Channel charting (CC) is an unsupervised machine learning framework for learning a lower-dimensional representation of Channel State Information (CSI), while preserving spatial relations between CSI samples. In this paper, we consider super-resolution features in the angle-delay domain in massive Multiple-Input Multiple-Output (MIMO) systems. We i) treat the angle and delay separately, ii) present the so-called “Normalized Polar Feature” utilizing the channel statistics of the CSI samples, iii) use the Euclidean distance to compute the dissimilarity matrix, and create the channel chart. Simulation results based on the DeepMIMO data-set show that the proposed super-resolution representation with the Euclidean distance leads to the state-of-the-art quality CC as compared to other CSI features and distances from the literature such as angle-delay-power features with earth mover distance.

This article extends the expectation-maximization (EM) formulation for the Gaussian mixture model (GMM) with a novel weighted dissimilarity loss. This extension results in the fusion of two different clustering methods, namely, centroid-based clustering and graph clustering in the same framework in order to leverage their advantages. The fusion of centroid-based clustering and graph clustering results in a simple "soft" asynchronous hybrid clustering method. The proposed algorithm may start as a pure centroid-based clustering algorithm (e.g., k -means), and as the time evolves, it may eventually and gradually turn into a pure graph clustering algorithm [e.g., basic greedy asynchronous distributed interference avoidance (GADIA) (Babadi and Tarokh, 2010)] as the algorithm converges and vice versa. The "hard" version of the proposed hybrid algorithm includes the standard Hopfield neural networks (and, thus, Bruck's Ln algorithm by (Bruck, 1990) and the Ising model in statistical mechanics), Babadi and Tarokh's basic GADIA in 2010, and the standard k -means (Steinhaus, 1956), (MacQueen, 1967) [i.e., the Lloyd algorithm (Lloyd, 1957, 1982)] as its special cases. We call the "hard version" of the proposed clustering as "hybrid-nongreedy asynchronous clustering (H-NAC)." We apply the H-NAC to various clustering problems using well-known benchmark datasets. The computer simulations confirm the superior performance of the H-NAC compared to the k -means clustering, k -GADIA, spectral clustering, and a very recent clustering algorithm structured graph learning (SGL) by Kang et al. (2021), which represents one of the state-of-the-art clustering algorithms.

In this article, we continue our very recent work by extending it to the complex case. Having been inspired by the real Hopfield neural network (HNN) results, our investigations here yield various novel results, some of which are as follows. First, extending the "biased pseudo-cut" concept to the complex HNN (CHNN) case, we introduce a "shadow-cut" that is defined as the sum of intercluster phased edges. Second, while the discrete-time real HNN strictly minimizes the "biased pseudo-cut" in each neuron state change, the CHNN "tends" to minimize the shadow-cut (as the CHNN energy function is minimized). Third, these definitions pose a novel L-phased graph clustering (partitioning) problem in which the sum of the shadow-cuts is minimized (or maximized) for the Hermitian complex and the directed graphs whose edges are (possibly arbitrary positive/negative) complex numbers. Finally, combining the CHNN and the pioneering algorithm GADIA of Babadi and Tarokh and their modified versions, we propose simple indirect algorithms to solve the defined shadow-cuts minimization/maximization problem. The proposed algorithms naturally include the CHNN as well as the GADIA as its special cases. The computer simulations confirm the findings.

Abstract In this paper, we present a general Gaussian N-relay network by allowing relays to communicate to each other and allowing a direct channel between source and destination as compared to the standard diamond network in Nazaroğlu et al. (IEEE Trans Inf Theory 60:6329–6341, 2014) at the cost of extra channel uses. Our main focus is to examine the min-cut bound capacities of the relay network. Very recently, the results in Uykan (IEEE Trans Neural Netw Learn Syst 31:3294–3304, 2020) imply that the GADIA in Babadi and Tarokh (IEEE Trans Inf Theory 56:6228–6252, 2010), a pioneering algorithm in the interference avoidance literature, actually performs max-cut of a given power-domain (nonnegative) link gain matrix in the 2-channel case. Using the results of the diamond network in Nazaroğlu et al. (2014) and the results in Uykan (2020), in this paper, we (i) turn the mutual information maximization problem in the Gaussian N-relay network into an upper bound minimization problem, (ii) propose a modified GADIA-based algorithm to find the min-cut capacity bound and (iii) present an upper and a lower bound to its min-cut capacity bound using the modified GADIA as applied to the defined “squared channel gain matrix/graph”. Some advantages of the proposed modified GADIA-based simple algorithm are as follows: (1) The Gaussian N-relay network can determine the relay clusters in a distributed fashion and (2) the presented upper bound gives an insight into whether allowing the relays to communicate to each other pays off the extra channel uses or not as far as the min-cut capacity bound is concerned. The simulation results confirm the findings. Furthermore, the min-cut upper bound found by the proposed modified-GADIA is verified by the cut-set bounds found by the spectral clustering based solutions as well.

Hopfield neural networks (HNNs) are one of the most well-known and widely used kinds of neural networks in optimization. In this article, the author focuses on building a deeper understanding of the working principle of the HNN during an optimization process. Our investigations yield several novel results giving some important insights into the working principle of both continuous and discrete HNNs. This article shows that what the traditional HNN actually does as energy function decreases is to divide the neurons into two classes in such a way that the sum of biased class volumes is minimized (or maximized) regardless of the types of the optimization problems. Introducing neuron-specific class labels, the author concludes that the traditional discrete HNN is actually a special case of the greedy asynchronous distributed interference avoidance algorithm (GADIA) [17] of Babadi and Tarokh for the 2-class optimization problems. The computer results confirm the findings.

Device-to-device (D2D) communications underlaying cellular networks is a promising concept that has several advantages over the traditional cellular networks. In the TDD system, the frame structure defines the order of uplink and downlink transmission slots. Typically, a TDD system is synchronized, and the same transmission order (TO) is used in all cells. In a direct D2D link, we have the freedom of selecting the TO of the devices freely. To our best knowledge, no paper has explicitly examined the TO optimization problem in D2D communications underlaying cellular network so far. In this paper, we focus exactly on this problem: once the proper co-channel D2D pairs are determined in the network, how do we minimize the network interference by optimally determining the TOs in all D2D links (together with co-channel cellular links) in the network, which is an NP-complete problem. In this paper, we formulate the TO optimization problem from a graph theoretic point of view: 1) we show that the TO optimization problem is equal to a constraint balanced min-cut graph partitioning problem of our defined augmented graph; and 2) we propose and analyze a distributed and a centralized efficient asynchronous clustering algorithm for solving the TO optimization problem equivalently for the min-cut of our proposed augmented graph. Computer simulations for the TDD-based D2D underlaying cellular network show that the proposed distributed and centralized algorithms, called ABCAMiC and CABCAMiC, respectively, 1) remarkably outperform the reference case where all TOs are fixed, 2) converge within a relatively small number of steps and generally converge in only a few epochs even for a large number of cellular and D2D users, and 3) the expected performance of the (partly/fully) distributed ABCAMiC is almost equal to that of the centralized solution CABCAMiC, which generally gives near-global optimal solution to the TO optimization problem.

Mobile Converged Heterogeneous Network (MCN) is seen as a viable solution to the exponentially increasing mobile traffic demand of near-future mobile services. Recently, a new dimension for improving the system performance of TDD based wireless systems has been introduced to the 3GPP standards: Dynamic TDD, which allows cell-specific frame configurations and cell-specific control of the Transmit Order (TO). In this paper, we propose unleashing the TO options in the context of MCNs where base stations are coordinated via a central controller for effective base-station-to-base-station interference cancellation (B2B-IC), and we investigate the corresponding performance improvements. Simulation results for an MCN including macro, micro, pico, femto and small cell networks operating in the same spectrum show that the TO with B2B-IC in MCN provide remarkable performance improvements at the expense of an increase in the signal exchange among the centralized controller and the base stations.

