Coarse Quantization Research Articles

Stochastic Hybrid Combining Design for Quantized Massive MIMO Systems

Both the power-dissipation and cost of massive multiple-input multiple-output (mMIMO) systems may be substantially reduced by using low-resolution analog-to-digital converters (LADCs) at the receivers. However, both the coarse quantization of LADCs and the inaccurate instantaneous channel state information (ICSI) degrade the performance of quantized mMIMO systems. To overcome these challenges, we propose a novel stochastic hybrid analog-digital combiner (SHC) scheme for adapting the hybrid combiner to the long-term statistics of the channel state information (SCSI). We seek to minimize the transmit power by jointly optimizing the SHC subject to average rate constraints. For the sake of solving the resultant nonconvex stochastic optimization problem, we develop a relaxed stochastic successive convex approximation (RSSCA) algorithm. Simulations are carried out to confirm the benefits of our proposed scheme over the benchmarkers.

A Widely Reconfigurable Piecewise-Linear ADC for Information-Aware Quantization

A two-step SAR ADC with a highly programmable transfer function is presented, extending the application domain of non-linear conversion from signal-specific scenarios to a wider range of data-constrained and information-aware applications. By utilizing a thermometer-encoded programmable capacitive DAC for coarse quantization, the converter can be reconfigured to achieve arbitrary piecewise-linear (PWL) transfer functions, and is not restricted to exponential and logarithmic conversion typical of non-linear ADCs. Analysis of the thermometer DAC design is provided to explore the trade-offs between flexibility, gained resolution, and resource overhead. A 7-bit prototype fabricated in 180nm CMOS validates the presented architecture; multiple measured linear and non-linear transfer functions showcase the flexibility of the reconfigurable PWL-ADC. The approach enables variable effective resolution across the full-scale range, providing up to 9.5-bit performance using a 7-bit ADC. Measurements using an ECG waveform are used to further highlight application-specific advantages enabled by the PWL-ADC.

Binary MIMO Detection via Homotopy Optimization and Its Deep Adaptation

In this paper we consider maximum-likelihood (ML) MIMO detection under one-bit quantized observations and binary symbol constellations. This problem is motivated by the recent interest in adopting coarse quantization in massive MIMO systems--as an effective way to scale down the hardware complexity and energy consumption. Classical MIMO detection techniques consider unquantized observations, and many of them are not applicable to the one-bit MIMO case. We develop a new non-convex optimization algorithm for the one-bit ML MIMO detection problem, using a strategy called homotopy optimization. The idea is to transform the ML problem into a sequence of approximate problems, from easy (convex) to hard (close to ML), and with each problem being a gradual modification of its previous. Then, our attempt is to iteratively trace the solution path of these approximate problems. This homotopy algorithm is well suited to the application of deep unfolding, a recently popular approach for turning certain model-based algorithms into data-driven, and performance enhanced, ones. While our initial focus is on one-bit MIMO detection, the proposed technique also applies naturally to the classical unquantized MIMO detection. We performed extensive simulations and show that the proposed homotopy algorithms, both non-deep and deep, have satisfactory bit-error probability performance compared to many state-of-the-art algorithms. Also, the deep homotopy algorithm has attractively low computational complexity.

A 99.15% energy-reduced switching scheme based on HSRS coarse–fine architecture for SAR ADCs

A trade-off switching scheme between high efficiency and considerable area overhead for successive approximation register (SAR) analog-to-digital converters (ADCs) is proposed. During the design process, the higher-side-reset-and-set (HSRS) coarse–fine architecture ensures significant energy saving. There is no energy consumption in the first two comparison cycles. The presented switching scheme achieves 99.15% savings in switching energy and 92.1% reduction in total capacitance, compared with the conventional SAR ADC. Benefit from the HSRS method, an improved HSRS scheme is proposed to reduce the switching energy in the coarse quantization process, achieving 1/16CVref2 energy saving for the third comparison cycle compared with HSRS method. Furthermore, the reset energy is verified to be 0.1367CVref2 due to the energy-free charge distribution and capacitor multiplexing (CDCM) technology adopted in the fine quantization process.

