We present an analytical framework for the channel estimation and the data detection in massive multiple-input multiple-output uplink systems with 1-bit analog-to-digital converters (ADCs) and i.i.d. Rayleigh fading. First, we provide closed-form expressions of the mean squared error (MSE) of the channel estimation considering the state-of-the-art linear minimum MSE estimator and the class of scaled least-squares estimators. For the data detection, we provide closed-form expressions of the expected value and the variance of the estimated symbols when maximum ratio combining is adopted, which can be exploited to efficiently implement minimum distance detection and, potentially, to design the set of transmit symbols. Our analytical findings explicitly depend on key system parameters such as the signal-to-noise ratio (SNR), the number of user equipments, and the pilot length, thus enabling a precise characterization of the performance of the channel estimation and the data detection with 1-bit ADCs. The proposed analysis highlights a fundamental SNR trade-off, according to which operating at the right noise level significantly enhances the system performance.
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This paper compares the sum rates and rate regions achieved by power-domain NOMA (non-orthogonal multiple access) and standard massive MIMO (multiple-input multiple-output) techniques. We prove analytically that massive MIMO always outperforms NOMA in i.i.d.~Rayleigh fading channels, if a sufficient number of antennas are used at the base stations. The simulation results show that the crossing point occurs already when having 20-30 antennas, which is far less than what is considered for the next generation cellular networks.
We study joint unicast and multigroup multicast transmission in single-cell massive multiple-input-multiple-output (MIMO) systems, under maximum ratio transmission. For the unicast transmission, the objective is to maximize the weighted sum spectral efficiency (SE) of the unicast user terminals (UTs) and for the multicast transmission the objective is to maximize the minimum SE of the multicast UTs. These two problems are coupled to each other in a conflicting manner, due to their shared power resource and interference. To address this, we formulate a multiobjective optimization problem (MOOP). We derive the Pareto boundary of the MOOP analytically and determine the values of the system parameters to achieve any desired Pareto optimal point. Moreover, we prove that the Pareto region is convex, hence the system should serve the unicast and multicast UTs at the same time-frequency resource.
Achieving high channel estimation accuracy and reducing hardware cost as well as power dissipation constitute substantial challenges in the design of massive multiple-input multiple-output (MIMO) systems. To resolve these difficulties, sophisticated pilot designs have been conceived for the family of energy-efficient hybrid analog-digital (HAD) beamforming architecture relying on adaptive-resolution analog-to-digital converters (RADCs). In this paper, we jointly optimize the pilot sequences, the number of RADC quantization bits and the hybrid receiver combiner in the uplink of multiuser massive MIMO systems. We solve the associated mean square error (MSE) minimization problem of channel estimation in the context of correlated Rayleigh fading channels subject to practical constraints. The associated mixed-integer problem is quite challenging due to the nonconvex nature of the objective function and of the constraints. By relying on advanced fractional programming (FP) techniques, we first recast the original problem into a more tractable yet equivalent form, which allows the decoupling of the fractional objective function. We then conceive a pair of novel algorithms for solving the resultant problems for codebook-based and codebook-free pilot schemes, respectively. To reduce the design complexity, we also propose a simplified algorithm for the codebook-based pilot scheme. Our simulation results confirm the superiority of the proposed algorithms over the relevant state-of-the-art benchmark schemes.
In this paper, we derive asymptotic expressions for the ergodic capacity of the keyhole multiple-input multiple-output (MIMO) channel at low SNR in independent and identically distributed (IID) Nakagami-$m$ fading conditions with perfect channel state information available at both the transmitter (CSI-T) and the receiver (CSI-R). We show that the low-SNR capacity of this keyhole channel scales proportionally as $\frac{\textrm{SNR}}{4} \log^2 \left(1/{\textrm{SNR}}\right)$. With this asymptotic low-SNR capacity formula, we find a very surprising result that the capacity of the MIMO fading channel at low-SNR increases in the presence of keyhole degenerate condition, which is in direct contrast of the degrading capacity behaviour under keyhole effect exhibited in the high-SNR regime. Finally, we show that a simple one-bit CSI-T based On-Off power scheme achieves this low-SNR capacity; surprisingly, it is robust against both moderate and severe fading conditions for a wide range of low SNR values. These results also extend to the Rayleigh keyhole MIMO channel as a special case.
