Correlated Source Signals Research Articles

The MMV tail null space property and DOA estimations by tail-[formula omitted] minimization

The tail-minimization approach is applied to the joint sparse multiple measurement vector (MMV) model and direction of arrival (DOA) estimations. The mechanism is to estimate the support T of the jointly sparse matrix and minimize the energy in the complement Tc of T during each iteration. An MMV tail-null-space property (MMV-tail-NSP) is derived, which is shown to be necessary and sufficient for the unique solution of the MMV tail minimization problem. The MMV-tail-NSP condition is also shown to be more likely to hold than that of the conventional MMV-NSP for any given MMV basis pursuit problem. Two recovery guarantees and error bound analyses are also derived based on the MMV-robust-tail-NSP condition and merely the MMV-tail-NSP assumption, respectively. Study shows that the MMV tail-minimization approach is among the most effective techniques for the MMV DOA model. In particular, the MMV tail-minimization approach is able to recover signals of rank-enriched sparsity level K0≡[spark(A)−1+rank(X)]/2. In fact, this approach can handle signal recovery of greater sparsity levels than that by others. The advantages of the MMV tail-minimization approach are also reflected in numerous aspects such as handling low signal-to-noise ratio (SNR), limited number of snapshots, and correlated source signals. Results are more accurate with higher resolution as well. It is also capable of detecting the number of sources and estimating DOAs simultaneously. All these characteristics and advantages are fully evidenced by extensive simulation studies.

A Two-Stage Separation Algorithm for Weak Correlation Source Signals

In this paper, we propose a separation algorithm for weakly correlated source signals. At present, there are many blind source separation algorithms based on independent component analysis, which can only deal with the separation of uncorrelated source signals. However, the assumption that the source signals are independent is too strict in practical application, so the application of the separation algorithm is limited. The proposed weak correlation source signal separation algorithm is divided into two stages. In the first stage, the correlation matrices of mixed signals are first decomposed into two parts, and then their image matrices are introduced. Finally, the objective function is constructed. Using the iterative algorithm to compute this function, we prove that when the function tends to zero, similar matrices of independent parts of the aforementioned correlation matrices are obtained. In the second stage, the joint diagonal matrix model is established by using these similarity matrices, and finally the separable separation matrix is obtained by optimizing the model so as to achieve the purpose of separating the source signals. Simulation experiments also verify the effectiveness of the algorithm.

Distributed Joint Source-Channel Coding-Based Adaptive Dynamic Network Coding

Distributed Source Coding (DSC) schemes rely on separate encoding but joint decoding of statistically dependent sources, which exhibit correlation. More specifically, Distributed Joint Source-Channel coding (DJSC) is associated with the scenario, where the correlated source signals are transmitted through a noisy channel. On one hand, employing DSC or DJSC schemes exploits the existing correlation between sensors resulting in minimising the transmission energy required by the sources, while maintaining reliable communication. On the other hand, Network Coding (NC) is an efficient data transport technique leveraging network efficiency, by allowing Relay Nodes (RNs) in a communication network to combine multiple data packets received via the incoming links before transmitting them to the Destination Node (DN). In this paper, the bandwidth-efficient Distributed Joint Turbo Trellis-Coded Modulation (DJTTCM) aided by both Dynamic Network Coding (DNC) and Adaptive DNC (ADNC)-based cooperative transmission schemes are proposed. Both systems are proposed for supporting correlated source transmissions over hostile channels experiencing both small-scale and large-scale fading in which the RNs dynamically transmit its non-binary linear combinations to the DN. A substantial gain of 19.5 dB was attained at a correlation coefficient of $\rho = 0.8$ over its counterpart dispensing with NC.

