This letter establishes a unified analytical framework to study the asymptotic average mutual information (AMI) of mixture gamma (MG) distributed fading channels driven by finite input signals in the high signal-to-noise ratio (SNR) regime. It is found that the AMI converges to some constant as the average SNR increases and its rate of convergence (ROC) is determined by the coding gain and diversity order. Moreover, the derived results are used to investigate the asymptotic optimal power allocation policy of a bank of parallel fading channels having finite inputs. It is suggested that in the high SNR region, the sub-channel with a lower coding gain or diversity order should be allocated with more power. Finally, numerical results are provided to collaborate the theoretical analyses.
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We study regression adjustments with additional covariates in randomized experiments under covariate-adaptive randomizations (CARs) when subject compliance is imperfect. We develop a regression-adjusted local average treatment effect (LATE) estimator that is proven to improve efficiency in the estimation of LATEs under CARs. Our adjustments can be parametric in linear and nonlinear forms, nonparametric, and high-dimensional. Even when the adjustments are misspecified, our proposed estimator is still consistent and asymptotically normal, and their inference method still achieves the exact asymptotic size under the null. When the adjustments are correctly specified, our estimator achieves the minimum asymptotic variance. When the adjustments are parametrically misspecified, we construct a new estimator which is weakly more efficient than linearly and nonlinearly adjusted estimators, as well as the one without any adjustments. Simulation evidence and empirical application confirm efficiency gains achieved by regression adjustments relative to both the estimator without adjustment and the standard two-stage least squares estimator.
To support the unprecedented growth of the Internet of Things (IoT) applications and the access of tremendous IoT devices, two new technologies emerge recently to overcome the shortage of spectrum resources. The first one, known as integrated sensing and communication (ISAC), aims to share the spectrum bandwidth for both radar sensing and data communication. The second one, called over-the-air computation (AirComp), enables simultaneous transmission and computation of data from multiple IoT devices in the same frequency. The promising performance of ISAC and AirComp motivates the current work on developing a framework that combines the merits of both called integrated sensing and AirComp (ISAA). Two schemes are designed to support multiple-input-multiple-output (MIMO) ISAA simultaneously, namely the shared and separated schemes. The performance metrics of radar sensing and AirComp are evaluated by the mean square errors of the estimated target response matrix and the received computation results, respectively. The design challenge of MIMO ISAA lies in the joint optimization of radar sensing beamformers and data transmission beamformers at the IoT devices, and data aggregation beamformer at the server, which results in complex non-convex problem. To solve this problem, an algorithmic solution based on the technique of semidefinite relaxation is proposed. The results reveal that the beamformer at each sensor needs to account for supporting dual-functional signals in the shared scheme, while dedicated beamformers for sensing and AirComp are needed to mitigate the mutual interference between the two functionalities in the separated scheme. The use case of target location estimation based on ISAA is demonstrated in simulation to show the performance superiority.
The use of a large excess of service antennas brings a variety of performance benefits to distributed MIMO C-RAN, but the corresponding high fronthaul data loads can be problematic in practical systems with limited fronthaul capacity. In this work we propose the use of lossy dimension reduction, applied locally at each remote radio head (RRH), to reduce this fronthaul traffic. We first consider the uplink, and the case where each RRH applies a linear dimension reduction filter to its multi-antenna received signal vector. It is shown that under a joint mutual information criteria, the optimal dimension reduction filters are given by a variant of the conditional Karhunen-Loeve transform, with a stationary point found using block co-ordinate ascent. These filters are then modified such that each RRH can calculate its own dimension reduction filter in a decentralised manner, using knowledge only of its own instantaneous channel and network slow fading coefficients. We then show that in TDD systems these dimension reduction filters can be re-used as part of a two-stage reduced dimension downlink precoding scheme. Analysis and numerical results demonstrate that the proposed approach can significantly reduce both uplink and downlink fronthaul traffic whilst incurring very little loss in MIMO performance.
Several div-conforming and divdiv-conforming finite elements for symmetric tensors on simplexes in arbitrary dimension are constructed in this work. The shape function space is first split as the trace space and the bubble space. The later is further decomposed into the null space of the differential operator and its orthogonal complement. Instead of characterization of these subspaces of the shape function space, characterization of the dual spaces are provided. Vector div-conforming finite elements are firstly constructed as an introductory example. Then new symmetric div-conforming finite elements are constructed. The dual subspaces are then used as build blocks to construct divdiv conforming finite elements.
