Cross-ambiguity Functions Research Articles

Unimodular Complete Complementary Sequence with Optimal Trade-off between Auto- and Cross-ambiguity Functions for MIMO Radars

Unimodular Complete Complementary Sequence with Optimal Trade-off between Auto- and Cross-ambiguity Functions for MIMO Radars

A novel design of multi-user sequence set for joint vehicular radar-communication based on Oppermann family

In this paper, a novel multi-user sequence set which are to be potentially used as communication preambles for joint vehicular radar and communication using Oppermann sequences is proposed. Herein, a set of Oppermann sequences with suitable auto-ambiguity functions (AF) and cross-ambiguity functions (AF) properties have been proposed. Moreover, a channel estimation algorithm using the designed Oppermann sequences is also proposed. The designed preamble, composed of optimized Oppermann sequences is an appropriate candidate for wireless standards, where both channel estimation and multi-user vehicular radar sensing are jointly pursued. The simulation results demonstrate that the designed sequences provide a significant performance improvement for vehicular radar sensing and don't degrade the channel estimation accuracy. The proposed optimized Oppermann sequences have better auto- and cross-AF compared existing Golay complementary sequences (used in IEEE 802.11ad as preamble), Zadoff-Chu sequences (used in 5G to generate preambles for the Physical Random Access Channel (PRACH)) and the non-optimized Oppermann sequences. Specifically, compared to the preamble composed of Golay complementary sequences in IEEE 802.11ad, the proposed sequences reduce the maximum sidelobe level of the auto-AF and maximum value level of cross-AF by at least 2 and 2.85 times, respectively. The target can still be accurately detected in mutual interference scenario caused by multiple radars in the vicinity. Both the sequences, when used for channel estimation achieve the CRLB limit. Both the proposed sequences and Golay complementary sequences, when used for channel estimation achieve the Cramer-Rao Lower Bound.

A Multi-Pulse Cross Ambiguity Function for the Wideband TDOA and FDOA to Locate an Emitter Passively

The time difference of arrival (TDOA) and frequency difference of arrival (FDOA) between two receivers are widely used to locate an emitter. Algorithms based on cross ambiguity functions can simultaneously estimate the TDOA and FDOA accurately. However, the algorithms, including the joint processing of received data, require transferring a large volume of data to a central computing unit. It can be a heavy load for the data link, especially for a wideband signal obtained at a high sampling rate. Thus, we proposed a multi-pulse cross ambiguity function (MPCAF) to compress the data before transmitting and then estimate the TDOA and FDOA with the compressed data. The MPCAF consists of two components. First, the raw data are compressed with a proposed two-dimensional compression function. Two methods to construct a reference pulse used in the two-dimensional compression function are considered: a raw data-based method constructs the pulse directly from the received signal, and a signal parameter-based method constructs it through the parameters of the received signal. Second, a wideband cross-correlation function is studied to refine the TDOA and FDOA estimates with the compressed data. The simulation and Cramer–Rao lower bound (CRLB) analyses show that the proposed method dramatically reduces the data transmission load but estimate the TDOA and FDOA well. The hardware-in-the-loop simulation confirms the method’s effectiveness.

Mutual Interference Mitigation for Multiple Connected Automotive Radar Systems

The number of commercial and civilian vehicles equipped with automotive radars is expected to rise rapidly in the forthcoming years and with that comes the problem of increased mutual interference between the radar sensors, which can result in severely reduced radar sensitivity and increased false alarm rates. The difficulty and complexity of the problem increase with MIMO radar systems and multiply even further with a growing number of vehicles present on the scene. A system of connected vehicles can efficiently address this problem by sharing information amongst themselves. In this paper, we propose an efficient waveform design algorithm that seeks to minimize a collective cross-ambiguity function. Vehicles that can <italic xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">talk</i> to each other, can perform the design online in a collaborative manner, or offline, in which case the radar codes can be designed and stored in a codebook for future use. The proposed coding scheme is computationally efficient for practical use and the incorporation of such schemes requires only a slight modification of the existing systems. Our numerical examples indicate that the proposed scheme can significantly reduce the interference power level in a desired area of the radar cross-ambiguity functions.

