Multi-tone Signals Research Articles

Photonic-Assisted Multi-Tone Microwave Frequency Measurement Based on Pulse Identification

We report a photonic-assisted method for measuring the frequencies of a multi-tone microwave with high accuracy based on pulse identification. The unknown microwave signal and a linearly chirped signal are modulated to an optical carrier using a dual-polarization Mach–Zehnder modulator. Carrier-suppressed single-sideband modulation avoids the generation of undesired frequency components after photodetection. An electrical bandpass filter with a narrow bandwidth selects the beat signal between the unknown signal and the linearly chirped optical tone. A pulse, generated by the beat signal, can be observed using an oscilloscope (OSC). By identifying the beating pulse position, we can accurately determine the frequency of the unknown signal. The single-tone and multi-tone microwave signal ranges of 6–16 GHz and 26–36 GHz are successfully measured, respectively. The measurement errors for single-tone and multi-tone signals are both less than ±1 MHz.

Fuzz-free ultra-wideband multitone signal instantaneous frequency measurement system based on simple optical frequency combs

Fuzz-free ultra-wideband multitone signal instantaneous frequency measurement system based on simple optical frequency combs

Real-time 60 Gb/s PS-64QAM SSB-DMT transceiver deploying a low-complexity distribution matcher in band-limited IM-DD system

In this work, we have implemented a low-complexity distribution matcher in real-time for bandwidth-limited intensity modulation and direct detection (IM/DD) system based on field programmable gate array (FPGA). For the hardware implementation of probabilistic shaping (PS), a simple and effective distribution matcher is the key to achieving the symbol of the target probability. Compared to traditional PS distribution matchers, our proposed distribution matcher has lower hardware implementation complexity and only requires a small amount of look-up table and registers to achieve target probability distribution. Meanwhile, an optical tunable filter is used to generate single sideband discrete multitone (SSB-DMT) signals for 50-km standard single-mode fiber (SSMF) transmission. By using PS technology and SSB modulation scheme, we successfully real-time realize 11-GHz PS-64QAM SSB-DMT signals over 25/50-km SSMF transmission in band-limited IM-DD system, achieving a line rate of approximately 65.7 Gbit/s.

Crest factor minimization of the multitone complex signal

In this paper we present the most effective algorithm for a crest factor minimization of multitone complex signals. The approach includes complex root selection of the amplitude function for the phase function rebuilding and then Gerchberg-Saxton algorithm application for a fine phase tuning. Phase optimization of a finite sum is fulfilled in case of the complex harmonics with equal amplitudes and equispaced frequencies. We compare our results with the earlier calculated best ones and remark its superiority. The main features of the approach are highlighted to underline the stability and performance capabilities for the global minimum achievement. Finally, we introduce some amplitude functions of multitone signals with lower crest factor than previously reported in the literature.

Mitigating signal interferences in quantum computing applications

The use of a crest factor reduction algorithm suppresses voltage peaks caused by multi-tone microwave signals, potentially allowing for advanced quantum computing applications

Self-measurement and calibration of amplitude-frequency response for coherent optical transmitters with limited DAC resolution

Precise measurement and calibration of the amplitude-frequency response (AFR) of coherent optical transmitters (Tx) are paramount for generating high-quality signals, especially when the transmitter has insufficient bandwidth. The previously proposed self-measurement and calibration (SMC) method based on multi-tone signals (MTS) is cost-effective, fast, and convenient. However, this method exhibits a compromised AFR measurement precision in high-frequency regions, especially when the digital-to-analog converters (DAC) of the Tx have a limited resolution. To solve this problem, we optimize the amplitudes and phases of the MTS by pre-emphasis and the sequential quadratic programming (SQP) algorithm to improve the accuracy in the high-frequency region. Numerical simulations show a notable reduction in AFR measurement error, from about 4 dB to 0.8 dB, when employing a DAC with a four-bit resolution. Additionally, experiments utilizing a 22 GHz 3-dB bandwidth transmitter to generate 61 GBaud dual-polarization 16QAM signals demonstrate a 60% BER reduction. The proposed SMC method is attractive for high-baud rate systems employing Tx with limited bandwidth and DAC resolution.

