BARANKIN BOUNDS ON PARAMETER ESTIMATION ACCURACY APPLIED TO COMMUNICATIONS AND RADAR PROBLEMS
MASSACHUSETTS INST OF TECH LEXINGTON LINCOLN LAB
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The Schwartz Inequality is used to derive the Barankin lower bounds on the covariance matrix of unbiased estimates of a vector parameter. The bound is applied to communications and radar problems in which the unknown parameter is imbedded in a signal of known form and observed in the presence of additive white Gaussian noise. Within this context it is shown that the Barankin bound reduces to the Cramer-Rao bound when the signal-to-noise ratio SNR is large. However, as the SNR is reduced beyond a critical value the Barankin bound deviates radically from the Cramer-Rao bound thereby exhibiting the so-called threshold effect. A particularly interesting signal, which has been widely used in practice to estimate the range of a target, is the linear FM waveform. The bounds were applied to this signal and within the resulting class of bounds it was possible to select one which led to a closed form expression for the lower bound on the variance of the range estimate. This expression clearly demonstrates the threshold behaviour one must expect when using a nonlinear modulation system. Tighter bounds were easily obtained but these had to be evaluated using numerical techniques. It is shown that the side-lobe structure of the linear FM compressed pulse leads to a significant increase in the variance of the estimate. For a practical linear FM pulse of 1 microsecond duration and 40 megahertz bandwidth it is shown that the radar must operate at an SNR greater than 10dB if meaningful range estimates are to be obtained.
- Active and Passive Radar Detection and Equipment