Abstract: Fractional Fourier Transform (FrFT)-based spectrum analyzers and spectrum analysis techniques are disclosed. Rather than using the standard Fast Fourier Transform (FFT), the FrFT may be used to view the signal content contained in a particular bandwidth. Usage of the FrFT in place of the frequency or time domain allows viewing of the signal in different dimensions, where “spectral” features of interest, or signal content, may appear where they were not visible in these domains before. This may allow signals to be identified and viewed in any domain within the continuous time-frequency plane, and may significantly enhance the ability to detect and extract signals that were previously hidden under interference and/or noise, provide or enhance the ability to extract signals from a congested environment, and enable operation in a signal-dense environment.

Abstract: Fractional Fourier Transform (FrFT)-based spectrum analyzers and spectrum analysis techniques are disclosed. Rather than using the standard Fast Fourier Transform (FFT), the FrFT may be used to view the signal content contained in a particular bandwidth. Usage of the FrFT in place of the frequency or time domain allows viewing of the signal in different dimensions, where “spectral” features of interest, or signal content, may appear where they were not visible in these domains before. This may allow signals to be identified and viewed in any domain within the continuous time-frequency plane, and may significantly enhance the ability to detect and extract signals that were previously hidden under interference and/or noise, provide or enhance the ability to extract signals from a congested environment, and enable operation in a signal-dense environment.

Abstract: A waveform analysis and vulnerability assessment (WAVE) tool is disclosed that can analyze the characteristics and vulnerabilities of waveforms. The WAVE tool may identify issues in waveforms prior to their implementation in a transmit device or building the back-end processing to receive the waveform at a ground station. The WAVE tool may quantify waveform vulnerabilities, address which vulnerabilities a particular waveform has, and enable the user to modify the waveform design to optimize its performance against threats prior to implementation. Additionally, the WAVE tool may save time and money since new waveforms can be vetted against the tool before implementation. Data from waveforms can be analyzed against a plurality of metrics and scores can be generated providing a quantitative assessment of waveform performance.

Abstract: Fractional Fourier Transform (FrFT)-based spectrum analyzers and spectrum analysis techniques are disclosed. Rather than using the standard Fast Fourier Transform (FFT), the FrFT may be used to view the signal content contained in a particular bandwidth. Usage of the FrFT in place of the frequency or time domain allows viewing of the signal in different dimensions, where “spectral” features of interest, or signal content, may appear where they were not visible in these domains before. This may allow signals to be identified and viewed in any domain within the continuous time-frequency plane, and may significantly enhance the ability to detect and extract signals that were previously hidden under interference and/or noise, provide or enhance the ability to extract signals from a congested environment, and enable operation in a signal-dense environment.

Abstract: Channel estimation using a chirp signal and the Fractional Fourier Transform (FrFT) is disclosed. A relatively short chirp may be transmitted, and its received components may be converted to tones using the FrFT, from which the channel tap magnitudes and delays can readily be computed. This may involve measuring peaks in the rotated spectrum, measuring the time between the peaks, and mapping the time in the rotated plane back to the original time. Such a technique has various advantages over conventional channel estimation techniques, such as providing high accuracy even in very poor multipath environments and requiring relatively few samples of a chirp, which hence can reduce pilot overhead.

Abstract: A signal-of-interest (SOI) may be separated from interference and/or noise using repeated reduced rank minimum mean-square error Fractional Fourier Transform (MMSE-FrFT) filtering and a low rank adaptive multistage Wiener filter (MWF). A number of stages in the MWF, L, may be chosen such that at the Lth stage, the MSE between the SOI estimate and the true SOI is less than or equal to an error threshold ? (e.g., ?=0.001). By combining these filtering techniques, significant improvement in reducing the mean-square error (MSE) may be realized over single stage MMSE-FrFT, repeated MMSE-FrFT, and MMSE-FFT algorithms—indeed, by an order of magnitude or more.

Abstract: A signal-of-interest (SOI) may be separated from interference and/or noise using repeated reduced rank minimum mean-square error Fractional Fourier Transform (MMSE-FrFT) filtering and a low rank adaptive multistage Wiener filter (MWF). A number of stages in the MWF, L, may be chosen such that at the Lth stage, the MSE between the SIM estimate and the true SW is less than or equal to an error threshold ? (e.g., ?=0.001). By combining these filtering techniques, significant improvement in reducing the mean-square error (MSE) may be realized over single stage MMSE-FrFT, repeated MMSE-FrFT, and MMSE-FFT algorithms—indeed, by an order of magnitude or more.

Abstract: A signal-of-interest (SOI) may be separated from interference and/or noise using repeated reduced rank minimum mean-square error Fractional Fourier Transform (MMSE-FrFT) filtering and a low rank adaptive multistage Wiener filter (MWF). A number of stages in the MWF, L, may be chosen such that at the Lth stage, the MSE between the SOI estimate and the true SOI is less than or equal to an error threshold ? (e.g., ?=0.001). By combining these filtering techniques, significant improvement in reducing the mean-square error (MSE) may be realized over single stage MMSE-FrFT, repeated MMSE-FrFT, and MMSE-FFT algorithms—indeed, by an order of magnitude or more.