An all-digital low-complexity blind background calibration of timing mismatch in time-interleaved ADCs

This paper proposed a novel all-digital blind background calibration to mitigate timing mismatch in time-interleaved analog-to-digital converter (TIADC). In estimation module, the adoption of a subtraction-based error extraction function and the design of Variable-Step-Size Least Mean Squares algorithm contribute to reducing the computational complexity and enhancing the convergence speed with optimal output accuracy respectively. In compensation module, a dual-stage Taylor series expansion structure has been introduced to effectively maintain the overall output performance. The proposed architecture is applied to a 12-bit 3 GS/s four-channel TIADC model. Its effectiveness for single-tone and multi-tone signals is proven through systematical testing and analysis. The simulation results exhibit that the Spurious Free Dynamic Range is significantly improved by 54.53 dB in the single-tone signal case, and the timing mismatch is converged after 1000 samples. The proposed calibration circuit has been synthesized utilizing a 28 nm standard cell library for assessing its hardware consumption, area (0.051 mm2) and average power dissipation (67.5 mW) within the integrated chip architecture. Our technology provides a viable optimization solution to improve efficiency of TIADC in high-speed systems.

Microwave-multiplexed qubit controller using adiabatic superconductor logic

Cryogenic qubit controllers (QCs) are the key to build large-scale superconducting quantum processors. However, developing scalable QCs is challenging because the cooling power of a dilution refrigerator is too small (~10 μW at ~10 mK) to operate conventional logic families, such as complementary metal-oxide-semiconductor logic and superconducting single-flux-quantum logic, near qubits. Here we report on a scalable QC using an ultra-low-power superconductor logic family, namely adiabatic quantum-flux-parametron (AQFP) logic. The AQFP-based QC, referred to as the AQFP-multiplexed QC (AQFP-mux QC), produces multi-tone microwave signals for qubit control with an extremely small power dissipation of 81.8 pW per qubit. Furthermore, the AQFP-mux QC adopts microwave multiplexing to reduce the number of coaxial cables for operating the entire system. As a proof of concept, we demonstrate an AQFP-mux QC chip that produces microwave signals at two output ports through microwave multiplexing and demultiplexing. Experimental results show an output power of approximately −80 dBm and on/off ratio of ~40 dB at each output port. Basic mixing operation is also demonstrated by observing sideband signals.

A cascaded bit-weighted distribution matching for LDPC-coded PS-64QAM DMT in a high-speed Unamplified IM-DD system

We experimentally demonstrate the generation and transmission of probabilistic shaping (PS) 64-ary quadrature amplitude modulation (64-QAM) discrete multi-tone (DMT) signal with low-density parity-check (LDPC)-coded modulation based on two-stage bit-weighted distribution matching (TS-BWDM) in a high-speed unamplified intensity modulation and direct detection system. The TS-BWDM scheme is based on a two-stage bit-weighted inversion algorithm, which has the advantages of no complex multiplication and division operations and low hardware implementation complexity. As the key content of TS-BWDM, before FEC coding, the bit-weighted intervention operation is used to change the bit probability of a specific sequence in the parallel binary sequence. The two-stage bit-weighted inversion operation and one-stage weight-labeling bit insertion is performed for achieving the target symbol probability distribution. As a result, it does not add a significant amount of extra redundant bits. Additionally, the high-accuracy training symbols-based sampling frequency offset (SFO) estimation method and digital interpolation are used to compensate SFO. In our experiments, the TS-BWDM-based PS-64QAM DMT signals with a net rate of 157.3-Gb/s transmission over 10-km non-zero dispersion- shifted fiber can be achieved. The system performance is investigated under two LDPC code rates (3/4 and 9/10) and three PS parameter values (k = 3, 5 and 9). The experimental results show that the receiver power sensitivity and the system fiber nonlinear effect tolerance can be significantly improved compared with uniformly-distributed signals.