Computationally Efficient 2D DOA Estimation for L-Shaped Array with Unknown Mutual Coupling

Although L-shaped array can provide good angle estimation performance and is easy to implement, its two-dimensional (2D) direction-of-arrival (DOA) performance degrades greatly in the presence of mutual coupling. To deal with the mutual coupling effect, a novel 2D DOA estimation method for L-shaped array with low computational complexity is developed in this paper. First, we generalize the conventional mutual coupling model for L-shaped array and compensate the mutual coupling blindly via sacrificing a few sensors as auxiliary elements. Then we apply the propagator method twice to mitigate the effect of strong source signal correlation effect. Finally, the estimations of azimuth and elevation angles are achieved simultaneously without pair matching via the complex eigenvalue technique. Compared with the existing methods, the proposed method is computationally efficient without spectrum search or polynomial rooting and also has fine angle estimation performance for highly correlated source signals. Theoretical analysis and simulation results have demonstrated the effectiveness of the proposed method.

Distributed Source Coding and Its Applications in Relaying-Based Transmission

Distributed source coding (DSC) schemes rely on separate encoding but joint decoding of statistically dependent sources, which exhibit correlation. DSC has numerous promising applications ranging from reduced-complexity handheld video communications to onboard hyperspectral image coding under computational limitations. The concept of separate encoding at the first sight compromises the attainable encoding performance. However, the DSC theory proves that independent encoding can in fact be designed as efficiently as joint encoding, as long as joint decoding is allowed. More specifically, distributed joint source-channel coding (DJSC) is associated with the scenario, where the correlated source signals are transmitted through a noisy channel. In this paper, we present a concise historic background of DSC concerning both its theory and its practical aspects. In addition, a series of turbo trellis-coded modulation (TTCM)-aided DJSC-based cooperative transmission schemes are proposed. DJSC scheme is conceived for the transmission of a pair of correlated sources to a destination node (DN). The first source sequence is TTCM encoded, and then, it is compressed before it is transmitted both over a Rayleigh fading channel, where the second source signal is assumed to be perfectly decoded side-information at the DN for the sake of improving the achievable decoding performance of the first source. The proposed scheme is capable of performing reliable communications for various levels of correlation near to the theoretical Slepian–Wolf/Shannon (SW/S) limit. Pursuing our objective of designing practical DJSC schemes, we further extended the above-mentioned arrangement to a more realistic cooperative communication system, where the pair of correlated sources are transmitted to a DN with the aid of a relay node (RN). Explicitly, the pair of correlated source sequences are TTCM encoded and compressed before transmission over a Rayleigh fading multiple access channel, where our proposed scheme is capable of operating within 0.55 dB from the SW/S limit for a correlation coefficient value of $\rho = 0.8$ , and within 0.07 bits of the minimum SW compression rate. The RN transmits both users’ signal with the aid of a powerful superposition modulation technique that judiciously allocates the transmit power between the two signals. The correlation is beneficially exploited at both the RN and the DN using our powerful iterative joint decoder, which is optimized using extrinsic information transfer characteristics charts.

Rotating Machine Monitoring Based on Blind Source Separation of Correlated Source Signals

Blind source separation (BSS) which separate the unknown sources from the observed signals is a new signal processing technique. The most methods for solving this problem rely on assumptions of independence or uncorrelation of source signals at least. However, the observed signal is always interfered by signals with common frequency in the rotating machine, and difficult to be separated by the conventional BSS method. In this paper, it is proved that the source signals with common frequencies are correlative, and the separating error brought by the cross-correlation of the source signals is analyzed. A new separating method for the correlated source signals with frequency overlapping is presented and it is successfully applied to separate the monitoring signals of rotor test stand.

Secret Key and Private Key Constructions for Simple Multiterminal Source Models

We propose an approach for constructing secret and private keys based on the long-known Slepian-Wolf code, due to Wyner, for correlated sources connected by a virtual additive noise channel. Our work is motivated by results of Csiszár and Narayan which highlight innate connections between secrecy generation by multiple terminals that observe correlated source signals and Slepian-Wolf near-lossless data compression. Explicit procedures for such constructions and their substantiation are provided. The performance of low-density parity check channel codes in devising a new class of secret keys is examined.

