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The echo signals of frequency diverse array multiple-input multiple-output (FDA-MIMO) feature angle-range coupling, enabling simultaneous discrimination and estimation of multiple targets at different locations. In light of this, based on FDA-MIMO, this paper explores an sensing-centric integrated sensing and communication (ISAC) system for multi-target sensing. On the transmitter side, the complex coefficients index modulation (CCIM) scheme is designed, which carries extra bits by selecting complex coefficients from the coefficient vector. At the sensing receiver, we propose the FDA-MIMO-based spatial spectrum multi-target estimation (SSMTE) method, which first jointly estimates the angle and distance of targets and then estimates the velocities. To reduce the sensing computational complexity, the low-complexity spatial spectrum estimation (LCSSE) algorithm is proposed. LCSSE reduces the complexity without degrading the sensing performance by converting the joint angle-range search into two one-dimensional searches. To address the range ambiguity caused by frequency offset, a frequency offset design criterion (FODC) is proposed. It designs the integer and fractional components of the frequency offset to ensure the ambiguity distance exceeds the maximum sensing range, thereby alleviating parameters pairing errors. Moreover, the closed-form expressions for the bit error rate (BER) tight upper bound and the Cram\'er-Rao bound (CRB) are derived. Simulation results show that the proposed system excels in multi-target sensing and communications.

The first part of this series introduced the effectiveness of frequency diverse array (FDA) jamming through direct wave propagation in countering airborne phased multiple-input multiple-output (Phased-MIMO) radar. This part focuses on the effectiveness of FDA scattered wave (FDA-SW) jamming on the space-time adaptive processing (STAP) for airborne phased-MIMO radar. Distinguished from the clutter signals, the ground equidistant scatterers of FDA-SW jamming constitute an elliptical ring, whose trajectory equations are mathematically derived to further determine the spatial frequency and Doppler frequency. For the phased-MIMO radar with different transmitting partitions, the effects of jamming frequency offset of FDA-SW on the clutter rank and STAP performance are discussed. Theoretical analysis provides the variation interval of clutter rank and the relationship between the jamming frequency offset and the improvement factor (IF) notch of phased-MIMO-STAP. Importantly, the requirements of jamming frequency offset for both two-part applications are discussed in this part. Numerical results verify these mathematical findings and validate the effectiveness of the proposed FDA jamming in countering the phased-MIMO radar.

Phased multiple-input multiple-output (Phased-MIMO) radar has received increasing attention for enjoying the advantages of waveform diversity and range-dependency from frequency diverse array MIMO (FDA-MIMO) radar without sacrificing coherent processing gain through partitioning transmit subarray. This two-part series proposes a framework of electronic countermeasures (ECM) inspired by frequency diverse array (FDA) radar, called FDA jamming, evaluating its effectiveness for countering airborne phased-MIMO radar. This part introduces the principles and categories of FDA jammer and proposes the FDA jamming signal model based on the two cases of phased-MIMO radar, phased-array (PA) radar and FDA-MIMO radar. Moreover, the effects of FDA jamming on matched filtering and spatial filtering of PA and FDA-MIMO radar are analyzed. Numerical results verify the theoretical analysis and validate the effectiveness of the proposed FDA jamming in countering phased-MIMO radar.

The combination of frequency diverse array (FDA) radar technology with the multiple input multiple output (MIMO) radar architecture and waveform diversity techniques potentially promises a high integration gain with respect to conventional phased array (PA) radars. In this paper, we propose an approach to the design of the transmitter and the receiver of a coherent FDA (C-FDA) radar, that enables it to perform the demodulation with spectral overlapping, due to the small frequency offset. To this purpose, we derive the generalized space-time-range signal model and we prove that the proposed C-FDA radar has a higher coherent array gain than a PA radar, and at the same time, it effectively resolves the secondary range-ambiguous (SRA) problem of FDA-MIMO radar, allowing for mainlobe interference suppression and range-ambiguous clutter suppression. Numerical analysis results prove the effectiveness of the proposed C-FDA radar in terms on anti-interference and anti-clutter capabilities over conventional radars.

