Quantization Bits Research Articles

A method of improving SFDRs of 1-bit signals for a monobit receiver

This paper proposes a method to improve the spurious-free dynamic ranges (SFDRs) of 1-bit sampled signals greatly, which is very beneficial to multi-tone signals detection. Firstly, the relationship between the fundamental component and the third harmonic component of 1-bit sampled signals is analyzed for determining four contiguous special frequency bands, which do not contain any third harmonics inside and cover 77.8% of the whole Nyquist sampling frequency band. Then, we present a special 4-channel monobit receiver model, where appropriate filter banks are used to obtain four desired pass bands before 1-bit quantization and each channel can sample and process sampled data independently to achieve a good instantaneous dynamic range without sacrificing the real-time performance or computing resources. The simulation results show that the proposed method effectively eliminates the effect of the most harmonics on SFDRs and the mean SFDR is increased to to 20 dB. Besides, the multi-signals simulation results indicate that the maximum amplitude separation (dynamic range) of two signals in each channel is 12 dB while the proposed monobit receiver can deal with up to eight simultaneous arrival signals. In general, the designing method proposed in this paper has a potential engineering value.

Threshold Uniformity Improvement in 1b Quanta Image Sensor Readout Circuit.

A new readout architecture for single-bit quanta image sensor (QIS) consisting of a capacitive transimpedance amplifier (CTIA) before a 1-bit quantizer to improve the threshold uniformity of the readout cluster is proposed in this paper. The 1-bit quantizer in the previous single-bit QIS had significant threshold non-uniformity likely caused by the fluctuation of the common-mode voltage of the jot output. To guarantee the stability of the common-mode voltage of input signals fed to the 1-bit quantizer, the CTIA is added before the 1-bit quantizer. A pipeline operation mode is also proposed so the CTIA and 1-bit ADC can work at the same time, thereby reducing the CTIA power consumption. A 2048 × 1024 high-speed test chip was implemented with 45 nm/65 nm stacked backside illuminated (BSI) CMOS image sensor (CIS) process and tested. According to the measured D-log-H results, a good threshold uniformity in the range of 0.3 to 0.8 e− for all readout clusters is demonstrated at 500 frame per second (fps) equivalent timing with 68 mW power consumption.

Analog-Domain Suppression of Strong Interference Using Hybrid Antenna Array.

The proliferation of wireless applications, the ever-increasing spectrum crowdedness, as well as cell densification makes the issue of interference increasingly severe in many emerging wireless applications. Most interference management/mitigation methods in the literature are problem-specific and require some cooperation/coordination between different radio frequency systems. Aiming to seek a more versatile solution to counteracting strong interference, we resort to the hybrid array of analog subarrays and suppress interference in the analog domain so as to greatly reduce the required quantization bits of the analog-to-digital converters and their power consumption. To this end, we design a real-time algorithm to steer nulls towards the interference directions and maintain flat in non-interference directions, solely using constant-modulus phase shifters. To ensure sufficient null depth for interference suppression, we also develop a two-stage method for accurately estimating interference directions. The proposed solution can be applicable to most (if not all) wireless systems as neither training/reference signal nor cooperation/coordination is required. Extensive simulations show that more than 65 dB of suppression can be achieved for 3 spatially resolvable interference signals yet with random directions.

Quantized photonic neural network modeling method based on microring modulators

Photonic chips have great potential for neural network computing due to their fast speed, low power consumption, and parallelism. We propose a quantized neural network modeling method based on microring resonators (MRR). We analyze the optical properties of the MRRs and utilize lasers with different wavelengths as inputs of the neural network. The quantization aware method is adopted to train the neural network, and the stochastic search method is utilized to determine hyperparameters of the network. We transform the network parameters and hyperparameters into MRR parameters to simulate neural network matrix multiplication operations. Finally, we used the Mixed National Institute of Standards and Technology database for testing the proposed model. For 4-, 5-, and 6-bit quantization of weight parameters, we obtain classification accuracies of 94.23%, 94.73%, and 96.11%, respectively. Thus our study demonstrates the feasibility of building a neural network inference system using a microring structure and provides a theoretical support for applying MRRs in neural networks.