Neural-Network Based Self-Initializing Algorithm for Multi-Parameter Optimization of High-Speed ADCs

This brief proposes a new automatic model parameter selection approach for determining the optimal configuration of high-speed analog-to-digital converters (ADCs) using a combination of particle swarm optimization (PSO) and stochastic gradient descent (SGD) algorithm. The proposed hybrid method first initializes the PSO algorithm to search for optimal neural-network configuration via the particles moving in finite search space with coarse quantization. Using the PSO estimates, the SGD algorithm then finds the global optimum solution. The global search ability of the PSO algorithm and the local search ability of the SGD are thus exploited to determine an optimal solution that is close to the global optimum with reduced latency. Several experiments were constructed to optimize the non-linearities in Nyquist flash and pipeline ADC datasets to show that the neural networks trained by the PSO-SGD algorithm outperform the random search-based performance optimization. Comparative resource analysis of the proposed algorithm is also conducted against the state-of-the-art that highlights improved latencies and performance with similar area and implementation complexity.

Dynamic speckle analysis with coarse quantization of the raw data.

Analysis of dynamic speckle formed on the surface of diffusely reflecting objects under laser illumination is a non-contact method for inspection of speed of processes. The paper deals with intensity-based implementation of the method that relies on statistical processing of correlated in time sequences of speckle images. A two-dimensional activity map is built for each sequence to visualize regions of different speed on the object surface at a given instant. A great number of images is required to track a process in time. We propose data compression by coarse quantization of the raw speckle data. Efficacy of quantization is analyzed by simulation and experiment for low- and high-contrast speckle patterns with bell-shaped and long-tailed distributions of intensity, respectively. Non-uniform quantization is proposed for long-tailed speckle intensity distributions. Decreasing the bit depth from 8 to 4 causes no change in the probability density function of the activity estimate.

Secure Massive MIMO Downlink With Low-Resolution ADCs/DACs in the Presence of Active Eavesdropping

In this paper we study the secrecy performance of a downlink massive multiple-input multiple-output (MIMO) system in the presence of pilot spoofing attack (PSA). Specifically, the base station (BS), which is equipped with low-resolution analog-to-digital converters (ADCs) and digital-to-analog converters (DACs), exploits the low-complexity random artificial noise (AN) to improve secrecy. With the aid of the additive quantization noise model, the ergodic secrecy rate is derived. Based on the derived results, we study the impact of ADCs' and DACs' resolutions on the secrecy performance for the two different scenarios: the scenarios with and without the knowledge of the PSA power. The optimal power allocation parameter, which allocates power between the information-bearing signal and AN, is derived for the scenario with the knowledge of the PSA power. For ADCs, our theoretical results indicate that high-resolution ADCs are always favorable for improving secrecy, regardless of the availability of the PSA power. However, the impact of DACs' resolution is related to the knowledge of the PSA power. For the scenario without the PSA power, enhancing the resolution of DACs does not necessarily improve the secrecy performance due to the inappropriate power allocation. For the scenario with the PSA power, DACs with different resolutions can achieve the same ergodic secrecy rate in most cases, since the optimal power allocation can make a balance between mitigating the rate loss due to coarse quantization and injecting AN for anti-eavesdropping. Only in the case where the PSA power is small, high-resolution DACs achieve a higher ergodic secrecy rate. Finally, we propose a PSA detection method and study the effect of low-resolution ADCs on the detection performance. It is found that the resolution of ADCs has little effect on the performance of PSA detection.

A Case for Digital Beamforming at mmWave

Due to the heavy reliance of millimeter-wave (mmWave) wireless systems on directional links, beamforming (BF) with high-dimensional arrays is essential for cellular systems in these frequencies. Thus, performing the array processing in a power-efficient manner is a fundamental challenge. Analog and hybrid BF require few analog-to-digital and digital-to-analog converters (ADCs and DACs), but can only communicate in a small number of directions at a time, limiting directional search, spatial multiplexing, and control signaling. Digital BF enables flexible spatial processing but must be operated at a low quantization resolution to stay within reasonable power levels. This decrease in quantizer resolution distorts the received as well as the transmitted signal. To assess the effect of coarse quantization at the receiver, this paper presents a system level analytic framework based on a simple additive quantization noise model (AQNM). The analysis verified through extensive simulations reveals that at moderate resolutions (3-4 bits per ADC), there is negligible loss in downlink cellular capacity from quantization. In essence, the low resolution ADCs limit the high SNR, where cellular systems typically do not operate. For the transmitter, it is shown that DACs with 4 or more bits of resolution can support high order modulations, and do not violate the adjacent carrier leakage limit set by 3 <sup xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">rd</sup> Generation Partnership Project (3GPP) New Radio (NR) standards for cellular operations. In fact, our findings suggest that low resolution digital BF architectures can be a power-efficient alternative to analog or hybrid BF for both transmitters and receivers at millimeter-wave.

