Analysis of the One-Pole Notch Filter for Interference Mitigation: Wiener Solution and Loss Estimations

The extreme weakness of the Galileo and GPS signals required the development of different interference mitigation techniques for the reduction of their impact in the receiver chain. One of the main classes of interfering is formed by all those narrowband signals that can be reasonably represented as pure sinusoids with respect to the Galileo/GPS bands. For this kind of interfering the notch filter has proved to be an efficient mitigation technique [3] This work is mainly focused on the analysis of the one-pole notch filter, first introduced in [8], and the case of a single interferer modelled as a complex sinusoid is analyzed. This kind of interferer implies the presence of a single spectral line that justify the single pole notch filter. The filter presents a single zero z(0) that is adaptively adjusted in order to minimize the output signal energy. The absolute value of z(0) is not constrained to 1 as in many works, but is adaptively adjusted, providing greater flexibility and an additional freedom degree. So, firstly the notch filter with its adaptive block is presented, and the employed LMS algorithm derived. Then the notch bandwidth and depth (transfer function maximum and minimum values) are analytically derived. Moreover, in order to analyze the asymptotical behaviour of the filter, the work provides a precise and generally valid Wiener solution, that is the optimal one (limit for the LMS). Simulations confirm the derived formulas, show that the interferer is properly individuated and cancelled, and validate the expression of the Wiener solution. Finally the loss introduced by the notch filter in absence of interferer is calculated on the basis of the ratio of the correlation output SNRs respectively in absence and in presence of notch filter.