On the asymptotic behavior of a complex adaptive line enchancer (CALE)

The Adaptive Line Enhancer (ALE) was first introduced by Widrow and has since been used in applications such as noise cancellation, coherent interference rejection, detection and estimation of sinusoid(s) in white noise, etc. In this paper, a Complex Adaptive Line Enhancer (CALE) is adopted to process complex-valued signals in their analytic form. The performance and asymptotic behavior of the CALE in cases of single and multiple sinusoid(s) in white noise are investigated in detail. It is shown that the frequency estimation obtained by CALE in the case of a single sinusoid is unbiased and independent of the bulk delay, Δ, the predictor length, L, and the Signal-to-Noise Ratio (SNR). If a conventional real ALE is used, this result, in general, cannot be obtained. A precise analysis is made for the case of two sinusoids. It is shown that an optimal choice of Δ, exists. For more than two sinusoids, an approximation is used to derive more insight into the analytical structure of a CALE. An intuitive explanation for the optimal choice of Δ, is given. Simulation results are also shown.