Low Probability Of Intercept Research Articles

Cramér‐Rao Lower Bounds for Joint Target Parameter Estimation in FM‐Based Distributed Passive Radar Network with Antenna Arrays

AbstractTo avoid the disadvantages of the active radar which utilizes its own transmitter to emit electromagnetic radiations, passive radars use the signals readily available in the environment and can provide superior capabilities of stealth target detection, low probability of intercept, low cost, and robustness. This paper investigates the joint target parameter (delay and Doppler) estimation performance for a frequency modulation (FM)‐based distributed passive radar network (DPRN) system with antenna arrays. The DPRN system consists of multiple FM‐based illuminators of opportunity and multiple radar receivers, which are placed on moving platforms. First, we consider the scenario where the target state parameters are unknown, the maximum likelihood estimator is developed, and the log‐likelihood ratio of the received signal for a complex Gaussian extended target is derived. Then, the Cramér‐Rao lower bounds (CRLBs) on the Cartesian coordinates of target position and velocity are computed for a DPRN system with MT FM‐based transmitters of Q antenna elements and MR multichannel receivers of P antenna elements. Finally, numerical examples demonstrate that grouping the receiving antenna elements into properly sized arrays can reduce estimation errors. It is also shown that the joint CRLB is a function of signal‐to‐noise ratio, the number of receiving antenna elements, the properties of the transmitted FM waveform, and the relative geometry between the target and the DPRN architecture. The analytically closed‐form expressions for CRLB are an important performance metric in that they enable the optimal placement of radar receivers to improve the target parameter estimation performance.

Microwave-photonics direction finding system for interception of low probability of intercept radio frequency signals

Direction finding (DF) systems are fundamental electronic support measures for electronic warfare. A number of DF techniques have been developed over the years; however, these systems are limited in bandwidth and resolution and suffer from a complex design for frequency downconversion. The design of a photonic DF technique for the detection and DF of low probability of intercept (LPI) signals is investigated. Key advantages of this design include a small baseline, wide bandwidth, high resolution, minimal space, weight, and power requirement. A robust postprocessing algorithm that utilizes the minimum Euclidean distance detector provides consistence and accurate estimation of angle of arrival (AoA) for a wide range of LPI waveforms. Experimental tests using frequency modulation continuous wave (FMCW) and P4 modulation signals were conducted in an anechoic chamber to verify the system design. Test results showed that the photonic DF system is capable of measuring the AoA of the LPI signals with 1-deg resolution over a 180 deg field-of-view. For an FMCW signal, the AoA was determined with a RMS error of 0.29 deg at 1-deg resolution. For a P4 coded signal, the RMS error in estimating the AoA is 0.32 deg at 1-deg resolution.

Target detection for a kind of troposcatter over‐the‐horizon passive radar based on channel fading information

The troposcatter over-the-horizon (OTH) passive radar plays an important role in the beyond-line-of-sight surveillance, for its high propagation reliability and low probability of interception. However, it has two major limitations, namely, large propagation losses and multipath scattering fading. Since the captured signals are non-stationary with low signal-to-noise ratio, high antenna gain is indispensable, which results in narrow beamwidth. To deal with the contradiction between narrow beamwidth and real-time wide spatial coverage, array receiving is promising. Then, the primary problem is the array signal detection under troposcatter fading correlations. Based on recent troposcatter fading model, this study addresses this passive detection problem in three cases: (i) the spatial–temporal correlation is known, and a Neyman–Pearson detector is proposed as benchmark; (ii) uncertain statistics exist in the spatial–temporal correlation, and a generalised likelihood ratio test is adopted to overcome this uncertainty; (iii) the fading correlation is totally unknown, and a spatial–temporal weighted covariance-based detector is proposed. The performances of the proposed detectors are verified by Monte-Carlo simulations and experiments in a linear array, which is instructive for this kind of passive radar design in practical. Comparisons with existing detectors and the benchmark confirm the feasibility and effectiveness for troposcatter OTH passive radar.