Abstract: A signal-of-interest (SOI) may be separated from interference and/or noise using repeated reduced rank minimum mean-square error Fractional Fourier Transform (MMSE-FrFT) filtering and a low rank adaptive multistage Wiener filter (MWF). A number of stages in the MWF, L, may be chosen such that at the Lth stage, the MSE between the SIM estimate and the true SW is less than or equal to an error threshold E (e.g., ?=0.001). By combining these filtering techniques, significant improvement in reducing the mean-square error (MSE) may be realized over single stage MMSE-FrFT, repeated MMSE-FrFT, and MMSE-FFT algorithms indeed, by an order of magnitude or more.

Abstract: The Fractional Fourier Transform (FrFT) may be used to extract multiple radar targets in clutter where some targets may be relatively weak. To do this, stronger targets may be removed by rotating to the proper axis ta using rotational parameter a, in which the target signal becomes a strong tone. By searching for the maximum peak over all values of a, stronger moving target echoes can be found and notched out, and weaker targets can then be extracted.

Abstract: The Fractional Fourier Transform (FrFT) may be used to extract multiple radar targets in clutter where some targets may be relatively weak. To do this, stronger targets may be removed by rotating to the proper axis ta using rotational parameter a, in which the target signal becomes a strong tone. By searching for the maximum peak over all values of a, stronger moving target echoes can be found and notched out, and weaker targets can then be extracted.

Abstract: A novel approach provides accurate estimation of the parameter a of a Fractional Fourier Transform (FrFT). A value of a may be selected for which the Wigner Distributions (WDs) of a signal-of-interest (SOI) and interference overlap as little as possible. However, instead of computing the WD for each signal, the FrFT may be computed for each WD, recognizing that the projection of the WD of a signal onto an axis ta is the energy of the FrFT along the same axis. Since the technique computes a using the SOI and a measure of the interference separately, significant improvements can be made in the estimate, especially at low signal-to-noise ratio (SNR). Once the estimate is obtained, a reduced rank filter may be applied to remove the interference, since minimum mean-square error (MMSE) approaches will again fail when using the low sample support required of non-stationary environments. The technique is not only computationally more efficient than MMSE, but far more robust as well.

Abstract: A novel approach provides accurate estimation of the parameter a of a Fractional Fourier Transform (FrFT). A value of a may be selected for which the Wigner Distributions (WDs) of a signal-of-interest (SOI) and interference overlap as little as possible. However, instead of computing the WD for each signal, the FrFT may be computed for each WD, recognizing that the projection of the WD of a signal onto an axis ta is the energy of the FrFT along the same axis. Since the technique computes a using the SOI and a measure of the interference separately, significant improvements can be made in the estimate, especially at low signal-to-noise ratio (SNR). Once the estimate is obtained, a reduced rank filter may be applied to remove the interference, since minimum mean-square error (MMSE) approaches will again fail when using the low sample support required of non-stationary environments. The technique is not only computationally more efficient than MMSE, but far more robust as well.

Abstract: An improved method for resolving interference between co-channel users is disclosed. A peak in a spectrum generated by a MUSIC algorithm is determined for a signal of interest (“SOI”) using a noise subspace. Also, an estimated carrier frequency offset (“CFO”) is determined for the SOI based on the determined peak in the spectrum.

Abstract: An improved method for resolving interference between co-channel users is disclosed. A peak in a spectrum generated by a MUSIC algorithm is determined for a signal of interest (“SOI”) using a noise subspace. Also, an estimated carrier frequency offset (“CFO”) is determined for the SOI based on the determined peak in the spectrum.

Abstract: Spreading code detection methods applying autoregressive spectrum estimation (ARSE) techniques to code division multiple access (CDMA) wireless communication systems allowing the subscriber device to estimate the other users' codes. According to one aspect, ARSE techniques are provided using an augmented Wiener-Hopf solution on a received forward link CDMA signal. The ARSE techniques produce a code spectrum transform yielding a power spectral density versus spreading code index relationship from which the spreading codes in the received forward link signal may be identified. According to another aspect, a reduced rank auto-regression (AR) implementation is provided to produce a code spectrum transform efficiently with improved false code detection rate. With knowledge of other users' spreading codes, interference cancellation can be performed on the forward link of CDMA systems.

Abstract: Adaptively analyzing an observed signal to estimate that part of the signal that best corresponds to a steering vector. Modifying the steering vector by convolution of the steering vector with a vector estimating the effect of multipath on the observed signal.

Abstract: Adaptively analyzing an observed signal to estimate that part of the signal that best corresponds to a steering vector. Modifying the steering vector by convolution of the steering vector with a vector estimating the effect of multipath on the observed signal.