Orthogonal Frequency Division Multiplexing Chirp Waveform Research Articles

An Integrated Orthogonal Frequency-Division Multiplexing Chirp Waveform Processing Method for Joint Radar and Communication Based on Low-Density Parity-Check Coding and Channel Estimation

With the advancement of information technology construction, the integration of radar and communication represents a crucial technological evolution. Driven by the research boom of integrated sensing and communications (ISACs), some scholars have proposed utilizing orthogonal frequency-division multiplexing (OFDM) to separately modulate radar and communication signals. However, the OFDM symbols in this paper incorporate a cyclic prefix (CP) and a virtual carrier (VC) instead of zero padding (ZP). This approach mitigates out-of-band power caused by ZP, in addition to reducing adjacent channel interference (ACI). In addition, we introduce low-density parity-check (LDPC) and use an improved normalized min-sum algorithm (NMSA) in decoding. The enhanced decoding efficiency and minimized system errors render the proposed waveform more suitable for complex environments. In terms of signal processing methods, this paper continues to use radar signals as a priori information to participate in channel estimation. Further, we consider the symbol timing offset (STO) and carrier frequency offset (CFO) issues. In order to obtain more reliable data, we use the minimum mean-square error (MMSE) estimation based on the discrete Fourier transform (DFT) to evaluate the channel. Simulation experiments verify that the system we propose not only realizes the transmission and detection functions but also improves the performance index of the integrated signal, such as the bit error rate (BER) of 7 × 10−5, the peak side lobe ratio (PSLR) of −13.81 dB, and the integrated side lobe ratio (ISLR) of −8.98 dB at a signal-to-noise ratio (SNR) of 10 dB.

An OFDM Chirp Waveform Design Method Based on Multiple Groups of Subchirp Durations Optimization for Clutter Suppression

Orthogonal frequency division multiplexing (OFDM) chirp waveform is considered a good choice in the waveform design for clutter suppression, which is due to its excellent characteristics such as spectral containment, phase diversity, great dynamic spectral allocation and high degree of freedom. Considering the purpose of clutter suppression, an OFDM chirp waveform design method based on multiple groups of subchirp durations optimization is proposed to improve the output signal-to-clutter-plus-noise ratio (SCNR) in this paper. The output SCNR is closely related to the waveform spectrum, so the waveforms’ energy spectral density functions are analyzed first to build the relation between the waveform parameters and spectra. Then, the multiple groups of subchirp durations optimization based on maximum SCNR is proposed and solved by an optimization method based on the sequential quadratic programming. Finally, the proposed method is verified and the optimized waveform is compared with the general waveform and the waveform with optimized single group of subchirp durations. The results show that the waveform optimized by the proposed method has higher output SCNR and the SCNR increment compared with the general waveform increases with the number of subcarriers. Besides, the high sidelobes of the general waveform are also greatly reduced.

A Method of Improving the Correlation Properties of OFDM Chirp Waveform Diversity

In this letter, an orthogonal frequency-division multiplexing (OFDM) chirp waveform diversity design scheme is proposed to achieve better correlation properties. First, the subchirp duration and bandwidth are optimized simultaneously to increase the degree of freedom in waveform diversity. Second, an optimization procedure is proposed based on the idea of Gram-Schmidt orthogonalization. To reduce the problem complexity, the design problem is separated into several subproblems. Each subproblem corresponds to designing an OFDM chirp composite waveform and is optimized by the Pareto optimization framework. Simulation results show that the proposed method outperforms the conventional methods in terms of both autocorrelation peak sidelobe level (APSL) and cross correlation peak level (CPL) under the circumstance of the same mainlobe width.

OFDM Chirp Waveform Design Based on Imitating the Time–Frequency Structure of NLFM for Low Correlation Interference in MIMO Radar

The orthogonal frequency division multiplexing (OFDM) chirp signal has its special merits of high-range resolution by exploiting a full bandwidth as multiple input multiple output (MIMO) radar signal. After simulation, there are some high peaks in the autocorrelation function and cross correlation function of conventional OFDM chirp signals, which may increase the correlation interference and reduce the detection performance of MIMO radar signal. This letter proposes to reduce the autocorrelation sidelobe peak (ASP) of OFDM chirp signal by subsection imitating the nonlinear frequency modulation (NLFM) signal's time-frequency structure. Since a suitable difference should be made between the subchirp rates and subchirp carrier frequencies of each of the two designed OFDM chirp signals for reducing the cross correlation peaks (CP), the imitated NLFM waveforms' design problem is solved by the proposed optimized method. At last, subchirps of the designed signals are coded by a group of optimized codes. The simulation shows the designed OFDM chirp signals have lower ASP and CP than the conventional ones and referenced previous OFDM signals, and their ASP decreases as the number of subchirps increases.

