This letter investigates the uplink of a multi-user millimeter wave (mmWave) system, where the base station (BS) is equipped with a massive multiple-input multiple-output (MIMO) array and resolution-adaptive analog-to-digital converters (RADCs). Although employing massive MIMO at the BS can significantly improve the spectral efficiency, it also leads to high hardware complexity and huge power consumption. To overcome these challenges, we seek to jointly optimize the beamspace hybrid combiner and the ADC quantization bits allocation to maximize the system energy efficiency (EE) under some practical constraints. The formulated problem is non-convex due to the non-linear fractional objective function and the non-convex feasible set which is generally intractable. In order to handle these difficulties, we first apply some fractional programming (FP) techniques and introduce auxiliary variables to recast this problem into an equivalent form amenable to optimization. Then, we propose an efficient double-loop iterative algorithm based on the penalty dual decomposition (PDD) and the majorization-minimization (MM) methods to find local stationary solutions. Simulation results reveal significant gain over the baselines.
Sparse signals, encountered in many wireless and signal acquisition applications, can be acquired via compressed sensing (CS) to reduce computations and transmissions, crucial for resource-limited devices, e.g., wireless sensors. Since the information signals are often continuous-valued, digital communication of compressive measurements requires quantization. In such a quantized compressed sensing (QCS) context, we address remote acquisition of a sparse source through vector quantized noisy compressive measurements. We propose a deep encoder-decoder architecture, consisting of an encoder deep neural network (DNN), a quantizer, and a decoder DNN, that realizes low-complexity vector quantization aiming at minimizing the mean-square error of the signal reconstruction for a given quantization rate. We devise a supervised learning method using stochastic gradient descent and backpropagation to train the system blocks. Strategies to overcome the vanishing gradient problem are proposed. Simulation results show that the proposed non-iterative DNN-based QCS method achieves higher rate-distortion performance with lower algorithm complexity as compared to standard QCS methods, conducive to delay-sensitive applications with large-scale signals.
We consider channel estimation for an uplink massive multiple-input multiple-output (MIMO) system where the base station (BS) uses an array with low-resolution (1-2 bit) analog-to-digital converters and a spatial Sigma-Delta ($\Sigma\Delta$) architecture to shape the quantization noise away from users in some angular sector. We develop a linear minimum mean squared error (LMMSE) channel estimator based on the Bussgang decomposition that reformulates the nonlinear quantizer model using an equivalent linear model plus quantization noise. We also analyze the uplink achievable rate with maximal ratio combining (MRC), zero-forcing (ZF), and LMMSE receivers and provide a lower bound for the achievable rate with the MRC receiver. Numerical results show superior channel estimation and sum spectral efficiency performance using the $\Sigma\Delta$ architecture compared to conventional 1- or 2-bit quantized massive MIMO systems.
In this paper, we propose a finite-precision decoding method that features the three steps of Reconstruction, Computation, and Quantization (RCQ). Unlike Mutual-Information-Maximization Quantized Belief Propagation (MIM-QBP), RCQ can approximate either belief propagation or Min-Sum decoding. One problem faced by MIM-QBP decoder is that it cannot work well when the fraction of degree-2 variable nodes is large. However, sometimes a large fraction of degree-2 variable nodes is necessary for a fast encoding structure, as seen in the IEEE 802.11 standard and the DVB-S2 standard. In contrast, the proposed RCQ decoder may be applied to any off-the-shelf LDPC code, including those with a large fraction of degree-2 variable nodes.Our simulations show that a 4-bit Min-Sum RCQ decoder delivers frame error rate (FER) performance around 0.1dB of full-precision belief propagation (BP) for the IEEE 802.11 standard LDPC code in the low SNR region.The RCQ decoder actually outperforms full-precision BP in the high SNR region because it overcomes elementary trapping sets that create an error floor under BP decoding. This paper also introduces Hierarchical Dynamic Quantization (HDQ) to design the non-uniform quantizers required by RCQ decoders. HDQ is a low-complexity design technique that is slightly sub-optimal. Simulation results comparing HDQ and an optimal quantizer on the symmetric binary-input memoryless additive white Gaussian noise channel show a loss in mutual information between these two quantizers of less than $10^{-6}$ bits, which is negligible for practical applications.
