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Why it is so hard to find small radio frequency signals in the presence of large signals
Abstract
The essence of radar, radio and wireless sensor engineering is extracting small information-bearing signals. This is notoriously difficult and engineers compensate by transmitting high power signals, reducing range, and spacing wireless systems in frequency and time. New understandings of passive intermodulation distortion, thermal effects, time-frequency effects, and noise are presented. It is seen that the familiar frequency-domain-based abstractions have missed important underlying physics. Through greater understanding, RF engineers can develop microwave systems with far lower levels of distortion and noise.
... In general nonlinear radar faces two major obstacles, (a) the transmit power of the nonlinear radar needs to be significantly higher than a linear radar for detection at the same range, 1, 2 and (b) nonlinear radar has is an increased susceptibility to self generated interference. 3 Harmonic radar is a type of nonlinear radar that transmits a single frequency f 0 and receives one or more integral multiples of that same frequency (e.g. 2f 0 , 3f 0 , 4f 0 ) [4][5][6][7][8][9][10] . ...
... where d T (i, k) is the delay from the transmit antenna to the pixel and c is the speed of light. The delay from the image pixel to the receive antenna is calculated as using Equation 3. ...
Nonlinear radar has proven to be a viable means of detecting devices that contain electrical nonlinearities. Electrical nonlinearities are present in dissimilar metals, metal to oxide junctions, semiconductors and more. This paper presents a linear and nonlinear synthetic aperture radar (SAR) system capable of imaging linear and nonlinear targets. The system creates images using data collected from fixed 16 channel receiver with a single transmitter. A custom 16:1 switching network was developed to collect the SAR data from a 16 antenna receive array. SAR images presented show a nonlinear target placed directly on the ground and imaged in multiple range and cross-range locations. Data is also presented showing the clutter rejection properties of nonlinear radar. Images show that the harmonic radar is able to ignore the strong linear response from a corner reflector, while retaining the nonlinear response from a target.
... Examples of sensing and imaging systems using vibratory sensing include landmine detection [1], evaluation of structural integrity [2], and medical imaging [2]. One of the challenges in remote RF probing is detecting the modulated reflected signal in the presence of the directly reflected carrier [3]. The power of the modulation sidebands can be much smaller than the reflected carrier signal with the usefulness of the GPR system dependent on the ability to resolve low level sidebands typically within ten to a few thousand hertz of the carrier frequency. ...
... Doppler modulation is expected to dominate the received modulated signal, with the carrier-normalized amplitude spectrum given by (3). The received signal will be further attenuated as described by the radar equation [13], so that the power of the received signal is (4) where is the transmitted signal power, and are the gains of the transmit and receive antennas, is the radar cross- section, and and are the distances between the reflector and the transmit and receive antennas, respectively. ...
A high-dynamic-range vibration detection system is presented based on analog cancellation. The prototype system operates at 900 MHz and is shown to detect vibrational displacement as low as 11 nm for a rectangular aluminum plate at a standoff distance of 2 m. By operating at a lower frequency than previous radar vibrometers, the system gains ground-penetrating capability and is shown to detect vibrations through 13 cm of sand. A fundamental relationship is introduced relating the minimum detectable vibration displacement to the standoff distance and system dynamic range.
... For landmine detection, the major challenge is that the landmine reflection signal is extremely weak due to the small magnitude displacement of landmine vibration. In addition, there exist RF interference signals that can impair Doppler radar performance, i.e. the direct coupling between the transmitter antenna and the receiving antenna, the intrinsic distortion factors in the system, and strong clutter in the sensing environment [12][13][14][15][16]. To achieve meaningful measurements, it is necessary to leverage the Doppler radar dynamic range by alleviating the interference and enhancing the small signal under measurement. ...
... Nonlinear radar provides high clutter rejection, 1, 2 but requires two major tradeoffs: (a) the power-on-target required to generate a signal-to-noise ratio comparable to linear radar is much higher than that of linear radar, 3,4 and (b) the radar must capture weak target responses in the presence of strong transmitted probes. 5 It is known that metal-to-metal contacts, corroded metal, and semiconductor junctions exhibit nonlinear scattering responses (in addition to linear scattering responses) when illuminated by electromagnetic waves. [6][7][8][9][10][11][12] Based on this phenomenology, the concept of nonlinear radar, primarily focusing on harmonic radar, has been under development since the 1970s. ...
