Reciprocity Calibration Research Articles

Deep Reciprocity Calibration for TDD mmWave Massive MIMO Systems Toward 6G

Deep Reciprocity Calibration for TDD mmWave Massive MIMO Systems Toward 6G

A primary wideband calibration method for noise hydrophones based on three-transducer spherical wave reciprocity in the frequency domain.

A primary wideband calibration method for noise hydrophones is developed, which can be applied to obtain noise acoustic spectral density sensitivity in the free-field. In this method, a wideband three-transducer spherical wave reciprocity calibration method is proposed in the frequency domain. A lowpass spatial domain filter is utilized to eliminate the reflecting acoustic waves from boundaries and water surface, and the wideband frequency responses of the transducer pair are calculated. Wideband calibrations are performed in a laboratory anechoic water tank, and two hydrophones with different reference sensitivities are calibrated in the frequency range of 250 Hz to 20 kHz using noise signals. The decidecade band sensitivities are obtained by the primary wideband calibration, which is in agreement with the single frequency sensitivities. The expended uncertainty of the primary wideband calibration is analyzed and estimated to be 8.9% (k = 2).

Reciprocity Calibration of Dual-Antenna Repeaters

Reciprocity Calibration of Dual-Antenna Repeaters

Free-field three-transducer spherical-wave reciprocity calibration for hydrophone at hydrostatic pressure of 10 MPa

Free-field three-transducer spherical-wave reciprocity method has been reviewed and employed to calibrate the hydrophone of TC4033 in a high hydrostatic pressure vessel. To reduce the measurement uncertainty, a reciprocal calibration bracket and reciprocal transducers were designed and developed. The calibration bracket can locate the transducers in the high hydrostatic pressure vessel. The reciprocal transducer can reduce the errors caused by the deviation of reciprocity. A correcting sensitivity method based on complex electrical impedance measurement has been described, which can obtain the original open-circuit sensitivity of a hydrophone. It is more accurate than correcting method based on the measurement of extension cable capacitance especially near the resonant frequency range. The TC 4033 hydrophone was calibrated in the one-third octave frequency points from 2 kHz to 200 kHz at a high hydrostatic pressure of 10 MPa. The calibration results were analyzed, and the measurement uncertainty was estimated to be 0.5 dB (k=2).

Diagnosing oral and maxillofacial diseases using deep learning

The classification and localization of odontogenic lesions from panoramic radiographs is a challenging task due to the positional biases and class imbalances of the lesions. To address these challenges, a novel neural network, DOLNet, is proposed that uses mutually influencing hierarchical attention across different image scales to jointly learn the global representation of the entire jaw and the local discrepancy between normal tissue and lesions. The proposed approach uses local attention to learn representations within a patch. From the patch-level representations, we generate inter-patch, i.e., global, attention maps to represent the positional prior of lesions in the whole image. Global attention enables the reciprocal calibration of path-level representations by considering non-local information from other patches, thereby improving the generation of whole-image-level representation. To address class imbalances, we propose an effective data augmentation technique that involves merging lesion crops with normal images, thereby synthesizing new abnormal cases for effective model training. Our approach outperforms recent studies, enhancing the classification performance by up to 42.4% and 44.2% in recall and F1 scores, respectively, and ensuring robust lesion localization with respect to lesion size variations and positional biases. Our approach further outperforms human expert clinicians in classification by 10.7 % and 10.8 % in recall and F1 score, respectively.

Performance of Cell-Free Massive MIMO Under Imperfect Channel State Information and Reciprocity Calibration

This article studies the downlink performance of a cell-free massive multiple-input–multiple-output (MIMO) system with imperfect channel estimation and reciprocity calibration. We present the statistical characteristics of the calibration error with the Argos algorithm and a relay-based calibration algorithm to obtain the calibration parameters of the whole network. Then, we derive approximate expressions of the downlink spectral efficiency for a cell-free massive MIMO system with imperfect channel state information and calibration error. The numerical results show the advantage of the proposed calibration algorithm and validate the accuracy of the theoretical expressions.

Amplitude prediction from uplink to downlink CSI against receiver distortion in FDD systems

In frequency division duplex (FDD) massive multiple-input multiple-output (mMIMO) systems, the reciprocity mismatch caused by receiver distortion seriously degrades the amplitude prediction performance of channel state information (CSI). To tackle this issue, from the perspective of distortion suppression and reciprocity calibration, a lightweight neural network-based amplitude prediction method is proposed in this paper. Specifically, with the receiver distortion at the base station (BS), conventional methods are employed to extract the amplitude feature of uplink CSI. Then, learning along the direction of the uplink wireless propagation channel, a dedicated and lightweight distortion-learning network (Dist-LeaNet) is designed to restrain the receiver distortion and calibrate the amplitude reciprocity between the uplink and downlink CSI. Subsequently, by cascading, a single hidden layer-based amplitude-prediction network (Amp-PreNet) is developed to accomplish amplitude prediction of downlink CSI based on the strong amplitude reciprocity. Simulation results show that, considering the receiver distortion in FDD systems, the proposed scheme effectively improves the amplitude prediction accuracy of downlink CSI while reducing the transmission and processing delay.

