TEMPORAL AND SPATIAL SAMPLING INFLUENCE ON THE ESTIMATES OF SUPERIMPOSED NARROW-BAND SIGNALS - WHEN LESS CAN MEAN MORE

This paper addresses the influence that the sampling locations have on the estimated frequencies of superimposed sinusoids, This problem has application in harmonic time-series analysis or direction-finding pha sed-array systems. Generalized mathematical bounds are developed in te rms that are independent of the array locations and have an intuitivel y appealing physical interpretation, They establish the influence of t he sampling locations on the variance of the frequency estimate and th e limit, at which two sources can be resolved using signal subspace es timators, For the resolution criteria, an expression dominated by the fourth central moment of the sensor locations expresses the resolving ability of the sensing array, irrespective of the array aperture or nu mber of sensors, Increasing the fourth central moment increases an arr ay's resolution ability, The commonly accepted notion that resolution necessarily depends on the array aperture is misleading and, indeed, t hat fewer snapshots from a reduced aperture array can outperform a lar ger array of more elements. For the estimator variance criteria, it is found that the product of the number of sensors and the second centra l moment (array variance) characterizes the estimator variance lower b ound, The metrics developed demonstrate that the;sampling topology is itself an important factor in determining the performance of the sampl ing system (and not the covariance lags sampled or the aperture spanne d).