Nonstationary Jammer Excision for GPS Receivers Using Sparse Reconstruction Techniques

Nonstationary jammer excision has been the subject of interest for anti-jam GPS receivers for many years. A large class of “smart” jammers assumes frequency modulated (FM) waveforms that are characterized by their instantaneous frequencies (IFs). Several anti-jam techniques rely on the instantaneously narrowband signal characteristic and use joint-variable signal representations to reveal the jammer signature in the time-frequency (TF) domain. In this case, jammer excision becomes a two-step process, i.e., estimation of the TF signature or the IF of the jammer, and then removal of the jammer signal based on such estimate and with minimum distortion of the desired signal. Jammer excision approaches commonly assume that the data is sampled uniformly at the Nyquist or higher sampling rate with all data samples available. There are situations, however, where the availability of the jammer signal sampled at the Nyquist rate is either unnecessary or impossible. For example, mitigating impulsive noise through discarding the high amplitude data samples renders the data to be “incomplete” or randomly sampled. In this case, FM jammer signals with missing data samples exhibit a high level of noise-like artifacts which clutter the entire TF domain, rendering TF signature and IF estimations difficult. This paper provides a novel sparse reconstructionbased approach for effective jammer excision from incomplete signal observations. Jammer TF signature estimation is achieved by exploiting the fact that the FM jammers are locally sparse in the TF domain. Reconstruction of such signals from few random observations falls under the emerging area of compressive sensing (CS) and sparse reconstruction. Within the CS framework, jammer TF signature estimation is built upon the linear Fourier relationship between the TF domain and other joint-variable domains. In particular, the instantaneous auto-correlation function and the TF representations are associated by a one-dimensional Fourier relationship. This paper also describes TF kernels and its effect in the sparse reconstruction and mitigation of jammers.