Effectiveness of Pulse Compression Signal Processing Techniques of Radar

Simple pulsed radar is limited in range sensitivity by the average radiation power and, in range resolution by the pulse length. The design of any radar always involves a compromise between the two constraints. Waveform design aims to seek an appropriate harmony that best suits the relevant application. The pulse compression theory has been introduced in order to get a high range resolution as well as a good detection probability. One of the basic types of pulse compression is binary phase coding which encodes the transmitted pulse with information that is compressed (decoded) in the receiver of the radar. The study of the peak sidelobe level (PSL) binary sequences occurs as a classical problem of signal design for digital communication and, in equivalent guise, in analytic number theory. It has also become a notorious problem of combinatorial optimization. For years mathematicians, engineers, physicists and chemists have sought a systematic way to construct long binary sequences with low PSL. In this Chapter, we describe pulse compression technique in radar waveform design. In order to make the presentation self-contained, we start by providing a short summary of waveform design and an introduction to principle behind pulse compression by compiling the basic tools required for analyzing and comparing different radar signals. After that, we talk about binary sequence, its desired properties and general types of methods for finding and generating such waveforms. We keep on by an overview and introducing the existing methods and search routine done. We conclude the chapter with a brief survey of the results exhibited yet for low autocorrelation binary sequences. We mention a table of complete results presented and also introduce a histogram to unscramble them visually and predict the future.

Bandwidth optimization and side-lobe levels reduction in PC radar using Legendre orthogonal polynomials

Radar system uses Pulse compression techniques to provide the benefits of larger range detection and high range resolution. The transmitted signal undergoes modulation to obtain this and after that matching is carried out with the echo signal (received signal) and transmitted signal. In the past several pulse compression techniques are used, out of which the well known method is linear frequency modulation (LFM). This paper deals with the design to develop and simulate pulse compression and matched filter algorithm in MATLAB to study the LFM pulse compression technique. Matched filter is used as the pulse compression filter which provides high SNR at the output. Matched Filter is mathematically equivalent to convolving the received signal with a conjugated time-reversed version of the reference signal. The main application of pulse compression Radars includes tracking of launch vehicles, abdicable components in space, Missile guidance etc. Here, in this paper we are discussing the pulse compression application in tracking the launch vehicle so as to check whether it had followed the predetermined path or not.

In a radar system, pulse compression technique permits us to overcome the trade-off between long and short duration pulses. Long duration pulses are used for good detection, whereas short duration pulses are used for better range resolution. During pulse compression, side-lobes exist with the main-lobe of the matched filter response. These side-lobes are unwanted because small targets might be hidden in the side-lobes which create the problem of accurate detection. When side-lobes are reduced, then main-lobe width is expanded which affects the range resolution. Linear frequency modulated waveforms and different polyphase codes, viz. Frank, P1, P2, P3 and P4 are used to reduce the side-lobes in the pulse compression. In this paper, polyphase codes are observed in pulse compression technique for side-lobe reduction. Ambiguity function is used to observe the polyphase codes behavior for side-lobes and range resolution. Simulation results show that P4 codes are best for side-lobe reduction as well as for better Doppler tolerance. The entire stated method is done with the aid of mathematical equations and simulation verification.

Linear Frequency Modulation (LFM) is a pulse compression method which is largely implemented in the radar applications. The high peak sidelobe is its main problem instead of its superiority on the simplicity and Doppler tolerance characteristics. The curve-shaped Nonlinear Frequency Modulation (NLFM) has been developed for overcoming this lack and prior investigation showed that this method provide lower sidelobe suppression than LFM. For obtaining the overall performance to be compared with LFM method, this research will investigate the curve-shaped NLFM in the case of Doppler effects and high level background noise. The Doppler effects considered in this research consist of two including center frequency shift and time dilation. Then, the background noise investigated is Gaussian distributed noise with signal to noise ratio (SNR) levels in range 0dB to −20dB. According to the simulation results, in the Doppler shift case, the curve-shaped NLFM is more sensitive than LFM as other NLFM drawbacks. However, this method is better than LFM in the time dilation scenario. Then, this pulse compression also has better detectability than LFM in the certain case of high level background noise condition.

Side-lobe reduction in pulse compression having a better range resolution

Nonlinear frequency modulated excitation signal and modified compressing filter for improved range resolution and side lobe level of ultrasound echoes

The theme of this paper is to present a novel technique for the reduction of the side-lobes in the pulse compression (PC) for the radar systems. The peak sidelobe level (PSL), integrated sidelobe level (ISL) and relative main-lobe width are computed using P4 polyphase codes, and compared the proposed technique results with other PC techniques such as Woo filter as well as modified Woo filter. This proposed PC technique is implemented by shifting the input P4 polyphase codes and multiplied it with reference signal in the frequency domain, after that the side-lobe behavior is analyzed by converting it into the time domain. Results show that the method introduced in this paper produces certain improvement in PSL and ISL.

The lateral resolution of a parametric acoustic array with narrow directivity is expected to be superior to that of a conventional linear sound source. The range resolution of the parametric array, however, is as low as the resolution of the linear source because of its long wavelength. To improve the range resolution in maintaining a high azimuth resolution for parametric sounds, a pulse compression technique using linear frequency-modulated signals or chirp signals is explored in the present study. The generation of chirp-modulated parametric sounds was experimentally confirmed in water, and then the auto-correlation of the parametric sound demonstrates short pulse widths up to 1/10 of the primary pulse duration. The results reveal that the pulse compression is feasible for a low-frequency parametric sound source with narrow directivity in the same manner as the compression of a linear sound wave.