Study on the Structure of an Efficient Receiver for Covert Underwater Communication Using Direct Sequence Spread Spectrum

This paper proposes an underwater communication receive model based on the spread spectrum technique in order to provide the characteristic of a low probability of interception. To do this, turbo equalization techniques employing Bahl-Cocke-Jelinek-Raviv (BCJR) decoding to improve performance through repetition are applied to offer excellent performance even at a low signal to noise ratio (SNR) of transmitted signals due to the spread spectrum technique. A turbo equalization model based on RAKE which increase signal power by summing the received signal through the multipath is proposed to compensate distorted data due to multipath channel and the performance improvements were proven by applying the threshold and weighted coefficient in the RAKE receiver model. The model was applied to covert underwater communication in a multi-sensor environment, and the efficiency of the proposed method was proven through underwater experiments.

LPI Radar Waveform Recognition Based on Multi-Branch MWC Compressed Sampling Receiver

In this paper, a new wideband digital receiver based on the modulated wideband converter compressed sampling (CS) system is proposed to replace a conventional wideband digital receiver, solve the cross-channel signal problem, and achieve intra-pulse modulation recognition for the low probability of intercept (LPI) radar signals. The proposed receiver uses cyclic-shifted pseudo-random sequences to mix the received signals to baseband. The mixed signals are low-pass filtered and down-sampled to obtain compressed sampling data containing the full information of the received signals. Since the phases of the multi-branch CS data are designed to change regularly, we propose a phase correction factor to correct the phases of the multi-branch CS data, which can be superposed to increase the output signal-to-noise ratio (SNR). Then, a recognition method based on the short-time Fourier transform (STFT) and spectrum energy focusing rate tests are proposed. First, the spectrum modulation bandwidth based on the STFT spectrum of the superposed CS data is tested to distinguish phase modulation signals and frequency modulation signals approximately. Then, the spectrum energy focusing rate of the superposed CS data is tested to determine the intra-pulse modulation type specifically. Finally, the superiority of the proposed recognition system for LPI radar signals and cross-channel signals is demonstrated by simulations and analysis. Simulation results show that the overall ratio of the successful recognition (RSR) is 100% when the SNR is greater than 0 dB.

Chaotic Phase-Coded Waveforms With Space-Time Complementary Coding for MIMO Radar Applications

A framework for designing orthogonal chaotic phase-coded waveforms with space-time complementary coding is proposed for multiple-input multiple-output (MIMO) radar applications. The phase-coded waveform set to be transmitted is generated with an arbitrary family size and an arbitrary code length by using chaotic sequences. Due to the properties of chaos, this chaotic waveform set has many advantages in performance, such as anti-interference and low probability of intercept. However, it cannot be directly exploited due to the high range sidelobes, mutual interferences, and Doppler intolerance. In order to widely implement it in practice, we optimize the chaotic phase-coded waveform set from two aspects. First, the autocorrelation property of the waveform is improved by transmitting complementary chaotic phase-coded waveforms, and an adaptive clonal selection algorithm is utilized to optimize a pair of complementary chaotic phase-coded pulses. Second, the crosscorrelation among different waveforms is eliminated by implementing space-time coding into the complementary pulses. Moreover, to enhance the detection ability for moving targets in MIMO radars, a method of weighting different pulses by a null space vector is utilized at the receiver to compensate the interpulse Doppler phase shift and accumulate different pulses coherently. Simulation results demonstrate the efficiency of our proposed method.

Automatic LPI Radar Waveform Recognition Using CNN

Detecting and classifying the modulation scheme of the intercepted noisy low probability of intercept (LPI) radar signals in real time is a necessary survival technique required in the electronic warfare systems. Therefore, LPI radar waveform recognition technique (LWRT) has gained an increasing attention recently. In this paper, we propose a convolutional neural network (CNN)-based LWRT, where the input and hyperparameters of the CNN, such as the input size, number of filters, filter size, and number of neurons are designed based on various signal conditions to guarantee the maximum classification performance. In addition, we propose a sample averaging technique to efficiently reduce the large computational cost required when the intercept receiver needs to process a large amount of signal samples to improve the detection sensitivity. We demonstrate the performance of the proposed LWRT with numerous Monte Carlo simulations based on the simulation conditions used in the recent LWRTs introduced in the literature. It is testified that the proposed LWRT offers significant improvement, such as robustness to noise and recognition accuracy, over the recent LWRTs.