Iterative HOS-SOS (IHOSS) Algorithm for Direction-of-Arrival Estimation and Sensor Localization

A new method for joint direction-of-arrival (DOA) and sensor position estimation is introduced. The sensors are assumed to be randomly deployed except two reference sensors. The proposed method exploits the advantages of both higher-order-statistics (HOS) and second-order-statistics (SOS) with an iterative algorithm, namely Iterative Higher-Order Second-Order Statistics (IHOSS). A new cumulant matrix estimation technique is proposed for the HOS approach by converting the multisource problem into a single source one. IHOSS performs well even in case of correlated source signals due to the effectiveness of the proposed cumulant matrix estimate. A cost function is defined for the joint DOA and position estimation. The iterative procedure is guaranteed to converge. The ambiguity problem in sensor position estimation is solved by observing the source signals at least in two different frequencies. The conditions on these frequencies are presented. Closed-form expressions are derived for the deterministic Cramér-Rao bound (CRB) for DOA and unknown sensor positions for noncircular complex Gaussian noise with unknown covariance matrix. Simulation results show that the performance of IHOSS is significantly better than the HOS approaches for DOA estimation and closely follows the CRB for both DOA and sensor position estimations.

Uniform and nonuniform V‐shaped planar arrays for 2‐D direction‐of‐arrival estimation

In this paper, isotropic and directional uniform and nonuniform V‐shaped arrays are considered for azimuth and elevation direction‐of‐arrival (DOA) angle estimation simultaneously. It is shown that the uniform isotropic V‐shaped arrays (UI V arrays) have no angle coupling between the azimuth and elevation DOA. The design of the UI V arrays is investigated, and closed form expressions are presented for the parameters of the UI V arrays and nonuniform V arrays. These expressions allow one to find the isotropic V angle for different array types. The DOA performance of the UI V array is compared with the uniform circular array (UCA) for correlated signals and in case of mutual coupling between array elements. The modeling error for the sensor positions is also investigated. It is shown that V array and circular array have similar robustness for the position errors while the performance of UI V array is better than the UCA for correlated source signals and when there is mutual coupling. Nonuniform V‐shaped isotropic arrays are investigated which allow good DOA performance with limited number of sensors. Furthermore, a new design method for the directional V‐shaped arrays is proposed. This method is based on the Cramer‐Rao Bound for joint estimation where the angle coupling effect between the azimuth and elevation DOA angles is taken into account. The design method finds an optimum angle between the linear subarrays of the V array. The proposed method can be used to obtain directional arrays with significantly better DOA performance.

Morphologically constrained ICA for extracting weak temporally correlated signals

Recently the constrained ICA (cICA) algorithm has been widely applied to many applications. But a crucial problem to the algorithm is how to design a reference signal in advance, which should be closely related to the desired source signal. If the desired source signal is very weak in mixed signals and there is no enough a priori information about it, the reference signal is difficult to design. With some detailed discussions on the cICA algorithm, the paper proposes a second-order statistics based approach to reliably find suitable reference signals for weak temporally correlated source signals. Simulations on synthetic data and real-world data have shown its validity and usefulness.

Iterative Source-Channel Decoding With Markov Random Field Source Models

We propose a joint source-channel decoding approach for multidimensional correlated source signals. A Markov random field (MRF) source model is used which exemplarily considers the residual spatial correlations in an image signal after source encoding. Furthermore, the MRF parameters are selected via an analysis based on extrinsic information transfer charts. Due to the link between MRFs and the Gibbs distribution, the resulting soft-input soft-output (SISO) source decoder can be implemented with very low complexity. We prove that the inclusion of a high-rate block code after the quantization stage allows the MRF-based decoder to yield the maximum average extrinsic information. When channel codes are used for additional error protection the MRF-based SISO source decoder can be used as the outer constituent decoder in an iterative source-channel decoding scheme. Considering an example of a simple image transmission system we show that iterative decoding can be successfully employed for recovering the image data, especially when the channel is heavily corrupted

Broadband Beamspace DOA Estimation: Frequency-Domain and Time-Domain Processing Approaches

