sforms beam pattern to the Effective and also in case of prior knowledge of the clusters from Aperture Distribution Function (EADF) domain which the signals originate. [LaRT04a], [LaRT04b]. The EADF matrix is calculated by a 2D Fourier transform by applying the Fourier ma- Beamformer optimisation step trices of the azimuth and the elevation to the discrete To avoid estimation results which are local minima of the beam patterns. The EADF concept allows a considerable cost function in [TLAP02] it is proposed to suppress the data compression since it is distinguished by a limited side lobes of the beamformer ck (x, O) = xk (O), where support area as shown in Figure 4.7-29 (right). On the Xk is the complete data of the kth path and a(O) is the other hand, it allows a simple analytic calculation of the normalised steering vector of the antenna array with re- derivatives with respect to the angular parameters. spect to the DoA O. In the initialisation step, from most Once one has the first-order derivatives with respect ML algorithms such as EM and SAGE this function is to the DoA the Fisher Information Matrix (FIM) and its calculated. For an example of a UCA with omnidirectional inverse the CRLB of an arbitrary test scenario can be beam patterns the best side lobe level suppression is calculated. The investigation and exploitation of the FIM achieved by a radius of: ropt 11 N1/16 < 7/4sin(n2/N). structure is essential to design a robust and efficient pa- Further suppression is possible through the joint optimi- rameter estimator. The simplest scenario is a single im- sation of the beam pattern of the antenna elements and the pinging path scenario, which is analysed in the following array radius. It is found that the radius of the UCA should example. It is related to an SPUCPA with 192 elements. be as big as possible in terms of a minimum CRLB of the In this scenario the FIM is diagonal. In Figure 4.7-30 the DoA. In terms of side lobe suppression of the beamformer CRLB of the azimuth angle is compared to the variance a