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Accuracy of Phase-Less Algorithms of Antenna Array Calibration
Authors
	Djigan V.I.
	Kurganov V.V.
Date of publication
	2021
DOI
	10.31114/2078-7707-2021-1-77-86
Abstract
	The Antenna Arrays (AA) are often used as the directional antennas in the modern radio systems. The usage became possible due to the achievements of the microwave microelectronics, which allow the manufacturing of the small-sized and reliable receivers and transmitters, distributed over the AA channels, and digital devices for the AA control. In the ideal case, the AA as a sort of the multi-channel system, has to have the identical channels, because the main characteristic of the AA, that is the Radiation Pattern (RP), is synthetized using the ideal model of the AA. However, the ensuring of the AA channels identity is not so simple task, because the main portion of the AA equipment is build using the analogue components. Unfortunately, the modern radio industry does not produce the active and passive radio frequency components with the identical characteristics. The characteristics variation grows with the operation frequency growing. Besides, the identity of the AA channels also depends on the accuracy and the quality of the devices assembling. All these factors lead to the variation of the AA channel characteristics.If the AA is produced using the discrete components, its characteristics can be improved by means of the traditional manual adjustment. However, due to the achievements of the modern microwave microelectronics the new sort of the AA is also appeared today. These AA are called the «anten-na in package» and the «antenna in chip». The manual ad-justments of these AA is impossible because there is no phys-ical access inside of these devices. However, the devices can be designed in such way, that some of the devices character-istics can be changed by means of the external electrical control. The automatic correction of the AA channel characteristics is called calibration. The purpose of the calibration is to adjust the characteristics close each other or even to make the characteristics identical in all channels of the AA. After the AA manufacturing and calibration, the measured char-acteristics are saved and used during the AA field operation. However, due to the influence of the environment, because the AA are usually used in the open-air, and the variation of the supplied voltages, the characteristics of the AA compo-nents may degrade. This may lead to the degradation of the characteristics of the AA channels. Due to this reason, an important task is not only to calibrate the AA in the special anechoic chambers by means of the expensive equipment after the manufacturing, but also to provide the ability of the calibration during the AA operation. During the calibration, it is required to adjust the AA signal phases and amplitudes. However, the amplitude calibration is rarely used, because the AA must have the controllable attenuators that reduce the power of the received or trans-mitted signals, or the microwave amplifiers with adjustable gain, which are still quite complicated in the design and the manufacturing. However, using the modern CAD systems, it is possible to design the microwave devices in such a way, that after the manufacturing, the spread of their transmis-sion coefficients does not exceed a several decibels. This af-fects not significantly on the level of the main lobe of the RP and the deviation of the RP shape from the one specified during the design of the AA. At the same time, the spread in the phases in the AA channels may vary from 0 to 360 °, since the spread in the phase characteristics of the radio components increases with the frequency increasing. In addition, the scatter of the physical lengths of transmission lines connecting the AA antennas with the receiving-transmitting devices and connecting these devices with ad-ders or power dividers does not allow to ensure the same values of the length in all channels. Therefore, the phase calibration of the AA is mandatory. Today there are a lot of phase calibration methods and algorithms. They are the traditional methods, which use the phase measurement equipment; the correlation methods; the method, based on adaptive signal processing; and so-called phase-less methods. The phase-less algorithms for the AA calibration do not use the phase measurement equipment. Using the algorithms, the AA channel phases are estimated by means of the processing of the limited number of the AA output power measurements. The measurements are conducted under the specific changes of the AA channel phases by means of the phase-shifters (PS). The phases are changed relatively the PS states priory the calibration. These algorithms are simple. Thus, they can be used not only for the AA calibration in the anechoic chambers, but also during the AA field operation. The algorithms are differed by the number of power measurements per the AA channel, by the mathematic relationships for the phase estimates computa-tion and by the accuracy that depends on the number of the power measurements and the number of bits of the PS in use. In this paper, the following calibration algorithms are compared: two algorithms based on the method of the Rotating-Element Electric Field Vector (REV), algorithms of Sorace and Leavitt, as well as three algorithms of the authors of this paper. Using the simulation, it was demonstrated, that the considered phase-less calibration algorithms can be arranged according to the criterion of decreasing accuracy as follows: the full REV; the paper authors’ one, that requires 6 + 2 the AA output power measurements per channel; two of the paper authors’ ones, that requires 3 of the AA output power measurements per channel; the simplified REV, that requires 3 of the AA output power measurements per chan-nel; Leavitt’s and Sorace’s ones. Despite the highest accuracy of the full REV algorithm, its complexity grows with the increase in the number of the discrete PS bits. Therefore, a close to this algorithm in terms of accuracy and complexity are the paper authors’ algorithms. The simplified REV algorithms demonstrates a lower accuracy comparing to above mentioned algorithms. The accuracy of the Leavitt’s and Sorace’s algorithms is the lowest among the all considered algorithms and, moreover, the accuracy is decreased with an increase in the number of AA channels. Nevertheless, all the considered algorithms can be used to calibrate the AA of an arbitrary geometric configuration after the manufacturing and during operation. In the last case, these algorithms also provide the simultaneous calibration of the AA and the tracking of the angular position of the signal source in the case of its movement or the movement of the AA. A feature of all these algorithms is that they do not require the AA channel disconnection. Thus, they can be used not only for calibration of the AA, but also for the tracking of the angular position of the signal source.
Keywords
	antenna array, array calibration, phase calibration, phase-less calibration.
Library reference
	Djigan V.I., Kurganov V.V. Accuracy of Phase-Less Algorithms of Antenna Array Calibration // Problems of Perspective Micro- and Nanoelectronic Systems Development - 2021. Issue 1. P. 77-86. doi:10.31114/2078-7707-2021-1-77-86
URL of paper
	http://www.mes-conference.ru/data/year2021/pdf/D008.pdf