The radar range equation for detecting targets using linear radar has been de�fined and derived many times for many di�fferent applications. The nonlinear radar range equation has been defi�ned in the literature but a step by step derivation is lacking and no experimental validation has been shown. This paper starts with a nonlinear system model and provides simulated and experimental validation for the model. Once the model is validated, the model is used to derive the nonlinear radar range equation for nonlinear radar. Key di�fferences between the linear and nonlinear radar range equation will be emphasized.
... Nonlinear radar is well-suited to the detection of electronic devices, typically those containing semiconductors and whose traditional (linear) radar cross sections are very low owing to their thin geometric profiles and are therefore usually obscured by nearby clutter. Nonlinear radar provides high clutter rejection, but requires two major tradeoffs: the power-on-target required to generate a signal-to-noise ratio comparable to linear radar is much higher than that of linear radar [1], and the radar must capture weak target responses in the presence of strong transmitted probes [2]. ...
The phase responses of nonlinear-radar targets illuminated by stepped frequencies are studied. Data is presented for an experimental radar and two commercial electronic targets at short standoff ranges. The amplitudes and phases of harmonics generated by each target at each frequency are captured over a 100-MHz-wide transmit band. As in the authors’ prior work, target detection is demonstrated by receiving at least one harmonic of at least one transmit frequency. In the present work, experiments confirm that the phase of a harmonic reflected from a radio-frequency electronic target at a standoff distance is linear versus frequency. Similar to traditional wideband radar, the change of the reflected phase with respect to frequency indicates the range to the nonlinear target.
... Nonlinear radar offers the feature of high clutter rejection, but this must be weighed against 2 disadvantages: 1) the harmonic response from the target is extremely weak, and thus difficult to capture, and 2) the incident power required to generate a detectable response is significantly higher than that of linear radar. 1,2 The nonlinear radar model used in my experiments is akin to a harmonic, stepped frequency radar. The radar transmits a single frequency, ω; if the radar receives a harmonic of this fundamental (i.e., 2ω and 3ω), a nonlinear target is present. ...
One of the latest challenges being investigated by the US Army Research Laboratory’s (ARL) Electronics and Radio Frequency (E&RF) Division is the development of a radar system that can accurately detect and range an electronically nonlinear target, such as a detonator of an improvised explosive device (IED). Previous nonlinear radar systems detect targets via transmission of a single frequency ω, stepping (incrementally increasing) this frequency through a wide bandwidth, and then listening for a response of the 2nd harmonic 2ω; however, the phase information that this harmonic contains and its relationship to target distance has been largely assumed and unconfirmed. Our most recent experimental tests, both wired and wireless, have confirmed that this harmonic phase response is constant versus frequency at the target. Using inverse Fourier transforms, the range of an electronic nonlinear target can be determined from that phase.
... Nonlinear radar provides high clutter rejection, 1 but requires two major tradeoffs: (a) the power-on-target required to generate a signal-to-noise ratio comparable to linear radar is much higher than that of linear radar, 2 and (b) the radar must capture weak target responses in the presence of strong transmitted probes. 3 It has been known for a while that metal-to-metal contacts, corroded metal, and semiconductor junctions exhibit nonlinear scattering responses (in addition to linear scattering responses) when illuminated by electromagnetic waves. [4][5][6][7][8][9][10][11] Based on this phenomenology, the concept of nonlinear radar, primarily focusing on harmonic radar, has been under development since the 1970s. ...
In a harmonic radar system design, one of the most important components is the filter used to remove the self-generated harmonics by the high-power transmitter power amplifier, which is usually driven close to its 1-dB compression point. The obvious choice for this filter is a low-pass filter. The low-pass filter will be required to attenuate stop band frequencies with 100 dB attenuation or more. Due to the high degree of attenuation required, multiple low-pass filter will likely be required. Most commercially available low-pass filters are reflective devices, which operate by reflecting the unwanted high frequencies. Cascading these reflective filter causes issues in attenuating stop band frequencies. We show that frequency diplexers are more attractive in place of reflective low-pass filters as they are able to terminate the stop band frequencies as opposed to reflecting them.