Low Probability of Intercept-Based Optimal OFDM Waveform Design Strategy for an Integrated Radar and Communications System

The integration of radar and communications systems can provide great advantages, such as enhanced efficiency, structure simplification, less occupied hardware resources, and interference mitigation, compared with traditional individual radar and communications applications. Extensive studies have presented achieving improved system performance, whereas the problem of low probability of intercept (LPI)-based waveform design for the integrated system is seldom discussed in the literature. In this paper, an LPI-based optimal orthogonal frequency multiplexing modulation (OFDM) waveform design strategy is developed for an integrated radar and communications system (IRCS). The dedicated transmitter in this system transmits integrated OFDM waveform for simultaneously target parameter estimation and downlink communications. The basis of the underlying strategy is to employ the optimization technique to design the integrated OFDM waveform of IRCS in order to minimize the total radiated power, while satisfying the specified requirements of target parameter estimation and data information rate. We analytically show that the resulting optimization problem is convex and can be solved by formulating the Karush–Kuhn–Tuckers optimality conditions. Numerical simulation results demonstrate that our proposed strategy can solve the waveform design problem in the IRCS with low complexity, and the LPI performance of the IRCS can efficiently be enhanced by utilizing the proposed integrated OFDM waveform design strategy.

Precoding‐Aided Spatial Modulation for the Wiretap Channel with Relay Selection and Cooperative Jamming

We propose in this paper a physical‐layer security (PLS) scheme for dual‐hop cooperative networks in an effort to enhance the communications secrecy. The underlying model comprises a transmitting node (Alice), a legitimate node (Bob), and an eavesdropper (Eve). It is assumed that there is no direct link between Alice and Bob, and the communication between them is done through trusted relays over two phases. In the first phase, precoding‐aided spatial modulation (PSM) is employed, owing to its low interception probability, while simultaneously transmitting a jamming signal from Bob. In the second phase, the selected relay detects and transmits the intended signal, whereas the remaining relays transmit the jamming signal received from Bob. We analyze the performance of the proposed scheme in terms of the ergodic secrecy capacity (ESC), the secrecy outage probability (SOP), and the bit error rate (BER) at Bob and Eve. We obtain closed‐form expressions for the ESC and SOP and we derive very tight upper‐bounds for the BER. We also optimize the performance with respect to the power allocation among the participating relays in the second phase. We provide examples with numerical and simulation results through which we demonstrate the effectiveness of the proposed scheme.

Морфологический подход к измерению временных параметров сигналов малозаметных РЛС по их частотно-временным портретам.

Морфологический подход к измерению временных параметров сигналов малозаметных РЛС по их частотно-временным портретам.

Mixing chaos modulations for secure communications in OFDM systems

In this paper, we consider a novel chaotic OFDM communication scheme is to improve the physical layer security. By secure communication we refer to physical layer security that provides low probability of detection (LPD)/low probability of intercept (LPI) transmission. A mixture of chaotic modulation schemes is used to generate chaotically modulated symbols for each subcarrier of the OFDM transmitter. At the receiver, different demodulators are combined together for the different modulation schemes for enhanced security. Time domain, frequency domain and statistical randomness tests show that transmit signals are indistinguishable from background noise. BER performance comparison shows that the physical layer security of the proposed scheme comes with a slight performance degradation compared to conventional OFDM communication systems.

Optimal Power Allocation Strategy in a Joint Bistatic Radar and Communication System Based on Low Probability of Intercept.

In this paper, we investigate a low probability of intercept (LPI)-based optimal power allocation strategy for a joint bistatic radar and communication system, which is composed of a dedicated transmitter, a radar receiver, and a communication receiver. The joint system is capable of fulfilling the requirements of both radar and communications simultaneously. First, assuming that the signal-to-noise ratio (SNR) corresponding to the target surveillance path is much weaker than that corresponding to the line of sight path at radar receiver, the analytically closed-form expression for the probability of false alarm is calculated, whereas the closed-form expression for the probability of detection is not analytically tractable and is approximated due to the fact that the received signals are not zero-mean Gaussian under target presence hypothesis. Then, an LPI-based optimal power allocation strategy is presented to minimize the total transmission power for information signal and radar waveform, which is constrained by a specified information rate for the communication receiver and the desired probabilities of detection and false alarm for the radar receiver. The well-known bisection search method is employed to solve the resulting constrained optimization problem. Finally, numerical simulations are provided to reveal the effects of several system parameters on the power allocation results. It is also demonstrated that the LPI performance of the joint bistatic radar and communication system can be markedly improved by utilizing the proposed scheme.