MobileNets Can Be Lossily Compressed: Neural Network Compression for Embedded Accelerators

Although neural network quantization is an imperative technology for the computation and memory efficiency of embedded neural network accelerators, simple post-training quantization incurs unacceptable levels of accuracy degradation on some important models targeting embedded systems, such as MobileNets. While explicit quantization-aware training or re-training after quantization can often reclaim lost accuracy, this is not always possible or convenient. We present an alternative approach to compressing such difficult neural networks, using a novel variant of the ZFP lossy floating-point compression algorithm to compress both model weights and inter-layer activations and demonstrate that it can be efficiently implemented on an embedded FPGA platform. Our ZFP variant, which we call ZFPe, is designed for efficient implementation on embedded accelerators, such as FPGAs, requiring a fraction of chip resources per bandwidth compared to state-of-the-art lossy compression accelerators. ZFPe-compressing the MobileNet V2 model with an 8-bit budget per weight and activation results in significantly higher accuracy compared to 8-bit integer post-training quantization and shows no loss of accuracy, compared to an uncompressed model when given a 12-bit budget per floating-point value. To demonstrate the benefits of our approach, we implement an embedded neural network accelerator on a realistic embedded acceleration platform equipped with the low-power Lattice ECP5-85F FPGA and a 32 MB SDRAM chip. Each ZFPe module consumes less than 6% of LUTs while compressing or decompressing one value per cycle, requiring a fraction of the resources compared to state-of-the-art compression accelerators while completely removing the memory bottleneck of our accelerator.

Quantisation‐based target detection for cooperative multiple input multiple output radar and communications with multiple stations

Target detection is investigated for the emerging integrated radar and communication (IRC) systems. Consider the case, where multiple radar and communication stations are physically separated, possibly widely spaced, while working in a cooperative way. To utilise all available information for a final decision making, the radar stations that receive signals send their local measurements to a fusion centre (FC) through a wireless channel, say the backhaul network. For the purpose of decreasing communication traffic, the local measurements are quantised and then transferred to the FC. Three strategies for the quantisation and fusion are considered, where for the first method, local sensors quantise their test statistics, which are linearly fused at the FC (quantising test statistics and linear combination fusion), for the second method, the test statistics are quantised at the local sensors and optimally fused at the FC (quantising test statistics and optimal fusion), and for the third method, the received signals are quantizsd at the local sensors and optimally fused at the FC (quantising received signals and optimal fusion). The detection probability for each method is derived for the cooperative IRC system and compared with that of the non-cooperative counterpart. It is proved that there is a detection performance gain through cooperation between the radar and communication systems and the cooperative IRC system can achieve the same performance as the non-cooperative system with a fewer number of quantisation bits. The correctness of theoretical analysis is verified by simulations.

AMBTC-based secret image sharing by simple modular arithmetic

A distortionless secret image sharing scheme using finite field GF(PG) (PG is the largest prime less than a given number) is investigated for sharing the absolute moment block truncation coding (AMBTC) images. Two adjusting operations are devised to modify the AMBTC trios (i.e., quantization pixels and bit maps) suitable for GF(PG) sharing. Polynomials under GF(PG) are constructed for encrypting the quantization pixels and bit maps. When sharing the trios under GF(PG), the AMBTC image is perfectly recovered. Moreover, the bit map sharing under GF(PG) can be extended to GF(PS) (PS is the smallest prime larger than a given number). Another scheme using GF(PS) is constituted by combining quantization pixel sharing under GF(PG) and bit map sharing under GF(PS). But the scheme using GF(PS) is not always lossless. Experimental results show that the proposed schemes are effective. Since GF(PG) and GF(PS) are simple modular arithmetic, improved computational efficiency is obtained.

Channel Estimation for Hybrid Massive MIMO Systems With Adaptive-Resolution ADCs

Achieving high channel estimation accuracy and reducing hardware cost as well as power dissipation constitute substantial challenges in the design of massive multiple-input multiple-output (MIMO) systems. To resolve these difficulties, sophisticated pilot designs have been conceived for the family of energy-efficient hybrid analog-digital (HAD) beamforming architecture relying on adaptive-resolution analog-to-digital converters (RADCs). In this paper, we jointly optimize the pilot sequences, the number of RADC quantization bits and the hybrid receiver combiner in the uplink of multiuser massive MIMO systems. We solve the associated mean square error (MSE) minimization problem of channel estimation in the context of correlated Rayleigh fading channels subject to practical constraints. The associated mixed-integer problem is quite challenging due to the nonconvex nature of the objective function and of the constraints. By relying on advanced fractional programming (FP) techniques, we first recast the original problem into a more tractable yet equivalent form, which allows the decoupling of the fractional objective function. We then conceive a pair of novel algorithms for solving the resultant problems for codebook-based and codebook-free pilot schemes, respectively. To reduce the design complexity, we also propose a simplified algorithm for the codebook-based pilot scheme. Our simulation results confirm the superiority of the proposed algorithms over the relevant state-of-the-art benchmark schemes.

