We consider the quantization of a transmit beamforming vector in multiantenna channels and of a signature vector in code division multiple access (CDMA) systems. Assuming perfect channel knowledge, the receiver selects for a transmitter the vector that maximizes the performance from a random vector quantization (RVQ) codebook, which consists of independent isotropically distributed unit-norm vectors. The quantized vector is then relayed to the transmitter via a rate-limited feedback channel. The RVQ codebook requires an exhaustive search to locate the selected entry. To reduce the search complexity, we apply generalized Lloyd or $k$-dimensional (kd)-tree algorithms to organize RVQ entries into a tree. In examples shown, the search complexity of tree-structured (TS) RVQ can be a few orders of magnitude less than that of the unstructured RVQ for the same performance. We also derive the performance approximation for TS-RVQ in a large system limit, which predicts the performance of a moderate-size system very well.
This paper investigates quantization of channel state information (CSI) and bit allocation across wireless links in a multi-source, single-relay cooperative cellular network. Our goal is to minimize the loss in performance, measured as the achievable sum rate, due to limited-rate quantization of CSI. We develop both a channel quantization scheme and allocation of limited feedback bits to the various wireless links. We assume that the quantized CSI is reported to a central node responsible for optimal resource allocation. We first derive tight lower and upper bounds on the difference in rates b…
Limited feedback is a paradigm for the feedback of channel state information in wireless systems. In multiple antenna wireless systems, limited feedback usually entails quantizing a source that lives on the Grassmann manifold. Most work on limited feedback beamforming considered single-shot quantization. In wireless systems, however, the channel is temporally correlated, which can be used to reduce feedback requirements. Unfortunately, conventional predictive quantization does not incorporate the non-Euclidean structure of the Grassmann manifold. In this paper, we propose a Grassmannian predic…
We study a heterogeneous two-tier wireless sensor network in which N heterogeneous access points (APs) collect sensing data from densely distributed sensors and then forward the data to M heterogeneous fusion centers (FCs). This heterogeneous node deployment problem is modeled as a quantization problem with distortion defined as the total power consumption of the network. The necessary conditions of the optimal AP and FC node deployment are explored in this paper. We provide a variation of Voronoi Diagram as the optimal cell partition for this network, and show that each AP should be placed be…
As the number of IoT devices continue to exponentially increase and saturate the wireless spectrum, there is a dire need for additional spectrum to support large networks of wireless devices. Over the past years, many promising solutions have been proposed but they all suffer from the drawback of new infrastructure costs, setup and maintenance, or are difficult to implement due to FCC regulations. In this paper, we propose a novel Wireless Quantization Index Modulation (QIM) technique which uses existing infrastructure to embed information into existing wireless signals to communicate with IoT…
Reconfigurable intelligent surface (RIS) can manipulate the wireless communication environment by controlling the coefficients of RIS elements. However, due to the large number of passive RIS elements without signal processing capability, channel estimation in RIS assisted wireless communication system requires high pilot overhead. In the second part of this invited paper, we propose to exploit the double-structured sparsity of the angular cascaded channels among users to reduce the pilot overhead. Specifically, we first reveal the double-structured sparsity, i.e., different angular cascaded c…
The performance of cloud radio access network (C-RAN) is constrained by the limited fronthaul link capacity under future heavy data traffic. To tackle this problem, extensive efforts have been devoted to design efficient signal quantization/compression techniques in the fronthaul to maximize the network throughput. However, most of the previous results are based on information-theoretical quantization methods, which are hard to implement due to the extremely high complexity. In this paper, we consider using practical uniform scalar quantization in the uplink communication of an orthogonal freq…
Optimal and suboptimal decentralized estimators in wireless sensor networks (WSNs) over orthogonal multiple-access fading channels are studied in this paper. Considering multiple-bit quantization before digital transmission, we develop maximum likelihood estimators (MLEs) with both known and unknown channel state information (CSI). When training symbols are available, we derive a MLE that is a special case of the MLE with unknown CSI. It implicitly uses the training symbols to estimate the channel coefficients and exploits the estimated CSI in an optimal way. To reduce the computational comple…
Discrete phase shifters of intelligent reflecting surface (IRS) generates phase quantization error (QE) and degrades the receive performance at the receiver. To make an analysis of the performance loss caused by IRS with phase QE, based on the law of large numbers, the closed-form expressions of signal-to-noise ratio (SNR) performance loss (PL), achievable rate (AR), and bit error rate (BER) are successively derived under line-of-sight (LoS) channels and Rayleigh channels. Moreover, based on the Taylor series expansion, the approximate simple closed form of PL of IRS with approximate QE is als…