A robust parameter estimation of FHSS signals using time–frequency analysis in a non-cooperative environment

Frequency hopping spread spectrum (FHSS) signals are widely implemented in both modern civilian and military applications. They are robust to channel impairments because of their low probability of interception. For applications that require the interception of FHSS signals, the signal parameters such as the hopping frequencies, hopping duration and hopping sequence should be accurately measured. In this paper, an accurate FHSS signal parameter estimation method is proposed based on quadratic time–frequency distributions (QTFDs). The extended modified B-distribution (EMBD) and the adaptive smoothed Wigner–Ville (SWWVD) are used which have the properties of high time–frequency resolution. The adaptive SWWVD requires no prior knowledge of the signal parameters since the kernel parameters are estimated from the signal characteristics and are compared to the EMBD which operates at the optimal kernel parameters. The proposed instantaneous frequency (IF) estimate method is compared to the time–frequency (TF) moments method and benchmarked with the Cramer–Rao lower bounds (CRLBs). The computational complexity of the IF estimation method is reduced by a factor of five compared to the TF moments method. Furthermore, the results show that the IF estimation method outperforms moments method where the mean-squared error (MSE) of the hopping frequencies estimate meets at minimum SNR of −3 dB and the hopping duration estimate MSE meets the CRLB at SNR of 0 dB.

LPI radar signal detection based on the combination of FFT and segmented autocorrelation plus PAHT

This paper proposes a desirable method to detect different kinds of low probability of intercept (LPI) radar signals, targeted at the main intra-pulse modulation method of LPI radar signals including the signals of linear frequency modulation, phase code, and frequency code. Firstly, it improves the coherent integration of LPI radar signals by adding the periodicity of the ambiguity function. Then, it develops a frequency domain detection method based on fast Fourier transform (FFT) and segmented autocorrelation function to detect signals without features of linear frequency modulation by virtue of the distribution characteristics of noise signals in the frequency domain. Finally, this paper gives a verification of the performance of the method for different signal-to-noise ratios by conducting simulation experiments, and compares the method with existing ones. Additionally, this method is characterized by the straightforward calculation and high real-time performance, which is conducive to better detecting all kinds of LPI radar signals.

LPI radar signal recognition based on BDS-GD

LPI radar signal recognition based on BDS-GD

Digital constant‐envelope modulation scheme for radar using multicarrier OFDM signals

Multicarrier signals using orthogonal frequency division multiplexing (OFDM) bring many advantages to radar such as low probability of intercept, improved target detection performance, optimisation of both radar transmitter and receiver etc. A major drawback of multicarrier OFDM signals is their high peak-to-mean envelope power ratio, which reduces the working efficiency of the used power amplifiers. To solve this problem, a digital constant-envelope modulation scheme is proposed for radar using multicarrier OFDM signals. The scheme can transmit multicarrier OFDM signals through power amplifiers being operated near saturation levels (and thus maximising power efficiency) with little spectral distortion, even in the presence of channel mismatch. Given the speed limitations of field programmable gate arrays (FPGAs), the proposed scheme is implemented in an FPGA at intermediate frequency level using a polyphase processing structure.

Cognitive FDA‐MIMO radar for LPI transmit beamforming

Active radar is vulnerable to illegal eavesdroppers due to its high-gain beam-scanning signals. To reduce active radar visibility and enhance its low probability of intercept (LPI) capability, this study proposes a cognitive LPI transmit beamforming scheme using frequency diverse array (FDA) and multiple-input multiple-output (MIMO) hybrid array antenna. The achievement of LPI is due to the unique range-angle-dependent transmitting beampattern of FDA-MIMO radar, which minimises the beam power at the target location to reduce its visibility and simultaneously maximise the power at the radar receiver without degrading the radar detection performance. Furthermore, the FDA-MIMO radar operates in a cognitive way: the receiver estimates the target range and the direction of arrival with a two-dimensional multiple signal classification algorithm, and feedbacks their estimates to the transmitter to update the FDA-MIMO transmit beamforming. As the transmit beamforming optimisation is non-convex problem, the authors propose three methods, namely linear combination, non-linear combination and closed form solution. All the proposed methods are verified by simulation results.

