Ambiguity function

We suggest a new interpretation of Woodward's ambiguity function as the expected value of an operator. The operator represents the physics of the interaction of the waveform with the object. This approach provides a new approach to understanding the return signal at the receiver and can reveal more detailed understanding of the underlying interactions within the return signal that are not usually brought out by standard signal processing techniques.

This paper, the first from a series of three papers on the application of coded excitation signals in medical ultrasound, discusses the basic principles and ultrasound-related problems of pulse compression. The concepts of signal modulation and matched filtering are given, and a simple model of attenuation relates the matched filter response with the ambiguity function, known from radar. Based on this analysis and the properties of the ambiguity function, the selection of coded waveforms suitable for ultrasound imaging is discussed. It is shown that linear frequency modulation (FM) signals have the best and most robust features for ultrasound imaging. Other coded signals such as nonlinear FM and binary complementary Golay codes also have been considered and characterized in terms of signal-to-noise ratio (SNR) and sensitivity to frequency shifts. Using the simulation program Field II, it is found that in the case of linear FM signals, a SNR improvement of 12 to 18 dB can be expected...

This paper presents a discussion on Passive Coherent Location (PCL) radar system using Digital-TV signals (Digital video broadcasting Terrestrial-DVB-T) as a means of radar transmission in Cape Town South Africa. It analyzes the quality of digital TV signals as an illuminator of opportunity for PCL. Digital TV signals being broadcasted in Cape Town South Africa will be analyzed by means of the ambiguity function. Furthermore, a system characterization with performance prediction.

The ambiguity function, which is used to determine the target resolution and parameter estimation capabilities of a radar, of discrete-time signals is discussed. Both continuous-time, continuous-frequency and discrete-time, discrete-frequency ambiguity functions are presented. To avoid aliasing, it is shown that the sampling rate must be twice the Nyquist rate associated with the sampled signal

In this paper the feasibility of a WiMAX transmissions based Passive Bistatic Radar (PBR) is analysed. The Ambiguity Function (AF) of the considered waveform of opportunity is characterized with reference to different transmission modes. The signal AF is shown to yield regularly spaced undesired peaks which might strongly limit the target detection capability of a WiMAX-based PBR. These sidelobe structures have a deterministic nature mainly related to the OFDM modulation exploited by WiMAX transmissions. A proper filter, based on the knowledge of the expected value of the signal Autocorrelation Function (ACF), is implemented to cope with this limitations and its performance is evaluated against simulated data generated according to the IEEE 802.16e Standard. The proposed approach is shown to yield an effective removal of the undesired peaks in the AF thus making the considered waveform more attractive for PBR medium range surveillance.

This paper, the last from a series of three papers on the application of coded excitation signals in medical ultrasound, investigates the possibility of increasing the frame rate in ultrasound imaging by using modulated excitation signals. Linear array-coded imaging and sparse synthetic transmit aperture imaging are considered, and the trade-offs between frame rate, image quality, and SNR are discussed. It is shown that FM codes can be used to increase the frame rate by a factor of two without a degradation in image quality and by a factor of 5, if a slight decrease in image quality can be accepted. The use of synthetic transmit aperture imaging is also considered, and it is here shown that Hadamard spatial encoding in transmit with FM emission signals can be used to increase the frame rate by 12 to 25 times with either a slight or no reduction in signal-to-noise ratio and image quality. By using these techniques a complete ultrasound-phased array image can be created using only two...

Modern ground penetrating radars (GPR), designed to determine the thickness of ice or search for the occurrence of aquifers in arid regions of the Earth, are installed either on helicopters or on the earth's surface. The use of a helicopter is economically expensive, and the installation of GPRs on the earth's surface is of a local nature. Modern GPRs mainly use video pulse probing signals and probing signals with linear frequency modulation. These signals have correlation noise, which makes it difficult to obtain a high-quality radar image. In this work, we propose to use a signal with a zero autocorrelation zone (ZACZ) as a probing signal for GPR installed on an unmanned aerial vehicle. In work, a polyphase probing signal with a ZACZ is synthesized and a comparative analysis of the correlation characteristics of the synthesized signal with the optimal phase-code shift keyed signal is carried out.

SUMMARY This paper presents an algorithm for GNSS carrier phase positioning based on some properties of Ambiguity Function Method. There is no stage of ambiguity search/resolution in the presented approach, since there is no ambiguity parameter in the proposed adjustment model. The integer nature of the ambiguities is ensured in the results through the least squares adjustment with condition equations in the functional model. Therefore the proposed method is robust to cycle slip effect. Also, an appropriate function for the condition equations is presented and tested here. The new approach requires subsequent processing of the linear combinations of GNSS signals in the cascade adjustment. The presented numerical tests were performed using in-house developed GINPOS software and GPS data sample collected by Polish GNSS network - ASG-EUPOS.

SUMMARY This paper presents an algorithm for GNSS carrier phase positioning based on some properties of Ambiguity Function Method. There is no stage of ambiguity search/resolution in the presented approach, since there is no ambiguity parameter in the proposed adjustment model. The integer nature of the ambiguities is ensured in the results through the least squares adjustment with condition equations in the functional model. Therefore the proposed method is robust to cycle slip effect. Also, an appropriate function for the condition equations is presented and tested here. The new approach requires subsequent processing of the linear combinations of GNSS signals in the cascade adjustment. The presented numerical tests were performed using in-house developed GINPOS software and GPS data sample collected by Polish GNSS network - ASG-EUPOS.

The multiple-input multiple-output (MIMO) radar delay-Doppler ambiguity function is introduced as the sum of all auto- and cross-ambiguity functions of the set of K spatially diverse waveforms. The integral of this function over the range-Doppler frequency region occupied by spread clutter relates to the clutter's power at the output of the matched MIMO receiver, and it serves as a measure

In this paper we suggest the improvement and generalization of the wideband ambiguity function for radar signals. Sounding waveforms and reflected radar signals have different probability density functions, and this fact is not taken into account in classical definition of an ordinary ambiguity function. The proposed generalization of the ambiguity function is based on the copula notion and does not depend on a probability density function. The generalized copula ambiguity function is useful for both analysis/synthesis of sounding waveforms (auto-ambiguity) and reflected signal detection/measurement (cross-ambiguity). Application of this approach gets rid of a dependence on the signal probability distribution, implementing actually non-parametric approach with CFAR.

A coherent processor to display the phase-space functions for 1-D signals is proposed. An elliptical zone plate is used as a single optical element. It is shown that, for a given 2-D input, the output plane shows the 1-D Fourier transform in one direction and the image in the other one. This lensless coherent processor can be used to display

A study is made of the sensitivity of range localization to several features, focusing on features recovered by temporal processing, and a metric that plays the role of an ambiguity function, now generalized to the multipath environment, is developed. In contrast with the matched wave-field approaches, which treat the channel as a black box, the modeling strategy effectively provides a manageable tool for understanding the role that different features can play in localization. Contour plots illustrate the sensitivity of ranging to the features and metric adopted.<<ETX>>

The conventional approach for tracking system design is to treat the detection and tracking subsystems as completely independent units. However, the two subsystems can be designed jointly to improve system (tracking) performance. It is known that different radar signal waveforms result in very different resolution cell shapes (for example, a rectangle versus an eccentric parallelogram) in the range/range-rate space, and