Under wide sense stationary uncorrelated scattering (WSSUS) conditions, the signal spreading due to a random channel may be described by the scattering function (SF). In an active acoustic system, the received signal is modeled as the superposition of delayed and Doppler spread replicas of the transmitted waveform. The SF completely describes the second-order statistics of a WSSUS channel and can be considered a density function that characterizes the average spread in delay and Doppler experienced by an input signal as it passes through the channel.The SF and its measurement will be reviewed. An estimator is proposed based on a two-dimensional autoregressive (AR) model for the scattering function. In order to implement this estimator we derive the minimum mean square error estimator of the time-varying frequency response of a linear channel. Unlike conventional Fourier methods the AR approach does not suffer from the usual convolutional smoothing due to the signal ambiguity function. Simulation results are given.

Under wide sense stationary uncorrelated scattering (WSSUS) conditions, the signal spreading due to a random channel may be described by the scattering function (SF). In an active acoustic system, the received signal is modeled as the superposition of delayed and Doppler spread replicas of the transmitted waveform. The SF completely describes the second-order statistics of a WSSUS channel and can be considered a density function that characterizes the average spread in delay and Doppler experienced by an input signal as it passes through the channel. The SF and its measurement will be reviewed. An estimator is proposed based on a two-dimensional (2-D) autoregressive (AR) model for the scattering function. In order to implement this estimator, we derive the conditional minimum variance unbiased estimator of the time-varying frequency response of a linear channel. Unlike conventional Fourier methods, the AR approach does not suffer from the usual convolutional smoothing due to the signal ambiguity function. Simulation results are given.

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A computer package, Automated Mirror Design, has been developed by us to automate the design of luminaire reflectors. In this paper, new improvements to the algorithm for Automated Mirror Design are presented. We have previously reported a study on a series of point-light source luminaire problems. We now report on the operation of Automated Mirror Design for non-trivial light sources. In particular, reflector designs are presented for an extended light source, which produce limited Lambertian output and return no radiation to the source. Finally, the operation of differential evolution relies on the use of an appropriate merit function to determine the quality of proposed mirror designs. Merit functions specific to the Lambertian output design problem are discussed.