This paper considers the use of fully homomorphic encryption for the realisation of distributed formation control of multi-agent systems via edge computer. In our proposed framework, the distributed control computation in the edge computer uses only the encrypted data without the need for a reset mechanism that is commonly required to avoid error accumulation. Simulation results show that, despite the use of encrypted data on the controller and errors introduced by the quantization process prior to the encryption, the formation is able to converge to the desired shape. The proposed architecture offers insight on the mechanism for realising distributed control computation in an edge/cloud computer while preserving the privacy of local information coming from each agent.
Product quantization (PQ) is a widely used technique for ad-hoc retrieval. Recent studies propose supervised PQ, where the embedding and quantization models can be jointly trained with supervised learning. However, there is a lack of appropriate formulation of the joint training objective; thus, the improvements over previous non-supervised baselines are limited in reality. In this work, we propose the Matching-oriented Product Quantization (MoPQ), where a novel objective Multinoulli Contrastive Loss (MCL) is formulated. With the minimization of MCL, we are able to maximize the matching probability of query and ground-truth key, which contributes to the optimal retrieval accuracy. Given that the exact computation of MCL is intractable due to the demand of vast contrastive samples, we further propose the Differentiable Cross-device Sampling (DCS), which significantly augments the contrastive samples for precise approximation of MCL. We conduct extensive experimental studies on four real-world datasets, whose results verify the effectiveness of MoPQ. The code is available at https://github.com/microsoft/MoPQ.
An effective recipe for building seq2seq, non-autoregressive, task-oriented parsers to map utterances to semantic frames proceeds in three steps: encoding an utterance $x$, predicting a frame's length |y|, and decoding a |y|-sized frame with utterance and ontology tokens. Though empirically strong, these models are typically bottlenecked by length prediction, as even small inaccuracies change the syntactic and semantic characteristics of resulting frames. In our work, we propose span pointer networks, non-autoregressive parsers which shift the decoding task from text generation to span prediction; that is, when imputing utterance spans into frame slots, our model produces endpoints (e.g., [i, j]) as opposed to text (e.g., "6pm"). This natural quantization of the output space reduces the variability of gold frames, therefore improving length prediction and, ultimately, exact match. Furthermore, length prediction is now responsible for frame syntax and the decoder is responsible for frame semantics, resulting in a coarse-to-fine model. We evaluate our approach on several task-oriented semantic parsing datasets. Notably, we bridge the quality gap between non-autogressive and autoregressive parsers, achieving 87 EM on TOPv2 (Chen et al. 2020). Furthermore, due to our more consistent gold frames, we show strong improvements in model generalization in both cross-domain and cross-lingual transfer in low-resource settings. Finally, due to our diminished output vocabulary, we observe 70% reduction in latency and 83% reduction in memory at beam size 5 compared to prior non-autoregressive parsers.
Current cellular systems use pilot-aided statistical-channel state information (S-CSI) estimation and limited feedback schemes to aid in link adaptation and scheduling decisions. However, in the presence of pulsed radar signals, pilot-aided S-CSI is inaccurate since interference statistics on pilot and non-pilot resources can be different. Moreover, the channel will be bimodal as a result of the periodic interference. In this paper, we propose a max-min heuristic to estimate the post-equalizer SINR in the case of non-pilot pulsed radar interference, and characterize its distribution as a function of noise variance and interference power. We observe that the proposed heuristic incurs low computational complexity, and is robust beyond a certain SINR threshold for different modulation schemes, especially for QPSK. This enables us to develop a comprehensive semi-blind framework to estimate the wideband SINR metric that is commonly used for S-CSI quantization in 3GPP Long-Term Evolution (LTE) and New Radio (NR) networks. Finally, we propose dual CSI feedback for practical radar-cellular spectrum sharing, to enable accurate CSI acquisition in the bimodal channel. We demonstrate significant improvements in throughput, block error rate and retransmission-induced latency for LTE-Advanced Pro when compared to conventional pilot-aided S-CSI estimation and limited feedback schemes.
Many of the systems that appear in various signal processing applications are non-linear, for example, due to hardware impairments such as non-linear amplifiers and finite-resolution quantization. The Bussgang decomposition is a popular tool for analyzing the performance of systems that involve such non-linear components. In a nutshell, the decomposition provides an exact probabilistic relationship between the output and the input of a non-linearity: the output is equal to a scaled version of the input plus uncorrelated distortion. The decomposition can either be used to compute exact performance results or lower bounds where the uncorrelated distortion is treated as independent noise. This lecture note explains the basic theory, provides key examples, extends the theory to complex-valued vector signals, and clarifies some potential misconceptions.