This is the second in a two-part series of papers on transmission order (TO) optimization in the presence of channel allocation (CA), i.e., joint optimization of the TO selection and CA problem, for interfering bidirectional wireless links. Part I of this paper thoroughly analyzes the joint optimization problem from a game theoretic perspective for a general deterministic setting. Here in Part II, we present novel distributed and centralized CA-TO algorithms, together with their performance analysis, for Device-to-Device (D2D) communications underlaying cellular networks based on the findings in Part I of this paper. Here, TO is a novel dimension for optimization. In Part II, we propose and analyze novel two distributed and one centralized joint CA-TO algorithms. Our investigations show that: i) our algorithms contain many of the existing TO algorithms and CA algorithms as its special cases and can thus be considered as a general framework for the joint CA and TO optimization. The computer simulations for TDD-based D2D communications underlaying cellular network show that the proposed distributed and centralized joint CA-TO algorithms remarkably outperform the reference algorithms.

In this two-part paper, we consider a system consisting of bidirectional wireless links that interfere with each other, which has been the of focus of intensive research recently in emerging wireless systems like Device-to-Device (D2D) communications underlaying cellular networks, heterogeneous networks, and small-cell networks. The problem is allocating the time resources (transmission orders) and frequency resources (channels) among the transmitters such that the overall network interference is minimized. Here, transmission order (TO) is a novel dimension for optimization. In Part I, we analyze the TO optimization problem in the presence of channel allocation (CA), i.e., joint CA and the TO optimization problem from a game theoretic perspective, and prove that the joint optimization problem can be formulated as an exact potential game, which has at least one “pure strategy Nash Equilibrium” for any subset of the complete CA-TO action set and for any initial CA and TO conditions. We also show that the proposed joint CA and TO game is equal to the max-cut of a novel TO-dependent holistic system interference graph. In Part II, we present novel joint CA-TO algorithms and their performance analysis in D2D communications underlays.

The Hopfield neural network (HNN) has been widely used in numerous different optimization problems since the early 1980s. The convergence speed of the HNN (already in high gain) eventually plays a critical role in various real-time applications. In this brief, we propose and analyze a generalized HNN which drastically improves the convergence speed of the network, and thus allows benefiting from the HNN capabilities in solving the optimization problems in real time. By examining the channel allocation optimization problem in cellular radio systems, which is NP-complete and in which fast solution is necessary due to time-varying link gains, as well as the associative memory problem, computer simulations confirm the dramatic improvement in convergence speed at the expense of using a second nonlinear function in the proposed network.

In this paper, we present a temporal round robin (TRR) packet scheduler. In default round robin (RR) scheduler, flows are scheduled in sequence one by one without prioritizing any flows assigning the same amount of time slots. The main idea in the proposed TRR is to exploit the temporal variations of a pre-defined utility argument (e.g. SINR or MCS in the context of cellular radio systems) while assigning the same amount of time slots to each flows. It's shown that the expected value of the utility argument of the scheduled flows in TRR case is equal to or greater than that of the traditional RR. In the context of the cellular radio networks, this translates into an equal or higher network throughput as compared to the traditional RR. The proposed scheduler algorithm can be easily implemented into many various cellular networks including WiMAX. Simple simulation results confirms the effectiveness of the algorithm.

