonparametric estimation of smooth spectra from irregularly sampled data
- Stoica, Babu
- 2011
(Show Context)
Citation Context ...nt, in the sense that the estimates of converge to the true values as becomes larger. In Fig. 3, the MSE is represented vs. along with the CRB, which is obtained from combining the bound for in [23], =-=[36]-=- with a linear transformation to obtain the bound in the PSD domain. See [19, Sec. 3.8] for more details about how to accomplish this computation. Note that is constrained to satisfy , which means tha... |

2 | A sparse covariance-based method for direction of arrival estimation - Stoica, Babu, et al. |

1 | Sparse spectral-line estimation for nonuniformly sampled multivariate time series - Babu, Stoica |

1 | Romero (S’11) received the telecommunication engineering and the M.S. degrees from University of Vigo (Spain) in 2009 and 2011, respectively. He is currently working towards the Ph.D. degree at the same university. In 2012, he visited the Circuits and Sys - Princeton, Press - 1996 |