To estimate angle, velocity, and range information of multiple targets jointly in FMCW MIMO radar, two-dimensional (2D) MUSIC with matched filtering and FFT algorithm is proposed. By reformulating the received FMCW signal of the colocated MIMO radar, we exploit 2D MUSIC to estimate the angle and Doppler frequency of multiple targets. Then by using a matched filter together with the estimated angle and Doppler frequency and FFT operation, the range of the target is estimated. To effectively estimate the parameters of multiple targets with large distance differences, we also propose a successive interference cancellation method that uses the orthogonal projection. That is, rather than estimating the multiple target parameters simultaneously using 2D MUSIC, we estimate the target parameters sequentially, in which the parameters of the target having strongest reflected power are estimated first and then, their effect on the received signal is canceled out by using the orthogonal projection. Simulations verify the performance of the proposed algorithm.

This letter presents an efficient hybrid direction of arrival (DOA) estimation scheme for massive uniform linear array. In this scheme, the DOA estimator based on a discrete Fourier transform (DFT) is first applied to acquire coarse initial DOA estimates for single data snapshot. And then, the fine DOA is accurately estimated through using the iterative search estimator within a very small region. It iteratively searches for correct DOA vector by minimizing the objective function using a Taylor series approximation of the DOA vector with the one initially estimated. Since the proposed scheme does not need to perform eigen-decomposition and spectrum search while maintaining better DOA estimates, it also has low complexity and real-time capability. Simulation results are presented to demonstrate the efficiency of the proposed scheme.

In order to solve the problem in Automatic Identification System (AIS) that the signal in the target slot cannot be correctly received due to partial overlap of signals in adjacent time slots, the paper introduces a new criterion: maximum expected signal power (MESP) and proposes a novel beamforming algorithm based on generalized singular value decomposition (GSVD) and orthogonal projection. The algorithm employs GSVD to estimate the signal subspace, and adopts orthogonal projection to project the received signal onto the orthogonal subspace of the non-target signal. Then, beamforming technique is used to maximize the output power of the target signal on the basis of MESP. Theoretical analysis and simulation results show the effectiveness of the proposed algorithm.

In this letter, we show the new signal power estimation method base on the subspace projection. This work mainly contributes to the SINR estimation problem because, in this research, the signal power estimation is implicitly or explicitly performed. The difference between our method and the conventional method related to this topic is the exploitation of the subspace character of the signals constructing the observed signal. As tools to perform subspace operation, we apply orthogonal projection and oblique projection which can extracts desired parameters. In the proposed scheme, the statistics of the projected observed signal by these projection are used to estimate the parameters.

In this letter, standard particle swarm optimization (PSO) with the center-symmetric trimmed correlation matrix and the orthogonal projection technique is firstly presented for blind carrier frequency offset estimation under interleaved orthogonal frequency division multiple access (OFDMA) uplink systems. It doesn't require eigenvalue decomposition and only needs a single OFDMA data block. Second, this letter also presents adaptive multiple inertia weights with Newton method to speed up the convergence of standard PSO iteration process. Meanwhile, the advantage of inherent interleaved OFDMA signal structure also is exploited to conquer the problems of local optimization and the effect of ambiguous peaks for the proposed approaches. Finally, several simulation results are provided for illustration and comparison.

In this letter, we show the recursive representation of the optimum projection matrix. The recursive representation of the orthogonal projection and oblique projection have been done in past references. These projections are optimum when the noise is only characterized by the white noise or the structured noise. However, in some practical applications, a desired signal is deteriorated by both the white noise and structured noise. In this situation, the optimum projection matrix has been given by Behrens. For this projection matrix, the recursive representation has not been done. Therefore, in this letter, we propose the recursive representation of this projection matrix.

In this letter, an iterative carrier frequency offset (CFO) estimation approach is presented which finds a new CFO vector based on first order Taylor series expansion of the one initially given for interleaved orthogonal frequency division multiple access uplink systems. The problem of finding the new CFO vector is formulated as the closed form of a generalized eigenvalue problem, which allows one to readily solve it. The proposed estimator combined center-symmetric trimmed correlation matrix and orthogonal projection technique, which doesn't require eigenvalue decomposition and it only needs single data block.

In this letter, the orthogonal projection (OP) estimation of the direction of arrival (DOA) and direction of departure (DOD) of multiple targets for bistatic multiple-input multiple-output radars is addressed. First, a two-dimensional direction finding estimator based on OP technique with automatic pairing is developed. Second, this letter also presents a modified reduced-dimension estimator by utilizing the characteristic of Kronecker product, which only performs two one-dimensional angle estimates. Furthermore, the DOA and DOD pairing is given automatically. Finally, simulation results are presented to verify the efficiency of the proposed estimators.

This letter presents an effective direction of arrival (DOA) estimator that is based on the orthogonal projection (OP) technique. When an OP matrix is attained, the proposed estimator, which dispenses with spatial smoothing (SS) preprocessing, can form the maximizing orthogonality for a single snapshot. Since this technique does not need to perform eigen-decomposition while maintaining better DOA estimates, it also has real-time DOA estimation capability. Numerical results are presented to illustrate the efficiency of this method.

We present an alternative approach to what we call the "standard optimization", which minimizes a cost function by searching a parameter space. Instead, our approach "projects" in the joint observation space onto the manifold defined by the "consistency constraint", which demands that any minimal subset of observations produce the same result. This approach avoids many difficulties encountered in the standard optimization. As typical examples, we apply it to line fitting and multiview triangulation. The latter produces a new algorithm far more efficient than existing methods. We also discuss the optimality of our approach.

In this paper we analytically investigate the generalization performance of learning using correlated inputs in the framework of on-line learning with a statistical mechanical method. We consider a model composed of linear perceptrons with Gaussian noise. First, we analyze the case of the gradient method. We analytically clarify that the larger the correlation among inputs is or the larger the number of inputs is, the stricter the condition the learning rate should satisfy is, and the slower the learning speed is. Second, we treat the block orthogonal projection learning as an alternative learning rule and derive the theory. In a noiseless case, the learning speed does not depend on the correlation and is proportional to the number of inputs used in an update. The learning speed is identical to that of the gradient method with uncorrelated inputs. On the other hand, when there is noise, the larger the correlation among inputs is, the slower the learning speed is and the larger the residual generalization error is.

The main purpose of this paper is to give a new representation method of the convergence characteristics of the LMS algorithm using tap-input vectors. The described representation method is an extended version of the interpretation method based on the orthogonal projection. Using this new representation, we can express the convergence characteristics in terms of tap-input vectors instead of the eigenvalues of the input signal. From this representation, we consider a general method for improving the convergence speed.