A Low-Profile Beam-Steering Reflectarray With Integrated Leaky-Wave Feed and 2-Bit Phase Resolution for Ka-Band SatCom

A novel reflectarray (RA) with ultralow-profile and 2-bit phase quantization beam-steering ability is presented in this article. To reduce the profile, a Leaky-wave feed is used to excite the RA with enhanced illumination efficiency. Moreover, simultaneous sum and difference patterns are also obtained to provide beam flexibility. The entire thickness of the proposed RA is less than 3&#x0025; of that of the conventional front-fed RA with the same aperture. To increase the efficiency of the RA, a novel unit cell consisting of a polarizer layer and a reflection layer is developed, which is configured to provide polarization rotation and 2-bit phase shifts by using a hybrid of tunable polarization and discrete resonator. The operation principle, theoretical explanation, and implementation of the proposed antenna are elaborated in this work. To prove the design concept and beam scanning performance, an array with <inline-formula> <tex-math notation="LaTeX">$9 \times 7$ </tex-math></inline-formula> unit cells operating at Ka-band is designed and simulated first. Two-dimensional beam scanning within the range of &#x00B1;30&#x00B0; has been verified. Then, a passive prototype with <inline-formula> <tex-math notation="LaTeX">$9\,\,\times67$ </tex-math></inline-formula> unit cells is designed, fabricated, and measured. Experimental results show aperture efficiency of 35.1&#x0025; and illumination efficiency of 43.4&#x0025;. The developed RA is scalable, and it provides a viable low-cost solution to develop low-profile, high-gain and beam-steering array antennas for satellite applications.

Quantized state feedback stabilization of nonlinear systems under Denial-of-Service

This paper studies the resilient control of networked systems in the presence of cyber attacks. In particular, we consider the state feedback stabilization problem for nonlinear systems when the state measurement is sent to the controller via a communication channel that only has a finite transmitting rate and is moreover subject to cyber attacks in the form of Denial-of-Service (DoS). We use a dynamic quantization method to update the quantization range of the encoder/decoder and characterize the number of bits for quantization needed to stabilize the system under a given level of DoS attacks in terms of duration and frequency. Our theoretical result shows that under DoS attacks, the required data bits to stabilize nonlinear systems by state feedback control are larger than those without DoS since the communication interruption induced by DoS makes the quantization uncertainty expand more between two successful transmissions. Even so, in the simulation, we show that the actual quantization bits can be much smaller than the theoretical value.

Full-duplex cell-free mMIMO networks with coarse ADCs/DACs over Ricean fading for beyond 5G

In this article, we explore a practical full-duplex (FD) cell-free massive multiple-input multiple-output (mMIMO) network equipped with coarse analog-to-digital converters/digital-to-analog converters (ADCs/DACs) at the access points (APs) over Ricean fading channels for beyond 5G communication. First, we suppose that the minimum mean square error scheme is applied to estimate channel state information. The accurate sum achievable rate expressions for both uplink (UL) and downlink (DL) are obtained in closed-form by performing the maximum ratio combining and conjugate beamforming at the APs, respectively. Then, the expressions of energy efficiency for UL and DL can be obtained in closed-form based on the established power dissipation model. Finally, the numerical results are conducted to demonstrate our analytical results about the spectral efficiency of considered system. It is also found that when the total number of coarse ADCs/DACs precision is fixed, employing the higher-precision ADCs at the receive end of APs can notably improve the FD sum rate of proposed networks. In addition, the simulation results also show the impacts of number of antennas at each AP and resolution of coarse ADCs/DACs on the energy efficiency (EE) performance. It is revealed that the moderate quantization bits can contribute to the optimal EE.

Redundancy cancellation of compressed measurements by QRS complex alignment.

The demand for long-term continuous care has led healthcare experts to focus on development challenges. On-chip energy consumption as a key challenge can be addressed by data reduction techniques. In this paper, the pseudo periodic nature of ElectroCardioGram(ECG) signals has been used to completely remove redundancy from frames. Compressing aligned QRS complexes by Compressed Sensing (CS), result in highly redundant measurement vectors. By removing this redundancy, a high cluster of near zero samples is gained. The efficiency of the proposed algorithm is assessed using the standard MIT-BIH database. The results indicate that by aligning ECG frames, the proposed technique can achieve superior reconstruction quality compared to state-of-the-art techniques for all compression ratios. This study proves that by aligning ECG frames with a 0.05% unaligned frame rate(R-peak detection error), more compression could be gained for PRD > 5% when 5-bit non-uniform quantizer is used. Furthermore, analysis done on power consumption of the proposed technique, indicates that a very good recovery performance can be gained by only consuming 4.9μW more energy per frame compared to traditional CS.

