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Error rate for our proposed algorithm as well as algorithms presented in Table 1 versus number of samples at SNR = −5 dB
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Estimating the number of sources is a key task in many array signal processing applications. Conventional algorithms such as Akaike’s information criterion (AIC) and minimum description length (MDL) suffer from underestimation and overestimation errors. In this paper, we propose four algorithms to estimate the number of sources in white Gaussian no...
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... evaluate the efficiency of our proposed algorithms in terms of error rate versus number of samples. It is desirable in practical scenarios to process the lower number of samples while achieving an adequate performance. Fig. 6 depicts the error rate for our proposed algorithms as well as the algorithms presented in Table 1 versus the number of samples at SNR = −5 dB and K = 2. The x- axis is the number of samples represented by log 2 ...
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... Traditionally, before performing the DOA estimation, signal detection methods are required [39]. Then, a source number estimator will be utilized, for instance, CorrM [40], BIC [41], and AIC [42]. Actually, source number estimation can be achieved through elementary column transformation, without any source number estimator. ...
A novel approach that does not require the number of sources as a priori is proposed to estimate the direction of arrival (DOA) based on a sparse non-uniform linear antenna array. To ensure the identifiability of the DOA, a specific configuration scheme of sparse array is designed. Based on this specific sparse array, firstly the fourth-order cumulant (FOC) is adopted to eliminate the impact imposed by Gaussian noise. Secondly, to circumvent eigenvalue decomposition or singular value decomposition, a propagator is constructed by using a Hermitian FOC matrix and a hyperparameter. Finally, a projection onto an irregular Toeplitz set is proposed to further improve estimation accuracy.
... Proposition 2: For the eigenvalues of the covariance matrix of the observed signals of the array antenna, it is found that the noise eigenvalues are very divergent in the colored noise environment, and diagonal loading can reduce the divergence of the noise eigenvalues and make them close to equality, and it does not have a significant effect on some of the eigenvalues of the signals. (25)(26)(27)(28) The eigenvalues of the covariance matrix are calculated as R(t) = X(t) • X H (t)/N, as do the eigen-decomposition to the covariance matrix R(t), and we can obtain the eigenvalues { } 1 ...
... On the contrary, overloading occurs, which results in the under estimation of the number of sources. (25)(26)(27)(28) Proposition 3: When the number of snapshots is not very large compared with that of antenna elements, both the eigenvalues of signals and sample noise are biased estimates of real values, and the fusion of the two types of eigenvalue cannot be separated, which leads to errors in the estimation of the number of sources by ITC methods. (23) The effects of the change in the proportional relationship between the number of antenna elements and that of snapshots on the signal and noise eigenvalues are analyzed as follows. ...
... A. Propagator based on Elementary Transformation: In general scenarios that the number of sources is unknown, signal detection methods are required before DOA estimation [20]. Subsequently, some signal source number estimators will be used, such as AIC [21], MDL, BIC [22] and CorrM [23]. In the case that propagator-based methods are adopted, K columns of R VS will be selected to construct the desired propagator, whereK is the estimated source number. ...
A novel direction of arrival (DOA) estimating method is proposed based on the coprime array, which can work without a priori information of the source number. The fourth-order statistics is adopted to construct a virtual array with a large aperture, which can also suppress Gaussian noise leading to a higher estimation accuracy and more importantly allowing the propagator construction. A propagator combining source number estimation and DOA estimation is presented firstly. Then considering the risk brought by the source number estimator, an improved propagator is constructed without the priori or estimated source number. The performance of the proposed method has been verified through some simulations.
... There are a large number of studies on source enumeration approaches, and they can be classified into information theoretic based and threshold based approaches, etc. [14]. AIC and MDL, which are the information theoretic based approaches, are the most popular approaches for source enumeration. ...
... Panel (c) shows the means of the accumulated gaps of eigenvalues, i.e., 1 i ∑ i k=1 ∆λ k from (14). The means of the NN gaps (when i is 1, 2 and 3) are relatively small, while the mean of the NN gaps and the NS gap (when i is 4) and the mean of the NN gaps, the NS gap, and the SS gap (when i is 5) are comparatively greater than the means of the NN gaps are; this reduces the value of AREG even if the greatest gap is the SS gap because the denominator of AREG is increased when the NS gap or SS gap are included. ...
