Movable Antenna Enhanced DF and AF Relaying Systems: Performance Analysis and Optimization

Movable antenna (MA) has been deemed as a promising technology to flexibly reconfigure wireless channels by adjusting the antenna positions in a given local region. In this paper, we investigate the application of the MA technology in both decode-and-forward (DF) and amplify-and-forward (AF) relaying systems, where a relay is equipped with multiple MAs to assist in the data transmission between two single-antenna nodes. For the DF relaying system, our objective is to maximize the achievable rate at the destination by jointly optimizing the positions of the MAs in two stages for receiving signals from the source and transmitting signals to the destination, respectively. To drive essential insights, we first derive a closed-form upper bound on the maximum achievable rate of the DF relaying system. Then, a low-complexity algorithm based on projected gradient ascent (PGA) and alternating optimization (AO) is proposed to solve the antenna position optimization problem. For the AF relaying system, our objective is to maximize the achievable rate by jointly optimizing the two-stage MA positions as well as the AF beamforming matrix at the relay, which results in a more challenging optimization problem due to the intricate coupling variables. To tackle this challenge, we first reveal the hidden separability among the antenna position optimization in the two stages and the beamforming optimization. Based on such separability, we derive a closed-form upper bound on the maximum achievable rate of the AF relaying system and propose a low-complexity algorithm to obtain a high-quality suboptimal solution to the considered problem. Simulation results validate the efficacy of our theoretical analysis and demonstrate the superiority of the MA-enhanced relaying systems to the conventional relaying systems with fixed-position antennas (FPAs) and other benchmark schemes.

Movable Antenna Aided NOMA: Joint Antenna Positioning, Precoding, and Decoding Design

This paper investigates movable antenna (MA) aided non-orthogonal multiple access (NOMA) for multi-user downlink communication, where the base station (BS) is equipped with a fixed-position antenna (FPA) array to serve multiple MA-enabled users. An optimization problem is formulated to maximize the minimum achievable rate among all the users by jointly optimizing the MA positioning of each user, the precoding matrix at the BS, and the successive interference cancellation (SIC) decoding indicator matrix at the users, subject to a set of constraints including the limited movement area of the MAs, the maximum transmit power of the BS, and the SIC decoding condition. To solve this non-convex problem, we propose a two-loop iterative optimization algorithm that combines the hippopotamus optimization (HO) method with the alternating optimization (AO) method to obtain a suboptimal solution efficiently. Specifically, in the inner loop, the complex-valued precoding matrix and the binary decoding indicator matrix are optimized alternatively by the successive convex approximation (SCA) technique with customized greedy search to maximize the minimum achievable rate for the given positions of the MAs. In the outer loop, each user's antenna position is updated using the HO algorithm, following a novel nature-inspired intelligent optimization framework. Simulation results show that the proposed algorithms can effectively avoid local optimum for highly coupled variables and significantly improve the rate performance of the NOMA system compared to the conventional FPA system as well as other benchmark schemes.

UAV-Enabled Passive 6D Movable Antennas: Joint Deployment and Beamforming Optimization

Intelligent reflecting surface (IRS) is composed of numerous passive reflecting elements and can be mounted on unmanned aerial vehicles (UAVs) to achieve six-dimensional (6D) movement by adjusting the UAV's three-dimensional (3D) location and 3D orientation simultaneously. Hence, in this paper, we investigate a new UAV-enabled passive 6D movable antenna (6DMA) architecture by mounting an IRS on a UAV and address the associated joint deployment and beamforming optimization problem. In particular, we consider a passive 6DMA-aided multicast system with a multi-antenna base station (BS) and multiple remote users, aiming to jointly optimize the IRS's location and 3D orientation, as well as its passive beamforming to maximize the minimum received signal-to-noise ratio (SNR) among all users under the practical angle-dependent signal reflection model. However, this optimization problem is challenging to be optimally solved due to the intricate relationship between the users' SNRs and the IRS's location and orientation. To tackle this challenge, we first focus on a simplified case with a single user, showing that one-dimensional (1D) orientation suffices to achieve the optimal performance. Next, we show that for any given IRS's location, the optimal 1D orientation can be derived in closed form, based on which several useful insights are drawn. To solve the max-min SNR problem in the general multi-user case, we propose an alternating optimization (AO) algorithm by alternately optimizing the IRS's beamforming and location/orientation via successive convex approximation (SCA) and hybrid coarse- and fine-grained search, respectively. To avoid undesirable local sub-optimal solutions, a Gibbs sampling (GS) method is proposed to generate new IRS locations and orientations for exploration in each AO iteration. Numerical results validate our theoretical analyses.

