Multi-antenna Base Station Research Articles

IRS-Based MEC for Delay-Constrained QoS Over RF-Powered 6G Mobile Wireless Networks

Mobile-edge computing (MEC) and intelligent reflecting surface (IRS) have been recognized as two key technologies for 6G mobile networks. Consequently, we propose the IRS-based MEC schemes for the delay-constrained quality-of-service (QoS) provisioning over radio frequency (RF) powered 6G mobile networks with <italic xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">non-linear</i> energy harvesting (EH) model. Using the IRS technique, multiple mobile users (MUs) first harvest energy from a multi-antenna base station (BS) equipped with an MEC server and then transmit their data to the BS for data-processing. We first formulate a delay minimization problem for MUs under their QoS requirements, by jointly optimizing the IRS's phase-shift matrices, the MEC server's finite computation resource allocation, the MIMO based BS's multi-MU detection (MUD) coefficients, and the energy/data transmission time and task allocation coefficient of each MU. We define the total delay of each MU as the sum of its EH time, data-transmission time, and data-processing time. Since our formulated joint-optimization problem is non-convex with multiple coupled variables, we apply the <italic xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">block coordinate descending</i> (BCD) method to decompose it into several subproblems which then can be iteratively solved by a low complexity algorithm. Moreover, we also extend our proposed scheme to IRS-based MEC over Terahertz (THz) wideband mobile networks. Finally, we validate and evaluate our developed delay minimization schemes through numerical analyses, which show that the total delay of the RF-powered MUs can be significantly reduced by using our proposed schemes.

Joint Receive and Passive Beamforming Optimization for RIS-Assisted Uplink RSMA Systems

In this letter, we investigate the joint optimization of transmit power allocation and receive/passive beamforming in a reconfigurable intelligent surface (RIS)-assisted uplink two-user rate-splitting multiple access (RSMA) system. Aiming at maximizing the achievable rate of one user subject to another user’s quality of service (QoS) requirements, RIS is deployed to assist the uplink transmissions from both users to a multi-antenna base station (BS). We decouple the non-convex rate maximization problem into three sub-problems and propose an alternating optimization (AO) algorithm to optimize the receive/passive beamforming and transmit power allocation. A closed-form expression is derived for the sub-problem of transmit power allocation by using the optimal decoding order and the concave-convex fractional programming beamforming problems are converted to convex ones by using the Charnes-Cooper transform. Then, a penalty term approach is applied to effectively solve the rank-1 constrained beamforming subproblems. Simulation results verify that the proposed AO algorithm attains a higher achievable rate than the existing benchmark schemes.

Hybrid Relay and Reconfigurable Intelligent Surface Assisted Multiuser MISO Systems

Reconfigurable intelligent surfaces (RISs) are viewed as key enablers for next-generation wireless communications. This paper investigates a multiuser downlink multiple-input single-output (MISO) system in which a multiantenna base station (BS) transmits information to multiple single-antenna users with the aid of both a half-duplex decode-and-forward (DF) relay and a full-duplex RIS. Active beamforming at the BS and the DF relay, as well as passive beamforming at the RIS, are jointly designed for system sum-rate maximization. The design problem is challenging to solve due to coupled beamforming variables. An alternating optimization (AO) based algorithm is proposed to tackle this complex co-design problem. Numerical results demonstrate the superior performance of the proposed hybrid relay–RIS system with a judicious joint beamforming design. Convergence and complexity analysis shows that the convergence rate of the proposed algorithm is dominated by the numbers of users and RIS elements, and the proposed scheme can converge in a few iterations even in the configuration of large numbers of users and RIS elements. Interesting tradeoffs posed in the joint design are discussed. An extension of the proposed design method to a related energy efficiency (EE) optimization problem is also outlined and implemented.