In smart city development, the automatic detection of structures and vehicles within urban or suburban areas via array radar (airborne or vehicle platforms) becomes crucial. However, the inescapable multipath effect adversely affects the radar's capability to detect and track targets. Frequency Diversity Array (FDA)-MIMO radar offers innovative solutions in mitigating multipath due to its frequency flexibility and waveform diversity traits amongst array elements. Hence, utilizing FDA-MIMO radar, this research proposes a multipath discrimination and suppression strategy to augment target detection and suppress false alarms. The primary advancement is the transformation of conventional multipath suppression into a multipath recognition issue, thereby enabling multipath components from single-frame echo data to be separated without prior knowledge. By offsetting the distance steering vectors of different objects to be detected, the accurate spectral information corresponding to the current distance unit can be extracted during spatial spectrum estimation. The direct and multipath components are differentiated depending on whether the transmitting and receiving angles match. Additionally, to mitigate high-order multipath, the echo intensity of multipath components is reduced via joint optimization of array transmit weighting and frequency increment. The numerical results show that the proposed algorithm can identify multipath at different distances in both single-target and multi-target scenarios, which is superior to the general MIMO radar., Comment: 14 pages

This paper addresses the problem of detecting a moving target embedded in Gaussian noise with an unknown covariance matrix for frequency diverse array multiple-input multiple-output (FDA-MIMO) radar. To end it, assume that obtaining a set of training data is available. Moreover, we propose three adaptive detectors in accordance with the one-step generalized likelihood ratio test (GLRT), two-step GLRT, and Rao criteria, namely OGLRT, TGLRT, and Rao. The LH adaptive matched filter (LHAMF) detector is also introduced when decomposing the Rao test. Next, all provided detectors have constant false alarm rate (CFAR) properties against the covariance matrix. Besides, the closed-form expressions for false alarm probability (PFA) and detection probability (PD) are derived. Finally, this paper substantiates the correctness of the aforementioned algorithms through numerical simulations.

The smart morphing wing aircraft (SMWA) is a highly adaptable platform that can be widely used for intelligent warfare due to its real-time variable structure. The flexible conformal array (FCA) is a vital detection component of SMWA, when the deformation parameters of FCA are mismatched or array elements are mutually coupled, detection performance will be degraded. To overcome this problem and ensure robust beamforming for FCA, deviations in array control parameters (ACPs) and array perturbations, the effect of mutual coupling in addition to looking-direction errors should be considered. In this paper, we propose a robust adaptive beamforming (RAB) algorithm by reconstructing a multi-domain interference plus noise covariance matrix (INCM) and estimating steering vector (SV) for FCA. We first reconstruct the INCM using multi-domain processing, including ACP and angular domains. Then, SV estimation is executed through an optimization procedure. Experimental results have shown that the proposed beamformer outperforms existing beamformers in various mismatch conditions and harsh environments, such as high interference-to-noise ratios, and mutual coupling of antennas., Comment: Conference extended version

Considering that frequency diverse array multiple-input multiple-output (FDA-MIMO) possesses extra range information to enhance sensing performance, this paper explores the FDA-MIMO-based integrated sensing and communication (ISAC) system. To reinforce the system communication capability, we propose the frequency offset permutation index modulation (FOPIM) scheme, which conveys extra information bits by selecting and permutating frequency offsets from a frequency offsets pool. For the system communication sub-functionality, considering the fact that the traditional maximum likelihood detection method suffers from high complexity and bit error rate (BER), the maximum likelihood-based two-stage detection (MLTSD) approach is presented to overcome this issue. For the system sensing sub-function, we employ the two-step maximum likelihood estimator (TSMLE) to stepwise estimate the angle and range of the interested target. Furthermore, we derive the closed-form expressions for the tight upper bound on the communication BER, along with the sensing Cram\'er-Rao bound (CRB). The simulation results validate the theoretical analysis, demonstrating that the proposed system exhibits lower BER and superior range resolution than independent MIMO communication and MIMO sensing modules.