... Evaluation Parameter Settings Because the numerical detectability extent of SORTE is M − 3, the maximum D is set to 4. Note thatγ of T-GANE is set to 0.0113, and the source enumeration procedure of T-GANE is performed with Algorithm 2. Figure 7 shows the estimation accuracy of AIC, MDL, SORTE, and our two proposed approaches (AREG, T-GANE) versus SNR. The performances are evaluated in the SNR range from −20 dB to 10 dB, which is roughly chosen in many other papers [4,[10][11][12]14,16,[23][24][25]31]. This paper is interested in improving accuracy of AIC at high SNR-where MDL has 100% accuracy, but AIC does not reach 100% accuracy-and it of MDL at low SNR-where the MDL accuracy begins to decrease sharply, but AIC maintais good accuracy. ...
Source enumeration is an important procedure for radio direction-of-arrival finding in the multiple signal classification (MUSIC) algorithm. The most widely used source enumeration approaches are based on the eigenvalues themselves of the covariance matrix obtained from the received signal. However, they have shortcomings such as the imperfect accuracy even at a high signal-to-noise ratio (SNR), the poor performance at low SNR, and the limited detection number of sources. This paper proposestwo source enumeration approaches using the ratio of eigenvalue gaps and the threshold trained by a machine learning based clustering algorithm for gaps of normalized eigenvalues, respectively. In the first approach, a criterion formula derived with eigenvalue gaps is used to determine the number of sources, where the formula has maximum value. In the second approach, datasets of normalized eigenvalue gaps are generated for the machine learning based clustering algorithm and the optimal threshold for estimation of the number of sources are derived, which minimizes source enumeration error probability. Simulation results show that our proposed approaches are superior to the conventional approaches from both the estimation accuracy and numerical detectability extent points of view. The results demonstrate that the second proposed approach has the feasibility to improve source enumeration performance if appropriate learning datasets are sufficiently provided.
... Let us discuss the assumption (15). If this assumption is not fulfilled, then also the following condition does not hold: ...
This paper describes how a priori information about the signal parameters can influence the accuracy of estimating the number of these signals. This study considers sinusoidal signals and it is supposed that the parameters (amplitudes, frequencies and phases) of the received signals are known up to a certain error. The error probability of the maximum likelihood estimation of the number of sinusoids is calculated under this condition.
... Furthermore, the transmission of random data in pilot phase impairs the channel estimate at the legitimate nodes due to interference from random data. The performance of sub-space approaches is poor in low signal-to-noise ratio (SNR) regimes [45]. ...
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... Let us discuss the assumption (15). If this assumption is not fulfilled, then also the following condition does not hold: ...
... ; and Nx is the number of snapshots. However, as mentioned in [23] and [24], AIC tends to asymptotically overestimate the number of echoes, while MDL performs poorly at low SNRs or a limited number of snapshots (leading to an underestimation of the number of echoes). To solve the problems coming from low SNRs as well as a limited number of snapshots, numerous adaptations of AIC and MDL have been proposed [23], [24]. ...
... However, as mentioned in [23] and [24], AIC tends to asymptotically overestimate the number of echoes, while MDL performs poorly at low SNRs or a limited number of snapshots (leading to an underestimation of the number of echoes). To solve the problems coming from low SNRs as well as a limited number of snapshots, numerous adaptations of AIC and MDL have been proposed [23], [24]. With the knowledge of the number of echoes, media parameter estimation methods are introduced in the following section. ...
Ground-penetrating radar (GPR) is a common technique for evaluating the structure and quality of civil engineering materials. The ever-increasing demand for higher GPR time resolution and better interpretation of GPR data has motivated the use of advanced signal processing methods for GPR applications. In this article, we review the major advances in signal processing techniques employed in civil engineering for different tasks, such as estimation of thickness, permittivity, and roughness. Their performance is tested and compared through numerical testing and using experimental data from laboratory measurements.
... However, estimation methods such as subspace methods or supervised machine learning based regression methods assume, either explicitly or implicitly, that the number of echoes (or the number of interfaces) is known beforehand. Some criteria (such as Akaike's information criterion (AIC) or Minimum Description Length (MDL) [11]) can be used to detect the number of echoes. Nevertheless, in practice, these criteria are not efficient enough due to the high coherence of the echoes. ...
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