In this paper, we propose an active calibration algorithm to tackle both gain-phase errors and position perturbations. Unlike many other active calibration methods, which fix the array while changing the location of the source, our approach rotates the array but does not change the location of the source, and knowledge of the direction-of-arrival (DOA) of the far-field calibration source is not required. The superiority of the proposed method lies in the fact that measurement of the direction of a far-field calibration source is not easy to carry out, while measurement of the rotation angle via the proposed calibration strategy is convenient and accurate. To obtain the receiving data from different directions, the sensor array is rotated to three different positions with known rotation angles. Based on the eigen-decomposition of the data covariance matrices, we can use the direction of the auxiliary source to represent the gain-phase errors and position perturbations. After that, we estimate the DOA of the calibration source by a one-dimensional search. Finally, the sensor gain-phase errors and position perturbations are calculated by using the estimated direction of the calibration source. Simulations verify the effectiveness and performance of the algorithm.

A robust adaptive beamforming algorithm is proposed based on the precise interference-plus-noise covariance matrix reconstruction and steering vector estimation of the desired signal, even existing large gain-phase errors. Firstly, the model of array mismatches is proposed with the first-order Taylor series expansion. Then, an iterative method is designed to jointly estimate calibration coefficients and steering vectors of the desired signal and interferences. Next, the powers of interferences and noise are estimated by solving a quadratic optimization question with the derived closed-form solution. At last, the actual interference-plus-noise covariance matrix can be reconstructed as a weighted sum of the steering vectors and the corresponding powers. Simulation results demonstrate the effectiveness and advancement of the proposed method.

For automotive millimeter radar, a method using a multi-input multi-output (MIMO) array antenna is essential for high angle resolution with module miniaturization. MIMO enables us to extend an antenna array with virtual antennas, and a large antenna array aperture enables high resolution angle estimation. Time division multiplex (TDM) MIMO, which is a method to generate virtual array antennas, makes it easy to design radar system integrated circuits. However, this method leads to two issues in signal processing; the phase error reduces the accuracy of angle estimation of a moving target, and the maximum detectable velocity decreases in inverse proportion to the number of Tx antennas. We analytically derived this phase error and proposed a method to correct the error. Because the phase error of TDM-MIMO is proportional to the target velocity, accurate estimation of the target velocity is an important issue for phase error correction. However, the decrease of the maximum detectable velocity in TDM-MIMO reduces the accuracy of both velocity estimation and angle estimation. To solve these issues, we propose new signal processing for range-velocity estimation for TDM-MIMO radar. By using the feedback result of the estimated direction of arrival (DoA), we can avoid decreasing the maximum detectable velocity. We explain our method with our simulation results.

An offline sensor gain-phase errors calibration method for a linear array using a source in unknown location is proposed. The proposed method is realized through three steps. First, based on the observed covariance matrix, we construct a function related to direction, and it is proved that when the function takes the minimum value, the corresponding value should be the direction of the calibration source. Second, the direction of calibration source is estimated by locating the valley from the constructed function. Third, the gain-phase errors are obtained based on the estimated direction. The proposed method offers a number of advantages. First, the accurate direction measurement of the calibration source is not required. Second, only one calibration source needs to be arranged. Third, it does not require an iterative procedure or a two-dimensional (2D) spectral search. Fourth, the method is applicable to linear arrays, not only to uniform linear arrays (ULAs). Numerical simulations are presented to verify the efficacy of the proposed method.

This letter proposes a blind phase compensation method for the phase errors in the Multi-Carrier Multiple-input multiple-output (MIMO) radar, which decouples the range and DOA coupling. The phase errors under the Linear Frequency Modulated Continuous Waveform (LFMCW) scheme are firstly derived, followed with the signal processing steps. Further, multiple targets with certain velocities can be handled uniformly without pre-knowledge of the actual range information of the targets. The evaluations of the DOA estimation performance are carried out through simulations, which validate the effectiveness of the proposed method.

Regarding the enlarged array size for the 5G new radio (NR) millimeter-wave phased-array transceivers, an improved phase tuning resolution will be required to support the accurate beam control. This paper introduces a CMOS implementation of an active vector-summing phase shifter. The proposed phase shifter realizes a 6-bit phase shifting with an active area of 0.32mm2. To minimize the gain variation during the phase tuning, a gain error compensation technique is proposed. After the compensation, the measured gain variation within the 5G NR band n257 is less than 0.9dB. The corresponding RMS gain error is less than 0.2dB. The measured RMS phase error from 26.5GHz to 29.5GHz is less than 1.2°. Gain-invariant, high-resolution phase tuning is realized by this work. Considering the error vector magnitude (EVM) performance, the proposed phase shifter supports a maximum data rate of 11.2Gb/s in 256QAM with a power consumption of 25.2mW.

