Array signal Processing in the known waveform and steering vector case

The amplitude estimation of a signal that is known only up to an unknown scaling factor, with interference and noise present, is of interest in several applications, including using the emerging quadrupole resonance (QR) technology for explosive detection. In such applications, a sensor array is often deployed for interference suppression. This paper considers the complex amplitude estimation of a known waveform signal whose array response is also known a priori. Two approaches, viz., the Capon and the maximum likelihood (ML) methods, are considered for the signal amplitude estimation in the presence of temporally white but spatially colored interference and noise. We derive closed-form expressions for the expected values and mean-squared errors (MSEs) of the two estimators. A comparative study shows that the ML estimate is unbiased, whereas the Capon estimate is biased downwards for finite data sample lengths. We show that both methods are asymptotically statistically efficient when the number of data samples is large but not when the signal-to-noise ratio (SNR) is high. Furthermore, we consider a more general scenario where the interference and noise are both spatially and temporally correlated. We model the interference and noise vector as a multichannel autoregressive (AR) random process. An alternating least squares (ALS) method for parameter estimation is presented. We show that in most cases, the ALS method is superior to the model-mismatched ML (M³L) method, which ignores the temporal correlation of the interference and noise.