Outage and Throughput Analysis of UAV-Assisted NOMA Relay Systems With Indoor and Outdoor Users

Non-orthogonal multiple access (NOMA) and unmanned aerial vehicle (UAV) are two promising technologies for the fifth generation (5G) and beyond networks. On the other hand, the transition environment from outdoor to indoor is an important problem in practical wireless communication. In this paper, we mathematically study a multi-antenna UAV-assisted communication system where a multi-antenna base station (BS) communicates with indoor and outdoor users through a multiantenna UAV using the power-domain NOMA technique. The metric used to evaluate the system performance are outage probability (OP) and throughput of indoor and outdoor users under different communication urban environments. Moreover, the impacts of the UAV's altitude and location and the light-of-sight (LoS) probability on system performance are also considered. We give the exact and asymptotic closed-form OP expressions and then optimize the transmission rate to maximize the throughput of each user and the overall system throughput. Numerical results show that better system performance can be achieved by controlling the altitudes and location of the UAV, selecting an appropriate transmission rate, or equipping BS and UAV with more antennas. Monte-Carlo simulation results are provided to demonstrate the performance of the investigated system and the accuracy of the developed analytical results.

Leveraging RIS-Enabled Smart Signal Propagation for Solving Infeasible Localization Problems: Scenarios, Key Research Directions, and Open Challenges

Reconfigurable intelligent surfaces (RISs) have tremendous potential for both communication and localization. While communication benefits are now well understood, the breakthrough nature of the technology may well lie in its capability to provide and support localization capabilities. We present an overview of RIS-enabled localization scenarios, considering various numbers of RISs, single- or multi-antenna base stations, narrowband or wideband transmissions, and near- and far-field operations. Based on this overview, we also highlight key research directions and open challenges specific to RIS-enabled localization and sensing.

Optimal Energy Signal Design for Multiuser MISO WPCNs With Non-Linear Energy Harvesting Circuits

The optimal energy signal design for wireless powered communication networks (WPCNs) enabling energy-sustainable communication for a large number of low-power devices is still an open problem in practical systems. In this work, we study a multi-user WPCN, where a multi-antenna base station (BS) sends an energy signal to multiple single-antenna users, which, in turn, harvest energy from the received signal and utilize it for information transmission in the uplink. In contrast to the existing works on multiple-input single-output (MISO) WPCN design, in this paper, we jointly optimize the energy signal waveform and downlink beamforming at the BS for energy harvesting (EH) devices described by non-linear circuit-based models. To this end, we assume that the BS broadcasts a pulse-modulated signal employing multiple energy signal vectors and we formulate an optimization problem for the joint design of the downlink transmit energy signal vectors, their number, the durations of the transmit pulses, and the time allocation policy for minimization of the average transmit power at the BS. We show that for single-user WPCNs, a single energy signal vector, which is collinear with the maximum ratio transmission (MRT) vector and drives the EH circuit at the user device into saturation, is optimal. Next, for the general multi-user case, we show that the optimal signal design requires a maximum number of energy signal vectors that exceeds the number of users by one and propose an algorithm to obtain the optimal energy signal vectors. Since the complexity of the optimal design is high, we also propose two suboptimal schemes for WPCN design. First, for asymptotic massive WPCNs, where the ratio of the number of users to the number of BS antennas, i.e., the system load, tends to zero, we show that the optimal downlink transmit signal can be obtained in closed-form and comprises a sequence of weighted sums of MRT vectors. Next, based on this result, for general WPCNs with finite system loads, we propose a suboptimal closed-form MRT-based design and a suboptimal semidefinite relaxation (SDR)-based scheme. Our simulation results reveal that the proposed optimal scheme and suboptimal SDR-based design achieve nearly identical performance and outperform two baseline schemes, which are based on linear and sigmoidal EH models. Furthermore, we show that, if the system load of the WPCN is low, the performance gap between the proposed suboptimal solutions is small and becomes negligible as the number of BS antennas tends to infinity.

Joint Data Transmission and Energy Harvesting for MISO Downlink Transmission Coordination in Wireless IoT Networks.