LPI Optimization Framework for Radar Network Based on Minimum Mean-Square Error Estimation

This paper presents a novel low probability of intercept (LPI) optimization framework in radar network by minimizing the Schleher intercept factor based on minimum mean-square error (MMSE) estimation. MMSE of the estimate of the target scatterer matrix is presented as a metric for the ability to estimate the target scattering characteristic. The LPI optimization problem, which is developed on the basis of a predetermined MMSE threshold, has two variables, including transmitted power and target assignment index. We separated power allocation from target assignment through two sub-problems. First, the optimum power allocation is obtained for each target assignment scheme. Second, target assignment schemes are selected based on the results of power allocation. The main problem of this paper can be considered in the point of views based on two cases, including single radar assigned to each target and two radars assigned to each target. According to simulation results, the proposed algorithm can effectively reduce the total Schleher intercept factor of a radar network, which can make a great contribution to improve the LPI performance of a radar network.

Power allocation for target detection in radar networks based on low probability of intercept: A cooperative game theoretical strategy

AbstractDistributed radar network systems have been shown to have many unique features. Due to their advantage of signal and spatial diversities, radar networks are attractive for target detection. In practice, the netted radars in radar networks are supposed to maximize their transmit power to achieve better detection performance, which may be in contradiction with low probability of intercept (LPI). Therefore, this paper investigates the problem of adaptive power allocation for radar networks in a cooperative game‐theoretic framework such that the LPI performance can be improved. Taking into consideration both the transmit power constraints and the minimum signal to interference plus noise ratio (SINR) requirement of each radar, a cooperative Nash bargaining power allocation game based on LPI is formulated, whose objective is to minimize the total transmit power by optimizing the power allocation in radar networks. First, a novel SINR‐based network utility function is defined and utilized as a metric to evaluate power allocation. Then, with the well‐designed network utility function, the existence and uniqueness of the Nash bargaining solution are proved analytically. Finally, an iterative Nash bargaining algorithm is developed that converges quickly to a Pareto optimal equilibrium for the cooperative game. Numerical simulations and theoretic analysis are provided to evaluate the effectiveness of the proposed algorithm.

Analysis of intra-pulse frequency-modulated, low probability of interception, radar signals

In this paper, we investigate the problem of analysis of low probability of interception (LPI) radar signals with intra-pulse frequency modulation (FM) under low signal-to-noise ratio conditions from the perspective of an airborne electronic warfare (EW) digital receiver. EW receivers are designed to intercept and analyse threat radar signals of different classes, received over large dynamic range and operating independently over large geographical spread to advice host aircraft to undertake specified actions. For an EW receiver, primary challenges in interception and analysis of LPI radar signals are low received power, intra-pulse modulations, multi-octave frequency range, wide signal bandwidth, long pulse width, vast and multi-parametric search space, etc. In the present work, a method based on match filterbank localization and Taylor’s series approximation for analysing the entire family of intra-pulse FM radar signals is proposed. The method involves progressive, joint time–frequency (TF) localization of the signal of interest (SOI), under piecewise linearity and continuity assumptions on instantaneous frequency, to effectively capture local TF signatures. Detection is by information-theoretic criterion based hypotheses testing, while estimation and classification are based on polynomial approximation. Fine signal analysis is followed by synthetic reconstruction of the received signal slope. Detection, estimation and classification performances for the prominent FM radar signal classes are quantified based on simulation study statistics. Stagewise implementation of analysis and FM slope reconstruction, in realistic radar threat scenarios, is demonstrated for the potential SOIs. Subject discussion is organized from the perspective of practical EW system design and presented within the realm of signal processing architecture of concurrent EW digital receivers.