On the Uplink Throughput of Zero Forcing in Cell-Free Massive MIMO With Coarse Quantization

The recently proposed Cell-Free massive MIMO architecture is studied for the uplink. In contrast to most previous works, joint detection is performed using global CSI. Therefore, we study strategies for transferring CSI to the CPU taking into account the fronthaul capacity which limits CSI quantization. Two strategies for pilot-based CSI acquisition are considered: estimate-and-quantize and quantize-and-estimate. These are analysed using the Bussgang decomposition. For a given quantization constraint for the data and CSI the achievable rate per user with Zero-Forcing is determined. Numerical results show that quantize-and-estimate (the simpler strategy) is similar to or better than estimate-and-quantize, especially for 1-bit resolution.

Impact of imperfect channel estimation and antenna correlation on quantised massive multiple‐input multiple‐output systems

This study examines the uplink performance of large-constellation multi-user massive multiple-input multiple-output systems with low-resolution analogue-to-digital converters (ADCs) in the presence of channel correlation and imperfect channel state information (CSI). The base station (BS) employs a large number of antennas for multiplexing and demultiplexing co-channel users with each antenna element having a dedicated radio frequency chain and two low-resolution ADCs. While such ADCs cause data loss due to coarse quantisation, the large number of antennas can be exploited not only to alleviate such a problem but also to make it possible to utilise large-constellation modulation schemes. The results provide an insight into the trade-off between various performance metrics and the number of quantisation bits under a wide range of realistic conditions. It will be shown that 1-bit quantisation provides sufficient resolution with 100 BS antennas to communicate with ten user equipments using quadrature phase shift keying, but the number of quantisation bits must be increased for larger constellations particularly to overcome CSI mismatch and channel correlation. The results also consider the trade-off between average mutual information and power consumption of the low-resolution ADCs. It will be shown that 16-quantum amplitude modulation with 2-bit quantisation may provide a good compromise between energy efficiency and average mutual information.

Design of Successively Refinable Unrestricted Polar Quantizer

This paper addresses the design of two-stage successively refinable unrestricted polar quantizers for bivariate circularly symmetric sources in the entropy-constrained and fixed-rate cases. The proposed solutions are globally optimal when the thresholds of the magnitude quantizers are confined to finite discretizations of the interval $\left[0,\infty\right)$ . The algorithm developed for the entropy-constrained case involves a series of stages, including solving the minimum-weight path problem for multiple node pairs in certain weighted directed acyclic graphs. The asymptotical time complexity is ${O}({K}_{1}{K}_{2}^{2}{P}_{max})$ , where ${K}_{1}$ and ${K}_{2}$ are the sizes of the sets of possible magnitude thresholds of the coarse and refined unrestricted polar quantizers (UPQs), respectively, while ${P}_{max}$ is an upper bound on the number of phase levels in any phase quantizer of the coarse UPQ. The solution algorithm for the fixed-rate case is based on solving a succession of dynamic programming problems for multiple coarse quantizer bins. The time complexity in the fixed-rate case amounts to ${O}({K}_{1}{K}_{2}{N}^{2}{N}_{1})$ , where ${N}_{1}$ is the number of cells of the coarse UPQ and $N$ is the ratio between the number of bins of the fine and coarse UPQs. The extensive experimental results on a bivariate circularly symmetric Gaussian source show the effectiveness of the proposed schemes.

A 96.88% area-saving and 99.72% energy-reduction switching scheme for SAR ADC with a novel two-step quantisation technique

This paper presents a novel area-saving and energy-efficient switching capacitor structure for successive approximation register analog-to-digital conversions, which uses a two-step quantisation logic control switching scheme. The two steps are coarse and fine quantisation respectively. During the coarse quantisation, there is no power consumption at the first two cycles. The fine quantisation does not increase the number of binary capacitors while consumes no energy. Therefore, the two-step quantisation switching scheme can significantly reduce both the power consumption and the capacitor area. Simulation results show that the structure can reduce the average energy and the capacitor area by 99.72% and 96.88% respectively over the conventional method.