In this paper, we study multi-agent consensus problems under Denial-of-Service (DoS) attacks with data rate constraints. We first consider the leaderless consensus problem and after that we briefly present the analysis of leader-follower consensus. The dynamics of the agents take general forms modeled as homogeneous linear time-invariant systems. In our analysis, we derive lower bounds on the data rate for the multi-agent systems to achieve leaderless and leader-follower consensus in the presence of DoS attacks, under which the issue of overflow of quantizer is prevented. The main contribution of the paper is the characterization of the trade-off between the tolerable DoS attack levels for leaderless and leader-follower consensus and the required data rates for the quantizers during the communication attempts among the agents. To mitigate the influence of DoS attacks, we employ dynamic quantization with zooming-in and zooming-out capabilities for avoiding quantizer saturation.
The paper presents a unified, flexible framework for the tasks of audio inpainting, declipping, and dequantization. The concept is further extended to cover analogous degradation models in a transformed domain, e.g. quantization of the signal's time-frequency coefficients. The task of reconstructing an audio signal from degraded observations in two different domains is formulated as an inverse problem, and several algorithmic solutions are developed. The viability of the presented concept is demonstrated on an example where audio reconstruction from partial and quantized observations of both the time-domain signal and its time-frequency coefficients is carried out.
We study the distributed average consensus problem in multi-agent systems with directed communication links that are subject to quantized information flow. The goal of distributed average consensus is for the nodes, each associated with some initial value, to obtain the average (or some value close to the average) of these initial values. In this paper, we present and analyze novel distributed averaging algorithms which operate exclusively on quantized values (specifically, the information stored, processed and exchanged between neighboring agents is subject to deterministic uniform quantization) and rely on event-driven updates (e.g., to reduce energy consumption, communication bandwidth, network congestion, and/or processor usage). We characterize the properties of the proposed distributed averaging protocols on quantized values and show that their execution, on any time-invariant and strongly connected digraph, will allow all agents to reach, in finite time, a common consensus value represented as the ratio of two quantized values that is equal to the exact average. We conclude with examples that illustrate the operation, performance, and potential advantages of the proposed algorithms.
Convolutional neural networks (CNNs) achieve state-of-the-art performance at the cost of becoming deeper and larger. Although quantization (both fixed-point and floating-point) has proven effective for reducing storage and memory access, two challenges -- 1) accuracy loss caused by quantization without calibration, fine-tuning or re-training for deep CNNs and 2) hardware inefficiency caused by floating-point quantization -- prevent processors from completely leveraging the benefits. In this paper, we propose a low-precision floating-point quantization oriented processor, named Phoenix, to address the above challenges. We primarily have three key observations: 1) 8-bit floating-point quantization incurs less error than 8-bit fixed-point quantization; 2) without using any calibration, fine-tuning or re-training techniques, normalization before quantization further reduces accuracy degradation; 3) 8-bit floating-point multiplier achieves higher hardware efficiency than 8-bit fixed-point multiplier if the full-precision product is applied. Based on these key observations, we propose a normalization-oriented 8-bit floating-point quantization method to reduce storage and memory access with negligible accuracy loss (within 0.5%/0.3% for top-1/top-5 accuracy, respectively). We further design a hardware processor to address the hardware inefficiency caused by floating-point multiplier. Compared with a state-of-the-art accelerator, Phoenix is 3.32x and 7.45x better in performance with the same core area for AlexNet and VGG16, respectively.
The use of machine learning methods to tackle challenging physical layer signal processing tasks has attracted significant attention. In this work, we focus on the use of neural networks (NNs) to perform pilot-assisted channel estimation in an OFDM system in order to avoid the challenging task of estimating the channel covariance matrix. In particular, we perform a systematic design-space exploration of NN configurations, quantization, and pruning in order to improve feedforward NN architectures that are typically used in the literature for the channel estimation task. We show that choosing an appropriate NN architecture is crucial to reduce the complexity of NN-assisted channel estimation methods. Moreover, we demonstrate that, similarly to other applications and domains, careful quantization and pruning can lead to significant complexity reduction with a negligible performance degradation. Finally, we show that using a solution with multiple distinct NNs trained for different signal-to-noise ratios interestingly leads to lower overall computational complexity and storage requirements, while achieving a better performance with respect to using a single NN trained for the entire SNR range.