Simultaneous Multi-frequency lock-in Thermography: A new flexible and effective Active Thermography scheme

A new active thermography scheme is here introduced, referred as ”‘Multi-Frequency Thermography”’, which uses an optimized multi-tone signal for simultaneously implementing lock-in analysis on a discrete and arbitrary set of linearly spaced frequencies. Such a signal, which modulates the intensity of the heating source here being a LED system in the visible range, results from the non-trivial summation of a desired number of odd and even harmonics of a fundamental tone, each of them having a specific initial phase value but equal amplitude, so as to deliver the same energy amount for all the chosen frequencies. In this way, a discrete set of thermal waves having different diffusion lengths are simultaneously excited within the inspected sample to probe different depths into it. With respect to standard lock-in thermography, it is demonstrated that the proposed approach can extract amplitude and phase features for all the excited frequencies from a single measurement, which lasts as long as a lock-in implemented at the fundamental tone. Both quantitative and qualitative comparisons with standard lock-in thermography are here reported, showing an excellent agreement. Hence, this new active thermography scheme can provide several advantages in practical implementations of thermography nondestructive evaluation.

Bias-drift insensitive full-field frequency response characterization of a thin-film lithium niobate-based intensity modulator.

We propose a rapid and precise scheme for characterizing the full-field frequency response of a thin-film lithium niobate-based intensity modulator (TFLN-IM) via a specially designed multi-tone microwave signal. Our proposed scheme remains insensitive to the bias-drift of IM. Experimental verification is implemented with a self-packaged TFLN-IM with a 3 dB bandwidth of 30 GHz. In comparison with the vector network analyzer (VNA) characterization results, the deviation values of the amplitude-frequency response (AFR) and phase-frequency response (PFR) within the 50 GHz bandwidth are below 0.3 dB and 0.15 rad, respectively. When the bias is drifted within 90% of the Vπ range, the deviation fluctuation values of AFR and PFR are less than 0.3 dB and 0.05 rad, respectively. With the help of the full-field response results, we can pre-compensate the TFLN-IM for the 64 Gbaud PAM-4 signals under the back-to-back (B2B) transmission, achieving a received optical power (ROP) gain of 2.3 dB. The versatility of our proposed full-field response characterization scheme can extend to various optical transceivers, offering the advantage of low cost, robust operation, and flexible implementation.

Separation of noisy multitone signals based on variational mode decomposition

We have observed that Variational Mode Decomposition (VMD) exhibits instability in the denoising and separation of noisy multitone signals. Specifically, minor changes in factors such as signal-to-noise ratio, frequency spacing, sampling rate, and probability distribution can significantly impact the decomposition results. To address this issue, we have developed the Dual-VMD-correlation algorithm. This algorithm effectively mitigates the impact of beat effects when harmonics of closely spaced frequencies are superimposed, enabling stable denoising of noisy multitone signals and the separation of each individual tone signal. The algorithm holds promise for applications in frequency-modulated continuous wave laser detection. It can address challenges related to denoising laser echo signals interfered with by aerosols and the difficulty in separating backscatter interference from the target reflected signal spectrum.

Experimental realization of one-dimensional single-atom array based on microscale optical dipole traps

Neutral atom array serves as a crucial experimental platform for studying many-body physics, quantum computing, and quantum simulation. In this work, we describe in detail the experimental process of preparing a one-dimensional homogeneous single atom array containing 40 Cs atoms, including the dipole trap array generation device, atomic array fluorescence imaging, and the uniformity optimization of the dipole trap array. The beam waist of the dipole trap is about 1.8 μm, and the spatial resolution of the imaging system is higher than 1.55 μm. The non-uniformity of dipole trap array is mainly caused by the intermodulation effect of multi-tone signal during amplification. The uniformity of the dipole trap array is optimized to 2% (Fig. (a)) by measuring the fluctuations of the dipole trap intensity and the light shift of trapped atom, and providing feedback to adjust the phase and amplitude applied to the multi-tone RF signal on acousto-optic deflectors. Furthermore, the uniformity of oscillation frequency, loading rate, and lifetime for trapped atom in the dipole trap array are measured. These results show that oscillation frequency has a uniformity within 2% (Fig. (b)); mean loading rate is around 58% with a uniformity within 3%; and mean lifetime of single atom in dark trap is around 6(1) s with a uniformity within 8%.

