Interference excision in DSSS based on the Undecimated Wavelet Packet Transform

This article presents an algorithm for suppressing narrowband interference in Direct-Sequence Spread-Spectrum Systems. It is based on a combination of frequency shifts with the Undecimated Wavelet Packet Transform. Simulation results show very robust and nearly optimal performance. Introduction: The interference rejection performance of a spread spectrum communication system can be improved by interference suppression techniques. The case of a Direct-Sequence Spread-Spectrum (DSSS) waveform received in the presence of narrowband interference is considered in this article. Transform domain excision is a suitable approach for interference suppression. Among the different transforms, those based on wavelet packets, which are intimately related to hierarchical filter banks [1, 2], have been shown to be especially useful. In particular, the adaptive hierarchical Tree Structuring Algorithm (TSA) proposed in [2] yields superior performance in comparison to conventional fixed transforms. The performance of the TSA depends on the position and bandwidth of the interference. In this article we propose an algorithm for interference excision in DSSS systems, based on the Undecimated Wavelet Packet Transform (UWPT) with performance independent of the interference frequency. It has been previously applied with success to FHSS systems [3]. The system considered is a coherent DS/BPSK [2][4] with narrowband interference and AWGN, thus the received signal is: (1) (t) n I(t) t) cos(w 2S c(t)d(t) r(t) w 0 + + = being d(t)=dm , mTb ≤ t ≤ (m+1)Tb , dm∈{-1,1} the data sequence and c(t)=cn , nTc ≤ t ≤ (n+1)Tc , cn∈{-1,1} the pseudo-noise sequence. Tb is the bit time and Tc is the chip time interval. K=Tb/Tc is the spreading factor. The receiver scheme is shown in Fig. 1. UWPT exciser: This is based on the application of frequency shifts to the signal in order to place the interference inside of one of the pass-band filters. Since the intervals in the UWPT expansion become smaller as resolution increases (Fig. 2b), the algorithm will begin with the highest resolution level to reduce the number of possible frequency shifts. Due to the fact that the transition and the pass-band intervals in successive resolution levels are aligned (see Fig. 2b), once the optimum frequency shift is obtained at the highest resolution level, the interference will remain centred at the other levels just by shifting either 0 or Bj/2, where Bj is the bandwidth of subbands at level j. Therefore, there is no longer any need to try with all possible frequency shifts. The following is a description of the UWPT exciser. Let J be the highest resolution level. For each d(J)∈[0,...,BJ] with step ∆d, the following actions are performed: 1. The input vector is frequency shifted. 2. It is then filtered to obtain the lowand high-pass subbands, WJ,0,d(J) and WJ,1,d(J). The filters for a generic level j are defined as: (2) ) (z H (z) H ) (z H (z) H 1 j 1 j 2 1 1j 2 0 0j − − = = where H0(z), H1(z) are the 2-band prototype analysis filters. 3. Finally, the energy difference between both subbands is calculated: