Thumbtack Ambiguity Function Research Articles

Chaotic waveform for optimal joint radar communication systems

Due to the increased spectrum congestion, there has been a tremendous interest in radar and communication devices operating on a shared platform. Therefore, the waveform design for joint radar communication (JRC) systems has recently gained significant attention. Despite several efforts, most state-of-the-art waveforms are far from achieving ideal radar and communication performance. To address this issue, we design a family of chaotic maps whose output yields waveforms with optimal JRC features. We adopt the antipodal chaos shift keying (ACSK) scheme, where the segments of the chaotic signal are multiplied by ±1 to encode the binary information. This ACSK waveform is further used for the JRC system transmission. Once the synchronization between the receiver and transmitter is established, the information is recovered by cross-correlating the received and the synchronized waveforms. This technique yields bit error rates (BER) similar to the theoretical values of the BPSK waveform. The same transmitted waveform results in a thumb-tack ambiguity function which is essential for high-resolution radar imaging. The variance analysis of the ambiguity function shows that the proposed waveform is comparable to the noise-modulated waveforms. We also show that the multiplexed ACSK waveforms yield similar optimal behavior. Furthermore, we demonstrate the potential of the family of chaotic maps for multiple-input, multiple-output (MIMO) JRC systems.

Waveform Design Based ECCM Scheme Against Interrupted Sampling Repeater Jamming for Wideband MIMO Radar in Multiple Targets Scenario

In this paper, we propose a waveform design based electronic counter-countermeasures (ECCM) scheme against interrupted sampling repeater jamming (ISRJ) for wideband multiple-input multiple-output (MIMO) radar. The ECCM scheme includes two steps: ISRJ parameters estimation and ISRJ signal suppression. The ISRJ signal interpretations based on time-frequency (TF) domain and Doppler domain are proposed respectively. Based on the Doppler interpretation, a waveform with thumbtack ambiguity function and a corresponding multiple Doppler channels processing structure are proposed to obtain ISRJ parameters. According to the TF interpretation and the known ISRJ parameters, a waveform with desired TF distribution and a corresponding frequency filter processing strategy are proposed to suppress ISRJ signal. The proposed ECCM scheme can be directly used in phased-array mode without waveform optimization. Considering the multiple targets scenario, the simultaneous multiple beams technology in MIMO radar is preferred. Therefore, a constant modulus waveform design method is proposed to match the desired transmit beampattern and TF distribution. Besides, in order to further suppress the sidelobe output of ISRJ signal, an extended version of the proposed ECCM scheme in the slow-time dimension is proposed. Finally, the numerical simulations are provided to demonstrate the effectiveness of the proposed ECCM scheme in multiple targets scenario.

Chaos Based Frequency Modulation for Joint Monostatic and Bistatic Radar-Communication Systems

In this article, we propose the utilization of chaos-based frequency modulated (CBFM) waveforms for joint monostatic and bistatic radar-communication systems. Short-duration pulses generated via chaotic oscillators are used for wideband radar imaging, while information is embedded in the pulses using chaos shift keying (CSK). A self-synchronization technique for chaotic systems decodes the information at the communication receiver and reconstructs the transmitted waveform at the bistatic radar receiver. Using a nonlinear detection scheme, we show that the CBFM waveforms closely follow the theoretical bit-error rate (BER) associated with bipolar phase-shift keying (BPSK). We utilize the same nonlinear detection scheme to optimize the target detection at the bistatic radar receiver. The ambiguity function for both the monostatic and bistatic cases resembles a thumbtack ambiguity function with a pseudo-random sidelobe distribution. Furthermore, we characterize the high-resolution imaging capability of the CBFM waveforms in the presence of noise and considering a complex target.

On the use of a multi-raster input of one-dimensional signals in two-dimensional optical correlators

A mathematical description of a coherent optical correlator for the multi-raster input of long signals is given. It is shown that such an input makes it possible to reduce the value of false correlation maxima that are generally found at the output of a correlator with a single-raster input. It is shown that false maxima do not appear when processing signals with a thumbtack ambiguity function, allowing one to do without a multi-raster input. The results of the theoretical analysis are confirmed by experiments with chirp signals and M-sequence type signals.