A fast-convergence, tree-structured, fully-parallel digital background timing mismatch calibration method for four-channel TIADC based on perfect reconstruction filter bank

This paper presents a fully-digital background timing mismatch calibration method for four-channel time-interleaved analog-to-digital converter (TIADC). Based on three improved dual-channel perfect reconstruction filter banks (PRFBs), the proposed method for correcting timing mismatch adopts the tree-structured four-channel PRFB. Unlike the direct four-channel PRFB, the improved structure utilizes fewer filter taps to achieve higher filter performance, making it suitable for real-time background calibration. Furthermore, timing mismatch is estimated by performing correlation calculations on the outputs of sub-channels with the variable step-size least mean squares (LMS) algorithm, being approximately eight times faster than the fixed step-size LMS algorithm. Our method verified by a 12-bit 3 GS/s TIADC test platform indicates that the spurs caused by the timing mismatch for single-tone and multi-tone signals can be effectively suppressed, close to 35 and 40 dB, respectively. The evaluation results on the Xilinx Vertix-7 VC707 platform indicate that the proposed method reduces FPGA hardware resources consumption by nearly 40% compared to the foreground pre-calibration method.

Modeling and analysis for group delay mismatch effect on wideband adaptive spatial interference cancellation

The adaptive interference cancellation technique has been widely utilized in radar, GPS, data link, etc., systems to address challenges from external interference, such as co-site and hostile interference. Since the anti-jamming performance of the adaptive interference cancellation technique is sensitive to group delay mismatch between channels, the group delay mismatch becomes one of the main factors that limit the system’s anti-jamming capability. However, the traditional adaptive interference cancellation system’s mathematical model cannot quantitatively characterize the group delay mismatch effect on the wideband interference cancellation performance. In this paper, the mathematical model of the wideband adaptive spatial interference cancellation (ASIC) system is established, which considers the group delay mismatch, to quantitatively analyze the impact of group delay mismatch on the hostile interference cancellation. The mathematical model utilizes the weighted multi-tone signals to fit the wideband interference, and then, delay differences are attached to each tone signal to simulate the group delay mismatch. Then, the analytic expressions of weight and interference cancellation ratio are derived, which consider the interference bandwidth and group delay mismatch, to quantitatively analyze the group delay mismatch effect on the anti-jamming performance of the wideband ASIC system. Simulation results indicate that the theoretical analysis based on the mathematical model of wideband ASIC system are accurate, which can achieve the quantitative analysis of the group delay mismatch effect on the WIC performance.

An improved wide-range, low-complexity, fully-parallel digital background timing mismatch calibration method for dual-channel TIADC based on perfect reconstruction filter bank

This paper presents a fully-digital background calibration method for calibrating timing mismatch in dual-channel time-interleaved analog-to-digital converter (TIADC). The proposed method estimates timing mismatch by performing correlation calculations on the outputs of sub-channels and corrects this mismatch using the improved perfect reconstruction filter bank (PRFB). The PRFB, which is improved by employing a polynomial fitting method, offers superior performance with fewer filter taps and extends the timing mismatch correction capability to almost the entire sampling clock cycle. The improved PRFB uses only one twentieth of the taps used in the original PRFB, and its dual-channel FIR filters have anti-symmetric taps. To enhance the real-time calibration capability of the system, this paper gives a fully-parallel hardware structure for calibrating offset, gain, bandwidth, and timing mismatches. The effectiveness of the proposed hardware structure is verified through a 10-bit 3GS/s dual-channel TIADC test platform. Simulation and measurement results show that the proposed calibration method significantly improves the signal-to-noise-and-distortion (SNDR) and spurious-free dynamic range (SFDR) of both single-tone and multi-tone input signals, which makes the proposed method a viable solution for practical TIADC applications.

Real-time reconfigurable on-chip photonic frequency decoder.

A group-delay-unit-based integrated silicon photonic integrated circuit (PIC) is employed as a reconfigurable analog radio frequency decoder, which provides a real-time temporal and spectral analysis of any arbitrary multi-tone signal in the micro- and mm-wave range. The circuit is based on cascaded Mach-Zehnder interferometer embedded silicon microring resonators as variable delay units. The temporal decoding of the multi-tone input signal is demonstrated by tuning the signal with respect to the ring resonator delay and resonance. A one-to-one conformal time-to-frequency mapping provides real-time spectral decoding of the signal under test without additional digital signal processing. The idea is validated by several experimental results with single-tone and two-tone input signals in a compact, low-power, silicon PIC. The proposed real-time temporal analog frequency decoder may be very intriguing for high-speed, low-latency wireless applications, such as autonomous driving and 6G.