Integrated Location Sensing and Communication for Ultra-Massive MIMO With Hybrid-Field Beam-Squint Effect

The advent of ultra-massive multiple-input-multiple output systems holds great promise for next-generation communications, yet their channels exhibit hybrid far- and near- field beam-squint (HFBS) effect. In this paper, we not only overcome but also harness the HFBS effect to propose an integrated location sensing and communication (ILSC) framework. During the uplink training stage, user terminals (UTs) transmit reference signals for simultaneous channel estimation and location sensing. This stage leverages an elaborately designed hybrid-field projection matrix to overcome the HFBS effect and estimate the channel in compressive manner. Subsequently, the scatterers' locations can be sensed from the spherical wavefront based on the channel estimation results. By treating the sensed scatterers as virtual anchors, we employ a weighted least-squares approach to derive UT' s location. Moreover, we propose an iterative refinement mechanism, which utilizes the accurately estimated time difference of arrival of multipath components to enhance location sensing precision. In the following downlink data transmission stage, we leverage the acquired location information to further optimize the hybrid beamformer, which combines the beam broadening and focusing to mitigate the spectral efficiency degradation resulted from the HFBS effect. Extensive simulation experiments demonstrate that the proposed ILSC scheme has superior location sensing and communication performance than conventional methods.

Codebook Design and Performance Analysis for Wideband Beamforming in Terahertz Communications

The codebook-based analog beamforming is appealing for future terahertz (THz) communications since it can generate high-gain directional beams with low-cost phase shifters via low-complexity beam training. However, conventional beamforming codebook design based on array response vectors for narrowband communications may suffer from severe performance loss in wideband systems due to the ``beam squint" effect over frequency. To tackle this issue, we propose in this paper a new codebook design method for analog beamforming in wideband THz systems. In particular, to characterize the analog beamforming performance in wideband systems, we propose a new metric termed wideband beam gain, which is given by the minimum beamforming gain over the entire frequency band given a target angle. Based on this metric, a wideband analog beamforming codebook design problem is formulated for optimally balancing the beamforming gains in both the spatial and frequency domains, and the performance loss of conventional narrowband beamforming in wideband systems is analyzed. To solve the new wideband beamforming codebook design problem, we divide the spatial domain into orthogonal angular zones each associated with one beam, thereby decoupling the codebook design into a zone division sub-problem and a set of beamforming optimization sub-problems each for one zone. For the zone division sub-problem, we propose a bisection method to obtain the optimal boundaries for separating adjacent zones. While for each of the per-zone-based beamforming optimization sub-problems, we further propose an efficient augmented Lagrange method (ALM) to solve it. Numerical results demonstrate the performance superiority of our proposed codebook design for wideband analog beamforming to the narrowband beamforming codebook and also validate our performance analysis.

Channel Estimation for Movable Antenna Aided Wideband Communication Systems

Movable antenna (MA) is an emerging technology that can significantly improve communication performance via the continuous adjustment of the antenna positions. To unleash the potential of MAs in wideband communication systems, acquiring accurate channel state information (CSI), i.e., the channel frequency responses (CFRs) between any position pair within the transmit (Tx) region and the receive (Rx) region across all subcarriers, is a crucial issue. In this paper, we study the channel estimation problem for wideband MA systems. To start with, we express the CFRs as a combination of the field-response vectors (FRVs), delay-response vector (DRV), and path-response tensor (PRT), which exhibit sparse characteristics and can be recovered by using a limited number of channel measurements at selected position pairs of Tx and Rx MAs over a few subcarriers. Specifically, we first formulate the recovery of the FRVs and DRV as a problem with multiple measurement vectors in compressed sensing (MMV-CS), which can be solved via a simultaneous orthogonal matching pursuit (SOMP) algorithm. Next, we estimate the PRT using the least-square (LS) method. Moreover, we also devise an alternating refinement approach to further improve the accuracy of the estimated FRVs, DRV, and PRT. This is achieved by minimizing the discrepancy between the received pilots and those constructed by the estimated CSI, which can be efficiently carried out by using the gradient descent algorithm. Finally, simulation results demonstrate that both the SOMP-based channel estimation method and alternating refinement method can reconstruct the complete wideband CSI with high accuracy, where the alternating refinement method performs better despite a higher complexity.