Advances in millimeter wave solid-state power amplifier technology over the past decade have led to the development of a new generation of compact, lightweight cloud and precipitation radars. Solid-state power amplifiers (SSPAs) have lower peak power than traditional vacuum tube transmitters, but generally are capable of operating at much higher duty cycle. Taking advantage of the high duty cycle of SSPAs usually requires some signal processing and/or pulse compression technique to achieve similar sensitivity at comparable range resolution. FMCW (frequency modulated continuous wave) radars take full advantage of SSPAs capable of CW (continuous wave) operation, but the usual requirement for separate transmit and receive antennas is often impractical. Radars that combine a pulse compression waveform with a short pulse offset in frequency are now commonly used to operate at duty cycles as high as 10–20%. This paper reviews the latest solid-state millimeter wave radar designs, benefits, and limitations and describes operating modes and signal processing techniques that are especially well suited for single antenna operation. High PRF (pulse repetition frequency) operation using coherent power (single lag covariance) provides automatic noise cancellation without requiring explicit noise sampling. A novel phase coding technique employing Chu-codes with quadratically-increasing phase can be used to separate ambiguous signals when running at MHz-level PRFs. Weather data measured using the quadratic phase coding (QPC) technique with a solid-state Ka-band radar running at 3.1 MHz PRF is presented. This data was gathered at a transmitter duty cycle of approximately 50 percent and exhibits a 20 dB sensitivity improvement when compared to conventional short pulse data gathered at the same range resolution.

In this paper, a novel algorithm is devised to reduce the peak side lobe level (PSLL) of the thinned planar antenna (TPA) array at antenna boresight as well as over the desired scan volume without occurrence of grating lobes when the beam is electronically scanned away from the boresight. Randomized symmetrical thinning is incorporated in the proposed algorithm to find the best combination of 'ON' and 'OFF' elements. Modified binary coded genetic algorithm (MBC-GA) is employed in the present study to solve this optimization problem. A 12×12-element TPA array is numerically examined to access the performance of proposed method. Results obtained through this study show that array under consideration renders maximum possible reduction in PSLL and also demonstrate the absence of grating lobes when the beam is scanned to 20 deg. and 40 deg. away from the boresight.

Feasibility of low-frequency ultrasound imaging using pulse compressed parametric ultrasound

Phase-coded waveforms, an important class of radar signals, exhibit low peak sidelobe level (PSL) but lack sufficient Doppler tolerance. Inspired by the excellent Doppler properties of chirp-like signals, researchers have developed Piecewise Polynomial Phase-Coded Waveforms (PPPCW), which model phase using quadratic polynomials within sections, employing different coefficients across intervals. This structure combines the Doppler tolerance of chirp-like signals with the enhanced correlation performance of piecewise design, enabling joint optimization of PSL and Doppler tolerance. However, when segment count increases beyond two, existing models fail to maintain the periodic Doppler tolerance characteristic of chirp-like waveforms, causing this desirable property to rapidly deteriorate with increasing frequency offset. In this paper, we overcome this limitation through systematic analysis of the relationships between polynomial coefficients and Doppler tolerance, leading to an optimization model that integrates tolerance metrics with coefficient constraints to preserve Doppler performance regardless of segment count. By approximating PSL using the Log-Sum-Exp (LSE) function and employing automatic differentiation techniques derived from neural networks, we effectively solve this model via gradient descent methods. Experimental results demonstrate that our proposed model yields waveforms with both low PSL and periodic Doppler tolerance regardless of segment count. Notably, the model readily extends to Multiple-Input MultipleOutput (MIMO) radar applications through simple orthogonality constraints.

Designing sparse arrays with fewer antenna elements and lower peak sidelobe level (PSLL) is critical and challenging for antenna arrays in terminal devices in Internet of Things (IoT) systems. This article presents a deep learning method based on denoising diffusion probabilistic models (DDPM) for synthesizing sparse arrays. With predefined constraints such as aperture size, number of elements, and minimum element spacing, a training dataset that enables the proposed DDPM is generated to directly learn the distribution characteristics of these sparse arrays. To simplify the network architecture, the backbone network U-Net is replaced by a multilayer perceptron (MLP). In addition, an innovative conditional generation strategy is introduced to enhance the training accuracy, categorizing the training data into diverse cross-conditional labels based on PSLL and sparse ratio. During the training process, two separate regression networks are employed to predict the sparse ratio and the PSLL, and a Pareto-optimal weighting scheme (PWS) is designed to address the trade-off between them. Examples of two planar sparse arrays and a conformal sparse array demonstrate the effectiveness of the proposed DDPM-based method, highlighting its superiority in reducing PSLL and increasing sparse ratio, reducing inference time compared with the existing methods.

A hybrid algorithm based on the invasive weed optimization (IWO) and the convex optimization (CVX) is proposed for minimizing the peak sidelobe level (PSLL) of linear array with focused and/or shaped beam pattern. In this approach, IWO is adopted to produce the array (described by element positions), and CVX is used to determine the excitations for each produced array. Then the corresponding PSLL acts as the fitness function of IWO to find the optimal positions which lead to the minimum PSLL. Numerical experiments are conducted to validate the effectiveness and robustness of the proposed hybrid approach. Compared with other techniques, a lower PSLL can be achieved with a fixed main beam width or with a shaped main beam using this hybrid algorithm. Moreover, this method can easily cope with some constraints on the aperture, such as the minimum element spacing and the total number of elements.