Research On Direction Finding And Array Calibration Techniques

Array signal processing is an important branch of signal processing, which iswidely applied to radar, sonar, communication, seismic exploration, radio astronomy,and biomedicine and so on.Direction finding with array, also named as the direction of arrival (DOA)estimation is one of the main reasearch areas of array signal processing.The existinghigh-resolution DOA estimation methods work well under the assumption of ideal arraymanifold. In practice, array errors are unavoidable. In the presence of array errors, mostof the existing high-resolution DOA estimation methods perform badly and even fail.Therefore, the existence of array errors is a bottleneck which impedes the practicabilityof the high-resolution DOA estimation methods. In addition, although most DOAresolution methods have high-resolution ability, the number of resolvable DOAs islimited to the number of antennas and cannot exceed the number of antennas. Inpractice, due to the limitation on the cost and volume of the system, the number ofantennas cannot be too many. Therefore, it is neccesarray to research and improve theexisting direction finding methods to identify as many sources as possible with limitedantennas.This dissertation mainly studies the self-calibrtion problem in the presence of arraygain-phase errors, array calibration applicable to the distributed small satellites, andDOA estimation wich can identify more sources than the number of antennas.The main contents of this dissertation are as follows.1. The conventional self-calibration method require the joint iteration betweenarray error estimation and DOA estimation, resulting in local convergence and degradedperformance in large phase errors. To overcome this problem, we propose aself-calibration method based on the fact that the dot product of the array output vectorand its conjugate is independent of phase errors. Theoretical analysis shows that theproposed method performs independently of phase errors and thus behaves wellregardless of phase errors. However, the resolution capability of the proposed method islower than the conventional method. In order to improve the resolution capability andmaintain phase error independence, a combined strategy is developed using theproposed and conventional methods. The advantage of the proposed methods is thatthey are independent of phase errors, leading to the cancellation of phase error calibration during the operation life of an array. Moreover, the proposed methods avoidthe problem of suboptimal solutions which occurs in the conventional method. Thedrawbacks of the proposed methods are their high computational complexity and theirrequirement for the condition that at least two signals are spatially far from each other,and they are not applicable to a linear array.2. In the conventional array estimation method for constellation SAR systems, theposition error estimation is based on the first-order Taylor series expansion of theposition-error exponential function. However, the first-order Taylor series expansioncauses an approximation error, resulting in the inaccuracy of the estimation by theconventional method. In this paper, an improved method is developed to overcome thisproblem, based on the fact that the aforementioned approximation error decreases withthe reduction of position errors. In the improved method, we first compensate theposition error estimates obtained at the kth iteration in order to reduce the remainingposition errors in the (k+1)th iteration. Then, the position error estimates obtained at alliterations are summed as the estimates of the true position errors. In this way, theimproved method removes the aforementioned approximation error, leading to estimateswith high accuracy. In addition, the improved method is more robust to position errorsthan the conventional method. Furthermore, the increase of the computational load ofthe improved method is negligible.3. The conventional array error estimation method requires joint iteration betweenposition error estimation and gain-phase error estimation, leading to suboptimalsolutions and weak robustness in large position errors. We observe that the steeringvectors of the spectrum components in one Doppler bin are conjugate with those of thespectrum components in its contrary Doppler bin on the condition that each SARoperates in the side-looking mode. We propose an array error estimation method basedon this observation and the uniqueness of the projection matrix. The proposed methoddirectly estimates phase and position errors without joint iteration between theestimations of phase and position errors, and overcomes the local convergence and theinstability of the conventional method. Furthermore, mathematical analysis indicatesthat the proposed method has less computation load. The only cost is that it employstwice as many Doppler bins as the conventional method does, which is endurablebecause there are numerous Doppler bins.4. The conventional MUSIC method cannot resolve more sources than the numberof antennas. To overcome this problem, a method is proposed by exploiting thedifference between the circularity of noncircular and circular signals. In the proposed method, we firstly estimate the DOAs of noncircular signals based on the nonconjugatecovariance matrix of the array output vector. Subsequently, we estimate the DOAs ofcircular signals based on the conventional covariance matrix. The maximum number ofdetectable directions by the proposed method is twice that by the MUSIC method.Furthermore, since the proposed method resolves noncircular and circular signals basedon the circularity difference rather than the DOA difference, the proposed methodperforms well regardless of the DOA separation between noncircular and circularsignals. Simulation results illustrate the effectiveness of the proposed method. Thedrawback of the proposed method is that in large DOA separation, its estimationaccuracy is lower than that of the MUSIC method.