Impact of Onset Ambiguity on SEM Signature and Reduction Approach by Scattering and Polarization Diversification

The paper assesses how multiple-static scattering mitigates the effect of late-time onset on the robustness of the extracted resonance modes in the context of radar target classification. The assessment exploits the mode distribution vs onset shift to verify the sensitivity of the mode’s extraction to the selected onset, especially higher-order, to onset. However, within some bistatic directions, the modes have enhanced energies with lesser specular energy, making the modes estimate less sensitive to onset shifts. Also, the mode distribution per bistatic and polarization configuration has demonstrated different onset windows of accurate and consistent mode extraction. Notably, the distribution of the mode energy distribution reveals that classification performance degrades with poorly selected onset.


Introduction
A primary role of a modern radar system is to perform classification or discrimination operation of unknown targets based on a radar signal model, for which the model parameters should faithfully reflect some physical attributes of the target [1] [2]. Therefore, the robust model parameters aim to decrease the separation distance between same-class targets, and increase the separation between different classes; subsequently, obtain better classification performance curve against perturbation sources like noise. Such a signal model is the Singularity Expansion Method (SEM) that represents the late time of a pulsed signal of tran-How to cite this paper: Aldhubaib, F. (2020) Impact of Onset Ambiguity on SEM Signature and Reduction Approach by Scattering and Polarization Diversification. sient nature as a set of multiple decaying exponentials, i.e., resonance modes, where a matrix pencil method (MPM) can extract the mode parameters [3] [4].
Then the reconstructed late-timesignalis expressed as follows:  (1) where ω ≡ angular resonant frequency, normalized δ ≡ the damping factor/ wave speed, n a ≡ associated residue. Henceforth, the ratio â δ , namely Residue/damping factor, stands for the mode energy normalized by the speed of light. The modal order parameter M represents the highest order in the model, and it should reflect the number of the cardinal structures of interest that should be excited by the pulse.
The computation includes a matrix pencil method (MPM) to extract the mode parameter set, namely (ω, δ , a), from the selected transient signal [3] [4]. The mode has enhanced return with its frequency related to the target's cardinal dimensions. Also, a low-order mode extends temporally revealing single structure interaction, whereas, a higher-order mode localizes temporally revealing multiple structure interactions [5]. Theoretically, each class of targets possesses a unique mode set which may help discriminate the class from the clutter and interference in a high-volume radar cell.
Nevertheless, as the specular portion is adjacent and preceding the late-time has a more substantial return, it is necessary to select a late-time onset that maximizes the separation between the modes and the specular component, without omitting high-order modes. Thus, onset ambiguity when extorting the mode set is considered a significant factor that could degrade the effectiveness of the SEM model. Notably, the onset ambiguity limits the validity of the intended classification operation in a noncooperative scenario, especially when the proposed operation is over a range of ambiguous target aspects, such as with concealed targets.
Hence, such SEM-based classification techniques will perform suboptimally due to the limitation imposed on the number of modes in the model when some modes are omitted by improper onset selection. Henceforth, the paper hypothesizes that the mode estimate energy can improve over some incident to scattering configuration and polarization channels.
Therefore, the assessment begins in the frequency domain to attain a reference (ideal) modal-regions from the magnitude peaks, and from which the twice reciprocal-frequency of the first peak gives a reference onset to benchmark in the time-domain analysis [11]. In the time domain, the assessment considers the MPM extracted modal-frequency distribution as a function of onset shift to reveal onset bins of well-estimated modes.
The aim is to find onset bins of robust mode extraction per the scattering direction and polarization channel. Finally, the assessment views the onset effect on the target classification by a scatter plot of the mode energy versus modal-frequency per scattering configuration and channel given three onset cases.

The Simulation
The commercial software FEKO can construct a generic aircraft target model and calculate the scattered E-field data by a method of moments solver [12].  Moreover, the simulation derives the scattering data for the modal frequencies for azimuth cut, i.e., 0-2-360˚. Table 1 summarizes FEKO simulation variables. A Gaussian pulse u(t) of a duration (t d ), peak amplitude (u o ), pulse delay (t o ) and pulse width (p w ), can be expressed as follows Table 2 describes the pulse parameters values with sampling time Δt for the discrete version.
The Fourier transformation converts the coherent frequency data to a temporal data (consisting of early (specular) and late (transient) portions). The convolution with a baseband Gaussian pulse (depicted in Figure 2.) synthesises a baseband excitation necessary to excite the fundamental modes.

