Ambiguity function and accuracy of the hyperbolic chirp: comparison with the linear chirp

In this paper, we derive the Ambiguity Function (AF) of a narrowband and a wideband hyperbolic chirp. We calculate the second derivatives of the squared amplitude of the narrowband Complex Ambiguity Function (CAF) and use them to calculate the Fisher Information Matrix (FIM) of the estimators of the target range and velocity. The FIM is then used to calculate the Cramer-Rao Lower Bounds (CRLB) of the variance of the estimators and to ´ carry out an analysis of estimation performance and a comparison with the case of a liner chirp with a rectangular and a Gaussian amplitude modulation. The analysis and the calculations of the CRLB are also extended to a train of hyperbolic chirps. Results corroborate that at narrowband the hyperbolic chirp is less Doppler tolerant than the linear chirp and show that the hyperbolic chirp provides a comparable measurement accuracy to the linear chirp. Results at wideband corroborate the superior Doppler tolerance of the hyperbolic chirp with respect to that of the linear chirp

High Speed Dim Air Target Detection Using Airborne Radar under Clutter and Jamming Effects

The challenging potential problems associated with using airborne radar in detection of high Speed Maneuvering Dim Target (HSMDT) are the highly noise, jamming and clutter effects. The problem is not only how to remove clutter and jamming as well as the range migration and Doppler ambiguity estimation problems due to high relative speed between the targets and airborne radar. Some of the recently published works ignored the range migration problems, while the others ignored the Doppler ambiguity estimation. In this paper a new hybrid technique using Optimum Space Time Adaptive Processing (OSTAP), Second Order Keystone Transform (SOKT), and the Improved Fractional Radon Transform (IFrRT) was proposed. The OSTAP was applied as anti-jamming and clutter rejection method, the SOKT corrects the range curvature and part of the range walk, then the IFrRT estimates the target’ radial acceleration and corrects the residual range walk. The simulation demonstrates the validity and effectiveness of the proposed technique, and its advantages over the previous researches by comparing its probability of detection with the traditional methods. The new approach increases the probability of detection, and also overcomes the limitation of Doppler frequency ambiguity

Method for shaping and aiming narrow beams

A sonar method and apparatus is discribed which utilizes a linear frequency chirp in a transmitter/receiver having a correlator to synthesize a narrow beamwidth pattern from otherwise broadbeam transducers when there is relative velocity between the transmitter/receiver and the target. The chirp is so produced in a generator in bandwidth, B, and time, T, as to produce a time bandwidth product, TB, that is increased for a narrower angle. A replica of the chirp produced in a generator is time delayed and Doppler shifted for use as a reference in the receiver for correlation of received chirps from targets. This reference is Doppler shifted to select targets preferentially, thereby to not only synthesize a narrow beam but also aim the beam in azimuth and elevation

Weighted Norms of Ambiguity Functions and Wigner Distributions

In this article new bounds on weighted p-norms of ambiguity functions and Wigner functions are derived. Such norms occur frequently in several areas of physics and engineering. In pulse optimization for Weyl--Heisenberg signaling in wide-sense stationary uncorrelated scattering channels for example it is a key step to find the optimal waveforms for a given scattering statistics which is a problem also well known in radar and sonar waveform optimizations. The same situation arises in quantum information processing and optical communication when optimizing pure quantum states for communicating in bosonic quantum channels, i.e. find optimal channel input states maximizing the pure state channel fidelity. Due to the non-convex nature of this problem the optimum and the maximizers itself are in general difficult find, numerically and analytically. Therefore upper bounds on the achievable performance are important which will be provided by this contribution. Based on a result due to E. Lieb, the main theorem states a new upper bound which is independent of the waveforms and becomes tight only for Gaussian weights and waveforms. A discussion of this particular important case, which tighten recent results on Gaussian quantum fidelity and coherent states, will be given. Another bound is presented for the case where scattering is determined only by some arbitrary region in phase space.Comment: 5 twocolumn pages,2 figures, accepted for 2006 IEEE International Symposium on Information Theory, typos corrected, some additional cites, legend in Fig.2 correcte

Approximate Computation of DFT without Performing Any Multiplications: Applications to Radar Signal Processing

In many practical problems it is not necessary to compute the DFT in a perfect manner including some radar problems. In this article a new multiplication free algorithm for approximate computation of the DFT is introduced. All multiplications $(a\times b)$ in DFT are replaced by an operator which computes $sign(a\times b)(|a|+|b|)$. The new transform is especially useful when the signal processing algorithm requires correlations. Ambiguity function in radar signal processing requires high number of multiplications to compute the correlations. This new additive operator is used to decrease the number of multiplications. Simulation examples involving passive radars are presented

WiFi-based PCL for monitoring private airfields

In this article, the potential exploitation of WiFi-based PCL systems is investigated with reference to a real-world civil application in which these sensors are expected to nicely complement the existing technologies adopted for monitoring purposes, especially when operating against noncooperative targets. In particular, we consider the monitoring application of small private airstrips or airfields. With this terminology, we refer to open areas designated for the takeoff and landing of small aircrafts that, unlike an airport, have generally short and possibly unpaved runways (e.g., grass, dirt, sand, or gravel surfaces) and do not necessarily have terminals. More important, such areas usually are devoid of conventional technologies, equipment, or procedures adopted to guarantee safety and security in large aerodromes.There exist a huge number of small, privately owned, and unlicensed airfields around the world. Private aircraft owners mainly use these “airports” for recreational, single-person, or private flights for small groups and training flight purposes. In addition, residential airparks have proliferated in recent years, especially inthe United States, Canada, and South Africa. A residential airpark, or “fly-in community,” features common airstrips where homes with attached hangars allow owners to taxi from their hangar to a shared runway. In many cases, roads are dual use for both cars and planes.In such scenarios, the possibility to employ low-cost, compact, nonintrusive, and nontransmitting sensors as a way to improve safety and security with limited impact on the airstrips' users would be of great potential interest. To this purpose, WiFi-based passive radar sensors appear to be good candidates [23]. Therefore, we investigate their application against typical operative conditions experienced in the scenarios described earlier. The aim is to assess the capability to detect, localize, and track authorized and unauthorized targets that can be occupying the runway and the surrounding areas