The advent of simultaneous wireless information and power (SWIPT) has been regarded as a promising technique to provide power supplies for an energy sustainable Internet of Things (IoT), which is of paramount importance due to the proliferation of high data communication demands of low-power network devices. In such networks, a multi-antenna base station (BS) in each cell can be utilized to concurrently transmit messages and energies to its intended IoT user equipment (IoT-UE) with a single antenna under a common broadcast frequency band, resulting in a multi-cell multi-input single-output (MISO) interference channel (IC). In this work, we aim to find the trade-off between the spectrum efficiency (SE) and energy harvesting (EH) in SWIPT-enabled networks with MISO ICs. For this, we derive a multi-objective optimization (MOO) formulation to obtain the optimal beamforming pattern (BP) and power splitting ratio (PR), and we propose a fractional programming (FP) model to find the solution. To tackle the nonconvexity of FP, an evolutionary algorithm (EA)-aided quadratic transform technique is proposed, which recasts the nonconvex problem as a sequence of convex problems to be solved iteratively. To further reduce the communication overhead and computational complexity, a distributed multi-agent learning-based approach is proposed that requires only partial observations of the channel state information (CSI). In this approach, each BS is equipped with a double deep Q network (DDQN) to determine the BP and PR for its UE with lower computational complexity based on the observations through a limited information exchange process. Finally, with the simulation experiments, we verify the trade-off between SE and EH, and we demonstrate that, apart from the FP algorithm introduced to provide superior solutions, the proposed DDQN algorithm also shows its performance gain in terms of utility to be up to 1.23-, 1.87-, and 3.45-times larger than the Advantage Actor Critic (A2C), greedy, and random algorithms, respectively, in comparison in the simulated environment.

Joint Location and Beamforming Design for STAR-RIS Assisted NOMA Systems

Simultaneously transmitting and reflecting reconfigurable intelligent surface (STAR-RIS) assisted non-orthogonal multiple access (NOMA) communication systems are investigated in its vicinity, where a STAR-RIS is deployed within a predefined region for establishing communication links for users. Both beamformer-based NOMA and cluster-based NOMA schemes are employed at the multi-antenna base station (BS). For each scheme, the STAR-RIS deployment location, the passive transmitting and reflecting beamforming (BF) of the STAR-RIS, and the active BF at the BS are jointly optimized for maximizing the weighted sum-rate (WSR) of users. To solve the resultant non-convex problems, an alternating optimization (AO) algorithm is proposed, where successive convex approximation (SCA) and semi-definite programming (SDP) methods are invoked for iteratively addressing the non-convexity of each sub-problem. Numerical results reveal that 1) the WSR performance can be significantly enhanced by optimizing the specific deployment location of the STAR-RIS; 2) both beamformer-based and cluster-based NOMA prefer asymmetric STAR-RIS deployment.

An Optimization Framework for General Rate Splitting for General Multicast

Immersive video, such as virtual reality (VR) and multi-view videos, is growing in popularity. Its wireless streaming is an instance of general multicast, extending conventional unicast and multicast, whose effective design is still open. This paper investigates general rate splitting for general multicast. Specifically, we consider a multi-carrier single-cell wireless network where a multi-antenna base station (BS) communicates to multiple single-antenna users via general multicast. We consider linear beamforming at the BS and joint decoding at each user in the slow fading and fast fading scenarios. In the slow fading scenario, we consider the maximization of the weighted sum average rate, which is a challenging nonconvex stochastic problem with numerous variables. To reduce computational complexity, we decouple the original nonconvex stochastic problem into multiple nonconvex deterministic problems, one for each system channel state. Then, we propose an iterative algorithm for each deterministic problem to obtain a Karush-Kuhn-Tucker (KKT) point using the concave-convex procedure (CCCP). In the fast fading scenario, we consider the maximization of the weighted sum ergodic rate. This problem is more challenging than the one for the slow fading scenario, as it is not separable. First, we propose a stochastic iterative algorithm to obtain a KKT point using stochastic successive convex approximation (SSCA) and the exact penalty method. Then, we propose two low-complexity iterative algorithms to obtain feasible points with promising performance for two cases of channel distributions using approximation and CCCP. The proposed optimization framework generalizes the existing ones for rate splitting for various types of services. Finally, we numerically show substantial gains of the proposed solutions over existing schemes in both scenarios and reveal the design insights of general rate splitting for general multicast.

Cooperative Beamforming for Antieavesdropping Communications Systems

This article introduces an antieavesdropping method named cooperative beamforming that simultaneously exploits the benefits of multiple-input multiple-output and coordinated multiple-point communications. Specifically, to enhance the security of the user terminal (UT), we propose to employ multiple multiantenna base stations to cooperatively form beams that intersect at a small area, where messages can only be well received. In particular, the original message intended for the UT is divided into submessages, each of which will be transmitted by different base stations. A counterintuitive phenomenon is discovered that the crossing point of beams is not the achievable rate highest point from the perspective of antieavesdropping communications. Correspondingly, an optimization problem is formulated to find beam azimuths and select proper serving base stations for maximizing the achievable rate under the security constraint. A Nelder–Mead-based algorithm is developed to optimize beam azimuths for maximizing the achievable rate of the UT for a given group of selected serving base stations. To address the mixed-integer nonlinear programming problem in selecting serving base stations, we further develop a low-complexity algorithm. Simulation results show that the performance of the proposed algorithm is near to the exhaustive search, which validates the effectiveness of the proposed antieavesdropping method.

Physical-Layer Security with Irregular Reconfigurable Intelligent Surfaces for 6G Networks.

The goal of 6G is to make far-reaching changes in communication systems with stricter demands, such as high throughput, extremely low latency, stronger security, and ubiquitous connectivity. Several promising techniques, such as reconfigurable intelligent surfaces (RISs), have been introduced to achieve these goals. An RIS is a 2D low-cost array of reflecting elements that can adjust the electromagnetic properties of an incident signal. In this paper, we guarantee secrecy by using an irregular RIS (IRIS). The main idea of an IRIS is to irregularly activate reflecting elements for a given number of RIS elements. In this work, we consider a communication scenario in which, with the aid of an IRIS, a multi-antenna base station establishes a secure link with a legitimate single-antenna user in the presence of a single-antenna eavesdropper. To this end, we formulate a topology-and-precoding optimization problem to maximize the secrecy rate. We then propose a Tabu search-based algorithm to jointly optimize the RIS topology and the precoding design. Finally, we present simulation results to validate the proposed algorithm, which highlights the performance gain of the IRIS in improving secure transmissions compared to an RIS. Our results show that exploiting an IRIS can allow additional spatial diversity to be achieved, resulting in secrecy performance improvement and overcoming the limitations of conventional RIS-assisted systems (e.g., a large number of active elements).

Energy Efficiency Optimization in Adaptive Transmit Antenna Selection Systems With Limited Feedback

We investigate the energy efficiency (EE) of cellular downlink transmissions with limited feedback, where the channel state information (CSI) assumed to be available at the destination is quantized and fed back to the multiantenna base station for transmitting precoding purposes. Typically, the employment of antennas with poor channel quality marginally enhances system performance but substantially consumes energy resources such as circuit power. Thus, we propose an adaptive transmit antenna selection (ATAS) scheme via setting a channel gain threshold to select transmit antennas with relatively good channel condition for reducing power resource consumption. Meanwhile, the conventional single transmit antenna (STAS) scheme is considered as a baseline. In order to improve EE while considering the impact of feedback overhead, we conduct the effective EE analysis for both ATAS and STAS schemes and show that a maximal effective EE of the proposed ATAS scheme can be achieved by jointly adjusting the channel gain threshold and transmit power. As a consequence, we propose the ergodic effective EE optimization of ATAS (eEEEO-ATAS) scheme to maximize the effective EE. Numerical simulation results demonstrate that the proposed ATAS scheme performs better than the STAS scheme in terms of effective EE.