Linear‐FM random radar waveform compressed by dechirping method

This research proposes a novel linear frequency modulation (Linear-FM) random radar waveform and introduces a dechirping compression method. The proposed linear-FM random waveforms possess a thumbtack ambiguity function and low cross-correlation properties which are good for fighting against digital radio frequency memory repeat jammer similar to random noise waveforms. The dechirping compression method for the proposed linear-FM random radar waveform works by mixing the random radar echo signal with a local reference linear frequency modulated (LFM) signal to reduce the echo bandwidth and thus allows to use low-speed analogue-to-digital converter similar to the dechirping method for LFM waveform compression. Both numerical simulation and high-resolution circular synthetic aperture radar imaging experiment are conducted to demonstrate the good performance of the proposed waveform and the proposed dechirping compression method.

Generation of Random NLFM Signals for Radars and Sonars and their Ambiguity Studies

Background/Objectives: In modern radars waveform design plays a vital role. In the design of radars the most significant parameter is the range resolution. With the help of the signal processing tools like auto correlation and ambiguity function various waveform designs can be achieved. Methods/Statistical Analysis: In the proposed paper the discrete frequency coding method of random NLFM (Non Linear Frequency Modulation) signal is described which results in a random like frequency evolution. Random NLFM enables to achieve the thumbtack ambiguity function while minimizing the crosstalk between frequencies. Findings: Random NLFM signals for different lengths are generated which are used in radars and sonars and also their ambiguity plots are obtained. The PSLR (Peak Side Lobe Ratio) and ISLR (Integrated Side Lobe Ratio) for these signals are evaluated and a comparison is made among these signals to identify best NLFM waveform. Application/Improvements: Non Linear Frequency Modulation waveforms using algebraic random number generators that are quite robust to electronic counter measures and have long duration for long range applications. In future applications of NLFM especially in RADAR/SONAR applications, this idea may result into new methodology

Frequency modulated radar signal with combined chaotic sequence based on Bernoulli map

Chaotic signal shows amounts of advantages in the application of radar systems for its easy generation and control. The model of combined chaotic maps based on Bernoulli map is proposed in this paper. Then, the chaos based frequency modulated (FM) radar signal is put forward and the frequency spectrum, ambiguity function are also analyzed in theory. In simulation, the phase spaces, Approximate entropy (ApEn) and balance of the combined chaotic maps are investigated, which shows the combined maps sequences have greater performances than the initial sequences. Additionally, the Peak side-lobe level (PSL) and Integrated side-lobe level (ISL) of signal autocorrelation are discussed, and they drop greatly with the combined chaotic maps after frequency modulation. Simulation results also show that the FM signal based on combined chaotic maps has flatter frequency spectrum in the whole frequency band and a thumbtack ambiguity function.

WIDE-BAND CHAOTIC NOISE SIGNAL FOR VELOCITY ESTIMATION AND IMAGING OF HIGH-SPEED MOVING TARGETS

This paper proposes a burst model of chaotic noise signals with randomly stepped carrier frequencies for velocity estimation and high-resolution range imaging of high-speed moving targets. The random stepping of carrier frequencies is controlled by a combination chaotic map (CCM), which is generated by embedding a Logistic map into a Bernoulli map. The baseband noise signal adopts the CCM based frequency-modulation (CCM-FM) signal, which has good randomness and a thumbtack ambiguity function as well. The velocity estimation includes a coarse search and a precise search, where the coarse search is conducted with a fixed step to makes the velocity deviation less than the velocity resolution, while the precise search adopts the Golden Section Search (GSS) algorithm to get an accurate estimation of velocity. What should be emphasized is that the velocity estimation process can be completed with just a burst of subpulses. Then the spectra are coherently synthesized to obtain ultra-wide bandwidth and high-resolution range imaging. Finally, numerical simulations demonstrate a good performance of the proposed signal model and the processing algorithm.

The generalized sinusoidal frequency modulated active sonar waveform ambiguity function: Theoretical and experimental results

The generalized sinusoidal FM (GSFM) waveform modifies the sinusoidal FM (SFM) waveform to use an instantaneous frequency (IF) function that resembles a FM chirp waveform and as a result of this the GSFM possesses a thumbtack ambiguity function (AF) [Hague, Buck, Asilomar (2012)]. This is a drastic improvement over the SFM, which suffers from poor range resolution as its AF contains many ambiguous peaks generated by the periodicity of the SFM's IF. Analyzing the Taylor Series expansion of the GSFM's AF near the origin proves that the GSFM achieves minimal range-Doppler coupling for single target measurements. This minimizes the error in jointly estimating target range and velocity. The GSFM's AF Peak Sidelobe Level (PSL) and Integrated Sidelobe Ratio (ISLR) are comparable to or better than that of other waveforms with a thumbtack AF. Consequently, the target masking effect experienced in multi-target environments is less severe for the GSFM than other thumbtack waveforms. Lastly, test tank experiments demonstrate that the GSFM's desirable AF properties are robust to the signal conditioning necessary for transmission on practical piezoelectric transducers. [Work supported by ONR and the SMART Scholarship Program.]