All digital phased arrays generate multiple beams concurrently through the digital beam forming technique, which features digital processing with multiple identical receiving/transmitting channels in RF or microwave frequencies. However, the performance of this process strongly depends on accurately matching the amplitude and phase of the channels, as mismatching is likely to degrade radar performance. In this paper, we present a method to calibrate receiving array by using NCO phase increasing algorithm, which simplifies array system by removing the external far-field calibration signals often needed in array systems. Both analysis and simulation results suggest that the proposed method attains better calibration performance than existing approaches, even with a low SNR input signal. Experiments also varify that the proposed calibration method is effective and achieves a desired radiation pattern. We can further boost calibration accuracy and reduce calibration time by programming NCO phase width and NCO phase resolution.

The influence of pump phase error on phase-sensitive optical amplifier (PSA) repeaters and the waveform degradation due to chromatic dispersion and fiber nonlinearities in the optical multi-relay transmission of quadrature phase-shift keying phase-conjugated twin waves are considered theoretically. First, the influence of noise from the pump phase error, optical local oscillator, receiver, and the amplified spontaneous-emission (ASE) in PSA repeaters is investigated with the assumption that transmission fibers are linear lossy channels. The bit-error rate (BER) is estimated as a function of the signal-to-noise ratio, and the relationship between the number of transmission relays and the fiber launch power is clarified. Waveform degradation due to chromatic dispersion and the optical fiber nonlinearities in transmission fibers are investigated with the noiseless condition, and the maximum repeatable number as a function of the fiber launch power is calculated. Finally, we show the relationship among the maximum repeatable number, standard deviation of pump phase error in PSA repeaters, and the fiber launch power to clarify the optimum transmission condition with consideration of the noise and the waveform degradation.

This study presents the design of a phase correlator for a digital frequency discriminator (DFD) that operates in the 2.0-6.0GHz frequency range. The accuracy of frequency discrimination as determined by the isolation of the correlator mixer was analyzed, and LO-RF isolation was found to have a significant effect on the frequency discrimination error by deriving various analytic equations related to the LO-RF isolation and phase performance. We propose a novel technique (phase sector compensation) to improve the accuracy of frequency discrimination. The phase sector compensation technique improved phase error by canceling the DC offset of the I and Q signals for only the frequency bands where the mixer's LO-RF isolation was below a specified limit. In the 2.0-6.0GHz range, the phase error of the designed phase correlator was decreased from 4.57° to 4.23° (RMS), and the frequency accuracy was improved from 1.02MHz to 0.95MHz (RMS). In the 4.8-6.0GHz range, the RMS phase error was improved from 5.59° to 4.12°, the frequency accuracy was improved from 1.24MHz to 0.92MHz, and the performance of the DFD correlator was improved by 26.3% in the frequency sector where LO-RF isolation was poor. Overall, the DFD correlator performance was improved by LO leakage compensation.

Digital phase shifters are widely used to achieve space scanning in phased array antenna, and beam pointing accuracy depends on the bit number and resolution of the digital phase shifter. This paper proposes a novel phase feeding method to reduce the phase quantization error effects. A linear formula for the beam pointing deviation of a linear uniform array in condition of phase quantization error is derived, and the linear programming algorithm is introduced to achieve the minimum beam pointing deviation. Simulations are based on the pattern of the phased array, which gives each element a certain quantization phase error to find the beam pointing deviation. The novel method is then compared with previous methods. Examples show that a 32-element uniform linear array with 5-bit phase shifters using the proposed method can achieve a higher beam-steering accuracy than the same array with 11-bit phase shifters.

Ranging is commonly used to measure the distance to a satellite, since it is one of the quickest and most effective methods of finding the position of a satellite. In general, ranging ambiguity is easily resolved using major and subsequent ambiguity-resolving tones. However, an induced unknown phase error could interfere with resolving the ranging ambiguity. This paper suggests an effective and practical method to resolve the ranging ambiguity without changing the original planned ranging tone frequencies when an unknown non-linear phase error exists. Specifically, the present study derives simple equations for finding the phase error from the physical relationship between the measured major and minor tones. Furthermore, a technique to select the optimal ambiguity integer and correct phase error is provided. A numerical analysis is performed using real measurements from a low earth orbit (LEO) satellite to show its suitability and effectiveness. It can be seen that a non-ambiguous range is acquired after compensating the unknown phase error.

