Probability Of Correct Resolution Research Articles

The method of forming virtual receiving channels in the automobile MIMO-radar

The article is intended for specialists in the field of radar, radio engineering and telecommunications. It considers the problem of forming virtual receiving channels in a car MIMO radar to increase the antenna aperture in the horizontal plane. The case is investigated when two cars fall into the main beam of the radar antenna pattern, and therefore, the application of super-resolution methods in azimuth is required. In modern vehicles, this option is required for vehicle collision avoidance and driver assistance systems. The use of MIMO technology makes it possible to form a larger antenna array (AR) for reception, the so-called virtual AR. This becomes possible due to a special choice of the topologies of the location of the transmitting and receiving channels, as well as due to the multiplication of the probing signals in each transmitting channel by an individual code. As a result, the resolving power of the AR increases in the direction finding of the target. A radar with “short” sounding chirp pulses is considered, in which the range is measured by the frequency method. The parameters of the signal in the radar are chosen so that the contribution of the terms associated with the speed of the target on the pulse duration to the beat frequency on the receiving side is negligible. Analytical expressions are obtained for the received signals under conditions of the Doppler frequency shift and “short” probing pulses. A method for generating signals in virtual receiving channels using an encoder only on the transmitting side and without a decoder on the receiving side is proposed. The use of various codes is investigated and their effectiveness is compared. For direction finding of targets, the method of the minimum polynomial of the correlation matrix of the received signals is applied. The method involves assessing the degree of the minimum polynomial of the correlation matrix of the input process in the AR based on a statistically valid root-mean-square criterion. This method allows adaptive estimation of the number of signal sources and has a super-resolution function. In contrast to the known works, the main attention is paid to the case of a short sample of the input process, when the number of samples is less than the dimension of the virtual AR. In this case, the sample correlation matrix is degenerate. The results of numerical modeling are given for the accuracy of azimuth measurement and the probability of correct resolution of two targets. A natural experiment was carried out. The presented results demonstrate the efficiency of the proposed concept, high accuracy of azimuth measurements, and the possibility of super resolution of two targets in the case of a short sample.

Determining the probability of correct resolution of the left–right ambiguity in towed array sonar

When a towed sonar array is straight, it has the difficulty that it cannot distinguish a contact on the left from one at the same angle on the right. When the array isnotstraight and its shape known, we calculate the probability that the left–right ambiguity is resolved correctly, using the Neyman–Pearson hypothesis testing framework, assuming a delay-sum beamformer, a single-frequency contact, and Gaussian noise. We also initially consider the noise field to be uncorrelated and show that the evaluation of the probability of correct resolution reduces to evaluating a one-dimensional integral. We find, as expected, that the probability increases, as the signal-to-noise ratio and the lateral deviation of the array from straight increase. For demonstration purposes, we also evaluate the probability of correct resolution for two representative shapes the array might assume in practice. Finally, we consider a more realistic, correlated noise field and we show that the initial assumption of an uncorrelated noise field provides a good approximation when the lateral deviation of the array is sufficiently large.

Resolution of left–right ambiguity in towed array sonars

A method is proposed for resolving the left–right ambiguity in passive sonar systems, a problem that arises in source localization when the array is straight. In practice, the array is not straight and a statistical analysis within the Neyman–Pearson framework is developed for a monochromatic signal in the presence of noise, assuming that the exact array shape is known. For any given array shape, an expression for the probability of correct resolution (PCR) is derived as a function of two parameters: the SNR and an array-lateral-displacement parameter. The first parameter measures the strength of the signal relative to the noise and the second the curvature of the array relative to the acoustic wavelength. The PCR is calculated numerically for a variety of array shapes of practical importance. The model results are found to agree with intuition; the PCR is 0.5 when the array is straight and is increasing as the signal is becoming louder and the array more curved. It is explained why the method is useful in practice and the effects of correlation between beams are discussed. [Research partially supported by Thomson Marconi Sonar Ltd.]