Antenna array mapping for DOA estimation in radio signal reconnaissance

Abstract: To counter radio signal reconnaissance, an efficient way of covert communication is to use subsecond duration burst transmissions in the congested HF band. Against this background, the present thesis treats fast direction finding (DF) using antenna arrays with known response only in a few calibration directions. In such scenarios the known method of array mapping (interpolation) may be used to transform the output data vectors from the existing array onto the corresponding output vectors of another (virtual) array that is mathematically defined and optimally chosen. But in signal reconnaissance the emitters are initially unknown and the mapping matrix must be designed as a compromise over a wide sector of DOAs. This compromise may result in large DOA estimate errors, both deterministic and random. Analyzing, analytically describing, and minimizing these DOA errors, is the main theme of the present thesis. The first part of the thesis analyzes the deterministic mapping errors, the DOA estimate bias, that is caused by dissimilarity between the two array geometries. It is shown that in a typical signal reconnaissance application DOA estimate bias can dominate over DOA estimate variance. Using a Taylor series expansion of the DOA estimator cost function an analytical expression for the bias is derived and a first order zero bias condition is identified. This condition is general, estimator independent, and can be applied to any type of data pre-processing. A design algorithm for the mapping matrix is thereafter presented that notably reduces mapped DOA estimate bias. A special version is also given with the additional property of reducing the higher order Taylor terms and thus the residual bias. Simulations demonstrate a bias reduction factor exceeding 100 in some scenarios. A version based on signal subspace mapping rather than array manifold mapping is also given. This version is of large practical interest since the mapping matrix can be designed directly from calibration data. In the second part of the thesis the derived bias minimization theory is extended into Mean Square Error (MSE) minimization, i.e. measurement noise is introduced. Expressions for DOA error variance and DOA MSE under general pre-processing are derived, and a design algorithm for the mapping matrix is formulated by which mapped DOA estimate MSE can be minimized. Simulations demonstrate improved robustness and performance for this algorithm, especially in low SNR scenarios. In the third and final part of the thesis the theoretical results are supported by experimental data. For an 8 element circular array mapped onto a virtual ULA across a 600 sector it is shown that the mapped DOA estimate errors can be suppressed down to the Cramér-Rao level.