... Nonlinear radar is well-suited to the detection of electronic devices, typically those containing semiconductors and whose traditional (linear) radar cross sections are very low owing to their thin geometric profile. Nonlinear radar provides high clutter rejection but requires two major tradeoffs: the power-on-target required to generate a signal-tonoise ratio comparable to linear radar is much higher than that of linear radar [9], and the radar must capture weak target responses in the presence of strong transmitted probes [10]. ...
Radio-frequency (RF) electronic targets, such as man-portable electronics, cannot be detected by traditional linear radar because the radar cross section of those targets is much smaller than that of nearby clutter. One technology that is capable of separating RF electronic targets from naturally-occurring clutter is nonlinear radar. Presented in this paper is the evolution of nonlinear radar at the United States Army Research Laboratory (ARL) and recent results of short-range over-the-air harmonic radar tests there. For the present implementation of ARL’s nonlinear radar, the transmit waveform is a chirp which sweeps one frequency at constant amplitude over an ultra-wide bandwidth (UWB). The receiver captures a single harmonic of this entire chirp. From the UWB received harmonic, a nonlinear frequency response of the radar environment is constructed. An inverse Fourier Transform of this nonlinear frequency response reveals the range to the nonlinear target within the environment. The chirped harmonic radar concept is validated experimentally using a wideband horn antenna and commercial off-the-shelf electronic targets.
... Nonlinear radar provides high clutter rejection, 1 but requires two major tradeoffs: 1) the power-on-target required to generate a signal-to-noise ratio comparable to linear radar is much higher than that of linear radar, 2 and 2) the radar must capture weak target responses in the presence of strong transmitted probes. 3 The nonlinear radar studied in this report transmits a single frequency at a time, denoted f0, and receives twice this value, 2f0; thus, the radar is harmonic. Prior work has focused on transmitting power at f0 sufficient to generate a harmonic target response while minimizing the amount of transmitter-generated harmonic that couples to the receiver. ...
This report describes a type of nonlinear radar that detects and locates nonlinear (electronic) targets using ultra-wideband transmission and harmonic reception. Data are presented for a successful test of an experimental harmonic radar at transmit frequencies between 700 and 900 MHz and an output power of 2 W. Detection is accomplished by measuring a signal reflected from the target at double the transmit frequency. Ranging is accomplished by sweeping the transmit frequencies across an ultrawide bandwidth, capturing the amplitude and phase of the harmonic return signal, and computing an inverse Fourier transform of the wideband harmonic response. Detection and ranging of 3 nonlinear targets are demonstrated at standoff distances of 6 and 12 ft.
This paper presents a time-domain simulation of phase noise in a varactor-tuned voltage-controlled oscillator. Flicker, thermal and shot noise are captured using transient sources of noise based on the principles of mathematical chaos. High levels of noise are handled by replacing the ordinary differential equations used in conventional transient circuit simulation by stochastic differential equations. The system of stochastic differential equations is interpreted in the sense of Stratonovich. Simulation runs are compared with measured phase noise of the oscillator and an accurate match is found for different levels of bias
Recent research has examined several novel radio frequency (RF) remote probing techniques. These new results are joined with the prior art leading to a unified understanding of RF remote probing that articulates the fundamental principles involved and allows extension to the analysis of additional “new” RF probing techniques. Two significant aspects in RF probing are emphasized: 1) information, coding, and signal theory considerations are identified as these establish bounds on probe performance against a specific information task and 2) building upon the well-known radar equation, the object cross section is generalized to be an interaction term describing a much broader range of interactions than simply reflection. These results are significant in enabling the rapid analysis and evaluation of “new” RF sensing techniques proposed to accomplish a variety of functions in the detection and identification of both natural and manmade objects.
An automated analog canceller is presented that uses feedforward cancellation in a bridge configuration. A minimum of 70 dB of analog cancellation is obtained. The canceller is used to construct an intermodulation distortion measurement system achieving up to 120 dBc of intermodulation dynamic range in two-port transmission testing and 140 dBc of intermodulation dynamic range in one-port reflection testing for frequency separations of at least 1 kHz. At a two-tone frequency separation of 1 Hz, the respective dynamic ranges are at least 94 and 111 dBc. The relationship of cancellation performance and dynamic range is examined in terms of application-specific definitions of dynamic range. The system is then used to measure passive intermodulation distortion using a two-tone test with a tone frequency separation from 1 Hz to 100 MHz.