Head-mounted holographic displays (HMHD) are projected to be the first commercial realization of holographic video display systems. HMHDs use liquid crystal on silicon (LCoS) spatial light modulators (SLM), which are best suited to display phase-only holograms (POH). The performance/watt requirement of a monochrome, 60 fps Full HD, 2-eye, POH HMHD system is about 10 TFLOPS/W, which is orders of magnitude higher than that is achievable by commercially available mobile processors. To mitigate this compute power constraint, display-ready POHs shall be generated on a nearby server and sent to the HMHD in compressed form over a wireless link. This paper discusses design of a feasible HMHD-based augmented reality system, focusing on compression requirements and per-pixel rate-distortion trade-off for transmission of display-ready POH from the server to HMHD. Since the decoder in the HMHD needs to operate on low power, only coding methods that have low-power decoder implementation are considered. Effects of 2D phase unwrapping and flat quantization on compression performance are also reported. We next propose a versatile PCM-POH codec with progressive quantization that can adapt to SLM-dynamic-range and available bitrate, and features per-pixel rate-distortion control to achieve acceptable POH quality at target rates of 60-200 Mbit/s that can be reliably achieved by current wireless technologies. Our results demonstrate feasibility of realizing a low-power, quality-ensured, multi-user, interactive HMHD augmented reality system with commercially available components using the proposed adaptive compression of display-ready POH with light-weight decoding.
In networked control systems, often the sensory signals are quantized before being transmitted to the controller. Consequently, performance is affected by the coarseness of this quantization process. Modern communication technologies allow users to obtain resolution-varying quantized measurements based on the prices paid. In this paper, we consider optimal controller synthesis of a Quantized-Feedback Linear-Quadratic-Gaussian (QF-LQG) system where the measurements are to be quantized before being transmitted to the controller. The system is presented with several choices of quantizers, along with the cost of operating each quantizer. The objective is to jointly select the quantizers and the controller that would maintain an optimal balance between control performance and quantization cost. Under certain assumptions, this problem can be decoupled into two optimization problems: one for optimal controller synthesis and the other for optimal quantizer selection. We show that, similarly to the classical LQG problem, the optimal controller synthesis subproblem is characterized by Riccati equations. On the other hand, the optimal quantizer selection policy is found by solving a certain Markov-Decision-Process (MDP).
In a wireless sensor network, multilevel quantization is necessary in order to find a compromise between the smallest possible power consumption of the sensors and the detection performance at the fusion center (FC). The general methodology is using distance measures such as J-divergence and Bhattacharyya distance in this quantization. This work proposes a different approach which is based on maximizing the average output entropy of the sensors under both hypotheses and utilizes it in a Neyman-Pearson criterion based distributed detection scheme in order to detect a point source. The receiver operating characteristics of the proposed maximum average entropy (MAE) method in quantizing sensor outputs was obtained for multilevel quantization both when the sensor outputs are available error-free at the FC and when non-coherent M-ary frequency shift keying communication is used for transmitting MAE based multilevel quantized sensor outputs over a Rayleigh fading channel. The simulation studies show the success of the MAE both in the cases of isolated error-free fusion and in the case where the effect of the wireless channel is incorporated. As expected the performance gets better as the level of quantization increases and with six-level quantization it approaches the performance of non-quantized data transmission.
We develop a two-stage deep learning pipeline architecture to estimate the uplink massive MIMO channel with one-bit ADCs. This deep learning pipeline is composed of two separate generative deep learning models. The first one is a supervised learning model and designed to compensate for the quantization loss. The second one is an unsupervised learning model and optimized for denoising. Our results show that the proposed deep learning-based channel estimator can significantly outperform other state-of-the-art channel estimators for one-bit quantized massive MIMO systems. In particular, our design provides 5-10 dB gain in channel estimation error. Furthermore, it requires a reasonable amount of pilots, on the order of 20 per coherence time interval.
Manifold models in data analysis and signal processing have become more prominent in recent years. In this paper, we will look at one of the main tasks of modern signal processing, namely, at analog-to-digital (A/D) conversion in connection with a simple manifold model - the circle. We will focus on Sigma-Delta modulation which is a popular method for A/D conversion of bandlimited signals that employs coarse quantization coupled with oversampling. Classical Sigma-Delta schemes provide mismatches and large errors at the initialization point if the signal to be converted is defined on the circle. In this paper, our goal is to get around these problems for Sigma-Delta schemes. Our results show how to design an update for the first and the second order schemes based on the reconstruction error analysis such that for the updated scheme the reconstruction error is improved.
This paper considers the problem of estimating the sparse mmWave massive multiple input - multiple output (MIMO) OFDM channel from one-bit quantized measurements. Unlike previous grid-based one-bit compressive sensing approaches, we present a gridless convex method to recover sparse channel form one-bit measurements via Binary Atomic Norm Minimization (BiANM) and Reweighted Binary Atomic Norm Minimization (ReBiANM). Simulation results verify the accuracy of the binary and reweighted binary atomic norm minimization techniques.
We develop a modelling framework for multiple yield curves driven by continuous-state branching processes with immigration (CBI processes). Exploiting the self-exciting behavior of CBI jump processes, this approach can reproduce the relevant empirical features of spreads between different interbank rates. In particular, we introduce multi-curve models driven by a flow of tempered alpha-stable CBI processes. Such models are especially parsimonious and tractable, and can generate contagion effects among different spreads. We provide a complete analytical framework, including a detailed study of discounted exponential moments of CBI processes. The proposed approach allows for explicit valuation formulae for all linear interest rate derivatives and semi-closed formulae for non-linear derivatives via Fourier techniques and quantization. We show that a simple specification of the model can be successfully calibrated to market data.
This paper investigates a downlink multiple-input single-output intelligent reflecting surface (IRS) aided non-orthogonal multiple access (NOMA) system, where a base station (BS) serves multiple users with the aid of IRSs. Our goal is to maximize the sum rate of all users by jointly optimizing the active beamforming at the BS and the passive beamforming at the IRS, subject to successive interference cancellation decoding rate conditions and IRS reflecting elements constraints. In term of the characteristics of reflection amplitudes and phase shifts, we consider ideal and non-ideal IRS assumptions. To tackle the formulated non-convex problems, we propose efficient algorithms by invoking alternating optimization, which design the active beamforming and passive beamforming alternately. For the ideal IRS scenario, the two subproblems are solved by invoking the successive convex approximation technique. For the non-ideal IRS scenario, constant modulus IRS elements are further divided into continuous phase shifts and discrete phase shifts. To tackle the passive beamforming problem with continuous phase shifts, a novel algorithm is developed by utilizing the sequential rank-one constraint relaxation approach, which is guaranteed to find a locally optimal rank-one solution. Then, a quantization-based scheme is proposed for discrete phase shifts. Finally, numerical results illustrate that: i) the system sum rate can be significantly improved by deploying the IRS with the proposed algorithms; ii) 3-bit phase shifters are capable of achieving almost the same performance as the ideal IRS; iii) the proposed IRS-aided NOMA systems achieve higher system sum rate than the IRS-aided orthogonal multiple access system.
In networked control systems, often the sensory signals are quantized before being transmitted to the controller. Consequently, performance is affected by the coarseness of this quantization process. Modern communication technologies allow users to obtain resolution-varying quantized measurements based on the prices paid. In this paper, we consider joint optimal controller synthesis and quantizer scheduling for a partially observed Quantized-Feedback Linear-Quadratic-Gaussian (QF-LQG) system, where the measurements are quantized before being sent to the controller. The system is presented with several choices of quantizers, along with the cost of using each quantizer. The objective is to jointly select the quantizers and synthesize the controller to strike an optimal balance between control performance and quantization cost. When the innovation signal is quantized instead of the measurement, the problem is decoupled into two optimization problems: one for optimal controller synthesis, and the other for optimal quantizer selection. The optimal controller is found by solving a Riccati equation and the optimal quantizer selection policy is found by solving a linear program (LP)- both of which can be solved offline.
Distributed graph signal processing algorithms require the network nodes to communicate by exchanging messages in order to achieve a common objective. These messages have a finite precision in realistic networks, which may necessitate to implement message quantization. Quantization, in turn, may generate distortion and performance penalty in the distributed processing tasks. This paper proposes a novel method for distributed graph filtering that minimizes the error due to message quantization without compromising the communication costs. It first bounds the exchanged messages and then allocates a limited bit budget in an optimized way to the different messages and network nodes. In particular, our novel quantization algorithm adapts to both the network topology and the message importance in a distributed processing task. Our results show that the proposed method is effective in minimizing the error due to quantization and that it permits to outperform baseline distributed algorithms when the bit budget is limited. They further show that errors produced in nodes with high eccentricity or in the first steps of the distributed algorithm contribute more to the global error. Also, sparse and irregular graphs require more irregular bit distribution. Our method provides one of the first quantization solutions for distributed graph processing, which is able to adapt to the target task, the graph properties and the communication constraints.
We develop a direction of arrival (DoA) and channel estimation algorithm for the one-bit quantized millimeter-wave (mmWave) massive multiple-input multiple-output (MIMO) system. By formulating the estimation problem as a noisy one-bit compressed sensing problem, we propose a computationally efficient gridless solution based on the expectation-maximization generalized approximate message passing (EMGAMP) approach. The proposed algorithm does not need the prior knowledge about the number of DoAs and outperforms the existing methods in distinguishing extremely close DoAs for the case of one-bit quantization. Both the DoAs and the channel coefficients are estimated for the case of one-bit quantization. The simulation results show that the proposed algorithm has effective estimation performances when the DoAs are very close to each other.