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We investigate the use of conventional angle of arrival (AoA) algorithms the Bartlett’s algorithm, the Minimum Variance Distortion Response (MVDR or Capon) algorithm, and the Minimum Norm algorithm for estimating the AoA theta together with our previously introduced algorithms linear regression (LR), inverse of the root sum squares of channel coefficients (ISQ), as well as a novel use of the MUSIC algorithm for estimating the distance from the base station, rho in the context of channel charting. We carry out evaluations in terms of the visual quality of the channel charts, the dimensionality reduction performance measures trustworthiness (TW) and connectivity (CT), as well as the execution time of the algorithms. We find that although the Bartlett’s algorithm, MVDR, and Minimum Norm algorithms have sufficiently close performance to techniques we studied earlier, the Minimum Norm algorithm has significantly higher computational complexity than the other two. Previously, we found that the use of the MUSIC algorithm for estimation of both theta and rho has a very high performance. In this paper, we investigated and quantified the performance of the Bartlett algorithm in its use for estimating both and , similar to the our previously introduced technique of using MUSIC for estimating both. 

A promising type of Reconfigurable Intelligent Surface (RIS) employs tunable control of its varactors using biasing transmission lines below the RIS reflecting elements. Biasing standing waves (BSWs) are excited by a time-periodic signal and sampled at each RIS element to create a desired biasing voltage and control the reflection coefficients of the elements. A simple rectifier can be used to sample the voltages and capture the peaks of the BSWs over time. Like other types of RIS, attempting to model and accurately configure a wave-controlled RIS is extremely challenging due to factors such as device non-linearities, frequency dependence, element coupling, etc., and thus significant differences will arise between the actual and assumed performance. An alternative approach to solving this problem is data-driven: Using training data obtained by sampling the reflected radiation pattern of the RIS for a set of BSWs, a neural network (NN) is designed to create an input-output map between the BSW amplitudes and the resulting sampled radiation pattern. This is the approach discussed in this paper. In the proposed approach, the NN is optimized using a Genetic Algorithm (GA) to minimize the error between the estimated and measured radiation patterns. The BSW amplitudes are then designed via Simulated Annealing (SA) to optimize a signal-to-leakage-plus-noise ratio measure by iteratively forward-propagating the BSW amplitudes through the NN and using its output as feedback to determine convergence. The resulting optimal solutions are stored in a lookup table to be used both as settings to instantly configure the RIS and as a basis for determining more complex radiation patterns. 

The problem of optimizing discrete phases in a reconfigurable intelligent surface (RIS) to maximize the received power at a user equipment is addressed. Necessary and sufficient conditions to achieve this maximization are given. These conditions are employed in an algorithm to achieve the maximization. New versions of the algorithm are given that are proven to achieve convergence in N or fewer steps whether the direct link is completely blocked or not, where N is the number of the RIS elements, whereas previously published results achieve this in KN or 2N number of steps where K is the number of discrete phases. Thus, for a discrete-phase RIS, the techniques presented in this paper achieve the optimum received power in the smallest number of steps published in the literature. In addition, in each of those N steps, the techniques presented in this paper determine only one or a small number of phase shifts with a simple elementwise update rule, which result in a substantial reduction of computation time, as compared to the algorithms in the literature. As a secondary result, we define the uniform polar quantization (UPQ) algorithm which is an intuitive quantization algorithm that can approximate the continuous solution with an approximation ratio of sinc2(1/K) and achieve low time-complexity, given perfect knowledge of the channel. 

To maximize the received power at a user equipment, the problem of optimizing a reconfigurable intelligent surface (RIS) with a limited phase range and nonuniform discrete phase shifts with adjustable gains is addressed. Necessary and sufficient conditions to achieve this maximization are given. These conditions are employed in two algorithms to achieve the global optimum in linear time. Depending on the phase range limitation, it is shown that the global optimality is achieved in NK or fewer and N(K + 1) or fewer steps, where N is the number of RIS elements and K is the number of discrete phase shifts which may be placed nonuniformly over the limited phase range. In addition, we define two quantization algorithms that we call nonuniform polar quantization (NPQ) algorithm and extended nonuniform polar quantization (ENPQ) algorithm, where the latter is a novel quantization algorithm for RISs with a significant phase range restriction. With NPQ, we provide a closed-form solution for the approximation ratio with which an arbitrary set of nonuniform discrete phase shifts can approximate the continuous solution. We also show that with a phase range limitation, equal separation among the nonuniform discrete phase shifts maximizes the normalized performance. Furthermore, for a larger RIS phase range limitation, we show that the gain of increasing K is only marginal, whereas, ON/OFF selection for the RIS elements can bring significant performance compared to the case when the RIS elements are strictly ON. 

A Reconfigurable Intelligent Surface (RIS) consists of many small reflective elements whose reflection properties can be adjusted to change the wireless propagation environment. Envisioned implementations require that each RIS element be connected to a controller, and as the number of RIS elements on a surface may be on the order of hundreds or more, the number of required electrical connectors creates a difficult wiring problem. A potential solution to this problem was previously proposed by the authors in which “biasing transmission lines” carrying standing waves are sampled at each RIS location to produce the desired bias voltage for each RIS element. This paper presents models for the RIS elements that account for mutual coupling and realistic varactor characteristics, as well as circuit models for sampling the transmission line to generate the RIS control signals. The paper investigates two techniques for conversion of the transmission line standing wave voltage to the varactor bias voltage, namely an envelope detector and a sample-and-hold circuit. The paper also develops a modal decomposition approach for generating standing waves that are able to generate beams and nulls in the resulting RIS radiation pattern that maximize either the Signal-to-Noise Ratio (SNR) or the Signal-to-Leakage-plus-Noise Ratio (SLNR). The paper provides five algorithms, two for the case of the envelope detector, one for the sample-and-hold circuit, one for pursuing the global minimum for both circuits, and one for simultaneous beam and null steering. Extensive simulation results show that while the envelope detector is simpler to implement, the sample-and-hold circuit has substantially better performance and runs in substantially less time. In addition, the wave-controlled RIS is able to generate strong beams and deep nulls in desired directions. This is in contrast with the case of arbitrary control of each varactor element and idealized RIS models. 

We present a new way of producing a channel chart for cellular wireless communications in polar coordinates. We estimate the angle of arrival θ and the distance between the base station and the user equipment ρ using the MUSIC algorithm and inverse of the root sum squares of channel coefficients (ISQ) or linear regression (LR). We compare this method with the channel charting algorithms principal component analysis (PCA), Samson’s method (SM), and autoencoder (AE). We show that ISQ and LR outperform all three in both performance and complexity. The performance of LR and ISQ are close, with ISQ having less complexity.