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Calibration of Antenna Arrays with Small Number of Antennas: Problems and Solutions
Authors
	Kurganov V.V.
	Djigan V.I.
Date of publication
	2020
DOI
	10.31114/2078-7707-2020-4-159-168
Abstract
	Today, Antenna Arrays (AA) are often used in the modern radio systems as the direction antennas. The commercial manufacturing of the AA became possible due to the achievements in modern physics of semiconductors, microe-lectronic technologies and design of the large scale integrated circuits. These achievements became the fundamentals for the manufacturing of the passive and active radio frequency components and digital integrated circuits, which are used in the radiofrequency blocks of the AA and the units for the AA control. The AA provides the non-mechanical beam steering, the ability to change the shape of the Radiation Pat-tern (RP), ensuring the required properties of the AA to-wards the desired signal source and the deep gaps of the RP towards the interference sources. An AA is a multichannel antenna system. The control of its RP shape is provided by means of the variable microwave elements, which change the amplitude and phase of the channel signals. These elements have some variation of their parameters. The variation is caused by discrete character of the AA control, the AA fre-quency band, operation frequency, range of operation tem-peratures, brake of active components, antennas mutual coupling etc. As the operation frequency of the AA grows, the mentioned variation becomes more noticeable. This influ-ences on the shape of the RP and other characteristics of the AA. It is especially important to keep the characteristics of the AA with the small number of antenna/channels. Any deviation of the complex gains of the AA channels leads to a noticeable change of the AA RP shape. In AA with a large number of channels, these deviations are almost averaged and the contribution of the each individual channel to the AA properties is not sensitive. However, some of the proper-ties are still important, like the value of received or transmit-ted power. Thus, to ensure the properties of the AA with low or large number of channels, it is required to compensate the abovementioned variations. This compensation is achieved by means of the AA calibration. The purpose of the paper is to provide the classification of the modern methods and algo-rithms of the AA calibration; to select the most suitable methods to calibrate the AA with a small numbers of anten-nas/channels; to consider the mathematic details of the meth-ods; to compare these methods and specify the conditions of the methods usage. The following so-called phaseless calibra-tion algorithms are considered in detail. They are the Rotat-ing-Element Electric Field Vector (REV), Measurement of Two Elements (MTE) algorithms [10]-[19] and three algo-rithms: by the paper authors [21]-[23], by Leavitt [24], by Sorace [25], [26] and correlation algorithm [27]-[29]. The REV and MTE algorithms allow to estimate the gains and phases of the AA channel signals. During the execution of these algorithms, the errors of the discrete Phase Shifters (PS) are averaged. These algorithms require at least three measurements of the AA output power per channel at three states of the channel PS. The algorithm accuracy is increased with the increasing of the number of the power measure-ments. The MTE algorithm requires to disable all AA chan-nels except a reference and a calibrated ones. The REV algo-rithm does not require the above mentioned disabling of the AA channels, but requires a preliminary inversion of some initial channel phases. The calibration algorithm, proposed by the paper authors, requires the eight measurements of power for per AA channel, does not require the channel sig-nals access or channel disabling and changes the phases only in two channels: reference and calibrated ones. The Leavitt’s algorithm is more complex, because it requires the phase changing in all channels of the AA during the calibration of each channel. It also requires eight measurements of power per AA channel. However, this algorithm does not take the PS quantization errors into account. The Sorace’s algorithm requires only four measurements of power per AA channel and uses the phase perturbation in two channels: reference and calibrated ones. However, the mathematic equation for channel phase estimation is an approximate one in this algo-rithm. So, the algorithm accuracy is lower comparing with that of the paper authors’ and Leavitt’s algorithms. The correlation algorithm is based on the correlation processing of the AA output signal, which consists of the combination of all channel signals. Each of channel signals is modulated by an own code sequence. The correlation processing allows to identify the complex-valued gain of each channel, that allows to estimate the gain spread and to use the information for AA calibration. This algorithm allows to calibrate the AA with analog and digital beamforming. So, even today an AA is a commercially available product, the AA calibration prob-lem is still important. The AA calibration ensures the AA parameters improvement. However, the most of the calibra-tion algorithms require the special anechoic chambers or fields for antenna measurements, as well as the expensive measuring equipment. At the same time, phaseless calibra-tion algorithms provide high enough accuracy, even are based on the indirect phase estimation. Besides, the algo-rithms do not require special conditions for the calibration and can be also used even during the AA operation. Due to this property, the phaseless calibration should be widely used in the commercially available AA, because this allows to make these AA inexpensive and simultaneously allows to ensure the AA design parameters during operation. In our opinion, the phaseless calibration methods and algorithms are the main trends in the AA technology development and the AA usage.
Keywords
	antenna array, array calibration, phaseless calibration, REV algorithm, MTE algorithm, correlation algorithm.
Library reference
	Kurganov V.V., Djigan V.I. Calibration of Antenna Arrays with Small Number of Antennas: Problems and Solutions // Problems of Perspective Micro- and Nanoelectronic Systems Development - 2020. Issue 4. P. 159-168. doi:10.31114/2078-7707-2020-4-159-168
URL of paper
	http://www.mes-conference.ru/data/year2020/pdf/D083.pdf