Research on Co-channel Interference Suppression Method for Passive Radar Based on the Jiont Processing of Primary and Reference Channels

The illuminators of passive radar based civil communication signals are densely distributed. As a result, the co-channel illuminator always interferes with the primary and reference channels, resulting in poor detection performance. To solve the aforementioned problem, an improved signal processing flow with co-channel interference suppression is proposed in this paper. First, signals from all channels were processed jointly. The direct-path wave of each illuminator was estimated using the multi-channel blind deconvolution algorithm. Then, the direct-path wave of the primary illuminator was identified as the reference signal by applying the difference in the proportion of the primary illuminator signal energy among channels. Then, the clutter of each illuminator in the primary channel was suppressed by utilizing each of the above estimated signals. Finally, the residual signal, after cancellation, was used to compute the cross-ambiguity functions with the identified direct-path wave of the primary illuminator for target detection. The improved flow can promote the cancellation ratio and reduce the bottom noise of the cross-ambiguity function and missed alarm. Co-channel interference can be effectively suppressed using the improved processing flow without changing the radar system’s hardware. The validity of the proposed method were confirmed by the results of the simulation and experiment.

Ambiguity function and imaging performance of coded FMCW waveforms with fast 4D receiver processing in MIMO radar

In this paper, a novel design and processing of nearly orthogonal waveforms based on frequency modulated continuous wave (FMCW) signals for multiple-input, multiple-output (MIMO) radars is presented. The design, implementation and results of the complete system, capable of detection and imaging of radar targets, are here described. The orthogonality of sounding signals is critical for multi-channel radar applications since the interference between signals can significantly limit the radar's ability for observation of weak targets in presence of stronger targets and background clutter. The orthogonal waveforms are designed by coding consecutive complex FMCW signals in a frame so that they can be sent to the different transmit antennas of the radar allowing the simultaneous operation of all transmit channels. Unlike time division switching approaches, the orthogonality in the proposed architecture, is achieved by applying several coding techniques, at a symbol level: Golay complementary, Zadoff Chu, Direct Spread Spectrum (DSS), Space-Time Block Coded, Discrete Fourier Transform (DFT) and Costas based sequences. Moreover, a radar receiver processing, based on a complex frame based convolution between transmit and received waveforms together with 4-dimensional Fast Fourier Transform (4D-FFT) beamforming, is presented. This allows for a fast and complete sensing of range, azimuth, elevation and Doppler in a single frame. The performance of the proposed waveforms is evaluated through the analysis of their cross ambiguity functions and imaging capabilities, while the general performance of the radar's receiver processing is shown through the use of multiple radar images. The flexibility in generating such orthogonal coded waveforms and the proposed general receiver architecture are an important first step for developing a future software programmable MIMO radar.

Orthogonal Waveform With Multiple Diversities for MIMO Radar

For multiple-input multiple-output radar employing the advantage of virtual array, the general assumption of the perfect orthogonality between multiple waveforms is proved to be unachievable. Therefore, to achieve good orthogonality, transmission schemes employing frequency diversity or chirp modulation diversity have been extensively investigated. Inspired by the idea of “diversity means superiority,” approach which integrates multiple diversities in a single waveform might be used to improve the orthogonality. In this paper, a novel waveform named discrete frequency and chirp-rate coding waveform (DFCCW) consisting of both frequency and chirp modulation diversities is proposed. Based on the auto- and cross-ambiguity functions of the DFCCW, we prove that the proposed approach is able to decrease the cross ambiguity peak values. To generate and optimize a set of Pareto-optimal DFCCWs, a many-objective optimization algorithm named nondominated sorting genetic algorithm with differential evolution is presented. Besides, the optimal criteria considering Doppler effects ensure that the DFCCW possess good performance in presence of moving targets. Numerical results show that the DFCCW achieves better orthogonality than the waveforms that utilize only single diversity type.

Random Access for Underwater Acoustic Cellular Systems.

In this paper, a random access preamble (RAP) design technique for underwater acoustic cellular systems is proposed. After showing that the conventional RAP used in long term evolution (LTE) systems is not appropriate for underwater acoustic cellular systems, two different types of RAPs (RAP 1 and RAP 2) are proposed to detect the identity of underwater equipment/nodes (UEs) and estimate the time delay between a UE and an underwater base station (UBS) at the physical layer. RAP 1 is generated using a Zadoff-Chu (ZC) sequence where the identity of the UE is mapped to its root index, whereas RAP 2 is generated using a linear frequency modulation (LFM) waveform where the identity of the UE is mapped to its frequency sweeping parameter and frequency shifting parameter. Ambiguity functions (AFs) and cross-ambiguity functions (CAFs) of RAP 1 and RAP 2 are derived to investigate their correlation properties under the effect of time delay and Doppler shift. The performance of RAP detection is investigated by analyzing the detection probabilities and false alarm probabilities of RAP 1 and RAP 2 in a Doppler environment. By evaluating the performances of RAP 1 and RAP 2 in various situations, it is concluded that RAP 2 is more suitable for underwater acoustic cellular systems. The AF and CAF analytically obtained in this paper are shown to be similar to those obtained using experimental data.