Toward a unified formulation of the acoustic transfer admittance of cylindrical cavities for reciprocity calibration of microphones

The pressure reciprocity technique for calibration of Laboratory Standard microphones provides the basis for primary measurement standards for sound pressure. This calibration method is described in the International Electrotechnical Commission (IEC) standard 61094-2:2009 where the key aspect relating to the calculation of the acoustic transfer admittance of couplers was recently completed and clarified in the amendment IEC 61094-2:2009/AMD1:2022. Three models are currently provided for calculating this quantity: the low-frequency solution suitable to low frequencies, the extended low-frequency solution suitable to low and medium frequencies, and the broadband solution suitable to medium and high frequencies. It is established that neither of these models is correct for all frequencies routinely considered in many National Metrology Institutes, namely from 2 Hz to 25 kHz, so that a transition must be made. Based on the fundamental equations of acoustics in thermoviscous fluid, this paper provides a unified formulation for the acoustic transfer admittance of cylindrical cavities. Under the common quasi-plane wave approximation, this paper provides a new form of solution for the Fourier equation, not restricted by any assumption on the pressure variation and leading to a new form of propagation equation in the coupler. Two techniques are used to solve the problem, the Laplace Adomian Decomposition Method and a stepped duct approximation technique. Numerical results are presented, providing substantial evidence to support the validity of these formulations. A high level of agreement is observed between the two models, approximately 10−6 dB for the amplitude and 10−4 degrees for the phase, excluding the resonance frequencies of couplers. Finally, this paper evaluates the compatibility of the extended low-frequency solution provided in the IEC amendment with the fundamental equations established in this study. A new simplified solution is provided, highlighting discrepancies in the application of the heat conduction corrective factor as compared to the guidelines outlined in the IEC amendment.

Experimental Performance Evaluation of Cell-Free Massive MIMO Systems Using COTS RRU With OTA Reciprocity Calibration and Phase Synchronization

Experimental Performance Evaluation of Cell-Free Massive MIMO Systems Using COTS RRU With OTA Reciprocity Calibration and Phase Synchronization

Ultrasonic needle hydrophone calibration in air by a parabolic off-axis mirror focused beam using three-transducer reciprocity

An acoustic field distribution investigation in air requires a small receiving sensor. Needle hydrophones seem to be an attractive solution, and it has previously been demonstrated that needle hydrophones designed for use in water can be used in air. The metrology problem is that an absolute sensitivity calibration is needed, because needle hydrophones are not characterized in air, especially for frequencies below 1 MHz, which is of interest for air-coupled ultrasound. Conventional, three-transducer/microphone reciprocity calibration requires measurements to be done in the far field. However, when transducer diameter is large and the frequency is high, the required measurement distance becomes very large: 3 m for a 20 mm source, transmitting at 1 MHz. Large propagation distance leads to high attenuation and nonlinear effects in air propagation, and distortion and losses accumulate. Small needle hydrophones have low sensitivity, so that high excitation amplitudes would be required, which can lead to transducer heating and increase nonlinearity effects. A derivative of the three-transducer reciprocity calibration method is proposed, where a large aperture transducer is focused onto a hydrophone, using hybrid of plane wave and spherical wave reciprocity. Use of a focused source minimizes the frequency-dependent diffraction effects, and the spherical wave approximation is valid at the focal distance, and low level excitation signals can be used. Focusing is accomplished using a parabolic off-axis mirror. Calibration is in transmission, which reduces the complexity of the electrical measurements. The corresponding equations have been derived for this setup. Calibration of the transducer and needle hydrophone absolute sensitivity is obtained.

Hierarchical-Absolute Reciprocity Calibration for Millimeter-Wave Hybrid Beamforming Systems

In time-division duplexing (TDD) millimeter-wave (mmWave) massive multiple-input multiple-output (MIMO) systems, the reciprocity mismatch severely degrades the performance of the hybrid beamforming (HBF). In this work, to mitigate the detrimental effect of the reciprocity mismatch, we investigate reciprocity calibration for the mmWave-HBF system with a fully-connected phase shifter network. To reduce the over-head and computational complexity of reciprocity calibration, we first decouple digital radio frequency (RF) chains and analog RF chains with beamforming design. Then, the entire calibration problem of the HBF system is equivalently decomposed into two subproblems corresponding to the digital-chain calibration and analog-chain calibration. To solve the calibration problems efficiently, a closed-form solution to the digital-chain calibration problem is derived, while an iterative-alternating optimization algorithm for the analog-chain calibration problem is proposed. To measure the performance of the proposed algorithm, we derive the Cramér-Rao lower bound on the errors in estimating mismatch coefficients. The results reveal that the estimation errors of mismatch coefficients of digital and analog chains are uncorrelated, and that the mismatch coefficients of receive digital chains can be estimated perfectly. Simulation results are presented to validate the analytical results and to show the performance of the proposed calibration approach.

