Abstract: The objective of this patent is to develop new signal processing algorithms for a wide-band circular electronically scanned array (CESA) or a wideband linear electronically scanned array (LESA) for use in surveillance and communications applications, where a sequence of pulses are transmitted and their returns are collected by the array for further processing. Instead of partitioning the entire wideband frequency into various subbands and then processing them separately using narrowband schemes, a frequency focusing method is proposed here to compensate and focus the wideband spatio-temporal data into a single narrow frequency band. This is made possible by operating with a pre-computed frequency focusing matrix that transforms the data from various frequency slots that are spread across the entire wideband region into a common narrowband frequency for the array outputs.

Abstract: A transmit signal is output from a transmitter towards a target and towards interference. A combination signal is received at a receiver, wherein the combination signal includes the transmit signal modified by interacting with the target and the interference along with noise. The receiver has a filter having a transfer function and the filter acts on the combination signal to form a receiver output signal having a receiver output signal waveform. The receiver output signal has a receiver output signal waveform that describes an output signal to interference to noise ratio (SINR) performance. Bandwidth and signal energy of the transmit signal are reduced simultaneously by modifying the transmit signal waveform and receiver output signal waveforms without sacrificing the output SINR performance level.

Abstract: Given a fixed amount of capital, how to invest it optimally by distributing it among a set of stocks and securities so as to maximize the return while minimizing the overall risk is addressed here. Given that one has full freedom in selecting the type of stocks, a new strategy is outlined here by maximizing the ratio of the gain to risk—rather than minimizing the risk alone—to determine the fraction of capital that must go to each stock. An optimum gain versus variance plot can be used to determine the type of stocks to be selected in addition to their relative quantity for maximum yield over the duration of interest. By modifying the definition of risk to include a function of the covariance matrix of secondary stocks that are sympathetic to the primary stocks of interest, an alternate investment strategy is also developed here. If short selling of stocks and securities is not allowed in a portfolio, then stock selection becomes important so as to maintain the desired fractions to be positive.

Abstract: Given a fixed amount of capital, how to invest it optimally by distributing it among a set of stocks and securities so as to maximize the return while minimizing the overall risk is addressed here. Given that one has full freedom in selecting the type of stocks, a new strategy is outlined here by maximizing the ratio of the gain to risk—rather than minimizing the risk alone—to determine the fraction of capital that must go to each stock. An optimum gain versus variance plot can be used to determine the type of stocks to be selected in addition to their relative quantity for maximum yield over the duration of interest. By modifying the definition of risk to include a function of the covariance matrix of secondary stocks that are sympathetic to the primary stocks of interest, an alternate investment strategy is also developed here. If short selling of stocks and securities is not allowed in a portfolio, then stock selection becomes important so as to maintain the desired fractions to be positive.

Abstract: A new method for transmitter-receiver design that enhances the desired signal output from the receiver by whitening the total interference and noise input to the receiver and maximizing the output Signal to Interference plus Noise power Ratio (SINR) is presented. As a result of the whitening process, the receiver “sees” a desired signal in white noise, and the receiver structure is then optimized to maximize the receiver output at the desired decision making instant. Furthermore the new design scheme proposed here can be used for transmit signal energy and bandwidth tradeoff. As a result, transmit signal energy can be used to tradeoff for “premium” signal bandwidth without sacrificing the system performance level in terms of the output Signal to Interference plus Noise power Ratio (SINR).

Abstract: A new method for transmitter-receiver design that enhances the desired signal output from the receiver while minimizing the total interference and noise output from the receiver at the desired decision making instant is presented. Further the new design scheme proposed here can be used for transmit signal energy and bandwidth tradeoff. As a result, transmit signal energy can be used to tradeoff for the “premium” signal bandwidth without sacrificing the system performance level in terms of the output Signal to Interference plus Noise power Ratio (SINR). The two designs—the one before and the one after the tradeoff—will result in two different transmitter-receiver pairs that have the same performance level. In many applications such as in telecommunications, since the available bandwidth is at premium, such a tradeoff will result in releasing otherwise unavailable bandwidth at the expense of additional signal energy.

Abstract: A new method for transmitter-receiver design that enhances the desired signal output from the receiver while minimizing the total interference and noise output from the receiver at the decision making instant is presented here. Further the new design scheme proposed here can be used for simultaneous savings of transmit signal energy and bandwidth compared to any traditional waveform without sacrificing the performance level. As a result, compared to a traditional transmit waveform, simultaneous savings in transmit signal energy as well as the more “premium” signal bandwidth can be realized without sacrificing the system performance level in terms of the output Signal to Interference plus Noise power Ratio (SINR).

Abstract: Given a fixed amount of capital, how to invest it optimally by distributing it among a set of stocks and securities so as to maximize the return while minimizing the overall risk is addressed here. Given that one has full freedom in selecting the type of stocks, a new strategy is outlined here by maximizing the ratio of the gain to risk—rather than minimizing the risk alone—to determine the fraction of capital that must go to each stock. An optimum gain versus variance plot can be used to determine the type of stocks to be selected in addition to their relative quantity for maximum yield over the duration of interest. By modifying the definition of risk to include a function of the covariance matrix of secondary stocks that are sympathetic to the primary stocks of interest, an alternate investment strategy is also developed here. If short selling of stocks and securities is not allowed in a portfolio, then stock selection becomes important so as to maintain the desired fractions to be positive.

Abstract: A new technique for re-computing shading parameters for low sidelobe levels for a radar or sonar system is disclosed. When some of the sensor elements become inoperative, remaining shading parameters are recomputed using a new constraint. This approach leads to an overall gain pattern that is superior compared to the one without re-computing the weights.