Volume Properties for the Wideband Ambiguity Function

It is shown that the volume under the wideband ambiguity function is close to the square of the signal energy. The ambiguity volume is asymptotically conserved as the signal approaches the narrowband case. The narrowband ambiguity volume is a lower bound for the volume of the wideband ambiguity function.     

Dynamic Effects of Signal Normalizing on Adaptive Algorithms

A method is shown for suppressing the adaptive switching transient that arises in complex adaptive (LMS and stochastic approximation) algorithms due to signal normalization with controlled switched gains. The method involves rescaling of the adaptive weights with the normalizing gains just prior to the first adaptation with the new gains. In addition, an effective method of rescaling the adaptive gain factor based on the maximum eigenvalues of the respective covariance matrices is shown.     

Time-Frequency HOP Signals Part II: Coding Based upon Quadratic Congruences

High-efficiency multicomponent signals for maximization of signalto-noise ratio are investigated. Maximization of signal-to-noise ratio in colored noise requires control of volume distribution of the signal ambiguity function and transmission of unity efficiency signals. Signal efficiency is defined as the ratio of average power to the peak power. It is concluded that the signals must be frequency hop pulse trains. Quadratic congruences are chosen to place the components in time-frequency space. The number-theoretic properties of these signals provide bounds on the position and amplitude of the various peaks of the signal ambiguity function. The tradeoffs are shown between volume removal, number of component signals, and the time-bandwidth product.     

Blind source separation and beamforming: algebraic technique analysis

Blind source separation (BSS) and blind beamforming schemes attempt to separate additive source signals, collected at a sensor array, and their direction-of-arrival (DOA). To this extent, many different and powerful algorithms have been produced to accomplish these tasks. However, unlike an optimal or adaptive method, an algebraic method for BSS and blind beamforming has the relative advantage of simplicity. This paper investigates such a technique that provides closed-form, algebraic expressions for BSS and beamforming in terms of performance and reliability. We provide these results, as well as a summary of the properties, and possible uses for this technique, in contrast to more optimal, adaptive techniques.