For a massive multiple-input-multiple-output (MIMO) system using intelligent reflecting surface (IRS) equipped with radio frequency (RF) chains, the multi-channel RF chains are expensive compared to passive IRS, especially, when the high-resolution and high-speed analog to digital converters (ADC) are used in each RF channel. In this letter, a direction of angle (DOA) estimation problem is investigated with low-cost ADC in IRS, and we propose a deep neural network (DNN) as a recovery method for the low-resolution sampled signal. Different from the existing denoising convolutional neural network (DnCNN) for Gaussian noise, the proposed DNN with fully connected (FC) layers estimates the quantization noise caused by the ADC. Then, the denoised signal is subjected to the DOA estimation, and the recovery performance for the quantized signal is evaluated by DOA estimation. Simulation results show that under the same training conditions, the better reconstruction performance is achieved by the proposed network than state-of-the-art methods. The performance of the DOA estimation using 1-bit ADC is improved to exceed that using 2-bit ADC.
We consider the problem of sparse signal reconstruction from noisy one-bit compressed measurements when the receiver has access to side-information (SI). We assume that compressed measurements are corrupted by additive white Gaussian noise before quantization and sign-flip error after quantization. A generalized approximate message passing-based method for signal reconstruction from noisy one-bit compressed measurements is proposed, which is then extended for the case where the receiver has access to a signal that aids signal reconstruction, i.e., side-information. Two different scenarios of side-information are considered-a) side-information consisting of support information only, and b) side information consisting of support and amplitude information. SI is either a noisy version of the signal or a noisy estimate of the support of the signal. We develop reconstruction algorithms from one-bit measurements using noisy SI available at the receiver. Laplacian distribution and Bernoulli distribution are used to model the two types of noises which, when applied to the signal and the support, yields the SI for the above two cases, respectively. The Expectation-Maximization algorithm is used to estimate the noise parameters using noisy one-bit compressed measurements and the SI. We show that one-bit compressed measurement-based signal reconstruction is quite sensitive to noise, and the reconstruction performance can be significantly improved by exploiting available side-information at the receiver.
The reconfigurable intelligent surface (RIS) is one of the promising technologies contributing to the next generation smart radio environment. A novel physics-based RIS channel model is proposed. Particularly, we consider the RIS and the scattering environment as a whole by studying the signal's multipath propagation, as well as the radiation pattern of the RIS. The model suggests that the RIS-assisted wireless channel can be approximated by a Rician distribution. Analytical expressions are derived for the shape factor and the scale factor of the distribution. For the case of continuous phase shifts, the distribution depends on the number of elements of the RIS and the observing direction of the receiver. For the case of continuous phase shifts, the distribution further depends on the quantization level of the RIS phase error. The scaling law of the average received power is obtained from the scale factor of the distribution. For the application scenarios where RIS functions as an anomalous reflector, we investigate the performance of single RIS-assisted multiple access networks for time-division multiple access (TDMA), frequency-division multiple access (FDMA) and non-orthogonal multiple access (NOMA). Closed-form expressions for the outage probability of the proposed channel model are derived. It is proved that a constant diversity order exists, which is independent of the number of RIS elements. Simulation results are presented to confirm that the proposed model applies effectively to the phased-array implemented RISs.
Recent years have witnessed growing interest in reduced cost radar systems operating with low power. Multiple-input multiple-output (MIMO) radar technology is known to achieve high performance sensing by probing with multiple orthogonal waveforms. However, implementing a low cost low power MIMO radar is challenging. One of the reasons for this difficulty stems from the increased cost and power consumption required by analog-to-digital convertors (ADCs) in acquiring the multiple waveforms at the radar receiver. In this work we study reduced cost MIMO radar receivers restricted to operate with low resolution ADCs. We design bit-limited MIMO radar (BiLiMO) receivers which are capable of accurately recovering their targets while operating under strict resolution constraints. This is achieved by applying an additional analog filter to the acquired waveforms, and designing the overall hybrid analog-digital system to facilitate target identification using task-based quantization methods. In particular, we exploit the fact that the target parameters can be recovered from a compressed representation of the received waveforms. We thus tune the acquisition system to recover this representation with minimal distortion, from which the targets can be extracted in digital, and characterize the achievable error in identifying the targets. Our numerical results demonstrate that the proposed BiLiMO receiver operating with a bit budget of one bit per sample achieves target recovery performance which approaches that of costly MIMO radars operating with unlimited resolution ADCs, while substantially outperforming MIMO receivers operating only in the digital domain under the same bit limitations.
