We first derive the property of strictly noncircular signals in the frequency domain.
Jiexin Yin, Ding Wang, Ying Wu 2018, 'An Efficient Direct Position Determination Method for Multiple Strictly NoncircularSources', Sensorshttp://www.mdpi.com/1424-8220/18/2/324. Retrieved from DOAJ CC BY 4.0 (https://creativecommons.org/licenses/by-sa/4.0/legalcode)
The constructed variable was approved to be second order noncircular (improper).
Panpan Peng, Liang An 2018, 'Widely Linear Adaptive Instantaneous Frequency Estimation in Vector Hydrophones',Sensorshttp://www.mdpi.com/1424-8220/18/10/3348. Retrieved from DOAJ CC BY 4.0 (https://creativecommons.org/licenses/by-sa/4.0/legalcode)
In the present study, the stop-hole method was investigated with creating a noncircular hole.
M. Fanni, N. Fouda, M.A.N. Shabara, M. Awad 2015, 'New crack stop hole shape using structural optimizing technique', Ain Shams Engineering Journalhttp://www.sciencedirect.com/science/article/pii/S2090447915000362. Retrieved from DOAJ CC BY 4.0 (https://creativecommons.org/licenses/by-sa/4.0/legalcode)
However, these receivers assume implicitly or explicitly circular (or proper) interferences and become suboptimal for noncircular (or improper) interferences.
Chevalier Pascal, Pipon François, Delaveau François 2007, 'Second-Order Optimal Array Receivers for Synchronization of BPSK, MSK, and GMSK SignalsCorrupted by Noncircular Interferences', EURASIP Journal on Advances in Signal Processinghttp://asp.eurasipjournals.com/content/2007/045605. Retrieved from DOAJ CC BY 4.0 (https://creativecommons.org/licenses/by-sa/4.0/legalcode)
This result can be understood in terms of the long-range quadrupolar wakes of noncircular vacuum chambers with finite resistivity.
Alexander Chao, Samuel Heifets, Bruno Zotter 2002, 'Tune shifts of bunch trains due to resistive vacuum chambers without circular symmetry',Physical Review Special Topics. Accelerators and Beamshttp://doi.org/10.1103/PhysRevSTAB.5.111001. Retrieved from DOAJ CC BY 4.0 (https://creativecommons.org/licenses/by-sa/4.0/legalcode)
Furthermore, the proposed algorithm can be applied to arbitrary arrays and works well without estimating the noncircular phases.
Weihua Lv, Huapu Sun, Xiaofei Zhang, Dazhuan Xu 2015, 'Reduced-Dimension Noncircular-Capon Algorithm for DOA Estimation of Noncircular Signals',International Journal of Antennas and Propagationhttp://dx.doi.org/10.1155/2015/348636. Retrieved from DOAJ CC BY 4.0 (https://creativecommons.org/licenses/by-sa/4.0/legalcode)