Design and Characteristic Analysis of Multicarrier Chaotic Phase Coded Radar Pulse Train Signal

By introducing phase code into multicarrier orthogonal frequency division multiplex signal, the multicarrier phase coded (MCPC) radar signal possesses a good spectrum utilization rate and can achieve a good combination of narrowband and wideband processing. Radar pulse train signal not only reserves the high range resolution of monopulse signal, but also has the same velocity resolution performance as continuous wave signal does. In this study, we use the chaotic biphase code generated by Chebyshev mapping to conduct a phase modulation on MCPC pulse train so as to design two different types of multicarrier chaotic phase coded pulse train signal. The ambiguity functions of the two pulse train signals are compared with that of P4 code MCPC pulse train. In addition, we analyze the influences of subcarrier number, phase-modulated bit number, and period number on the pulse train’s autocorrelation performance. The low probability of intercept (LPI) performance of the two signals is also discussed. Simulation results show that the designed pulse train signals have a thumbtack ambiguity function, a periodic autocorrelation side lobe lower than P4 code MCPC pulse train, and excellent LPI performance, as well as the feature of waveform diversity.

Feasibility analysis of utilizing the ‘8k mode’ DVB-T signal in passive radar applications

One non-cooperative illuminator recently considered for passive radar applications is the DVB-T (Digital Video Broadcasting-Terrestrial) signal. The thumbtack ambiguity function of the DVB-T signal, in addition to being stationary over time, makes such a signal a good candidate for such applications. However, certain ambiguities in its ambiguity function necessitates certain issues to be carefully considered when the DVB-T signal is to be utilized in these scenarios. Methods have been already proposed to resolve them. In this paper, after studying the origins of these ambiguities, we propose special processing schemes to reduce the complexity of the parts associated with resolving these ambiguities efficiently. Then, the DVB-T’s Cross Ambiguity Function (CAF) processing gain is carefully studied, and it is shown that its noisy nature results in a high processing gain and resolution. Finally, the detection range of the DVB-T based passive radar is examined, besides simulations, to show the practical feasibility of this signal for cases of passive coherent location.

Ambiguity Functions for Monostatic and Bistatic Radar Systems using UWB Throb Signal

Waveform design and ambiguity function are significant tools for the performance analysis of radar systems. We first describe the principle of waveform design for ultrawideband (UWB) impulse waveforms and present the signal model and the advantages of a UWB-throb signal. The ambiguity function of the UWB-throb signal for monostatic radar is derived in detail and analyzed by computer simulation to show its capabilities for enhanced radar performance in terms of target detection, resolution, accuracy of range and velocity measurements, and clutter suppression. The resolution theory for bistatic radar using UWB-throb signal is also presented. The dependence of delay and Doppler shift, associated with a moving target, on the parameters that constitute the geometry of bistatic radar is formulated and used to obtain the bistatic ambiguity function of the UWB-throb signal. Computer simulation plots are generated that clearly illustrate the effects of change in radar-target geometry on the overall characteristics of the bistatic ambiguity function. The computer plots of the monostatic and the bistatic ambiguity functions of the UWB-throb signal demonstrate that such signal can achieve the "thumbtack ambiguity function," that is desirable for the numerous applications of UWB-impulse radar.

Multifrequency complementary phase-coded radar signal

A multifrequency radar signal is considered. It uses M subcarriers simultaneously. The subcarriers are phase modulated by M different sequences that constitute a complementary set. Such a set can be constructed, for example, from the M cyclic shifts of a perfect phase-coded sequence of length M (e.g. P4). The subcarriers are separated by the inverse of the duration of a phase element t/sub b/, yielding orthogonal frequency division multiplexing (OFDM), well known in communications. A single pulse of such a signal exhibits a thumbtack ambiguity function with delay resolution of t/sub b//M. The power spectrum is relatively flat, with width of M/t/sub b/. The signal can be constructed by power combining M fixed-amplitude signals. The resulting signal, however, is of variable amplitude. The peak-to-mean envelope power ratio can be maintained below 2. A train of complementary pulses and a weight function along the frequency axis are useful for further sidelobe reduction.