A 0.5–1.1-V Adaptive Bypassing SAR ADC Utilizing the Oscillation-Cycle Information of a VCO-Based Comparator

A successive approximation register (SAR) analog-to-digital converter (ADC) with a voltage-controlled oscillator (VCO)-based comparator is presented in this paper. The relationship between the input voltage and the number of oscillation cycles (NOC) to reach a VCO-comparator decision is explored, implying an inherent coarse quantization in parallel with the normal comparison. The NOC as a design parameter is introduced and analyzed with noise, metastability, and tradeoff considerations. The NOC is exploited to bypass a certain number of SAR cycles for higher power efficiency of VCO-based SAR ADCs. To cope with the process, voltage, and temperature (PVT) variations, an adaptive bypassing technique is proposed, tracking and correcting window sizes in the background. Fabricated in a 40-nm CMOS process, the ADC achieves a peak effective number of bits of 9.71 b at 10 MS/s. Walden figure of merit (FoM) of 2.4–6.85 fJ/conv.-step is obtained over a wide range of supply voltages and sampling rates. Measurement has been carried out under typical, fast-fast, and slow-slow process corners and 0 °C–100 °C temperature range, showing that the proposed ADC is robust over PVT variations without any off-chip calibration or tuning.

Quantized stabilization of stochastic systems with multiplicative noise under Markovian switching

A problem of quantized state feedback quadratic mean-square stabilization of discrete-time stochastic processes under Markovian switching and multiplicative noise is considered. A static quantizer is used in the feedback channel and the jump Markovian switching is modeled by a discrete-time Markov chain. The control input is simultaneously applied to both the rate vector and the diffusion term. It is shown that the coarsest quantization density that permits quadratic mean-square stabilization of this system is achieved with the use of a logarithmic quantizer, and the coarsest quantization density is determined by an algebraic Riccati equation, which is also the solution to a special linear stochastic Markovian switching control system. Also, sufficient conditions for exponential mean-square stabilization of such systems are also explored. An example is given to demonstrate the obtained results.

Deep Wide-Activated Residual Network Based Joint Blocking and Color Bleeding Artifacts Reduction for 4:2:0 JPEG-Compressed Images

Blocking and color bleeding are two well-known artifacts for 4:2:0 JPEG-compressed images. Blocking mainly results from the block-level quantization of the luma component, while color bleeding is mainly caused by the subsampling and quantization of chroma components. Restoring luma can reduce blocking distortion, but with little influence on color bleeding. On the contrary, color bleeding can be removed via chroma components restoration. This letter proposes a deep wide-activated residual network for reducing blocking and color bleeding artifacts simultaneously, in which the luma and chroma components are jointly restored. Chroma components usually suffer from more severe distortion than the luma component due to subsampling and coarse quantization. Thus, we use the luma component to guide the restoration of chroma components. Moreover, we reduce blocking and color bleeding artifacts in low-resolution space via pixel shuffle-based decimation and assembling, which allows to obtain high restoration speed. Experimental results show that the proposed approach achieves state-of-the-art performance on joint blocking and color bleeding artifacts reduction.

Low-Resolution ADCs for Wireless Communication: A Comprehensive Survey

With the rapid growth of wireless data traffic and antennas configuration, higher spectrum efficiency and lower power consumption processing have evoked remarkable attention from the research and industry community for the deployment of future wireless communication. It has become a heated topic quickly in recent years and gives rise to the widespread interest around the world. As a core technology of the fifth-generation (5G) mobile communication, massive multi-input multi-output (MIMO) technology can fully exploit the space resources and greatly improve the spectral and energy efficiency. However, massive MIMO systems are faced with the problems of mass data processing, high hardware cost, and huge total power consumption. To cope with these problems, a useful solution is that the receiver equips with finite resolution analog-to-digital (ADC) converters. A large number of research results show that the low-resolution quantization technology brings significant performance within the allowable loss of capacity. This promising technique has attracted many scholars to do tremendous endeavor on it. As a motivation, we make a comprehensive survey about low-resolution ADCs for wireless communication. This paper summarizes the latest developments in the design of low-resolution communication systems, focusing on system performance analysis, some key technologies of the receiver, and typical application scenarios for the low-resolution ADCs. In view of the adverse effects caused by coarse quantization, some potential implementations are presented to alleviate this dilemma. Future research directions are also given and suggested in this paper. This overview contributes significantly to providing an informative and tutorial reference for the key technologies of low-resolution ADCs as well as its applications in practical systems.

