Detection performance of the reduced-rank linear predictor ROCKET

This paper assesses the frequency detection capabilities of a new signal-dependent reduced-rank linear predictor applied to autoregressive spectrum estimation. The new technique is called reduced-order correlation kernel estimation technique (ROCKET). Its detection performance is examined by comparison to a full-rank autoregressive (FR-AR) estimator and two reduced-rank principal component autoregressive (PC-AR) estimators based on both the standard signal-independent version and a modified signal-dependent method. The performance of the new autoregressive estimator is also compared as a function of rank to the popular pseudo-spectrum estimator MUSIC. The performance metrics examined are the probability of detection (P_D) and the false alarm rate (FAR) of detecting the spatial frequencies of plane waves impinging on a uniform line array in additive white Gaussian noise. These metrics are studied as a function of subspace rank, sample support, and signal-to-noise ratio (SNR). Simulations show that the signal-dependent reduced-rank estimators significantly outperform both the signal-independent version of PC-AR and the FR-AR estimator for low sample support and low SNR environments. One notable characteristic of ROCKET that highlights its distinct subspace selection is its performance as a function of subspace rank. It is observed that for equal powered signals, its peak performance is nearly invariant to signal rank and that at almost any subspace rank ROCKET meets or exceeds FR-AR performance. This provides an extra degree of robustness when the signal rank is unknown.