Computer Science

Recently, Chen and Sbert proposed a general divergence measure. This report presents some interim findings about the question whether the divergence measure is a metric or not. It has been postulated that (i) the measure might be a metric when (0 < k <= 1), and (ii) the k-th root of the measure might be a metric when (k > 1). The report shows that for a 2-letter alphabet, postulation (i) can be proved. The possible pathway for obtaining a proof for (i) in n-letter cases is also discussed. The authors hope that the report may stimulate more scholarly effort to study the mathematical properties of this divergence measure.

This paper tackles the problem of joint active and passive beamforming optimization for an intelligent reflective surface (IRS)-assisted multi-user downlink multiple-input multiple-output (MIMO) communication system. We aim to maximize spectral efficiency of the users by minimizing the mean square error (MSE) of the received symbol. For this, a joint optimization problem is formulated under the minimum mean square error (MMSE) criterion. First, block coordinate descent (BCD) is used to decouple the joint optimization into two sub-optimization problems to separately find the optimal active precoder at the base station (BS) and the optimal matrix of phase shifters for the IRS. While the MMSE active precoder is obtained in a closed form, the optimal phase shifters are found iteratively using a modified version (also introduced in this paper) of the vector approximate message passing (VAMP) algorithm. We solve the joint optimization problem for two different models for IRS phase shifts. First, we determine the optimal phase matrix under a unimodular constraint on the reflection coefficients, and then under the constraint when the IRS reflection coefficients are modeled by a reactive load, thereby validating the robustness of the proposed solution. Numerical results are presented to illustrate the performance of the proposed method using multiple channel configurations. The results validate the superiority of the proposed solution as it achieves higher throughput compared to state-of-the-art techniques.

This letter investigates the joint active and passive beamforming optimization for intelligent reflecting surface (IRS) aided multiuser multiple-input multiple-output systems with the objective of maximizing the weighted sum-rate. We show that this problem can be solved via a matrix weighted mean square error minimization equivalence. In particular, for the optimization of the passive IRS beamforming, we first propose an iterative algorithm with excellent performance based on the manifold optimization. By using the matrix fractional programming technique to obtain a more tractable object function, we then propose a low complexity algorithm based on the majorization-minimization method. Numerical results verify the convergence of our proposed algorithms and the significant performance improvement over the communication scenario without IRS assistance.

Intelligent reflecting surface (IRS) offers a cost effective solution to link blockage problem in mmWave communications, and the prerequisite of which is the accurate estimation of (1) the optimal beams for base station/access point (BS/AP) and mobile terminal (MT), (2) the optimal reflection patterns for IRSs, and (3) link blockage. In this paper, we carry out beam training design for IRSs assisted mmWave communications to estimate the aforementioned parameters. To acquire the optimal beams and reflection patterns, we firstly perform random beamforming and maximum likelihood estimation to estimate angle of arrival (AoA) and angle of departure (AoD) of the line of sight (LoS) path between BS/AP (or IRSs) and MT. Then, with the estimate of AoAs and AoDs, we propose an iterative positioning algorithm that achieves centimeter-level positioning accuracy. The obtained location information is not only a fringe benefit but also enables us to cross verify and enhance the estimation of AoA and AoD, and facilitates the prediction of blockage indicator. Numerical results show the superiority of our proposed beam training scheme and verify the performance gain brought by location information.

This paper considers unmanned aerial vehicle (UAV)-carried intelligent reflecting surface (IRS) for secure data collection in wireless sensor networks. An eavesdropper (Eve) lurks within the vicinity of the main receiver (Bob) while several randomly placed sensor nodes beamform collaboratively to the UAV-carried IRS that reflects the signal to the main receiver (Bob). The design objective is to maximise the achievable secrecy rate in the noisy communication channel by jointly optimizing the collaborative beamforming weights of the sensor nodes, the trajectory of the UAV and the reflection coefficients of the IRS elements. By designing the IRS reflection coefficients with and without the knowledge of the eavesdropper's channel, we develop a non-iterative sub-optimal solution for the secrecy rate maximization problem. It has been shown analytically that the UAV flight time and the randomness in the distribution of the sensor nodes, obtained by varying the sensor distribution area, can greatly affect secrecy performance. In addition, the maximum allowable number of IRS elements as well as a bound on the attainable average secrecy rate of the IRS aided noisy communication channel have also been derived. Extensive simulation results demonstrate the superior performance of the proposed algorithms compared to the existing schemes.