DOA Estimation for Echo Signals and Experimental Results in the AM Radio-Based Passive Radar

The direction of arrival (DOA) of the target’s echo signal is extremely important for passive detection and tracking. However, it is a challenge to estimate the echo signal’s DOA due to the low signal-to-noise ratio of the echo signal and the serious masking effect. In this paper, a novel method is developed to estimate the DOA of the echo signal through enhancing the desired echo signal and attenuating the interference in range-Doppler domain before performing the DOA estimation. Firstly, the cross-ambiguity functions of the direct path signal and the received array signal are calculated. Then, they are combined to form a single-snapshot virtual array signal. Under certain conditions, the desired echo signal can be enhanced, and the interference can be attenuated simultaneously. After extending the single-snapshot virtual array signal to multi-snapshots, the conventional MUSIC approach can be performed, and the clutter interference can be suppressed significantly through subspace orthogonal meanwhile. Finally, the DOAs of echo signals as well as their corresponding Doppler shifts can be measured on a 2-D direction-Doppler map. The virtual array signal’s construction principle and the gain of echo signal are analyzed theoretically, and some experimental results are presented to verify the effectiveness of the proposed method.

Multi‐user radar waveforms based on doubly coded Costas signals

In multi-user radar applications, waveforms that show low cross-correlation and cross-ambiguity sidelobes are needed. In this study, the authors propose to generate novel multi-user waveforms using a modified version of Costas signals, namely doubly coded Costas signals. The modification principle consists in combining two Costas codes by coding the sub-pulses of the main code by another code. First, the sub-pulse Costas code diversity is used to generate waveforms with low cross-correlation sidelobes and good auto-correlation properties while using the same main Costas code. Conditions on sub-pulse codes are drawn by optimising the auto- and cross-ambiguity functions around the mainlobe. Subsequently, the authors extended the approach to the use of several main Costas codes selected according to particular criteria. Hence, since both main and sub-pulse Costas codes are exploited, the total number of generated signals is increased significantly compared with a usage of standard Costas codes. This can be suitable for multi-user radar applications with a large number of simultaneous users.

Anti-jamming property of Colpitts-based direct chaotic through-wall imaging radar

A direct chaotic through-wall imaging (TWI) radar using chaotic signal generated by improved Colpitts oscillator is proposed, and its good anti-jamming performance is investigated theoretically and experimentally. Compared with conventional TWI radar, the proposed radar has the advantages of very high range resolution, low probability of intercept, and immunity from jamming and interference. The characteristics of the chaotic signal are presented. According to the delta function-like autocorrelation of the chaotic signal, the range resolution of the radar is 6 cm. The cross-ambiguity functions with no discernible peaks are used to theoretically certify its interference immunity performance, and then the anti-jamming properties in the Colpitts jamming, linear frequency modulated chirp jamming, and noise jamming environments are demonstrated by numerical electromagnetic simulations using finite difference time domain, and the corresponding experiments. The simulation and experimental results show that the chaotic waveform possesses excellent jamming immunity to the noise and radio frequency interference. This feature makes the chaotic signal perform superbly in multi-radar environments.

Cross-ambiguity characterization of communication waveform features for passive radar

We examine ambiguity functions of long-term evolution (LTE), digital video broadcast (DVB), and digital audio broadcast (DAB) signals. For passive radar, we propose exploiting deterministic signal features. Degradation in cross-ambiguity functions using deterministic features is characterized with respect to the full self-ambiguity function. In some applications, performance trade-offs may be suitable, allowing cost-effective radar implementation, utilizing simplified receivers (without a direct-path channel) and partial matched filters with deterministic features of LTE, DVB, or DAB.

Estimating maxima of generalized cross ambiguity functions, and uncertainty principles

In certain signal processing problems, it is customary to estimate parameters in distorted signals by approximating what is termed a cross ambiguity function and estimating where it attains its maximum modulus. To unify and generalize these procedures, we consider a generalized form of the cross ambiguity function and give error bounds for estimating the parameters, showing that these bounds are lower if we maximize the real part rather than the modulus. We also reveal a connection between these bounds and certain uncertainty principles, which leads to a new type of uncertainty principle.

Cross-ambiguity function domain multipath channel parameter estimation

A new array signal processing technique is proposed to estimate the direction-of-arrivals (DOAs), time delays, Doppler shifts and amplitudes of a known waveform impinging on an array of antennas from several distinct paths. The proposed technique detects the presence of multipath components by integrating cross-ambiguity functions (CAF) of array outputs, hence, it is called as the cross-ambiguity function direction finding (CAF-DF). The performance of the CAF-DF technique is compared with the space-alternating generalized expectation–maximization (SAGE) and the multiple signal classification (MUSIC) techniques as well as the Cramér–Rao lower bound. The CAF-DF technique is found to be superior in terms of root-mean-squared-error (rMSE) to the SAGE and MUSIC techniques.