Determination of microphone acoustic center from sound field projection measured by optical interferometry.

This article presents a method for determining the acoustic center of a microphone from a sound field measured by optical interferometry. The acoustic center defines the equivalent point source position of a microphone serving as a sound source where the spherical waveform starts to diverge. The value is used to determine the effective distance between microphones for free-field reciprocity calibration. Conventionally, it is determined from the inverse distance law properties of a point source using the transfer function method. In this study, the acoustic center was determined from the projection of the sound field of the microphone. Parallel phase-shifting interferometry was used to measure the line integration of the sound pressure from a microphone. The acoustic center is determined as the position where the squared error between the measured data and the projection model of a point source is minimized. Experiments with the B&K 4180 (Brüel & Kjær, Nærum, Denmark) microphone were performed for frequencies from 10 to 50 kHz. The best acoustic center estimation was obtained at a microphone distance of 0 mm, with a difference of 0.17 mm to the IEC 61094-3 value and 0.36 mm to the Barrera-Figueroa et al. [J. Acoust. Soc. Am. 120(5), 2668-2675 (2006)] result at a measurement frequency of 20 kHz.

Correctly Modeling TX and RX Chain in (Distributed) Massive MIMO—New Fundamental Insights on Coherency

This letter shows that the TX and RX models commonly used in literature for downlink (distributed) massive MIMO are inaccurate, leading also to inaccurate conclusions. In particular, the Local Oscillator (LO) effect should be modeled as <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"> <tex-math notation="LaTeX">$+\varphi $ </tex-math></inline-formula> in the transmitter chain and <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"> <tex-math notation="LaTeX">$-\varphi $ </tex-math></inline-formula> in the receiver chain, i.e., different signs. A common misconception in literature is to use the same sign for both chains. By correctly modeling TX and RX chain, one realizes that the LO phases are included in the reciprocity calibration and whenever the LO phases drift apart, a new reciprocity calibration becomes necessary (the same applies to time drifts). Thus, free-running LOs and the commonly made assumption of perfect reciprocity calibration (to enable blind DL channel estimation) are both not that useful, as they would require too much calibration overhead. Instead, the LOs at the base stations should be locked and relative reciprocity calibration in combination with downlink demodulation reference symbols should be employed.

Deep Unfolded Extended Conjugate Gradient Method for Massive MIMO Processing with Application to Reciprocity Calibration

In this paper, we consider deep unfolding the standard iterative conjugate gradient (CG) algorithm to solve a linear system of equations. Instead of being adjusted with known rules, the parameters are learned via backpropagation to yield the optimal results. However, the proposed unfolded CG (UCG) is extended wherein a scalar parameter is substituted by a matrix-parameter to augment the degrees of freedom per layer. Once the training is completed, the UCG has revealed to require far a smaller number of layers than the number of iterations needed using the standard iterative CG. It is also shown to be very robust to noise and outperforms the standard CG in low signal to noise ratio (SNR) region. A key merit of the proposed approach is the fact that no explicit training data is dedicated to the learning phase as the optimization process relies on the residual error which is not explicitly expressed as a function of the desired data. As an example, the proposed UCG is applied to solve the reciprocity calibration problem encountered in massive MIMO (Multiple-Input Multiple-Output) systems.

Calibration of hydrophones using a frequency domain filter processing method: theory and experiment

To eliminate the interferences coming from the boundaries of a water tank and extend its low frequency calibration limit, a frequency domain filter processing (FDFP) method is proposed for hydrophone calibration measurements. The frequency domain filter function is designed according to the a priori spatial position of projector and hydrophone pair in a water tank. A simultaneous comparison method is used for calibration, and a wideband pink noise pulse signal is transmitted. After application of the FDFP method, the transfer impedances of projector and hydrophone pairs in a quasi-free-field are obtained, and interferences reflected from the boundaries of the water tank are effectively eliminated. To verify the FDFP method, an experimental system is established for calibration of the free-field sensitivity of a TC 4033 hydrophone. For a non-anechoic water tank of 1.5 m × 0.88 m × 0.90 m, the lowest calibration frequency is extended from 20 kHz to 3.15 kHz, and the calibration result is consistent with the free-field reciprocity calibration result obtained in an anechoic water tank of 50 m × 15 m × 10 m in the frequency range 3.15 kHz to 31.5 kHz.