OFDM Chirp Waveform Design Based on Subchirp Bandwidth Overlap and Segmented Transmitting for Low Correlation Interference in MIMO Radar

There are some special merits for the orthogonal frequency division multiplexing (OFDM) chirp waveform as multiple input multiple output (MIMO) signals. This signal has high range resolution, good Doppler tolerance, and constant modulus superiority since it exploits a full bandwidth and is based on chirp signals. The correlation sidelobe peaks level are critical for the detection requirement of MIMO radar signals, however conventional OFDM chirp signals produce high autocorrelation sidelobe peaks (ASP) and cross-correlation peaks (CP), which reduces detection performance. In this paper, we explore the structure of OFDM chirp signals’ autocorrelation function and proposed a scheme to reduce the designed signal’s ASP by a designing suitable range of subchirp bandwidth and a segmented transmit-receive mode. Next, we explore a suitable range of interval between the chirp rates of each two signals to reduce the CP. The simulation of designed signals verifies the effectiveness of the proposed methods in the reduction of ASP and CP, with the correlation performance being compared with recent relate studies. In addition, the multiple signals detection and one-dimensional range image simulation show the good detection performance of a designed signal in MIMO radar detection.

OFDM chirp radar for adaptive target detection in low grazing angle

Low-altitude target detection is of great importance in radar applications, especially for military radar to counter the targets penetrated from low grazing angles. However, it is a challenge to detect the targets in low grazing angle area due to severe multipath reflection effects. In this study, the authors propose orthogonal frequency division multiplexing (OFDM) chirp waveform for target detection in low grazing angle region. The OFDM chirp waveform has better peak-to-average-power ratio level and provides larger time-bandwidth product than that of conventional OFDM waveform, which is beneficial for target detection. Two different radar schemes, namely, OFDM chirp radar and OFDM chirp multiple-input multiple-output (MIMO) radar, are studied under the Earth's curvature geometry model with the consideration of realistic multipath reflection effects. The generalised likelihood ratio test algorithm is developed by jointly exploiting the advantages of OFDM chirp waveform and MIMO configuration in increased degrees of freedom. In addition, an adaptive algorithm is further applied to enhance the target detection performance. All proposed schemes are verified by numerical results.

OFDM Chirp Waveform Diversity Design With Correlation Interference Suppression for MIMO Radar

The orthogonal frequency-division multiplexing (OFDM) chirp waveform has attracted much attention due to its high range resolution, low peak-to-average ratio, and large time-bandwidth product. In its application to multiple-input multiple-output radar, the correlation property of multiple OFDM chirp waveforms should be considered primarily for good detection performance. The simulation results show that high sidelobes exist in correlation functions of the conventional waveforms. In this letter, the reason for high correlation sidelobes is explored first, which is the equal subchirp durations and the same subcarrier bandwidth. Second, two new OFDM chirp waveform diversity design schemes are proposed to suppress the correlation interference. Via designing the various subchirp durations or subcarrier bandwidths specially, the high sidelobes are depressed and the correlation property is improved. Both simulation results and comparisons verify the effectiveness of the proposed methods.

MIMO SAR OFDM chirp waveform design and GMTI with RPCA based method

Multiple-input multiple-output synthetic aperture radar (MIMO SAR) has drawn wide attention for its increased degrees of freedom (DOFs) compared to the traditional multi-channel SAR (MC-SAR) system. The MIMO SAR system, which makes each antenna illuminate one subswath, can widen the range swath without decreasing PRF. One of the foremost tasks involved in the MIMO SAR system is the waveform design at the transmitter. Moreover, at the receiver, how to accurately separate the auto-correlation signal from the cross-correlation interferences is the other important issue. In this paper, an orthogonal frequency division multiplexing (OFDM) chirp signal designing method is firstly proposed, which is based on low cross-correlation interferences and good peak-to-sidelobe ratio (PSLR) rules. Using the designed OFDM chirp signals, the focused signal of MIMO SAR system matched the robust principal component analysis (RPCA) basic model. The moving target (sparse signal), clutter (low-rank signal) and noise (noise signal) can be separated directly. Hence, RPCA based method can be employed for ground moving target indication (GMTI) with no need for extracting the matched signal or suppressing the unmatched interferences. Extensive simulations demonstrate the effectiveness of the waveform designing method and GMTI with RPCA based method for MIMO SAR system.

Spread Spectrum-Coded OFDM Chirp Waveform Diversity Design

This paper proposes an approach to design multiple-input multiple-output radar waveforms that are orthogonal on both the transmitter and receiver. The proposed method jointly utilizes the direct sequence spread spectrum coding and orthogonal frequency division multiplexing (OFDM) chirp signaling techniques. We name it spread spectrum-coded OFDM chirp waveform diversity design. The performance of the designed waveforms is analyzed by examining the ambiguity function and correlation function. The influences of the spread spectrum code choice and the OFDM chirp parameters are also investigated. It is verified that the proposed design scheme can ensure these waveforms stay orthogonal on the receiver and have large time-bandwidth product which is beneficial to separate closely spaced targets.