Frequency-domain and time-domain processing approaches to direction-of-arrival (DOA) estimation for multiple broadband far field signals using beamspace preprocessing structures are proposed. The technique is based on constant mainlobe response beam-forming. A set of frequency-domain and time-domain beamformers with constant (frequency independent) mainlobe response and controlled sidelobes is designed to cover the spatial sector of interest using optimal array pattern synthesis technique and optimal FIR filters design technique. These techniques lead the resulting beampatterns higher mainlobe approximation accuracy and yet lower sidelobes. For the scenario of strong out-of-sector interfering sources, our approaches can form nulls or notches in the direction of them and yet guarantee that the mainlobe response of the beamformers is constant over the design band. Numerical results show that the proposed time-domain processing DOA estimator has comparable performance with the proposed frequency-domain processing method, and that both of them are able to resolve correlated source signals and provide better resolution at lower signal-to-noise ratio (SNR) and lower root-mean-square error (RMSE) of the DOA estimate compared with the existing method. Our beamspace DOA estimators maintain good DOA estimation and spatial resolution capability in the scenario of strong out-of-sector interfering sources.

Iterative joint source-channel decoding of variable-length codes using residual source redundancy

We present a novel symbol-based soft-input a posteriori probability (APP) decoder for packetized variable-length encoded source indexes transmitted over wireless channels where the residual redundancy after source encoding is exploited for error protection. In combination with a mean-square or maximum APP estimation of the reconstructed source data, the whole decoding process is close to optimal. Furthermore, solutions for the proposed APP decoder with reduced complexity are discussed and compared to the near-optimal solution. When, in addition, channel codes are employed for protecting the variable-length encoded data, an iterative source-channel decoder can be obtained in the same way as for serially concatenated codes, where the proposed APP source decoder then represents one of the two constituent decoders. The simulation results show that this iterative decoding technique leads to substantial error protection for variable-length encoded correlated source signals, especially, when they are transmitted over highly corrupted channels.

Convergence properties of the multistage constant modulus array for correlated sources

A steady-state analysis of the multistage constant modulus (CM) array is presented for the case of correlated source signals. Using a Wiener model for the converged adaptive algorithms, it is demonstrated that because of the cascade structure, signal cross-correlation causes phantom sources to be present. The resulting signal leakage in the adaptive cancellers between stages causes an increase in the minimum mean-square error. A parallel implementation that overcomes this loss in performance is described; it requires an initialization strategy to ensure that each stage captures a different source. Computer simulations are presented to illustrate the convergence properties of the cascade and parallel CM array systems and to verify the theoretical results.

Unitary ESPRIT: how to obtain increased estimation accuracy with a reduced computational burden

ESPRIT is a high-resolution signal parameter estimation technique based on the translational invariance structure of a sensor array. Previous ESPRIT algorithms do not use the fact that the operator representing the phase delays between the two subarrays is unitary. The authors present a simple and efficient method to constrain the estimated phase factors to the unit circle, if centro-symmetric array configurations are used. Unitary ESPRIT, the resulting closed-form algorithm, has an ESPRIT-like structure except for the fact that it is formulated in terms of real-valued computations throughout. Since the dimension of the matrices is not increased, this completely real-valued algorithm achieves a substantial reduction of the computational complexity. Furthermore, Unitary ESPRIT incorporates forward-backward averaging, leading to an improved performance compared to the standard ESPRIT algorithm, especially for correlated source signals. Like standard ESPRIT, Unitary ESPRIT offers an inexpensive possibility to reconstruct the impinging wavefronts (signal copy). These signal estimates are more accurate, since Unitary ESPRIT improves the underlying signal subspace estimates. Simulations confirm that, even for uncorrelated signals, the standard ESPRIT algorithm needs twice the number of snapshots to achieve a precision comparable to that of Unitary ESPRIT. Thus, Unitary ESPRIT provides increased estimation accuracy with a reduced computational burden.< <ETX xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">&gt;</ETX>