Widely Linear Beamforming Algorithms Based On Noncircularity Coefficient Estimation

Beamforming technique is one of the most important issues in the array signal processing, which utilizes the array constituted by multiple sensors to transmit or receive the space signals, and has been widely used in the area of radar, sonar, communication and etc. Conventional beamforming technique generally assumes that the signals are circular and statistically stationary and only utilizes the covariance matrix of the observation vector. However, in the area of communication system, many artificial modulation signals are noncircular and nonstationary, which only have covariance matrix but also have conjugated covariace matrix. Although the conventional beamforming technique based on the circular assumption can be used for the reception of noncircular signals, the reception performance cannot attain the optimum. Recently, in the area of modern signal processing, the development of widely linear (WL) technique attains more and more researchers to reconsider the problem of the beamforming technique for the reception of noncircular signals. By analyzing the noncircularity of noncircular signals, the WL beamforming technique simultaneously utilizes the covariance matrix and conjugated covariance matrix of the observation vector and the corresponding WL beamforming methods were successively proposed.Based on the overview of WL beamforming technique, this paper aims at carrying out the study of the WL beamforming methods for the key issues in the development of WL beamforming technique. The target of our research is to solve the problem of noncircularity coefficient estimation and then propose corresponding WL beamforming methods under different scenarios. The main contributions and innovative points of this dissertation are listed as follows:1. For the problem of noncircularity coefficient estimation, we propose a method to estimate the noncircularity coefficient of the desired signal, and then a robust weight vector by using the diagonal loading technique. We consider the the principle of minimum Variance Distortionless response (MVDR) and turn out this problem into a parameter estimation problem. We find out the parameter to make the output power maximal as a rough estimate of noncircularity coefficient by taking the conjugate derivative of the objective function. Then, through analyzing the effect of interferences and noise on the rough estimate of noncircularity coefficient, we obtain the final modified estimate of the noncircularity coefficient. After obtaining the modified estimate of the noncircularity coefficient, the diagonal loading technique is used to suppress the effect of the estimation error on the optimal WL MVDR beamformer.2. For the situation that the desired signal has a non-null offset frequency, we propose a frequency-shift (FS) WL beamforming method for the reception of noncircular signals. Considering that the noncircularity rate of desired signal with a non-null offset frequency changes and approaches to0with the increment of observation time, the correlation information of the desired signal between the conjugated observation vector and observation decreases. We propose to use the conjugated cyclic observation vector and the corresponding conjugated cyclic coefficient instead of the conjugated observation vector and the noncircularity coefficient in the optimal WL beamformer. When the offset frequency of the desired signal is null. the proposed method is equivalent to the optimal WL MVDR beamformer. When the offset frequency of the desired signal is non-null.the proposed method outperforms the optimal WL MVDR beamformer. In addition, we propose two methods for the estimation of offset frequency based on relationship between the time-averaged noncircularity coefficient and offset frequency.3. Considering the situation that the offset frequencies of the desired signal and interferences are different, we propose an Mth-order FS WL beamfoming method. The FS WL beamfomer only utilizes the conjugated coefficient of the desired signal. When the offset frequencies of the desired signal and interferences are different, the proposed method uses multiple conjugated cyclic observation vectors and suppresses the output powers of interferences on their own cyclic frequency by adding M constraints. The proposed method is the extended version of the FS WL MVDR beamformer and the0th-order FS WL MVDR beamformer corresponds to the proposed FS WL MVDR beamformer. When the offset frequencies of the desired signal and interferences are different.the proposed method outperforms the FS WL MVDR beamformer.4. For the situation that there exists steering vector mismatch, we propose a robust WL beamforming method, in which the spatial spectrum of noncircularity coefficient is firstly introduced. The proposed method constructs the interfere-plus-noise covariance matrix (1NCM) and conjugated1NCM. Hence, the desired signal component is removed from the extended covariance matrix. Under the high signal-to-noise ratio (SNR) and small snapshots size, the output signal-to-interference-plus-noise ratio (SINR) of the proposed robust WL MVDR beamformer always approaches the optimal value.