Implementation of the OFDM Chirp Waveform on MIMO SAR Systems

Attention has been devoted to multiple-input multiple-output (MIMO) synthetic aperture radar (SAR) systems in recent years. The applications of MIMO SAR systems, which involve high-resolution wide-swath remote sensing, 3-D imaging, and multibaseline interferometry, are seriously limited by the available sets of orthogonal waveforms. Although orthogonal frequency-division multiplexing (OFDM) chirp waveforms are proposed to avoid intrapulse interferences, this waveform scheme has not been investigated for practical implementation. In this paper, challenges in implementing the OFDM chirp waveforms on practical systems are analyzed and solved. First, the small extra carrier frequency between the mutually orthogonal waveforms, which renders the OFDM chirp waveforms not strictly on common spectral support, is avoided by improving the modulation of the OFDM chirp waveform. Second, the tedious demodulation, which is realized by circular-shift addition in the time domain and subcarrier extraction in the frequency domain, is improved. Third, the radar systematic error and the Doppler shift, which introduce bandwidth leakage and degrade the waveform orthogonality significantly, are compensated. Finally, taking all these challenges into consideration, a novel signal processing algorithm along with a MIMO SAR system model is proposed. Theoretical analysis is validated by simulations and systematic calibration measurements based on a C-band system.

MIMO radar OFDM chirp waveform diversity design with sparse modeling and joint optimization

In multiple-input multiple-output radar systems, the employed waveforms should have a large time-bandwidth product, good correlation property and satisfactory ambiguity function performance. This paper proposes a orthogonal frequency division multiplexing (OFDM) chirp waveform diversity design scheme with sparse modeling and joint optimization of the waveform code matrix and amplitude matrix. First, we formulate the waveform diversity design as a mathematical optimization problem with sparse modeling and optimally design a code matrix to select the hopping frequencies for each waveform. Thereafter, the waveform amplitudes are adaptively designed by minimizing the cross-correlation peaks with genetic algorithm. The proposed method can easily generate multiple pseudo-orthogonal waveforms with satisfactory correlation and ambiguity function performance. Additionally, the impacts of waveform number, hopping frequency interval and selectable frequency index are discussed. The superiority of the proposed OFDM chirp waveform design over existing methods is verified by extensive simulation results.

MIMO SAR OFDM Chirp Waveform Diversity Design With Random Matrix Modulation

Multiple-input multiple-output (MIMO) synthetic aperture radar (SAR) has received much attention due to its interesting application potentials, but effective waveform diversity design is still a technical challenge. In a MIMO SAR, each antenna should transmit a unique waveform, orthogonal to the waveforms transmitted by other antennas. The waveforms should have a large time-bandwidth product, low cross-correlation interferences, and a low peak-average ratio. To reach these aims, this paper proposes an orthogonal frequency division multiplexing (OFDM) chirp waveform with random matrix modulation. The designed waveforms are time-delay and frequency-shift decorrelated. Referring to MIMO SAR high-resolution imaging, the proposed OFDM chirp waveform parameters are optimally designed, and their performances are analyzed through the ambiguity function and range-Doppler-based MIMO SAR imaging algorithm. Extensive and comparative simulation results show that the waveforms have the superiorities of high range resolution, constant time domain and almost constant frequency-domain modulus, large time-bandwidth product, low peak-average ratio, and low time-delay and frequency-shift correlation peaks. More importantly, this scheme can easily generate over three orthogonal waveforms with a large time-bandwidth product.

Large time-bandwidth product OFDM chirp waveform diversity using for MIMO radar

Multiple-input multiple-output radar waveform diversity design has received much attention, but many of existing waveforms are lack of a large time-bandwidth product. This paper proposes an orthogonal frequency division multiplexing (OFDM) chirp waveform diversity design scheme to generate four waveforms with good correlation properties, ambiguity performance and Doppler tolerance. The method jointly utilizes classic chirp waveform and OFDM to conduct multi-carrier modulation. This scheme enables us to exploit full bandwidth for each waveform and thus has an high frequency utilization efficiency. The modulation and demodulation of the four OFDM chirp waveforms are presented. The performance of the designed waveforms is analyzed by the correlation and ambiguity functions. Simulation results validate that our proposal can generate more orthogonal waveforms without significant performance degradation.

An improved OFDM chirp waveform used for MIMO SAR system

Special attention has been devoted to multi-input multi-output (MIMO) synthetic aperture radar (SAR) systems in recent years. The applications of MIMO SAR systems which involve 3D imaging, highresolution wide-swath remote sensing, and multi-baseline interferometry are seriously limited to the orthogonal waveforms. Although orthogonal frequency division multiplexing (OFDM) chirp waveforms can be used for MIMO SAR systems to avoid intra-pulse interferences, there is a small frequency shift between the transmitted OFDM pulses. This vulnerable shift, which can not only affect the waveform orthogonality, but also introduce residual phase error, renders the OFDM waveforms impractical. In this paper, an improved OFDM chirp waveform which works without the mentioned shift is presented, along with the novel modulation and efficient demodulation procedures. Comparison between the improved and the conventional OFDM chirp waveforms is detailed. The influence of random noise, quantization error, and Doppler shift on the orthogonality of OFDM waveform is also investigated in this paper. Theoretical analysis and simulation results illustrate the feasibility of this waveform scheme.