An acoustic tone isonifying an antenna is shown to produce radio frequency (RF) distortion in a log-periodic dipole array. This distortion is capable of interfering with a sensitive receiver. The passive distortion produces two sidebands, the powers of which have a 1:1 relationship with both the RF and acoustic tone, but have nonmonotonic behavior with respect to RF and acoustic frequency.
The ability to model the effect of non-negligible levels of white noise superimposed on a carrier is investigated when this signal–noise combination is fed to the input of an MMIC power amplifier. Transient simulation using stochastic differential equations is introduced here to handle large levels of noise of arbitrary frequency characteristics. The effectiveness of the modelling is ascertained by looking at measured gain-compression plots at the output of the amplifier and comparing these with simulated results. It is found that increasing levels of noise introduce increased compression of the output power characteristic. Copyright © 2008 John Wiley & Sons, Ltd.
This paper explores the generation of passive intermodulation distortion products through the self heating of resistive elements in a microwave attenuator. A compact electrothermal resistor model requiring only two physical parameters is developed for platinum resistors and applied to a resistive attenuator pi network to predict electrothermal PIM. The electrothermal model is verified by comparing measured and predicted results when the attenuator is excited by a two tone signal at 400MHz with tone spacing from 1 to 100 Hz
An analytic formulation of dynamic electro-thermally induced nonlinearity is developed for a general resistive element, yielding a self-heating circuit model based on a fractional derivative. The model explains the 10 dB/decade slope of the intermodulation products observed in two-tone testing. Two-tone testing at 400 MHz of attenuators, microwave chip terminations, and coaxial terminations is reported with tone spacing ranging from 1 to 100 Hz.
The long-tail transient responses of a bandpass network to pulsed and switched-tone stimuli are examined and a time-domain closed-form expression of the envelope response is developed. It is shown that the long-tail response leads to interference in frequency-hopping communication systems. Interference, and in particular co-site interference, can result in any radar, communication, or RF sensor system becoming exposed to unintentional pulsed RF signals. In the experimental study, 900-MHz Chebyshev bandpass filters are considered.
A theoretical treatment of distributed electro-thermally induced intermodulation distortion is developed for microstrip transmission lines. The growth of passive intermodulation distortion (PIM) along the length of a line is derived accounting for both loss and electrical dispersion. PIM dependencies on width, length, thickness, and substrate parameters are analyzed leading to design guidelines for low distortion lines. Single metal silver transmission lines are fabricated on sapphire and fused-quartz substrates to isolate the electro-thermal effect and validate the model. Electro-thermal PIM is measured in a two-tone test with tone separation ranging from 4 Hz to 10 kHz.
The contribution of bandpass filter memory to intermodulation distortion in narrowband amplifier circuits is examined. A method for generating multisines from filtered switched tones is presented, and techniques for measuring an amplifier's IP3 and extracting a filter's passband using these multisines are developed. It is shown that amplified filtered pulses produce intermodulation distortion in frequency-hopping communication systems. In the experimental study, 465 and 900-MHz Chebyshev bandpass filters are considered.
This paper presents an intermodulation distortion measurement system based on automated feedforward cancellation that achieves 113 dB of broadband spurious-free dynamic range for discrete tone separations down to 100 Hz. For 1-Hz tone separation, the dynamic range is 106 dB, limited by carrier phase noise. A single-tone cancellation formula is developed requiring only the power of the probing signal and the power of the combined probe and cancellation signal so that the phase shift required for cancellation can be predicted. The technique is applied to a two-path feedforward cancellation system in a bridge configuration. The effects of reflected signals and of group delay on system performance is discussed. Spurious frequency content and interchannel coupling are analyzed with respect to system linearity. Feedforward cancellation and consideration of electromagnetic radiation coupling and reverse-wave isolation effects extends the dynamic range of spectrum and vector analyzers by at least 40 dB. Application of the technique to the measurement of correlated and uncorrelated nonlinear distortion of an amplified wideband code-division multiple-access signal is presented.