Bounds on the Volume and Height Distributions for the MIMO Radar Ambiguity Function

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 of orthogonality of the waveforms in this region. We derive the upper bound on the attainable "clear area" for the ambiguity function, and we show that, with respect to the conventional single-waveform ambiguity function, the maximum clear area is K times smaller for the MIMO system.

Ambiguity functions of laser-based chaotic radar

The ambiguity functions of a newly developed laser-based chaotic radar (CRADAR) system are studied. In the CRADAR system, the chaotic waveforms can be generated either by an optically injected (OI) semiconductor laser, or a semiconductor laser with optoelectronic feedback (OEF). The ambiguity functions of the chaotic pulsation and chaotic oscillation waveforms obtained experimentally from the CRADAR system with the respective OEF and the OI schemes are examined and compared. In the cross-ambiguity functions, both types of the chaotic waveforms demonstrate their excellent capabilities in the electrical counter-countermeasures (ECCM) that civilian and military applications desire. In the auto-ambiguity functions, the chaotic oscillation waveform shows better unambiguous detection quality than the chaotic pulsation waveform that an ideal thumbtack-like ambiguity function with minimal sidelobes is found. Moreover, variations in the peak value and the full width at half-maximum of the auto-ambiguity function of the chaotic oscillation waveform along the principal axes are also investigated. By having the features of both ultrawideband radar and random signal radar, the chaotic oscillation waveform of the CRADAR system with the OI scheme is shown to possess the advantages of high range resolution, excellent ECCM capability, ideal thumbtack-like ambiguity function, and uncoupled range and range rate resolution functions.

Distinguishing between materials in terahertz imaging using wide-band cross ambiguity functions

Terahertz pulsed imaging is a novel imaging technique whereby sub pico-second broadband THz pulses are used in the analysis of samples, through transmission and reflection modalities. This paper briefly introduces terahertz pulsed imaging and its potential medical applications, before exploring how wavelet analysis may be used in categorising terahertz imaged samples, specifically the use of the terahertz reference pulse as a mother function through wide-band cross ambiguity functions. We show that analysis using ambiguity functions can distinguish between a nylon and a resin step wedge phantom, and furthermore that the results obtained are consistent with those of traditional time domain and Fourier based techniques.

Fast computation of the ambiguity function and the Wigner distribution on arbitrary line segments

By using the fractional Fourier transformation of the time-domain signals, closed-form expressions for the projections of their auto or cross ambiguity functions are derived. Based on a similar formulation for the projections of the auto and cross Wigner distributions and the well known two-dimensional (2-D) Fourier transformation relationship between the ambiguity and Wigner domains, closed-form expressions are obtained for the slices of both the Wigner distribution and the ambiguity function. By using discretization of the obtained analytical expressions, efficient algorithms are proposed to compute uniformly spaced samples of the Wigner distribution and the ambiguity function located on arbitrary line segments. With repeated use of the proposed algorithms, samples in the Wigner or ambiguity domains can be computed on non-Cartesian sampling grids, such as polar grids.

Frames of cross ambiguity functions

Frames of two-dimensional (2-D) signals arising from frames of signals in one dimension are proposed. Such 2-D frames are obtained by computing the cross ambiguity function between frame elements in one dimension and elements of the corresponding reciprocal frame.

Generation of binaural information using cross ambiguity functions

This paper describes a method to generate binaural information. First of all, the accuracy of a conventional linear interpolation was examined by using signal-to-deviation ratio (SDR) and spectrum distortion. It was found that the accuracy of left and right direction HRTFs (60−120°) did not deteriorate despite the presence of a wide directional interval (SDR ≂ 23 dB). However, the accuracy of front and back direction HRTFs (0−−60° and 120−180°) deteriorated as the interval broadened. For the shade-side ear’s HRTFs, particularly, it was confirmed that the accuracy of linear interpolation deteriorated dramatically (SDR≂8 dB). Therefore, a method was investigated for generating a shade-side ear’s HRTF by using cross ambiguity functions (CAFs) whose model is related to dichotic listening. A shade-side HRTF could be generated with about a 10-dB SDR from a sunny-side HRTF, while the SDR becomes about 8 dB for a conventional linear interpolation estimation method. In this paper, the independence of HRTFs is also discussed, using the singular value decomposition from the point of view that it is possible to generate a new vector from a linear combination of vectors. In this article the accuracy of a linear interpolation from a base of HRTFs by SDR and spectrum distortion is examined.