Carrier-free signal design for look-down radars

The detection of low flying targets with small radar cross section (RCS), known as low observables, such as cruise missiles and stealth airplanes adds a new dimension to radar signal design and radar signal processing. A high resolution look-down radar is very attractive since it takes advantage of target shape to overcome difficulties encountered with small RCS. The look-down geometry, however, imposes three requirements: 1) the radar should detect targets with small relative velocities from almost zero to about the velocity of sound with no blind speeds, 2) it should minimize ground clutter by using short pulses, and 3) the radar signal must have a thumbtack ambiguity function. We investigate a look-down radar that eliminates time side lobes of compressed signal correlation functions to improve range resolution, reduces ground clutter to enhance receiver dynamic range, and uses thumbtack resolution function to resolve moving low observable targets from the surface of the Earth. The side lobe elimination technique transforms the correlation function of a coded waveform, based on complementary codes, to the correlation function of a single pulse. Features of side lobe elimination technique along with clutter cancellation circuits are presented in terms of blind speeds and range-velocity resolution function.< <ETX xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">&gt;</ETX>

Resolution function of nonsinusoidal radar signals. I. Range-velocity resolution with rectangular pulses

A generalization of a previously published ambiguity function that applies to radar known as large-relative-bandwidth radar, carrier-free radar, impulse radar, or nonsinusoidal radar is discussed. This radar has attracted attention because of its ability to penetrate absorbing materials used in the stealth technology. Another good application is the detection of moving targets with a small radar cross section by a look-down radar, which calls for a thumbtack ambiguity function. Since a small radar cross section in this application is typically due to the small size of the target that is coated with absorbing material, the antistealth feature of the nonsinusoidal radar is implicitly being used. The principle is presented of a resolution function (tentatively called the range-velocity or the range-Doppler resolution function) based on processing a nonsinusoidal signal consisting of N characters with a time separation T/sub D/ and each character consisting of a sequence of L binary pulses of duration T. It is shown that range-velocity resolution functions approaching the ideal thumbtack function are easy to obtain. The blind speeds of the pulse-Doppler radar with sinusoidal carrier do not inherently occur, and all velocities are observed as true velocities rather than as velocities modulo the first blind speed (velocity ambiguity). >

Principles of high-resolution radar based on nonsinusoidal waves. II. Generalized ambiguity function

For pt.I see ibid., vol.31, no.4, p.359-68 (1989). A generalized ambiguity function for nonsinusoidal coded waveforms that are represented as a train of properly weighted Gaussian pulses is derived and analyzed to study its properties. Computer plots of generalized ambiguity functions of different binary codes, e.g. Barker, complementary, and pseudorandom codes, are presented. The various computer plots show that the desired thumbtack ambiguity function is achievable by nonsinusoidal coded waveforms.< <ETX xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">&gt;</ETX>

A study of a class of detection waveforms having nearly ideal range—Doppler ambiguity properties

A special class of permutation matrices is considered. It is shown that these matrices may be beneficially used to determine the frequency-time pattern of a uniform pulse train. Proper choice of burst waveform parameters is shown to result in a detection wave-form having range and Doppler resolution properties consistent with the overall signal duration and bandwidth. The range-Doppler sidelobe peaks are well-controlled so that the ideal thumbtack ambiguity function behavior is closely approximated by the synthesis procedure presented.

Synthetic-Aperture Radar Based on Nonsinusoidal Functions: VI-Pulse-Position and Pulse-Shape Coding

Previous papers of this series have used coded radio signals with desirable features, without explaining how these signals were obtained. This paper supplies the explanation. The concept of coding is generalized from the baseband signals, modulated onto sinusoidal carriers, to the radio signals actually transmitted. The conventional radar signals have coded baseband signals, which are referred to as the fine structure of the radar signals, while the carrier, referred to as the hyperfine structure, has always sinusoidal time variation. The more general radio signals discussed here have both a coded fine structure and hyperfine structure. Two classic problems of radar are readily solved by this generalized coding. 1) A class of signals is derived that approaches the ideal thumbtack ambiguity function in the range-Doppler domain as closely as one wants to. 2) The same class of signals makes it possible to increase the average-to- peak power ratio significantly over that achievable with frequency- modulated sinusoidal carriers. An estimate of the number of terms of a Fourier-series expansion of the signals, as well as the number of components of each term, is given; this estimate shows that a Fourier representation is too complicated for practical purposes, but also that the signals are ideal for frequency-sharing and spread-spectrum transmission.