When a target is masked by mainlobe clutter with the same Doppler frequency, it is difficult for conventional airborne radars to determine whether a target is present in a given observation using regular space-time adaptive processing techniques. Different from phased-array and multiple-input multiple-output (MIMO) arrays, frequency diverse arrays (FDAs) employ frequency offsets across the array elements, delivering additional range-controllable degrees of freedom, potentially enabling suppression for this kind of clutter. However, the reception of coherent FDA systems employing small frequency offsets and achieving high transmit gain can be further improved. To this end, this work proposes an coherent airborne FDA radar receiver that explores the orthogonality of echo signals in the Doppler domain, allowing a joint space-time processing module to be deployed to separate the aliased returns. The resulting range-space-time adaptive processing allows for a preferable detection performance for coherent airborne FDA radars as compared to current alternative techniques., Comment: 11 pages, 9 figures

Current literature show that frequency diverse arrays (FDAs) are able of producing range-angle-dependent and time-variant transmit beampatterns, but the resulting time and range dependencies and their characteristics are still not well understood. This paper examines the FDA transmission model and the model for the FDA array factor, considering their time-range relationship. We develop two FDA transmit beampatterns, both yielding the auto-scanning capability of the FDA transmit beams. The scan speed, scan volume, and initial mainlobe direction of the beams are also analyzed. In addition, the equivalent conditions for the FDA integral transmit beampattern and the multiple-input multiple-output (MIMO) beampattern are investigated. Various numerical simulations illustrate the auto-scanning property of the FDA beampattern and the proposed equivalent relationship with the MIMO beampattern, providing the basis for an improved understanding and design of the FDA transmit beampattern., Comment: 31 pages, 9 figures

Frequency diverse array (FDA) differs from conventional array techniques in that it imposes an additional frequency offset (FO) across the array elements. The use of FO provides the FDA with the controllable degree of freedom in range dimension, offering preferable performance in joint angle and range localization, range-ambiguous clutter suppression, and low probability of intercept, as compared to its phased-array or multiple-input multiple-output (MIMO) counterparts. In particular, the FO of the coherent FDA is much smaller than the bandwidth of the baseband waveform, capable of obtaining higher transmit gain and output signal-to-interference-plus-noise ratio (SINR). In this paper, we investigate the problem of joint design of the transmit and receive weights for coherent FDA radar systems. The design problem is formulated as the maximization of the ratio of the power in the desired two-dimensional range-angle space to the power in the entire area, subject to an energy constraint that limits the emitted energy of each transmit antenna and a similarity constraint such that a good transmit beampattern can be guaranteed. Due to the resultant problem is NP-hard, therefore, a sequential optimization method based on semidefinite relaxation (SDR) technique is developed. Numerical simulations are provided to demonstrate the effectiveness of the proposed scheme., Comment: 28 pages, 10 figures

This paper considers the problem of jointly designing the transmit waveforms and weights for a frequency diverse array (FDA) in a spectrally congested environment in which unintentional spectral interferences exist. Exploiting the properties of the interference signal induced by the processing of the multi-channel mixing and low-pass filtering FDA receiver, the interference covariance matrix structure is derived. With this, the receive weights are formed using the minimum variance distortionless response (MVDR) method for interference cancellation. Owing to the fact that the resulting output signal-to-interference-plus-noise ratio (SINR) is a function of the transmit waveforms and weights, as well as due to the ever-greater competition for the finite available spectrum, a joint design scheme for the FDA transmit weights and the spectrally compatible waveforms is proposed to efficiently use the available spectrum while maintaining a sufficient receive SINR. The performance of the proposed technique is verified using numerical simulations in terms of the achievable SINR, spectral compatiblity, as well as several aspects of the synthesized waveforms., Comment: 13 pages, 14 figures

In this paper, we focus on the design of the transmit waveforms of a frequency diverse array (FDA) in order to improve the output signal-to-interference-plus-noise ratio (SINR) in the presence of signal-dependent mainlobe interference. Since the classical multi-carrier matched filtering-based FDA receiver cannot effectively utilize the waveform diversity of FDA, a novel FDA receiver framework based on multi-channel mixing and low-pass filtering is developed to keep the separation of the transmit waveform at the receiver side, while preserving the FDA range-controllable degrees of freedom. Furthermore, a range-angle minimum variance distortionless response beamforming technique is introduced to synthesize receiver filter weights with the ability to suppress a possible signal-dependent mainlobe interference. The resulting FDA transmit waveform design problem is initially formulated as an optimization problem consisting of a non-convex objective function and multiple non-convex constraints. To efficiently slove this, we introduce two algorithms, one based on a signal relaxation technique, and the other based on the majorization minimization technique. The preferable performance of the proposed multi-channel low-pass filtering receiver and the optimized transmit waveforms is illustrated using numerical simulations, indicating that the resulting FDA system is not only able to effectively suppress mainlobe interference, but also to yield estimates with a higher SINR than the FDA system without waveform optimization., Comment: 37 pages, 11 figures