Leveraging Secondary Reflections and Mitigating Interference in Multi-IRS/RIS Aided Wireless Networks

Reconfigurable surfaces (RS) have recently emerged as an enabler for smart radio environments where they are used to actively tailor/control the radio propagation (e.g., to support users under adverse channel conditions). If multiple RSs are deployed (e.g., coated on various buildings) to support different groups of users, it is critical to jointly optimize the phase-shifts of all the RSs to mitigate interference amongst them as well as to leverage the secondary reflections amongst them. Motivated by these considerations, this paper considers the uplink transmissions of multiple users that are grouped and supported by multiple RSs to communicate with a multi-antenna base station (BS). We first formulate two optimization problems: the weighted sum-rate maximization and the minimum achievable rate (from all users) maximization. Unlike existing works that considered single user or single RS or multiple RSs without inter-RS reflections, the considered problems require the joint optimization of the phase-shifts of all RS elements and all beamformers at the multi-antenna BS. The two problems turn out to be non-convex and thus are difficult to be solved in general. Moreover, the inter-RS reflections give rise to the coupling of the phase-shifts amongst the RSs, making the optimization problems even more challenging to solve. To tackle them, we design alternating optimization algorithms that provably converge to locally optimal solutions. Simulation results reveal that by effectively mitigating interference and leveraging the secondary reflections amongst the RSs, there is a great benefit of deploying more RSs to support different groups of users so as to achieve a higher rate per user. This gain is even more significant with a larger number of elements per RS. Without properly dealing with the secondary reflections, by contrast, increasing the number of RSs can adversely impact the network throughput, especially for high transmit power.

Joint Beamforming Design for RIS-Assisted Integrated Sensing and Communication Systems

Integrated sensing and communication (ISAC) has been envisioned as a promising technology to tackle the spectrum congestion problem for future networks. In this correspondence, we investigate to deploy a reconfigurable intelligent surface (RIS) in an ISAC system for achieving better performance. In particular, a multi-antenna base station (BS) simultaneously serves multiple single-antenna users with the assistance of a RIS and detects potential targets. The active beamforming of the BS and the passive beamforming of the RIS are jointly optimized to maximize the achievable sum-rate of the communication users while satisfying the constraint of beampattern similarity for radar sensing, the restriction of the RIS, and the transmit power budget. An efficient alternating algorithm based on the fractional programming (FP), majorization-minimization (MM), and manifold optimization methods is developed to convert the resulting non-convex optimization problem into two solvable sub-problems and iteratively solve them. Simulation studies illustrate the advancement of deploying RIS in ISAC systems and the effectiveness of the proposed algorithm.

Throughput Optimization in Adaptive Transmit Antenna Selection Systems With Limited Feedback

We investigate the performance of a downlink wireless system with a multiantenna base station under the effect of limited channel feedback. In order to inactivate transmit antennas with poor channel quality and, thus, reduce the feedback overhead, a channel gain threshold-based multiantenna selection (CGT-MAS) scheme is proposed without optimization (NOCGT-MAS) and the corresponding single-antenna scheme (NOCGT-SAS) is considered as a baseline. Considering that the number of selected antennas affects both data transmission rate and the feedback overhead, an effective throughput defined as the difference between the data transmission rate and feedback rate is employed for evaluating the system performance. We conduct an effective throughput analysis for both the NOCGT-SAS and NOCGT-MAS schemes and show that an optimal channel gain threshold exists to maximize the effective throughput of the proposed NOCGT-MAS scheme. As a consequence, we propose the optimal instantaneous CGT-MAS algorithm (OICGT-MAS) to maximize the instantaneous effective throughput. Besides, we derive a closed-form expression of an average effective throughput for the CGT-MAS scheme and propose an optimal average channel gain threshold-based multiantenna selection algorithm (OACGT-MAS) for maximizing the derived average effective throughput. Numerical results demonstrate that the effective throughput of the proposed NOCGT-MAS is substantially better than that of conventional NOCGT-SAS. Moreover, although the OICGT-MAS scheme has a slight advantage over OACGT-MAS in terms of the effective throughput, it has a much higher computational complexity than the latter method.

