## 1 Introduction
Assuming the integral knowledge about the narrow band interference is known, when there is a set of narrow band interferences and the central frequency or the amplitude of the narrow band interferences is varying, methods utilizing analog notch filters or notch antennas may lose their practicality. In addition, utilizing traditional fixed analog filters in the frequency domain will no doubt increase the computation complexity, size, power consumption and cost of the ultra-wide band wireless sensor networks. In this article, we present a novel complex-coefficient in-band adaptive NBI-avoiding scheme for time hopping coding division impulse ultra-wide band wireless sensor networks. To simplify the reception processing, a novel adaptive complex-coefficient iteration relationship based on Taylor series of the one order complex value notch filter unit with a single zero-pole pair is derived. Based on our previous works [35; 36], to cope with multiple in-band strong NBIs in the same ultra-wide band wireless sensor networks, a complex-coefficient linear cascaded high order adaptive notch filter (ANF) and a novel cyclic cascaded high order matrix adaptive notch filter (CCHOMAF) NBI-elimination algorithm based on the proposed basic ANF units are presented. The proposed method is able to elevate the reception performance of UWB wireless sensor networks, not only in additive white Gaussian noise (AWGN) environments, but also in the ultra-wide band multipath fading channels. Since the proposed interference suppression processing can be executed before signal demodulation, it is also fit for the non-coherent impulse UWB wireless sensors [47]. The theoretical analysis and numerical simulation results indicate that the proposed CCMOMAF algorithm has perfect performance in ultra-wide band wireless sensor networks under strong in-band NBIs, in which an ideal average bit error probability performance versus signal to interference and noise ratio (SINR) enhancement is acquired. Overall, the proposed complex-coefficient adaptive notch filter the in-band NBI-elimination scheme can greatly elevate the immunity against NBIs for the ultra-wide band wireless sensors, which is quite suitable for improving the reception performance of low-cost low-power consumption cognitive ultra-wide band wireless sensor networks. The remainder of the article is outlined as follows. The time hopping code division pulse position modulation (PPM)-based impulse radio (IR) ultra-wide band wireless signal model is presented in Section 2. The reception performance under the AWGN channel and under the multipath fading propagation channel in the presence of narrow band interferences are discussed and compared in Section 3. The detailed procedure of the basic complex-coefficient adaptive notch filter unit with a single zero-pole pair is developed, and the closed form relationship of the weight coefficient based on Taylor series expansion is derived in Section 4. To cope with multiple in-band narrow band interferences, a linear cascaded high order adaptive notch filter and a novel cyclic cascaded high order adaptive notch filter interference elimination algorithm based on the proposed basic one order adaptive notch filter unit are also considered in Section 4. The numerical results are presented and the reception performances and performance elevated under different channel conditions are discussed in Section 4. Finally, Section 5 draws the conclusions of the article.