Delay sampling theorem: A criterion for the recovery of multitone signal

Periodic nonuniform sampling (PNS) is widely used in sub-Nyquist sampling schemes of multitone signals. However, what sampling pattern of PNS enables the signal to recover from the sub-Nyquist samples? Although this problem has been discussed in different schemes, the corresponding answers vary greatly. In this paper, we introduce the recurrent delay times to describe a PNS and provide a mathematical definition of signal recoverability from the perspective of delay. On this basis, we review the well-known Shannon–Nyquist sampling theorem and suggest a delay sampling theorem (DST) that a multitone signal bandlimited to [0,fmax] can be perfectly reconstructed from its periodic nonuniform samples when its minimum combined delay time τmin is not more than the Nyquist interval 1/2fmax. To explain and demonstrate the DST, subspace theory-based algorithms and active aliasing and de-aliasing algorithm (AADA) are proposed and used to recover the spectrum or waveform of multitone signals. The high consistency between practical and theoretical results evidently verifies the correctness of DST. In terms of sampling and recovery of multitone signal, DST extends the Shannon–Nyquist sampling theorem and naturally unifies several existing sampling strategies from the perspective of delay. DST provides a new guideline for the sub-Nyquist sampling of multitone signals. According to the DST criterion, we can optimize the sampling patterns to reduce cosets and improve the supremum frequency such that the reconstructed spectrum is alias-free. By generalizing the sampling theorem from the view of delay, DST opens many avenues for the development of multitone signal processing.

An All-Digital Background Calibration Technique for M-Channel Downsampling Time-Interleaved ADCs Based on Interpolation

An all-digital background calibration technique for gain, timing, and bandwidth mismatches in the time-interleaved analog-to-digital converter (TI-ADC) is presented in this brief. The proposed calibration technique employs an interpolation filter and a Hilbert filter to generate a reference sequence for each sub-ADC. Subsequently, adaptive filters are used to calibrate the mismatch errors, the coefficients of which are updated by the least mean square (LMS) algorithm. The advantage of the technique is that it only requires the output sequence of the TI-ADC without any additional information or extra reference channels. Moreover, it is effective for the M-channel TI-ADC sampling of single-tone, multi-tone, and wideband signals in any Nyquist Band. The frequency shifting is analyzed via filter bank theory, avoiding the complex signal introduction. The simulation for 4-channel TI-ADC with 5 sinusoidal input signals, shows that the proposed technique can improve the SNDR and SFDR by 37 dB and 54 dB, respectively.

Pre-Equalized DMT Signal Transmission Utilizing Low-Resolution DAC With Channel Response Dependent Noise Shaping Technique

In this paper, a channel response dependent noise shaping (CRD-NS) technique is proposed and experimentally demonstrated for the pre-equalized discrete multi-tone (DMT) signal transmission in intensity modulation and direct detection (IM/DD) system with a low-resolution digital-to-analog converter (DAC). Compared with traditional NS technique, the proposed CRD-NS technique can bring signal-to-quantization noise ratio (SQNR) improvement and solve the unevenly distributed SQNR problem in pre-equalized DMT signal induced by residual quantization noise without introducing additional computational complexity. Transmission and reception of 100 Gb/s 16 quadrature amplitude modulation (QAM)-DMT signal generated by a 3-bit DAC are experimentally demonstrated to verify the effectiveness of the proposed CRD-NS technique. The experimental results show that the bit-error ratio (BER) performance of 100 Gb/s 16 QAM-DMT signal with CRD-NS technique outperforms the corresponding signal with traditional NS technique. Compared with digital resolution enhancer (DRE) technique, in which channel response is also considered, the CRD-NS technique shows a similar noise shaping capability with DRE in pre-equalized DMT signal transmission, while the computational complexity can be significantly reduced, the number of real multiplications per sample is reduced from 81 to 7.