Adaptive Radar for Uncooperative Spectrum Sharing: GLRT Asymptotic Performance

Abstract

The increasing demand for spectrum has paved the way to spectral coexistence of different radio systems, in particular radar and communications (namely 5G mobile systems and beyond). In coexistence scenarios the communication signal affects both the cell under test (primary data) and the training (secondary) data used by the radar to estimate the clutter covariance matrix, making it difficult to obtain an adequate number of samples due to the nonstationarity of the interference. To prevent the consequent degradation of the probability of detection, earlier work proposed a generalized likelihood ratio test (GLRT)-based detector that does not require secondary data, by modeling the interference in terms of an autoregressive filter. However, the analysis was given only through Monte Carlo simulations due to the intractability of the detection statistic, thus lacking understanding of the relationships with the fundamental parameters at play, and possibility to set the threshold (and predict the corresponding performance) especially for low values of the probability of false alarm. In the present paper we provide an asymptotic statistical characterization and assess to what extent it can be a valid tool for performance prediction. By means of Wilks’ theorem, the asymptotic distribution of the GLRT statistic is derived, which requires calculation of the Fisher information matrix associated with the Cramér-Rao bound for the estimation of data model parameters. The resulting closed-form expression is simple and elegant, and can be easily computed to both obtain approximate threshold setting for a desired probability of false alarm and to analyze the resulting performance in terms of probability of detection. The theoretical predictions show reasonable agreement with the numerical results, and reveal relevant dependency on system parameters, in particular the number of samples of both radar and communication signals, the signal-to-noise ratio, and the normalized frequencies of both communications and target steering vectors.