The robust symmetrical number system (RSNS) is a number theoretic transform based on N ≥ 2 sequences that can extract the maximum amount of information from symmetrical folding waveforms. The sequences, based on coprime moduli, exhibit an integer gray code property making the RSNS well suited for many applications that benefit from an inherent error detection and correction capability, such as analog-to-digital converters, direction finding arrays, and radar waveform design. To use the RSNS, it is necessary to know the greatest length of combined sequences without ambiguities, called the dynamic range M̂, for which only a few closed-form expressions currently exist. In this paper, an efficient algorithm for computing M and its position within the combined set of sequences is presented and shown to be independent of the size of the moduli. The algorithm is used to generate the equations for several groups of additional moduli arrangements. Closed-form expressions for M are conjectured and proved using the obtained congruence equations that define the ambiguity locations.

This paper develops a new expression for a network node capability value used to quantify the node's ability to maintain an optimal information flow in a mobile communication network. The capability value is adaptable and is a function of the bandwidth efficiency, the data rate, the energy-per-bit to noise spectral density power ratio and reflects how effectively the node can receive, process and transmit data. To evaluate the capability expression a generalized connectivity metric is used which integrates the node capability values along with their connections scaled by the length of the routes (including their directionality) in order to measure the maximum information exchange rate (characteristic tempo) of the network. Simulation results are shown for a prototype four-node dynamic scenario to numerically evaluate the node capability values and the resulting network characteristic tempo.

The robust symmetrical number system (RSNS) is a number theoretic transform formed using N ≥ 2 integer sequences and ensures that two successive RSNS vectors (paired terms from all N sequences) differ by only one integer - integer Gray code property. The dynamic range M of the RSNS is defined as the greatest length of combined sequences that contain no ambiguities or repeated paired terms. For all but a select few RSNS sequences there is no closed-form solution to compute the dynamic range and its position. This paper presents an efficient algorithm for computing the dynamic range and its position. The dynamic range is shown to satisfy Mfwhere Pfis the RSNS fundamental period Pf= 2N Πmi. It then follows that Miis the dynamic range of the residue number system. An example is presented to demonstrate the algorithm. The efficiency of the algorithm is examined by comparing the speed of computation to a naive search algorithm (using MATLAB on a PC).

Often used in low probability of intercept continuous waveform (CW) emitters, polyphase modulations can have extremely long code lengths (large processing gain), good sidelobe performance and robust Doppler tolerance. This paper presents an efficient algorithm to autonomously extract the polyphase radar modulation parameters from an intercepted waveform using a Wigner-Ville Radon transform. Results show that our method results in a small relative error in the extracted parameters for signal-to-noise ratios as low as - 6dB.

This paper describes a bandpass sampling architecture for direct RF conversion that is reconfigurable and efficient. The receiver architecture avoids the requirement for high clock speeds and fast quantizers by using a two-stage sampling process. In the first stage, the RF signal is bandpass filtered and sampled using an impulse-like sampling device without quantizing the signal. After continuous time low-pass or bandpass filtering, the resulting analog signal is then sampled and quantized by a traditional analog-to-digital converter. This architecture also provides a high degree of reconfigurablity in tuning range and bandwidth by using a tunable or selectable anti-aliasing filter before the first stage of sampling and by using a tunable sample clock in the first stage of sampling.

The robust symmetrical number system (RSNS) is a modular system formed using$N \geq 2$integer sequences and ensures that two successive RSNS vectors (paired terms from all$N$sequences) differ by only one integer. This integer Gray-code property reduces the possibility of encoding errors and makes the RSNS useful in applications such as folding analog-to-digital converters (ADCs), direction finding antenna architectures, and photonic processors. This paper determines the length of combined sequences that contain no vector ambiguities. This length or longest run of distinct vectors we call the RSNS dynamic range$(\mathhat{M})$. The position of$\mathhat{M}$which is the starting point in the sequence is also derived. Computing$\mathhat{M}$and the position of$\mathhat{M}$allows the integer Gray-code properties of the RSNS to be used in practical applications. We first extend our two-sequence results to develop a closed-form expression for$\mathhat{M}$for a three-sequence RSNS with moduli of the form$2^r -1, 2^r, 2^r+1$. We then extend the results to solving the$N$-sequence RSNS ambiguity locations in general.