In this paper, we apply well-known variable structure systems control theory to power control problem in mobile radio systems. The aim is to make the power control operation insensitive to unknown changes in the link gains. Some of well-known distributed power control algorithms (Foschini and Miljanic algorithm, fixed step, etc) are obtained as special cases of the proposed algorithm. Simulation results suggest that the proposed algorithm is relatively fast and robust. The algorithm is also verified with an advanced dynamic system simulator

This paper presents the HSDPA system performance of an optical fiber distributed antenna system (ODAS) in an office indoor environment using an advanced dynamic system simulator. Our simulation results show that the investigated ODAS with a low remote unit output power supports high data rate communication for interactive HSDPA in indoor environments and meets QoS requirements

In this paper we present and analyze a new structure for designing a radial basis function neural network (RBFNN). In the training phase, input layer of RBFNN is augmented with desired output vector. Generalization phase involves the following steps: (1) identify the cluster to which a previously unseen input vector belongs; (2) augment the input layer with an average of the targets of the input vectors in the identified cluster; and (3) use the augmented network to estimate the unknown target. It is shown that, under some reasonable assumptions, the generalization error function admits an upper bound in terms of the quantization errors minimized when determining the centers of the proposed method over the training set and the difference between training samples and generalization samples in a deterministic setting. When the difference between the training and generalization samples goes to zero, the upper bound can be made arbitrarily small by increasing the number of hidden neurons. Computer simulations verified the effectiveness of the proposed method.

Gradient-descent type supervised learning is the most commonly used algorithm for design of the standard sigmoid perceptron (SP). However, it is computationally expensive (slow) and has the local-minima problem. Moody and Darken (1989) proposed an input-clustering based hierarchical algorithm for fast learning in networks of locally tuned neurons in the context of radial basis function networks. We propose and analyze input clustering (IC) and input-output clustering (IOC)-based algorithms for fast learning in networks of globally tuned neurons in the context of the SP. It is shown that "localizing'' the input layer weights of the SP by the IC and the IOC minimizes an upper bound to the SP output error. The proposed algorithms could possibly be used also to initialize the SP weights for the conventional gradient-descent learning. Simulation results offer that the SPs designed by the IC and the IOC yield comparable performance in comparison with its radial basis function network counterparts.

A previous paper has derived a clustering-based upper bound on mean squared output error of radial basis function networks that explicitly depends on the network parameters. In this study we focus on single-hidden-layer-sigmoid perceptron. Using the analysis of the previous paper, this paper (i) presents a similar upper bound on output error of the sigmoid perceptron and the upper bound can be made arbitrarily small by increasing the number of sigmoid units, and (ii) proposes unsupervised type learning of input-layer (synaptic) weights in contrast to traditional gradient-descent type supervised learning, i.e., the proposed method minimizes the upper bound by a clustering algorithm for determining the input-layer weights in contrast to the gradient-descent type algorithm minimizing the output error, which is traditionally used in the design of the perceptron. The simulation results show that (i) the proposed hierarchical method requires less time for learning when compared to gradient-descent-type supervised algorithm, (ii) it yields comparable performance in comparison with radial basis function network, and (iii) the upper bounds minimized during the clustering are quite tight to the output error function.

The key point in design of radial basis function networks is to specify the number and the locations of the centers. Several heuristic hybrid learning methods, which apply a clustering algorithm for locating the centers and subsequently a linear leastsquares method for the linear weights, have been previously suggested. These hybrid methods can be put into two groups, which will be called as input clustering (IC) and input-output clustering (IOC), depending on whether the output vector is also involved in the clustering process. The idea of concatenating the output vector to the input vector in the clustering process has independently been proposed by several papers in the literature although none of them presented a theoretical analysis on such procedures, but rather demonstrated their effectiveness in several applications. The main contribution of this paper is to present an approach for investigating the relationship between clustering process on input-output training samples and the mean squared output error in the context of a radial basis function netowork (RBFN). We may summarize our investigations in that matter as follows: 1) A weighted mean squared input-output quantization error, which is to be minimized by IOC, yields an upper bound to the mean squared output error. 2) This upper bound and consequently the output error can be made arbitrarily small (zero in the limit case) by decreasing the quantization error which can be accomplished through increasing the number of hidden units.