ADCs sit at the interface of the analog and digital worlds and fundamentally determine what information is available in the digital domain for processing. This paper shows that a configurable ADC can be designed for signals with non constant information as a function of frequency such that within a fixed power budget the ADC maximizes the information in the converted signal by frequency shaping the quantization noise. Quantization noise shaping can be realized via loop filter design for a single channel delta sigma ADC and extended to common time and frequency interleaved multi channel structu…
Reconfigurable intelligent surface (RIS) has received widespread attention owing to the superiority of changing the wireless propagation environment intelligently. Channel feedback is essential in frequency division duplex (FDD) RIS-assisted wireless communications, since the downlink channel state information (CSI) needs to be acquired by the base station (BS) from the user equipment (UE) for the joint beamforming at the BS and the RIS. In this paper, we exploit the single-structured sparsity of RIS channel, which means that the sparse angular-domain channels of different users share the same…
MIMO systems are considered as most promising for wireless communications. However, with an increasing number of radio front ends the corresponding energy consumption and costs become an issue, which can be relieved by the utilization of low-resolution quantizers. In this study we propose an optimal precoding algorithm constrained to constant envelope signals and phase quantization that maximizes the minimum distance to the decision threshold at the receivers using a branch-and-bound strategy. The proposed algorithm is superior to the existing methods in terms of bit error rate. Numerical resu…
This paper studies the optimal bit allocation for shape-gain vector quantization of wireless channels in multiuser (MU) multiple-input multiple-output (MIMO) downlink systems based on linear precoding. Our design minimizes the mean squared-error between the original and quantized channels through optimal bit allocation across shape (direction) and gain (magnitude) for a fixed feedback overhead per user. This is shown to significantly reduce the quantization error, which in turn, decreases the MU interference. This paper makes three main contributions: first, we focus on channel gain quantizati…
The future wireless network, such as Centralized Radio Access Network (C-RAN), will need to deliver data rate about 100 to 1000 times the current 4G technology. For C-RAN based network architecture, there is a pressing need for tremendous enhancement of the effective data rate of the Common Public Radio Interface (CPRI). Compression of CPRI data is one of the potential enhancements. In this paper, we introduce a vector quantization based compression algorithm for CPRI links, utilizing Lloyd algorithm. Methods to vectorize the I/Q samples and enhanced initialization of Lloyd algorithm for codeb…
In this paper, we consider a multi-antenna system where the receiver should harvest energy from the transmitter by wireless energy transfer to support its wireless information transmission. In order to maximize the harvesting energy, we propose to perform adaptive energy beamforming according to the instantaneous channel state information (CSI). To help the transmitter to obtain the CSI for energy beamforming, we further propose a win-win CSI quantization feedback strategy, so as to improve the efficiencies of both power and information transmission. The focus of this paper is on the tradeoff …
Wireless positioning systems that are implemented by means of a Cloud Radio Access Networks (C-RANs) may provide cost-effective solutions, particularly for indoor localization. In a C-RAN, the baseband processing, including localization, is carried out at a centralized control unit (CU) based on quantized baseband signals received from the RUs over finite-capacity fronthaul links. In this paper, the problem of maximizing the localization accuracy over fronthaul quantization/compression is formulated by adopting the Cramér-Rao bound (CRB) on the localization accuracy as the performance metric o…
Multi-antenna or multiple-input multiple-output (MIMO) technique can significantly improve the efficiency of radio frequency (RF) signal enabled wireless energy transfer (WET). To fully exploit the energy beamforming gain at the energy transmitter (ET), the knowledge of channel state information (CSI) is essential, which, however, is difficult to be obtained in practice due to the hardware limitation of the energy receiver (ER). To overcome this difficulty, under a point-to-point MIMO WET setup, this paper proposes a general design framework for a new type of channel learning method based on t…
The orthogonal time frequency space (OTFS) modulation has emerged as a promising modulation scheme for high mobility wireless communications. To enable efficient OTFS detection in the delay-Doppler (DD) domain, the DD domain channels need to be acquired accurately. To achieve the low latency requirement in future wireless communications, the time duration of the OTFS block should be small, therefore fractional Doppler shifts have to be considered to avoid significant modelling errors due to the assumption of integer Doppler shifts. However, there lack investigations on the estimation of OTFS c…
In frequency division duplex (FDD) multiple-input multiple-output (MIMO) wireless communications, limited channel state information (CSI) feedback is a central tool to support advanced single- and multi-user MIMO beamforming/precoding. To achieve a given CSI quality, the CSI quantization codebook size has to grow exponentially with the number of antennas, leading to quantization complexity, as well as, feedback overhead issues for larger MIMO systems. We have recently proposed a multi-stage recursive Grassmannian quantizer that enables a significant complexity reduction of CSI quantization. In…
