Asymptotically optimal detection in unknown colored noise via autoregressive modeling

The problem of detecting a known signal in colored Gaussian noise of unknown covariance is addressed. The noise is modeled as an autoregressive process of known order but unknown coefficients. By employing the theory of generalized likelihood ratio testing, a detector structure is derived and then analyzed for performance. It is proven that for large data records the detection performance is identical to that of an optimal prewhitener and matched filter, and therefore the detector itself is optimal. Simulation results indicate that the data record length necessary for the asymptotic results to apply can be quite small. Thus, the proposed detector is well suited for practical applications.