An autonomous (no human operator intervention) feature extraction algorithm that can be used for classification of low probability of intercept (LPI) radar modulations using time-frequency (T-F) images is presented. The approach uses erosion and a new adaptive threshold binarization algorithm embedded within a recursive dilation process to autonomously determine the modulation energy centroid (radar's carrier frequency). The modulation is then cropped from the original T-F image and the adaptive algorithm is used again to compute a binary feature vector for input into a multi-layer perceptron classification network. Classification results for five simulated radar modulations are shown to demonstrate the feature extraction approach and quantify the performance of the algorithm.

Without dispute, symmetrical folding waveforms are the most common type of waveform in engineering science (e.g., cosine, sine). symmetrical number systems (SNS) have been formed to extract the maximum amount of information from symmetrically folded waveforms. The robust symmetrical number system (RSNS) is formed using N ges 2 sequences and ensures that two successive RSNS vectors differ by only one digit. This Gray-code property reduces the possibility of encoding errors and makes the RSNS useful in applications such as folding analog-to-digital converters, direction finding antenna architectures and photonic processors. This paper determines the length of combined sequences that contain no ambiguities (Mcirc) which we call the RSNS dynamic range. The position of M is also derived. We first extend our two-sequence results to develop Mcirc for a three-sequence RSNS with moduli of the form 2r- 1, 2r, 2r+ 1. We then extend the results to solving the N-channel RSNS redundancy locations in general

In this paper, the orbit selection and configuration of the space-based exo-atmospheric kill vehicle (EKV) launch platforms are determined for three example launch sites. These include North Korea, China and Iran. The trajectories of the intercontinental ballistic missiles (ICBMs) are derived and the resulting trajectory parameters are used to determine the orbit necessary for a successful intercept. The parameters calculated include the inclination angle i, right ascension of the ascending node Q and the altitude r/sub a/ of the orbit. The calculations are based on the ICBM locations, capability of the space launch vehicle and the capabilities of the EKV. We show that for the launch locations given, a successful intercept requires 40 launch platforms in a circular orbit with altitude r/sub a/ = 1000 km, inclination angle i = 43.5 degrees and a right ascension angle of /spl Omega/ = 15.3 degrees.

In this paper, the different electronic attack (EA) techniques that can be deployed to reduce the effectiveness of boost-phase target sensing, tracking, and intercepting are examined. The purpose is to investigate the effects of the EA on the performance of the radio frequency (RF) sensors used within a boost-phase ballistic missile defense sensor system. The EA types investigated include barrage noise, chaff tactics, and the use of expendable decoys. The reduction of the radar cross-section is also addressed and predicted using a physical optics approach. The desired effect of the EA against the RF sensors is degradation of the target track quality, thereby forcing the sensors to use other methods to estimate the target position (e.g., triangulation). An inadequately designed sensor fusion scheme can lead to loss of target track, which is undesirable in a boost-phase ballistic missile intercept system.

This paper investigates the performance of a quadrature mirror filter (QMF) in detecting two low-probability of intercept (LPI) emitter waveforms: a triangular Frequency Modulation Continuous Wave (FMCW) waveform and a P-4 polyphase code CW waveform. Detection performance for signal-to-noise ratios (SNRs) of +10 dB, 0 dB, −10 dB, and −20 dB is examined. Signal features that can be extracted are also quantified. Results indicate that QMF processing can provide good detection of LPI waveforms even in the presence of a moderate amount of noise.

This paper examines the performance of the Wigner distribution in detection of two low-probability of intercept (LPI) emitter waveforms: a triangular Frequency Modulation Continuous Wave (FMCW) and a P-4 polyphase code CW signal. Detection performance for signal-to-noise ratios (SNRs) of +10 dB, 0 dB, −10 dB, and −20 dB are examined. Results indicate that time-frequency processing can provide good detection of LPI waveforms even in the presence of a moderate amount of noise.

The symmetrical number system (SNS) can be used as an efficient preprocessing technique to reduce the number of comparators in a folding ADC. This paper examines the issue of encoding errors that result when the separate channels m/sub i/ are brought back together to derive the input analog voltage. As an example, a unipolar 7-bit SNS ADC using pairwise relatively prime (PRP) moduli m/sub 1/=4, m/sub 2/=5 and m/sub 3/=7 is evaluated numerically. Steady state transfer functions are shown which detail encoding errors that occur when the folded input samples lie at one of the code transition points. To discard the encoding errors that occur, a decimation band is constructed at each transition point. The effectiveness of the decimation band in eliminating the encoding errors is also quantified.