We consider distributed estimation of a Gaussian vector with a linear observation model in an inhomogeneous wireless sensor network, where a fusion center (FC) reconstructs the unknown vector, using a linear estimator. Sensors employ uniform multi-bit quantizers and binary PSK modulation, and communicate with the FC over orthogonal power- and bandwidth-constrained wireless channels. We study transmit power and quantization rate (measured in bits per sensor) allocation schemes that minimize mean-square error (MSE). In particular, we derive two closed-form upper bounds on the MSE, in terms of th…
This paper introduces a new quantization scheme for real and complex Grassmannian sources. The proposed approach relies on a structured codebook based on a geometric construction of a collection of bent grids defined from an initial mesh on the unit-norm sphere. The associated encoding and decoding algorithms have very low complexity (equivalent to a scalar quantizer), while their efficiency (in terms of the achieved distortion) is on par with the best known structured approaches, and compares well with the theoretical bounds. These properties make this codebook suitable for high-resolutions, …
Corrupted sensing concerns the problem of recovering a high-dimensional structured signal from a collection of measurements that are contaminated by unknown structured corruption and unstructured noise. In the case of linear measurements, the recovery performance of different convex programming procedures (e.g., generalized Lasso and its variants) is well established in the literature. However, in practical applications of digital signal processing, the quantization process is inevitable, which often leads to non-linear measurements. This paper is devoted to studying corrupted sensing under qu…
Massive MIMO wireless FDD systems are often confronted by the challenge to efficiently obtain downlink channel state information (CSI). Previous works have demonstrated the potential in CSI encoding and recovery by take advantage of uplink/downlink reciprocity between their CSI magnitudes. However, such a framework separately encodes CSI phase and magnitude. To improve CSI encoding, we propose a learning-based framework based on limited CSI feedback and magnitude-aided information. Moving beyond previous works, our proposed framework with a modified loss function enables end-to-end learning to…
Compressed sensing has been employed to reduce the pilot overhead for channel estimation in wireless communication systems. Particularly, structured turbo compressed sensing (STCS) provides a generic framework for structured sparse signal recovery with reduced computational complexity and storage requirement. In this paper, we consider the problem of massive multiple-input multiple-output (MIMO) orthogonal frequency division multiplexing (OFDM) channel estimation in a frequency division duplexing (FDD) downlink system. By exploiting the structured sparsity in the angle-frequency domain (AFD) a…
Large-scale multiple-antenna systems have been identified as a promising technology for the next generation of wireless systems. However, by scaling up the number of receive antennas the energy consumption will also increase. One possible solution is to use low-resolution analog-to-digital converters at the receiver. This paper considers large-scale multiple-antenna uplink systems with 1-bit analog-to-digital converters on each receive antenna. Since oversampling can partially compensate for the information loss caused by the coarse quantization, the received signals are firstly oversampled by…
Existing secret key extraction techniques use quantization to map wireless channel amplitudes to secret bits. This pa- per shows that such techniques are highly prone to environ- ment and local noise effects: They have very high mismatch rates between the two nodes that measure the channel be- tween them. This paper advocates using the shape of the channel instead of the size (or amplitude) of the channel. It shows that this new paradigm shift is significantly ro- bust against environmental and local noises. We refer to this shape-based technique as Puzzle. Implementation in a software-defined…
This paper studies a wireless powered mobile edge computing (MEC) system with fluctuating channels and dynamic task arrivals over time. We jointly optimize the transmission energy allocation at the energy transmitter (ET) for WPT and the task allocation at the user for local computing and offloading over a particular finite horizon, with the objective of minimizing the total transmission energy consumption at the ET while ensuring the user's successful task execution. First, in order to characterize the fundamental performance limit, we consider the offline optimization by assuming that the pe…
Beijing National Research Center for Information Science and Technology（北京信息科学与技术国家研究中心）；Tsinghua University（清华大学）
In this paper, we study a federated learning system at the wireless edge that uses over-the-air computation (AirComp). In such a system, users transmit their messages over a multi-access channel concurrently to achieve fast model aggregation. Recently, an AirComp scheme based on digital modulation has been proposed featuring one-bit gradient quantization and truncated channel inversion at users and a majority-voting based decoder at the fusion center (FC). We propose an improved digital AirComp scheme to relax its requirements on the transmitters, where users perform phase correction and trans…
This paper introduces a novel concept from coalitional game theory which allows the dynamic formation of coalitions among wireless nodes. A simple and distributed merge and split algorithm for coalition formation is constructed. This algorithm is applied to study the gains resulting from the cooperation among single antenna transmitters for virtual MIMO formation. The aim is to find an ultimate transmitters coalition structure that allows cooperating users to maximize their utilities while accounting for the cost of coalition formation. Through this novel game theoretical framework, the wirele…
