Adaptive enhancement of finite bandwidth signals in white Gaussian noise

The steady-state behavior of the adaptive line enhancer (ALE) is analyzed for stationary inputs consisting of finite bandwidth signals embedded in a white Gaussian noise (WGN) background. Analytic expressions for the weights and output of the LMS adaptive filter are derived as functions of input signal bandwidth and SNR, as well as ALE length and bulk delay. The steady-state gain in broad-band SNR from input to output is derived as a function of these same four variables. For fixed ALE parameters and input SNR, it is shown that this gain increases as the input signal becomes narrower and approaches the sinusoidal limit. It is emphasized that because the correlation time of finite bandwidth signals is limited, excessively large values of the ALE bulk delay parameter result in diminished gain. Furthermore, there is an optimal filter length, whose value depends upon signal bandwidth and SNR, for which the broad-band gain is maximized. These results demonstrate the importance of including the effects of algorithm noise in analyzing the performance of real-time adaptive processors.