Estimating the number of signals (NIS) is an important goal in array signal processing, such as direction-of-arrival (DOA) estimation. A common approach for solving this problem is to use an eigenvalue of the array covariance matrix and information criterion, such as the Akaike information criterion (AIC) and minimum description length (MDL). However they suffer serious degradation, when the incoming signals are coherent. To estimate the NIS of the coherent signals impinging on a uniform linear array (ULA), a method for estimating the number of signals without eigendecomposition (MENSE) is proposed. The accuracy of the NIS estimation performance of MENSE is superior to the other algorithms equipped with preprocessing such as the spatial smoothing preprocessing (SSP) and forward/backward spatial smoothing techniques (FBSS) to decorrelate the coherency of signals. Instead of using SSP or FBSS preprocessing, MENSE uses the Hankel correlation matrices. The Hankel correlation matrices can not only decorrelate the coherency of signals but also suppress the influence of noise. However, in severe conditions like low signal-to-noise ratio (SNR) or a closely spaced signals impinging on a ULA, the NIS estimation metric of MENSE has some bias which causes estimation error. In this paper, we pay attention to the multiplicity defined by the ratio of the geometric mean to the arithmetic mean. Accordingly, we propose a new estimation metric that has less bias than that in MENSE. The Computer simulation results show that the proposed method is superior to MENSE in the above severe conditions.

In this paper, we consider the problem of estimating the time-varying directions-of-arrival (DOAs) of coherent narrowband cyclostationary signals impinging on a uniform linear array (ULA). By exploiting the cyclostationarity of most communication signals, we investigate a new computationally efficient subspace-based direction estimation method without eigendecomposition and spatial smoothing (SS) processes. The proposed method uses the inherently temporal property of incident signals and a subarray scheme to decorrelate the signal coherency and to suppress the noise and interfering signals, while the null subspace is obtained from the resulting cyclic correlation matrix through a linear operation. Then an on-line implementation of this method is presented for tracking the DOAs of slowly moving coherent signals. The proposed algorithm is computationally simple and has a good tracking performance. The effectiveness of the proposed method is verified through numerical examples.

This study is aimed to explore a fast convergence method of blind equalization using higher order statistics (cumulants). The efforts are focused on deriving new theoretical solutions for blind equalizers rather than investigating practical algorithms. Under the common assumptions for this framework, it is found that the condition for blind equalization is directly associated with an eigenproblem, i. e. the lag coefficients of the equalizer can be obtained from the eigenvectors of a higher order statistics matrix. A method of blind phase recovery is also proposed for QAM systems. Computer simulations show that very fast convergence can be achieved based on the approach.

This paper describes a new Artificial Neural Network (ANN), UNItary Decomposition ANN (UNIDANN), which can perform the unitary eigendecomposition of the synaptic weight matrix. It is shown both analytically and quantitatively that if the synaptic weight matrix is Hermitian positive definite, the neural output, based on the proposed dynamic equation, will converge to the principal eigenvectors of the synaptic weight matrix. Compared with previous works, the UNIDANN possesses several advantageous features such as low computation time and no synchronization problem due to the underlying analog circuit structure, faster convergence speed, accurate final results, and numerical stability. Some simulations with a particular emphasis on the applications to high resolution bearing estimation problems are also furnished to justify the proposed ANN.