Research On Sensor Errors Auto-calibration Algorithms For Non-circular Signals

Direction of arrival(DOA) estimation is an important area in the field of array signal processing. Most of the super-resolution estimation algorithms are proposed given that steering vectors are precisely known and thus they have a good theoretical performance. However, inevitable sensor errors will lead to considerable deterioration of estimation performance in reality, and those super-resolution estimators even fail the desired performance. Therefore, the study on sensor error calibration technologies becomes particularly significant. Among all the calibration methods, auto-calibration is prosperous for it can achieve online estimation of both DOAs and sensor error parameters. At present, there is a lack of auto-calibration methods using the additional information of sources, and thus the number of sources that they can distinguish is limited and their estimation accuracy has yet to be improved. Non-circular signal is one type of sources widely used in modern communication systems. Considering that the unconjugated covariance matrix of non-circular signals increases available information, the auto-calibration methods with the use of non-circular feature will have higher accuracy of estimation or be capable of dealing with much more unknowns. This dissertation aims to combine non-circular feature of signals to further improve the auto-calibration performance. Our research consists of three parts: the study on non-circular feature and sensor error modeling, the analysis of the influence of sensor errors on theoretical performance of DOA estimation for non-circular signals, and the design of auto-calibration algorithms for non-circular signals. The main research work and contributions are outlined as follows:1. The study is made with regard to non-circular feature and sensor error modeling. The array signal models are presented under the effects of gain/phase errors including channel gain/phase errors and angularly dependent gain/phase errors, mutual coupling between sensors, sensor position perturbation, and the existence of multiple sensor errors, respectively. Then a unified expression of these models is given. Furthermore, the model of non-circular signals with maximum non-circularity rate, the model of non-circular signals with arbitrary non-circularity rate, and the model of temporally correlated non-circular signals are all established in the presence of sensor errors.2. The research is made in regard to the Cramér–Rao bound(CRB) for non-circular signals in the presence of sensor errors. Based on the deterministic model of non-circular signals with maximum non-circularity rate, the stochastic model of non-circular signals with arbitrary non-circularity rate and the stochastic model of temporally correlated non-circular signals, the associated expressions of CRB matrices are derived respectively. Then comparisons between CRB for non-circular signals and that for circular signals are presented.3. Two kinds of extended rank reduction estimator(RARE) for uncorrelated non-circular sources with maximum non-circularity rate are proposed to calibrate mutual coupling and angularly dependent gain/phase errors, respectively. The performance study provides a necessary condition for identifiability of parameters and a theoretical derivation for the closed-form expression of mean square error(MSE) of DOA estimation. Assuming that the noise is spatially uncorrelated, the proposed algorithm can achieve ―decoupling‖ estimation of both DOAs and sensor error parameters by using the special structure of the extended covariance matrix of non-circular signals with maximum non-circularity rate. Not only can the extended RARE avoid multi-dimensional search or iteration, but also its estimation accuracy is higher and the number of distinguished sources is larger compared with traditional RARE.4. An auto-calibration algorithm is proposed based on the extended covariance matching estimation technique(COMET) for non-circular sources with arbitrary non-circularity rate, which is called NC-COMET algorithm. The identifiability of parameters is discussed and its asymptotic performance is analyzed. This algorithm requires the knowledge of noise model. It first extends the covariance matrix by applying unconjugated covariance matrix of non-circular signals, and then estimates unknowns according to extended COMET. The proposed algorithm is effective in the absence of statistical information as well as in the presence of statistically independent information of sources. Its optimization relies on a Newton alternating iteration procedure. In addition, the variance of NC-COMET estimator under Gaussian assumption is asymptotically equal to the stochastic Cramér–Rao Bound for non-circular signals. The proposed algorithm can also realize auto-calibration when the incident non-circular sources are mixed with circular signals. It is more robust with respect to low signal-to-noise ratio, and its estimation is much more precise in the presence of statistically independent information of sources.5. An auto-calibration algorithm in unknown noise field is proposed, which is one kind of weighted signal subspace fitting(WSSF) method for non-circular sources based on 2-sided instrumental variable(2-sided IV-NCWSSF). The identifiability of parameters is discussed and the asymptotic performance of this algorithm is also analyzed. By combining the non-circular feature and temporal correlation of sources, an objective function with optimal weighting matrices is constructed according to the principle of WSSF. Then the function is reduced to a tractable expression so as to estimate parameters of DOAs and sensor errors through an improved alternating projection procedure. The specified algorithm works for mixed sources of non-circular and circular signals. What is more, it needs no knowledge of the spatial correlation structure of the noise, and thus it is effective for separating spatially and temporally correlated non-circular sources from unknown colored(i.e., spatially correlated) noise.