Investigation of key factors of Blackman-Harris window and interpolation algorithm in TTU frequency estimation module

In order to provide a reference for the selection of related parameters when the Blackman-Harris window and interpolation algorithm is applied to the frequency estimation for voltage and current signals in transformer terminal unit (TTU), the principle of the algorithm is introduced, the implementation is preliminarily discussed, and the influence of signal parameters and measurement parameters on the frequency error is investigated based on the numerically generated voltage signals. The results reveal that the error is proportional to the frequency deviation of the signal. The frequency error decreases exponentially with signal-to-noise ratio (SNR) and sampling duration. Total harmonic distortion, sampling frequency and analog-to-digital converter (ADC) quantization bit have almost no impact on frequency error.

Hybrid Grey Wolf Optimization with Cuckoo Search‐based optimal channel estimation for energy efficient massive multiple input multiple output

SummaryThe massive multiple input multiple output (mMIMO) provides reliable base station (BS) for the mobile users (MUs) with CSI (channel state information) and jointly offers spectral efficiency (SE) and energy efficiency (EE). Conversely, because of the existence of multiple transceivers at both the transmitter and receiver side, the channel estimation (CE) issue is increasingly complex and expensive in terms of hardware and energy utilization. Hence, we have proposed an effective Hybrid Grey Wolf Optimization with Cuckoo Search (GWO‐CS) based optimal channel estimation for developing energy efficient mMIMO. The proposed GWO‐CS selects the optimal channel by jointly optimizing the spectral efficiency and reduces the SINR (signal to interference plus noise ratio). Experimental analysis of the performance of the proposed approach is carried out using existing approaches. The results obtained show that, the EE of the proposed GWO‐CS based CE provides 15–37 Mbits for varying quantization bits, 22.5–25 Mbits for different user equipment (UE) ranges and 7–24 Mbits for various SE. However, the existing approaches fail to provide such EE and this proves the efficiency of proposed approach.

Quantization-Error-Robust Deep Neural Network for Embedded Accelerators

Quantization with low precision has become an essential technique for adopting deep neural networks in energy-and memory-constrained devices. However, there is a limit to the reducing precision by the inevitable loss of accuracy due to the quantization error. To overcome this obstacle, we propose methods reforming and quantizing a network that achieves high accuracy even at low precision without any runtime overhead in embedded accelerators. Our proposition consists of two analytical approaches: 1) network optimization to find the most error-resilient equivalent network in the precision-constrained environment and 2) quantization exploiting adaptive rounding offset control. The experimental results show accuracies of up to 98.31% and 99.96% of floating-point results in 6-bit and 8-bit quantization networks, respectively. Besides, our methods allow the lower precision accelerator design, reducing the energy consumption by 8.5%.

Fully Onboard AI-Powered Human-Drone Pose Estimation on Ultralow-Power Autonomous Flying Nano-UAVs

Many emerging applications of nano-sized unmanned aerial vehicles (UAVs), with a few cm² form-factor, revolve around safely interacting with humans in complex scenarios, for example, monitoring their activities or looking after people needing care. Such sophisticated autonomous functionality must be achieved while dealing with severe constraints in payload, battery, and power budget (&#x007E;<b>100mW</b>). In this work, we attack a complex task going from perception to control: to estimate and maintain the nano-UAV&#x2019;s relative 3-D pose with respect to a person while they freely move in the environment&#x2014;a task that, to the best of our knowledge, has never previously been targeted with fully onboard computation on a nano-sized UAV. Our approach is centered around a novel vision-based deep neural network (DNN), called Frontnet, designed for deployment on top of a parallel ultra-low power (PULP) processor aboard a nano-UAV. We present a vertically integrated approach starting from the DNN model design, training, and dataset augmentation down to 8-bit quantization and deployment in-field. PULP-Frontnet can operate in real-time (up to <b>135 frame/s</b>), consuming less than <b>87 mW</b> for processing at peak throughput and down to <b>0.43 mJ/frame</b> in the most energy-efficient operating point. Field experiments demonstrate a closed-loop top-notch autonomous navigation capability, with a tiny 27-g Crazyflie 2.1 nano-UAV. Compared against an ideal sensing setup, onboard pose inference yields excellent drone behavior in terms of median absolute errors, such as positional (onboard: <b>41cm</b>, ideal: <b>26 cm</b>) and angular (onboard: <b>3.7&#x00B0;</b>, ideal: <b>4.1&#x00B0;</b>). We publicly release videos and the source code of our work.