Over-the-Air Computation via 2D Movable Antenna Array

Movable antenna (MA) has emerged as a promising technology for improving the performance of wireless communication systems, which enables local movement of the antennas to create more favorable channel conditions. In this letter, we advance its application for over-the-air computation (AirComp) network, where an access point is equipped with a two-dimensional (2D) MA array to aggregate wireless data from massive users. We aim to minimize the computation mean square error (CMSE) by jointly optimizing the antenna position vector (APV), the receive combining vector at the access point and the transmit coefficients from all users. To tackle this highly non-convex problem, we propose a two-loop iterative algorithm, where the particle swarm optimization (PSO) approach is leveraged to obtain a suboptimal APV in the outer loop while the receive combining vector and transmit coefficients are alternately optimized in the inner loop. Numerical results demonstrate that the proposed MA-enhanced AirComp network outperforms the conventional network with fixed-position antennas (FPAs).

Movable Antennas Meet Intelligent Reflecting Surface: When Do We Need Movable Antennas?

Intelligent reflecting surface (IRS) and movable antenna (MA)/fluid antenna (FA) techniques have both received increasing attention in the realm of wireless communications due to their ability to reconfigure and improve wireless channel conditions. In this paper, we investigate the integration of MAs/FAs into an IRS-assisted wireless communication system. In particular, we consider the downlink transmission from a multi-MA base station (BS) to a single-antenna user with the aid of an IRS, aiming to maximize the user's received signal-to-noise ratio (SNR), by jointly optimizing the BS/IRS active/passive beamforming and the MAs' positions. Due to the similar capability of MAs and IRS for channel reconfiguration, we first conduct theoretical analyses of the performance gain of MAs over conventional fixed-position antennas (FPAs) under the line-of-sight (LoS) BS-IRS channel and derive the conditions under which the performance gain becomes more or less significant. Next, to solve the received SNR maximization problem, we propose an alternating optimization (AO) algorithm that decomposes it into two subproblems and solve them alternately. Numerical results are provided to validate our analytical results and evaluate the performance gains of MAs over FPAs under different setups.

Movable Antenna Enhanced AF Relaying: Two-Stage Antenna Position Optimization

The movable antenna (MA) technology has attracted increasing attention in wireless communications due to its capability for flexibly adjusting the positions of multiple antennas in a local region to reconfigure channel conditions. In this paper, we investigate its application in an amplify-and-forward (AF) relay system, where a multi-MA AF relay is deployed to assist in the wireless communications from a source to a destination. In particular, we aim to maximize the achievable rate at the destination, by jointly optimizing the AF weight matrix at the relay and its MAs' positions in two stages for receiving the signal from the source and transmitting its amplified version to the destination, respectively. However, compared to the existing one-stage antenna position optimization, the two-stage position optimization is more challenging due to its intricate coupling in the achievable rate at the destination. To tackle this challenge, we decompose the considered problem into several subproblems by invoking the alternating optimization (AO) and solve them by using the semidefinite programming and the gradient ascent. Numerical results demonstrate the superiority of our proposed system over the conventional relaying system with fixed-position antennas (FPAs) and also drive essential insights.

CSI-Free Position Optimization for Movable Antenna Communication Systems: A Black-Box Optimization Approach

Movable antenna (MA) is a new technology which leverages local movement of antennas to improve channel qualities and enhance the communication performance. Nevertheless, to fully realize the potential of MA systems, complete channel state information (CSI) between the transmitter-MA and the receiver-MA is required, which involves estimating a large number of channel parameters and incurs an excessive amount of training overhead. To address this challenge, in this paper, we propose a CSI-free MA position optimization method. The basic idea is to treat position optimization as a black-box optimization problem and calculate the gradient of the unknown objective function using zeroth-order (ZO) gradient approximation techniques. Simulation results show that the proposed ZO-based method, through adaptively adjusting the position of the MA, can achieve a favorable signal-to-noise-ratio (SNR) using a smaller number of position measurements than the CSI-based approach. Such a merit makes the proposed algorithm more adaptable to fast-changing propagation channels.