The use of low-resolution data converters in the radio-frequency (RF) chains of all-digital massive multiple-input multiple-output (MIMO) basestations promises significant reductions in power consumption, hardware costs, and interconnect bandwidth. We propose a quantization-aware data-detection algorithm which mitigates the performance loss of 1-bit quantized massive MIMO orthogonal frequency-division multiplexing (OFDM) systems. Since the system performance heavily depends on the quality of channel estimates, we also develop a nonlinear 1-bit channel estimation algorithm that builds upon the proposed data detection algorithm. We show that the proposed algorithms significantly outperform linear data detectors and channel estimators in terms of bit error rate. For the proposed nonlinear data detection algorithm, we develop a very large scale integration (VLSI) architecture and present implementation results on a Xilinx Virtex-7 field programmable gate array (FPGA). Our implementation results are, to the best of our knowledge, the first for 1-bit massive MU-MIMO-OFDM systems and demonstrate comparable hardware efficiency with respect to state-of-the-art linear data detectors designed for systems with high-resolution data converters, while achieving lower bit error rate.
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.
Target detection is an important problem in multiple-input multiple-output (MIMO) radar. Many existing target detection algorithms were proposed without taking into consideration the quantization error caused by analog-to-digital converters (ADCs). This paper addresses the problem of target detection for MIMO radar with one-bit ADCs and derives a Rao's test-based detector. The proposed method has several appealing features: 1) it is a closed-form detector; 2) it allows us to handle sign measurements straightforwardly; 3) there are closed-form approximations of the detector's distributions, which allow us to theoretically evaluate its performance. Moreover, the closed-form distributions allow us to study the performance degradation due to the one-bit ADCs, yielding an approximate $2$ dB loss in the low-signal-to-noise-ratio (SNR) regime compared to $\infty$-bit ADCs. Simulation results are included to showcase the advantage of the proposed detector and validate the accuracy of the theoretical results.
Consider a robust multiple-input single-output downlink beamforming optimization problem in a frequency division duplexing system. The base station (BS) sends training signals to the users, and every user estimates the channel coefficients, quantizes the gain and the direction of the estimated channel and sends them back to the BS. Suppose that the channel state information at the transmitter is imperfectly known mainly due to the channel direction quantization errors, channel estimation errors and outdated channel effects. The actual channel is modeled as in an uncertainty set composed of two inequality homogeneous and one equality inhomogeneous quadratic constraints, in order to account for the aforementioned errors and effects. Then the transmit power minimization problem is formulated subject to robust signal-to-noise-plus-interference ratio constraints. Each robust constraint is transformed equivalently into a quadratic matrix inequality (QMI) constraint with respect to the beamforming vectors. The transformation is accomplished by an equivalent phase rotation process and the strong duality result for a quadratically constrained quadratic program. The minimization problem is accordingly turned into a QMI problem, and the problem is solved by a restricted linear matrix inequality relaxation with additional valid convex constraints. Simulation results are presented to demonstrate the performance of the proposed method, and show the efficiency of the restricted relaxation.
By reconfiguring the propagation environment of electromagnetic waves artificially, reconfigurable intelligent surfaces (RISs) have been regarded as a promising and revolutionary hardware technology to improve the energy and spectrum efficiency of wireless networks. In this paper, we study a RIS aided multiuser multiple-input multiple-output (MIMO) wireless power transfer (WPT) system, where the transmitter is equipped with a constant-envelope analog beamformer. First, we maximize the total received power of the users by jointly optimizing the beamformer at transmitter and the phase-shifts at the RIS, and propose two alternating optimization based suboptimal solutions by leveraging the semidefinite relaxation (SDR) and the successive convex approximation (SCA) techniques respectively. Then, considering the user fairness, we formulate another problem to maximize the total received power subject to the users' individual minimum received power constraints. A low complexity iterative algorithm based on both alternating direction method of multipliers (ADMM) and SCA techniques is proposed to solve this problem. In the case of multiple users, we further analyze the asymptotic performance as the number of RIS elements approaches infinity, and bound the performance loss caused by RIS phase quantization. Numerical results show the correctness of the analysis results and the effectiveness of the proposed algorithms.