In this paper, we analyze the performance of a reconfigurable intelligent surface (RIS)-assisted unmanned aerial vehicle (UAV) wireless system that is affected by mixture-gamma small-scale fading, stochastic disorientation, and misalignment, as well as transceivers hardware imperfections. First, we statistically characterize the end-to-end channel for both cases, i.e., in the absence as well as in the presence of disorientation and misalignment, by extracting closed-form formulas for the probability density function (PDF) and the cumulative distribution function (CDF). Building on the aforementioned expressions, we extract novel closed-form expressions for the outage probability (OP) in the absence and the presence of disorientation and misalignment as well as hardware imperfections. In addition, high signal-to-noise ratio OP approximations are derived, leading to the extraction of the diversity order. Finally, an OP floor due to disorientation and misalignment is presented.
Energy efficiency (EE) plays a key role in future wireless communication network and it is easily to achieve high EE performance in low SNR regime. In this paper, a new high EE scheme is proposed for a MIMO wireless communication system working in the low SNR regime by using two dimension resource allocation. First, we define the high EE area based on the relationship between the transmission power and the SNR. To meet the constraint of the high EE area, both frequency and space dimension are needed. Besides analysing them separately, we decided to consider frequency and space dimensions as a unit and proposed a two-dimension scheme. Furthermore, considering communication in the high EE area may cause decline of the communication quality, we add quality-of-service(QoS) constraint into the consideration and derive the corresponding EE performance based on the effective capacity. We also derive an approximate expression to simplify the complex EE performance. Finally, our numerical results demonstrate the effectiveness of the proposed scheme.
In this paper, we are interested in the performance of a variable-length stop-feedback (VLSF) code with $m$ optimal decoding times for the binary-input additive white Gaussian noise (BI-AWGN) channel. We first develop tight approximations on the tail probability of length-$n$ cumulative information density. Building on the work of Yavas \emph{et al.}, we formulate the problem of minimizing the upper bound on average blocklength subject to the error probability, minimum gap, and integer constraints. For this integer program, we show that for a given error constraint, a VLSF code that decodes after every symbol attains the maximum achievable rate. We also present a greedy algorithm that yields possibly suboptimal integer decoding times. By allowing a positive real-valued decoding time, we develop the gap-constrained sequential differential optimization (SDO) procedure. Numerical evaluation shows that the gap-constrained SDO can provide a good estimate on achievable rate of VLSF codes with $m$ optimal decoding times and that a finite $m$ suffices to attain Polyanskiy's bound for VLSF codes with $m = \infty$.
In this paper, we investigate a cell-free massive MIMO system with both access points and user equipments equipped with multiple antennas over the Weichselberger Rayleigh fading channel. We study the uplink spectral efficiency (SE) based on a two-layer decoding structure with maximum ratio (MR) or local minimum mean-square error (MMSE) combining applied in the first layer and optimal large-scale fading decoding method implemented in the second layer, respectively. To maximize the weighted sum SE, an uplink precoding structure based on an Iteratively Weighted sum-MMSE (I-WMMSE) algorithm using only channel statistics is proposed. Furthermore, with MR combining applied in the first layer, we derive novel achievable SE expressions and optimal precoding structures in closed-form. Numerical results validate our proposed results and show that the I-WMMSE precoding can achieve excellent sum SE performance.
Downlink precoding is considered for multi-path multi-user multi-input single-output (MU-MISO) channels where the base station uses orthogonal frequency-division multiplexing and low-resolution signaling. A quantized coordinate minimization (QCM) algorithm is proposed and its performance is compared to other precoding algorithms including squared infinity-norm relaxation (SQUID), multi-antenna greedy iterative quantization (MAGIQ), and maximum safety margin precoding. MAGIQ and QCM achieve the highest information rates and QCM has the lowest complexity measured in the number of multiplications. The information rates are computed for pilot-aided channel estimation and a blind detector that performs joint data and channel estimation. Bit error rates for a 5G low-density parity-check code confirm the information-theoretic calculations. Simulations with imperfect channel knowledge at the transmitter show that the performance of QCM and SQUID degrades in a similar fashion as zero-forcing precoding with high resolution quantizers.
In this paper, we study the optimal convergence rate for distributed convex optimization problems in networks. We model the communication restrictions imposed by the network as a set of affine constraints and provide optimal complexity bounds for four different setups, namely: the function $F(\xb) \triangleq \sum_{i=1}^{m}f_i(\xb)$ is strongly convex and smooth, either strongly convex or smooth or just convex. Our results show that Nesterov's accelerated gradient descent on the dual problem can be executed in a distributed manner and obtains the same optimal rates as in the centralized version of the problem (up to constant or logarithmic factors) with an additional cost related to the spectral gap of the interaction matrix. Finally, we discuss some extensions to the proposed setup such as proximal friendly functions, time-varying graphs, improvement of the condition numbers.
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