The Global Position System (GPS), which is well known as a global tool for positioning, is also the primary system for time transfer. GPS can deliver very precise time to every corner of the world. Usually, a GPS receiver indicates the precise time by means of the 1PPS (one pulse per second) signal. This paper studies the precise time transfer system structure of GPS receivers and then proposes an effective PPS signal generation method with predictive synchronous loop, combining phase error prediction and dynamic threshold adjustment. A GPS time transfer system is implemented and measured in detail to demonstrate the validity of the proposed algorithm. Assuming the receiver clock rate of 16.368MHz, the proposed method can achieve the accuracy of ±20ns in the scope 1δ which can meet the requirements of the vast majority of occasions. Through a long period of testing, we prove the feasibility of this algorithm experimentally.

A double-capacitor phase error compensation configuration is proposed for Gm-C and MOSFET-C filters. The use of two capacitors enables the effective compensation capacitance to track with the tuning resistance, thereby making it more effective over a wider frequency tuning range as compared to the conventional single-capacitor configuration. Simulations of 5th-order Chebyshev filters in a 0.18 µm CMOS process with more than one octave tuning range were carried out to demonstrate the viability of the proposed double-capacitor configuration for both Gm-C and MOSFET-C filters.

A novel CMOS LC quadrature oscillator (QO) which adopts complementary-coupling circuitry has been proposed. The performance improvement in I/Q phase error and phase noise of the proposed QO, is explained in comparison with conventional QOs. The proposed QO is implemented in 0.18 µm CMOS technology along with conventional QOs. The measurement result of the proposed QO shows -133.5 dBc/Hz of phase noise at 1 MHz offset and 0.6 I/Q phase difference, while oscillating at 1.77 GHz. The proposed QO shows more than 6.5 dB phase noise improvement compared to that of the conventional QOs over the offset frequency range of 10 K-1 MHz, while dissipating 4 mA from 1.4 V supply.

In this letter, we derive an analytical expression for computing the symbol error probability (SEP) of the M-ary quadrature amplitude modulation (M-QAM) in the joint presence of phase/quadrature error and I/Q gain imbalance over an additive white Gaussian noise (AWGN) channel. The derived expression containing only the two-dimensional Gaussian Q-function can be used to compute the SEP of M-QAM in various fading channels by making use of the moment-generating function (MGF) approach.

A second order charge pump (SOCP) scheme is proposed in this letter. Compared with the conventional single charge pump, the second order charge pump does not suffer phase errors caused by the output voltage dependent current mismatches. Also, the second order charge pump can be implemented in a mixed-mode type, enabling the fast lock and the various operation modes simultaneously. The proposed SOCP has been adopted into the duty cycle corrector (DCC) loops of DDR2 DRAM, and shows a much widened correction range owing to the removal of the parasitic effects.

A novel phase error correction scheme is proposed for the high rate OFDM-based wireless local area networks (WLANs). The proposed scheme makes the system capable of efficiently compensating the whole phase error due to the residual sampling clock offset and frequency offset estimation error after timing and frequency offset compensation, as well as the phase noise.

This letter presents an alternative analytical expression for the symbol error probability (SEP) of the coherent M-ary phase shift keying (M-PSK) system when an arbitrary phase error exists in an additive white Gaussian noise (AWGN) channel. Unlike the previous work, it is shown that the SEP performance of the M-PSK system can be completely characterized by the one- and two-dimensional Gaussian Q-functions. The new expression is numerically more convenient to manipulate than the previous results by replacing the integral operations with the built-in functions commonly available in various mathematical software tool libraries.

This paper describes an all-digital DLL (Delay Locked Loop) circuit with a high phase resolution. The proposed architecture is based on three-stage phase tuning blocks for coarse, fine and ultra fine phase control. Each block has a phase detector, a phase selection block and a delay line, respectively. It was simulated in a 0.35 µm CMOS technology under 3.3 V power supply. The simulation result shows the maximum phase error can be reduced to 13-42 ps with the operating range of 250 MHz to 800 MHz.

Detection loss due to phase error in a carrier tracking loop is analyzed and simulated for a code division multiple access system with BPSK and QPSK modulations in a Rayleigh fading channel. For a specific BER, the detection loss due to phase error is defined as an increase of required SNR to maintain the same BER without phase error. A nonlinear Fokker-Planck method is employed to analyze first-order PLL (phase locked loop) performance. From the simulation results, it is confirmed that the phase noise induces significant detection loss, which eventually leads to degradation of the BER performance.