Rejection Capability of Anti-Jamming Wiener Filter for Multi-Tone Interference in DSSS Systems

In the context of military communications, anti-jamming techniques are of paramount importance to protect against potential interferences. Within this framework, the anti-jamming Wiener filter is particularly well-suited for rejecting stationary narrow-band jammers that disrupt wideband systems such as Direct-Sequence Spread Spectrum (DSSS). This paper presents a unified matrix-form derivation of the optimal Wiener solution to the anti-jamming filter design problem. Therefrom, the closed-form expression of the rejection capability of such anti-jamming filter is obtained for an arbitrary multi-tone jamming signal. This allows for identifying the worst-case scenarios where the Wiener filter may fail in rejecting the jamming signal. This theoretical analysis finally leads to some recommendations of minimal length of the anti-jamming filter to guarantee a minimum rejection capability.