Mean‐based reciprocity calibration in TDD massive MIMO system

Non-reciprocity limits the potential of time division duplexing (TDD) massive multiple-input and multiple-output (MIMO) systems. Due to the reciprocal channel, there is no need for downlink (DL) pilot transmission implies computational complexity reduction and saving precious time resources. In this study, the DL channel matrix is estimated using the uplink channel matrix by a novel reciprocity calibration technique. Non-reciprocity arises due to the hardware mismatch (HM) across the base station (BS) and the user terminal (UT)/both. Its detrimental effect causes amplitude and phase impairment in the downlink signal transmission. Since a massive MIMO network has a large number of antenna elements across the BS, hence the instantaneous HM coefficient cannot be determined accurately. For solving such a problem, the authors use the statistical response of the hardware unit. Considering a complex Gaussian hardware response across each antenna terminal, the probability density function (PDF) of amplitude and phase mismatch is derived. They also derive the joint PDF of amplitude and phase mismatch, considering the HM. Simulation results address the sensitivity and complexity for evaluating the sum-rate capacity under three linear precoders (matched filter, regularized zero-forcing, and zero-forcing), which validate their effectiveness in this scenario.

Downlink Pilots for Hybrid Massive MIMO Under Reciprocity Imperfections

In this letter, we study the performance of a time division duplex (TDD) hybrid massive multiple input multiple output (MIMO) system with imperfect calibration of the transmit and receive radio frequency chains. Using deterministic equivalent (DE) analysis, we establish the loss in the achievable rates due to calibration imperfections. We then discuss limited downlink training to estimate the effective downlink channel, and compare the relative merits of this method against frequency division duplexed (FDD) operation. Finally, via detailed numerical simulations, we evaluate the relative performance of no downlink training, limited downlink training, and FDD mode operation in the presence of reciprocity calibration errors.

Relaying Systems With Reciprocity Mismatch: Impact Analysis and Calibration

Cooperative beamforming can provide significant performance improvement for relaying systems with the help of the channel state information (CSI). In time-division duplexing (TDD) mode, the estimated CSI will deteriorate due to the reciprocity mismatch. In this work, we examine the impact and the calibration of the reciprocity mismatch in relaying systems. To evaluate the impact of the reciprocity mismatch for all devices, the closed-form expression of the achievable rate is first derived. Then, we analyze the performance loss caused by the reciprocity mismatch at sources, relays, and destinations respectively to show that the mismatch at relays dominates the impact. To compensate the performance loss, a two-stage calibration scheme is proposed for relays. Specifically, relays perform the intra-calibration based on circuits independently. Further, the inter-calibration based on the discrete Fourier transform (DFT) codebook is operated to improve the calibration performance by cooperation transmission, which has never been considered in previous work. Finally, we derive the achievable rate after relays perform the proposed reciprocity calibration scheme and investigate the impact of estimation errors on the system performance. Simulation results are presented to verify the analytical results and to show the performance of the proposed calibration approach.

Beyond 5G: Leveraging Cell Free TDD Massive MIMO Using Cascaded Deep Learning

This letter deals with the calibration of Time Division Duplexing (TDD) reciprocity in an Orthogonal Frequency Division Multiplexing (OFDM) based Cell Free Massive MIMO system where the responses of the (Radio Frequency) RF chains render the end to end channel non-reciprocal, even though the physical wireless channel is reciprocal. We further address the non-availability of the uplink channel estimates at locations other than pilot subcarriers and propose a single-shot solution to estimate the downlink channel at all subcarriers from the uplink channel at selected pilot subcarriers. We propose a cascade of two Deep Neural Networks (DNN) to achieve the objective. The proposed method is easily scalable and removes the need for relative reciprocity calibration based on the cooperation of antennas, which usually introduces dependency in Cell Free Massive MIMO systems.

Reciprocity Calibration of TDD MIMO Channel for Interference Alignment

Interference alignment (IA) is a promising technique to boost the Multiple-input Multiple-output (MIMO) network throughput. Concurrent data transmission links between multiple pairs of transmitters (TX) and receivers (RX) can be established in the same spectrum via cooperation. To make the channel state information (CSI) available on the transmitter side, channel reciprocity in time division duplex (TDD) networks is assumed by a large number of distributed IA algorithms. The physical channel is reciprocal, but nevertheless the channel considered by IA is not, because it also involves the radio frequency (RF) front ends of the transceiver, which are different circuits for transmit and receive modes individually. The difference between the two circuits yields mismatch between the forward and backward channels. Given the mutual coupling effect of the antenna array, the channel's non-symmetry is further complicated. In this paper, we provide the modeling of the non-reciprocity for the TDD MIMO channels and propose a corresponding calibration method to minimize the mismatch. Experimental validation has been conducted with classic distributed IA algorithms. The results highlight the indispensability of the reciprocity calibration for approaching the network capacity gain promised by IA.