The latest theoretical advances in the field of unlimited sampling framework (USF) show the potential to avoid clipping problems of analog-to-digital converters (ADC). To date, most of the related works have focused on real-valued modulo samples, but little has been reported about the impact of quantization. In this paper, we study more practical USF system where modulo samples are quantized to a finite number of bits. In particular, we present a new requirement about the lower bound of sampling rate to ensure exact recovery of original signals from quantized modulo samples. The minimum sampling rate is jointly determined by signal bandwidth and quantization bits. Numerical results show that in the presence of quantization noise, signals with different waveforms and bandwidths are recovered perfectly at the new minimum sampling rate while the recovery fails at minimum sampling rate before modification, which also verifies the correctness of the theory. The trade-offs of sampling rates, quantization bits and computational complexity of recovery algorithm are also given for practitioners to weigh.
In this letter, we investigate the uplink of a reconfigurable intelligent surface (RIS)-aided millimeter-wave (mmWave) multi-user system. In the considered system, however, problems with hardware cost and power consumption arise when massive antenna arrays coupled with power-demanding analog-to-digital converters (ADCs) are employed. To account for practical hardware complexity, we consider that the access point (AP) is equipped with resolution-adaptive analog-to-digital converters (RADCs). We maximize the achievable rate under hardware constraints by jointly optimizing the ADC quantization bits, the RIS phase shifts, and the beam selection matrix. Due to the non-convexity of the feasible set and objective function, the formulated problem is non-convex and difficult to solve. To efficiently tackle this problem, a block coordinated descent (BCD)-based algorithm is proposed. Simulations demonstrate that an RIS can mitigate the hardware loss due to use of RADCs, and that the proposed BCD-based algorithm outperforms state-of-the-art algorithms.
In this paper, we derive the uplink achievable rate expression of intelligent reflecting surface (IRS)-aided millimeter-wave (mmWave) systems, taking into account the phase noise at IRS and the quantization error at base stations (BSs). We show that the performance is limited only by the resolution of analog-digital converters (ADCs) at BSs when the number of IRS reflectors grows without bound. On the other hand, if BSs have ideal ADCs, the performance loss caused by IRS phase noise is a constant. Finally, our results validate the feasibility of using low-precision hardware at the IRS when BSs are equipped with low-resolution ADCs.
In this paper, the zero-forcing (ZF) precoder with max-min power allocation is proposed for cell-free millimeter wave (mmWave) massive multiple-input multiple-output (MIMO) systems using low-resolution digital-to-analog converters (DACs) with limited-capacity fronthaul links. The proposed power allocation aims to achieve max-min fairness on the achievable rate lower bounds of the users obtained by the additive quantization noise model (AQNM), which mimics the effect of low-resolution DACs. To solve the max-min power allocation problem, an alternating optimization (AO) method is proposed, which is guaranteed to converge because the global optima of the subproblems that constitute the original problem are attained at each AO iteration. The performance of cell-free and small-cell systems is explored in the simulation results, which suggest that not-too-small fronthaul capacity suffices for cell-free systems to outperform small-cell systems.
We propose a method of data quantization of finite discrete-time signals which optimizes the error estimate of low frequency Haar coefficients. We also discuss the error/noise bounds of this quantization in the Fourier space. Our result shows one can quantize any discrete-time analog signal with high precision at low frequencies. Our method is deterministic, and it employs no statistical arguments, nor any probabilistic assumptions.
Implanted devices providing real-time neural activity classification and control are increasingly used to treat neurological disorders, such as epilepsy and Parkinson's disease. Classification performance is critical to identifying brain states appropriate for the therapeutic action. However, advanced algorithms that have shown promise in offline studies, in particular deep learning (DL) methods, have not been deployed on resource-restrained neural implants. Here, we designed and optimized three embedded DL models of commonly adopted architectures and evaluated their inference performance in a case study of seizure detection. A deep neural network (DNN), a convolutional neural network (CNN), and a long short-term memory (LSTM) network were designed to classify ictal, preictal, and interictal phases from the CHB-MIT scalp EEG database. After iterative model compression and quantization, the algorithms were deployed on a general-purpose, off-the-shelf microcontroller. Inference sensitivity, false positive rate, execution time, memory size, and power consumption were quantified. For seizure event detection, the sensitivity and FPR (h-1) for the DNN, CNN, and LSTM models were 87.36%/0.169, 96.70%/0.102, and 97.61%/0.071, respectively. Predicting seizures for early warnings was also feasible. The implemented compression and quantization achieved a significant saving of power and memory with an accuracy degradation of less than 0.5%. Edge DL models achieved performance comparable to many prior implementations that had no time or computational resource limitations. Generic microcontrollers can provide the required memory and computational resources, while model designs can be migrated to ASICs for further optimization. The results suggest that edge DL inference is a feasible option for future neural implants to improve classification performance and therapeutic outcomes.