Adaptive enhancement of finite bandwidth signals in white Gaussian noise

The steady-state behavior of the adaptive line enhancer (ALE) is studied using stationary inputs which consist of finite bandwidth signals embedded in a white Gaussian noise background. Analytic expressions are derived for the weights and output of the least mean squares adaptive filter as functions of input signal bandwidth, signal to noise ratio (SNR), ALE length, and bulk delay. The steady-state gain in broad-band SNR from input to output is also derived as a function of these four variables. It is found that for fixed ALE parameters and input SNR, this gain increases as the input signal becomes narrower and approaches the sinusoidal limit. Excessively large values of the ALE bulk delay parameter are found to result in diminished gain due to the limited correlation time of the finite bandwidth signals. In addition, an optimal filter length, whose value depends upon the signal bandwidth and SNR, is found for which the broadband gain is maximized. It is concluded that these results demonstrate the importance of including the effects of algorithm noise in analyzing the performance of real-time adaptive processors.