Reconfigurable Intelligent Surface (RIS) has becoming a useful tool in future wireless communication systems for close-distance communication network. This paper we use Reconfigurable Intelligent Surface (RIS) for downlink multi-user communication designed to improve energy collection performance while satisfying wireless information and Power Transfer (WIPT). The designed system consists of an IRS-assisted system consists of a multi-antenna assisted base station (BS) and two opposite multi-antenna assisted information receiver cooperated (RIS) as energy receiver (ERs) that meets energy collection requirements. Based on the electromagnetic property of Reconfigurable Intelligent Surface (RIS), like two mirrors that are opposite each other, setting two Reconfigurable Intelligent Surface (RIS) attached to the city buildings to reflect the sending signals. The transmitting precoding of the Multi-antenna Auxiliary Base Station (BS) and the angular phase transfer matrix of the multi-antenna Auxiliary Information Receiver (IRs) need to be optimized together to maximize the energy harvesting of IoT devices for energy efficiency (EE) of the IRs system and to provide users with the efficiency of the received signal. In order to solve the joint optimization problem effectively, we turn the non-convex maximize problem into the equivalent formal error method based on the mean square, and finally use the iterative algorithm for optimization. As for algorithm, we respectively use MSE method, semidefinite relaxation techniques to simplify transmitting beamforming matrix and the matrix phase shift. Through the observation of simulation data, it can be concluded that the performance optimization method of SDR based on RIS is effective.

Reconfigurable intelligent surface (RIS) provides a promising way to build the programmable wireless transmission environments in the future. Owing to the large number of reflecting elements used at the RIS, joint optimization for the active beamforming at the transmitter and the passive reflector at the RIS is usually complicated and time-consuming. To address this problem, this paper proposes a low-complexity joint beamforming and reflecting algorithm based on fractional programing (FP). Specifically, we first consider a RIS-aided multi-user communication system with perfect channel state information (CSI) and formulate an optimization problem to maximize the sum rate of all users. Since the problem is nonconvex, we decompose the original problem into three disjoint subproblems. By introducing favorable auxiliary variables, we derive the closed-form expressions of the beamforming vectors and reflecting matrix in each subproblem, leading to a joint beamforming and reflecting algorithm with low complexity. We then extend our approach to handle the case when transmitter-RIS and RIS-receiver channels are not perfect and develop corresponding low-complexity joint beamforming and reflecting algorithm with practical channel estimation. Simulation results have verified the effectiveness of the proposed algorithms as compared to various benchmark schemes.

The millimeter wave (mmWave) multiuser multiple-input multiple-output (MU-MIMO) systems with discrete lens arrays (DLA) have received great attention due to their simple hardware implementation and excellent performance. In this work, we investigate the joint design of beam selection and digital precoding matrices for mmWave MU-MIMO systems with DLA to maximize the sum-rate subject to the transmit power constraint and the constraints of the selection matrix structure. The investigated non-convex problem with discrete variables and coupled constraints is challenging to solve and an efficient framework of joint neural network (NN) design is proposed to tackle it. Specifically, the proposed framework consists of a deep reinforcement learning (DRL)-based NN and a deep-unfolding NN, which are employed to optimize the beam selection and digital precoding matrices, respectively. As for the DRL-based NN, we formulate the beam selection problem as a Markov decision process and a double deep Q-network algorithm is developed to solve it. The base station is considered to be an agent, where the state, action, and reward function are carefully designed. Regarding the design of the digital precoding matrix, we develop an iterative weighted minimum mean-square error algorithm induced deep-unfolding NN, which unfolds this algorithm into a layerwise structure with introduced trainable parameters. Simulation results verify that this jointly trained NN remarkably outperforms the existing iterative algorithms with reduced complexity and stronger robustness.

This paper considers a reconfigurable intelligent surface (RIS)-aided millimeter wave (mmWave) downlink communication system where hybrid analog-digital beamforming is employed at the base station (BS). We formulate a power minimization problem by jointly optimizing hybrid beamforming at the BS and the response matrix at the RIS, under signal-to-interference-plus-noise ratio (SINR) constraints. The problem is highly challenging due to the non-convex SINR constraints as well as the non-convex unit-modulus constraints for both the phase shifts at the RIS and the analog beamforming at the BS. A penalty-based algorithm in conjunction with the manifold optimization technique is proposed to handle the problem, followed by an individual optimization method with much lower complexity. Simulation results show that the proposed algorithm outperforms the state-of-art algorithm. Results also show that the joint optimization of RIS response matrix and BS hybrid beamforming is much superior to individual optimization.

Accurate channel parameter estimation is challenging for wideband millimeter-wave (mmWave) large-scale hybrid arrays, due to beam squint and much fewer radio frequency (RF) chains than antennas. This paper presents a novel joint delay and angle estimation approach for wideband mmWave fully-connected hybrid uniform cylindrical arrays. We first design a new hybrid beamformer to reduce the dimension of received signals on the horizontal plane by exploiting the convergence of the Bessel function, and to reduce the active beams in the vertical direction through preselection. The important recurrence relationship of the received signals needed for subspace-based angle and delay estimation is preserved, even with substantially fewer RF chains than antennas. Then, linear interpolation is generalized to reconstruct the received signals of the hybrid beamformer, so that the signals can be coherently combined across the whole band to suppress the beam squint. As a result, efficient subspace-based algorithm algorithms can be developed to estimate the angles and delays of multipath components. The estimated delays and angles are further matched and correctly associated with different paths in the presence of non-negligible noises, by putting forth perturbation operations. Simulations show that the proposed approach can approach the Cramér-Rao lower bound (CRLB) of the estimation with a significantly lower computational complexity than existing techniques.