Prototype Verification of Self-Interference Suppression for Constant-Amplitude Full-Duplex Phased Array with Finite Phase Shift

In view of the strong self-interference problem when the practical phased array system is simultaneously applied for transmission and reception, under the constraints including limited quantization number, constant envelope amplitude, scanning mode, wideband signal mode, etc., this work studies it and proposes the amplitude-phase joint adjustment method and the phase-only method for beamforming optimization. Through digital simulation design, electromagnetic simulation evaluation and principle test verification, under the actual array system conditions, including 6-bit phase quantization or phase step size of 5.625° and amplitude 0.5 dB quantization step, when the transmitting beam is pointing (0°, 0°), the research has achieved a performance of 11.9~14.4 dB for self-interference suppression; at the same time, the optimized beam shape is maintained well, and the ratio of the main lobe to the side lobes does not change significantly, but the beam gain has a loss of about 2~3 dB. In addition, we studied the interference suppression performance and beam feature retention performance of the optimized beamforming weights in the case of array scanning and broadband signals, and analyzed the influence of the changes in the mutual coupling characteristics between elements caused by scanning and frequency changes on the cancellation performance. This provides a reference for the application research of the simultaneous transmitting and receiving self-interference suppression technology in the actual array system state.

Topological gaps in quasiperiodic spin chains: A numerical and K-theoretic analysis

Topological phases supported by quasi-periodic spin-chain models and their bulk-boundary principles are investigated by numerical and K-theoretic methods. We show that, for both the un-correlated and correlated phases, the operator algebras that generate the Hamiltonians are non-commutative tori, hence the quasi-periodic chains display physics akin to the quantum Hall effect in two and higher dimensions. The robust topological edge modes are found to be strongly shaped by the interaction and, generically, they have hybrid edge-localized and chain-delocalized structures. Our findings lay the foundations for topological spin pumping using the phason of a quasi-periodic pattern as an adiabatic parameter, where selectively chosen quantized bits of magnetization can be transferred from one edge of the chain to the other.

Joint Phase and Timing Estimation With 1-Bit Quantization and Oversampling

Digital receivers based on 1-bit quantization and oversampling w.r.t. the transmit signal bandwidth promise lower energy consumption. However, since 1-bit quantization is a highly non-linear operation, standard off the shelf receiver algorithms cannot be applied. In this paper we consider an unknown phase rotation and timing offset and a fully digital receiver. To reduce the non-linear behavior introduced by 1-bit quantization, we assume that the receiver applies uniform phase and sample dithering, which can be implemented by sampling at an irrational normalized intermediate frequency and with an irrational oversampling factor, respectively. Based on the least squares objective function we derive a typical digital matched filter receiver with a data- and timing-aided phase estimator and square time recovery based timing estimation. Our main contribution is to show that both estimators are consistent under very general assumptions, e.g., arbitrary colored noise and stationary ergodic transmit symbols. Performance evaluations are done via simulations and are compared against a numerically computable upper bound of the Cram&#x00E9;r&#x2013;Rao lower bound. For low signal-to-noise ratio the estimators perform well but for high signal-to-noise ratio they run into an error floor. The performance loss of the phase estimator due to decision-directed operation or estimated timing information is marginal.

Secure performance analysis and pilot spoofing attack detection in cell-free massive MIMO systems with finite-resolution ADCs

In this article, the secure communication in cell-free massive multiple-input multiple-output system with low-resolution analog-to-digital converters is investigated in the presence of an active eavesdropper. Specifically, in this article, the deterioration caused by the analog-to-digital converter imperfections on the accuracy of the channel estimation and secure transmission performance is studied. Besides, the additive quantization noise model is utilized to analyze the impacts of the low-resolution analog-to-digital converters. The minimum mean square error channel estimation results show that there is a nonzero floor caused by the coarse analog-to-digital converters. Then, the closed-form expressions for both the legitimate users achievable ergodic rate and the information leakage to the eavesdropper are derived, respectively. Moreover, tight approximated ergodic secrecy rate expression is also presented with respect to analog-to-digital converters quantization bits, number of antennas, pilot power, and so on. To degrade the impacts of the pilot spoofing attack, an active attack detection approach based on random matrix theory is proposed which can only be operated at one access point. Simulation results are provided to corroborate the obtained results and analyze the impacts of various parameters on system secrecy performance. Also, the superiority of the proposed active attacks detection method is confirmed via simulation results.