A Contribution to Efficient Direction Finding using Antenna Arrays

It is save to say that there is no such thing as the direction finding (DF) algorithm. Rather, there are algorithms that are tuned to resolve hundreds of paths, algorithms that are designed for uniform linear arrays or uniform circular arrays, and algorithms that strive for efficiency. The doctoral thesis at hand deals with the latter type of algorithms. However, the approach taken does not only incorporate the actual DF algorithm but approaches the problem from different perspectives. The first perspective concerns the description of the array manifold. Current interpolation schemes have no notion of polarization. Hence, the array manifold interpolation is performed separately for each state of polarization. In this thesis, we adopted the idea of interpolation via a 2-D discrete Fourier transform. However, we transform the problem into the quaternionic domain. Here, a 2-D discrete quaternionic Fourier transform is applied. Hence, both states of polarization can be viewed as a single quantity. The resulting interpolation is applied to a signal model which is essentially compatible to conventional complex model. The second perspective in this thesis is to look at the fundamental DF capability of an antenna array. For that, we use the deterministic Cram?r-Rao Lower Bound (CRLB). We point out the differences between not considering polarimetric parameters and taking them as desired parameters or nuisance parameters. Such differences lead to three different CRLBs. Moreover, insight is given how a CRLB can be used to optimize an antenna array already during the design process to improve its DF performance. The actual DF algorithm constitutes the third perspective that is considered in this thesis. A MUSIC-based cost function is used to derive efficient estimators. To this end, a modified Levenberg search and Levenberg-Marquardt search are employed. Since the original cost function is not eligible to be used in this framework, we replace it by four different functions that locally show the same behavior. These functions are based on a linearization of Kronecker products of two polarimetric array steering vectors. It turns out that at least one of these functions usually exhibits very fast convergence leading to real-time capable algorithms.