Procedures
The following steps describe the procedures: a) Use Feko calculate the coherent frequency response for the four orthogonal scattering direction of interest. b) Consider that the reference frequencies as the frequencies of the peaks, then derive their azimuthal pattern to verify that the mode enhances in some scattering and polarization directions. c) Define a reference onset as the reciprocal of the first frequency plus the delay time and pulse width (for backward scattering). d) Use the Fourier transformation then the convolution with the Gaussian pulse to transform the coherent frequency data to time data, namely 0 y , consisting of early and late time parts. e) Truncate the whole signal by a unit step function shifted by an onset time, namely l T , to create a truncatedsignal, namely l y , as follows: f) Repeatedly apply the MPM to the truncated signal while shifting the onset to derive the mode frequency distribution per polarization and scattering directions of interests. g) Derive the distribution of the residue/damping factor versus frequency for earlier, reference and later onsets for model A per scattering direction, then for both models per polarization channel.     have enhanced magnitude return compared to the backward direction, especially at the second mode where the wing and stabilizer interaction dominates. For the HH channel, the modes have all enhanced magnitude near the 180 forward direction, i.e., φ = 55˚. In overall, the 11 MHz mode has the highest total return in the HH channel due to the wing interaction, whereas the 23 MHz mode has the highest total radiation in the VV-channel due to the tail interaction. Notably, as the higher mode reveals more interactions between the target's structures, the mode's radiation pattern becomes more directive in the forward and side directions.   which extends for about 120 ns between the onset interval of 100 -220 ns within the co-polarized channel. However, the third mode extends for about 350 ns between the onset interval of 0 to 350 ns with better consistency within the cross-polarized channel. Notably, the onset interval between 225 -350 ns within the cross-polarized channel demonstrates better consistency for all three modes. Figure 9 depicts the distribution of the first three modes with onset shift within the forward directions in the hh channel. The onset shift intervals of 200 -300 ns demonstrate stable extraction of the three modes. Practically, delaying the onset interval will eventually decrease the transient energy to the specular level to the extent that the MPM cannot robustly extract the modes. Next, the dependence of the energy of the modes on the scattering direction is noticeable as depicted in shows modes of lower energies that have less resemblance and noticeable fluctuations along the different scattering direction. In general, shifting the onset to later times causes omitting overdamped modes because they are highly localized in time, as seen in the case of the third mode in Figure 10(b), in which the modes beyond 16 MHz disappear. Figure 11 depicts the energy distribution of the modes per polarization channel for both models. For T l = 113 ns and 210 ns, the modes distributions of both models are relatively similar compared to T l = 347 ns; hence, proper onset selection is essential to classify a target correctly.

Conclusion
In general, the high-order modes are of low energy and localized natures which commence adjacent to the end of the specular portion. The estimation of the higher-order modes is more susceptible to onset shift, which in turn adversely affects the modal order of the signature, i.e., level of information. Even more, delaying the onset to avoid specular spill over the transient portion causes the higher modes to be excluded from the signature, i.e., limit the signature modal order. Thus, the higher-order modes are more sensitive to the transient onset shift, and the risk of the modes been estimated incorrectly or even excluded from the signature is high. In general, the forward directions have enhanced the accuracy and consistency of the estimated resonance with a lesser specular return. The results have demonstrated that a generic aircraft model posses distinct modes in the vicinity of 8.89, 11.18 and 23 MHz as expected, where the transient return had duration twice the specular duration of approximately 120 ns. There exist a transient window, almost half its duration, were the modes are most consistent and accurate for the chosen azimuth angle. To further improve the transient return and suppress the specular, we suggest using several modulated pulses of lower resolution, i.e., longer duration, at the frequencies of the target's modes of interest.