Analysis of Ergodic Rate for Transmit Antenna Selection in Low-Resolution ADC Systems

In this paper, we analyze the ergodic rate of single transmit antenna selection (TAS) in low-resolution analog-to-digital converter (ADC) systems. Using low-resolution ADCs is a potential power-reduction solution for multiple antenna systems. Low-resolution ADC systems with TAS can further reduce cost and power consumption in wireless transceivers. Considering such systems, we derive the approximated lower bound of the ergodic rate with TAS. Here, we exploit the approximated distribution of the sum of Weibull random variables to address the challenge involved in analyzing the quantization error. We, then, derive the approximated ergodic rate with TAS for a single receive antenna in closed form, which reveals the TAS gain in low-resolution ADC systems. The upper bound of a single transmit and single receive antenna system under coarse quantization is derived to compare with the ergodic rate of the TAS system. The analysis shows that the TAS method achieves a large improvement in ergodic rate with a moderate number of transmit antennas. Simulation results validate the derived ergodic rates and resulting intuition.

A New Cell-Level Search Based Non-Exhaustive Approximate Nearest Neighbor (ANN) Search Algorithm in the Framework of Product Quantization

Non-exhaustive search is widely used in the approximate nearest neighbor (ANN) search. In this paper, we propose a new cell-level search-based non-exhaustive ANN search algorithm in the framework of product quantization (PQ) called cell-level PQ to speed up the ANN search. The cell-level search is introduced by searching all the PQ cells of the query vector on the cell level, and the length of the candidate list can be significantly reduced with negligible computational costs. Instead of using the high time-consuming coarse quantizers, which are necessary in all of the existing non-exhaustive ANN search algorithms such as inverted files (IVFs) and inverted multi-index (IMI), our proposed cell-level PQ reuses the PQ cells of query vector to reject database vectors so that the ANN search in the framework of PQ can be efficiently speeded up. In addition, because our proposed cell-level PQ does not need to store the auxiliary indexes of coarse quantizers for each database vector, no extra memory consumption is required. The experimental results on different databases demonstrate that our proposed cell-level PQ can significantly speed up the ANN search in the framework of PQ, and meanwhile, the search accuracy is almost the same as that of the standard PQ.

Secure Nearest Neighbors Query for High-Dimensional Vectors in Outsourced Environments

Due to the explosive increase of data in both the aspects of dimensionality and volume, performing $k$ nearest neighbors search over cloud environments has been progressively receiving more attention among researchers in the field of database cloud computing. However, the key challenge for switching $k$ nearest neighbors search from the local server (i.e., traditional way) to the third-party cloud is, that the database which always contains series of sensitive information has to be kept secret against the cloud. In this work, we present a pair of solutions towards Secure $k$ Nearest Neighbors (S $k$ NN) query in outsourced environments. By skillfully utilizing coarse quantization and the cryptography techniques Advanced Encryption Standard (AES) and Paillier homomorphic encryption, we construct a secure Inverted File (IVF) and compute encrypted approximate distances directly to search for high-dimensional data in the third-party cloud provider, and finally find the better tradeoff between the search quality and security. Empirical study over real datasets and practical environments validate our solutions’ feasibility, completeness, and practicality. Compared to the state-of-the-art, the proposed solutions resolve the S $k$ NN of high-dimensional data novelly, have very limited response time and provide high privacy protection on the side of both the User and the cloud provider.

Massive MIMO 1-Bit DAC Transmission: A Low-Complexity Symbol Scaling Approach

We study multi-user massive multiple-input single-output systems and focus on downlink transmission for PSK modulation, where the base station employs a large antenna array with low-cost 1-bit digital-to-analog converters (DACs). The direct combination of existing beamforming schemes with 1-bit DACs is shown to lead to an error floor at medium-to-high SNR regime, due to the coarse quantization of the DACs with limited precision. In this paper, based on the constructive interference, we consider both a quantized linear beamforming scheme where we analytically obtain the optimal beamforming matrix and a non-linear mapping scheme where we directly design the transmit signal vector. Due to the 1-bit quantization, the formulated optimization for the non-linear mapping scheme is shown to be non-convex. The non-convex constraints of the 1-bit DACs are first relaxed into convex, followed by an element-wise normalization to satisfy the 1-bit DAC transmission. We further propose a low-complexity symbol scaling scheme that consists of three stages, in which the quantized transmit signal on each antenna element is selected sequentially. Numerical results show that the proposed symbol scaling scheme achieves a comparable performance to the optimization-based non-linear mapping approach, while the corresponding performance-complexity tradeoff is more favorable for the proposed symbol scaling method.