Given many popular functional forms for the Lorenz curve do not have a closed-form expression for the Gini index and no study has utilized the observed Gini index to estimate parameter(s) associated with the corresponding parametric functional form, a simple method for estimating the Lorenz curve is introduced. It utilizes 3 indicators, namely, the Gini index and the income shares of the bottom and the top in order to calculate the values of parameters associated with the specified functional form which has a closed-form expression for the Gini index. No error minimization technique is required in order to estimate the Lorenz curve. The data on the Gini index and the income shares of 4 countries that have different level of income inequality, economic, sociological, and regional backgrounds from the United Nations University-World Income Inequality Database are used to illustrate how the simple method works. The overall results indicate that the estimated Lorenz curves fit the actual observations practically well. This simple method could be useful in the situation where the availability of data on income distribution is low. However, if more data on income distribution are available, this study shows that the specified functional form could be used to directly estimate the Lorenz curve. Moreover, the estimated values of the Gini index calculated based on the specified functional form are virtually identical to their actual observations.
Reconfigurable intelligent surface (RIS) is very promising for wireless networks to achieve high energy efficiency, extended coverage, improved capacity, massive connectivity, etc. To unleash the full potentials of RIS-aided communications, acquiring accurate channel state information is crucial, which however is very challenging. For RIS-aided multiple-input and multiple-output (MIMO) communications, the existing channel estimation methods have computational complexity growing rapidly with the number of RIS units $N$ (e.g., in the order of $N^2$ or $N^3$) and/or have special requirements on the matrices involved (e.g., the matrices need to be sparse for algorithm convergence to achieve satisfactory performance), which hinder their applications. In this work, instead of using the conventional signal model in the literature, we derive a new signal model obtained through proper vectorization and reduction operations. Then, leveraging the unitary approximate message passing (UAMP), we develop a more efficient channel estimator that has complexity linear with $N$ and does not have special requirements on the relevant matrices, thanks to the robustness of UAMP. These facilitate the applications of the proposed algorithm to a general RIS-aided MIMO system with a larger $N$. Moreover, extensive numerical results show that the proposed estimator delivers much better performance and/or requires significantly less number of training symbols, thereby leading to notable reductions in both training overhead and latency.
Efficient channel estimation is challenging in full-dimensional multiple-input multiple-output communication systems, particularly in those with hybrid digital-analog architectures. Under a compressive sensing framework, this letter first designs a uniform dictionary based on a spherical Fibonacci grid to represent channels in a sparse domain, yielding smaller angular errors in three-dimensional beamspace than traditional dictionaries. Then, a Bayesian inference-aided greedy pursuit algorithm is developed to estimate channels in the frequency domain. Finally, simulation results demonstrate that both the designed dictionary and the proposed Bayesian channel estimation outperform the benchmark schemes and attain a lower normalized mean squared error of channel estimation.
We study the asymptotic normality of two estimators of the integrated volatility of volatility based on the Fourier methodology, which does not require the pre-estimation of the spot volatility. We show that the bias-corrected estimator reaches the optimal rate 1/4, while the estimator without bias-correction has a slower convergence rate and a smaller asymptotic variance. Additionally, we provide simulation results that support the theoretical asymptotic distribution of the rate-efficient estimator and show the accuracy of the Fourier estimator in comparison with a rate-optimal estimator based on the pre-estimation of the spot volatility. Finally, we reconstruct the daily volatility of volatility of the S&P500 and EUROSTOXX50 indices over long samples via the rate-optimal Fourier estimator and provide novel insight into the existence of stylized facts about its dynamics.
It was recently shown that under smoothness conditions, the squared Wasserstein distance between two distributions could be efficiently computed with appealing statistical error upper bounds. However, rather than the distance itself, the object of interest for applications such as generative modeling is the underlying optimal transport map. Hence, computational and statistical guarantees need to be obtained for the estimated maps themselves. In this paper, we propose the first tractable algorithm for which the statistical $L^2$ error on the maps nearly matches the existing minimax lower-bounds for smooth map estimation. Our method is based on solving the semi-dual formulation of optimal transport with an infinite-dimensional sum-of-squares reformulation, and leads to an algorithm which has dimension-free polynomial rates in the number of samples, with potentially exponentially dimension-dependent constants.
We introduce an algorithmic method for population anomaly detection based on gaussianization through an adversarial autoencoder. This method is applicable to detection of `soft' anomalies in arbitrarily distributed highly-dimensional data. A soft, or population, anomaly is characterized by a shift in the distribution of the data set, where certain elements appear with higher probability than anticipated. Such anomalies must be detected by considering a sufficiently large sample set rather than a single sample. Applications include, but not limited to, payment fraud trends, data exfiltration, disease clusters and epidemics, and social unrests. We evaluate the method on several domains and obtain both quantitative results and qualitative insights.
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