Transmit Beamforming for Ambient Backscatter Communication Enabled Wireless Body Area Network in Multiuser MISO System

Wireless Body Sensor Network (WBAN) is a promising technology which can provide pervasive E-health services. However, the power consumption of wireless communications in WBAN greatly restricts its applications. Recently Ambient Backscatter Communication (AmBC) technology has been introduced to realize ultra-low power passive wireless communication, thus it is highly desirable for WBAN. In this paper we consider that AmBC, powered by a multi-antenna Base Station (BS), is incorporated in WBAN to achieve ultra-low power intra-WABN communication. To fully exploit the potential of the AmBC in WBAN, the transmit beamforming at BS, the AmBC information symbol period as well as the transmission time allocation are jointly designed, taking into account Quality of Service (QoS) requirement of WBAN and cellular users, and BS power budget. The formulated optimization problem is highly nonconvex and very challenging to solve. To tackle this issue, we employ Inner Approximate (IA) framework to reformulate the original problem and solve it in an iterative manner. Finally, numerical results are provided to show the effectiveness of the proposed algorithm under various of system parameters settings.

Intelligent Reflecting Surface Enabled Multi-Target Sensing

Besides improving communication performance, intelligent reflecting surfaces (IRSs) are also promising enablers for achieving larger sensing coverage and enhanced sensing quality. Nevertheless, in the absence of a direct path between the base station (BS) and the targets, multi-target sensing is generally very difficult, since IRSs are incapable of proactively transmitting sensing beams or analyzing target information. Moreover, the echoes of different targets reflected via the IRS-established virtual links share the same directionality at the BS. In this paper, we study a wireless system comprising a multi-antenna BS and an IRS for multi-target sensing, where the beamforming vector and the IRS phase shifts are jointly optimized to improve the sensing performance. To meet the different sensing requirements, such as a minimum received power and a minimum sensing frequency, we propose three novel IRS-assisted sensing schemes: Time division (TD) sensing, signature sequence (SS) sensing, and hybrid TD-SS sensing. First, for TD sensing, the sensing tasks are performed in sequence over time. Subsequently, a novel signature sequence (SS) sensing scheme is proposed to improve sensing efficiency by establishing a relationship between directions and SSs. To strike a flexible balance between the beam pattern gain and sensing efficiency, we also propose a general hybrid TD-SS sensing scheme with target grouping, where targets belonging to the same group are sensed simultaneously via SS sensing, while the targets in different groups are assigned to orthogonal time slots. By controlling the number of groups, the hybrid TD-SS sensing scheme can provide a more flexible balance between beam pattern gain and sensing frequency. Moreover, ...

Symbol-Level Precoding Design in IRS-Aided Secure Wireless Communication Systems

This letter investigates an intelligent reflective surface (IRS) aided secure wireless communication system, in which a multi-antenna base station (BS) transmits confidential messages to multiple users via symbol-level precoding (SLP). We consider the two cases where the eavesdropper (Eve) has no channel state information (CSI) and global CSI, respectively, to investigate the possible worst and best eavesdropping performance, and the security improvement brought by the joint SLP-IRS design. For the former, we consider the user-receive signal-to-interference-noise ratio (SINR) balancing problem under the constraints of transmission power and security, and prove that SLP is inherently safe. For the latter, we assume that a smart Eve can intercept signals using brute-force and maximum likelihood detection methods. First, its received SINR is derived under the artificial noise framework, and then a two-step design scheme for SLP and IRS is proposed. In particular, an iterative penalty method is proposed for the IRS design step. Simulation results verify the analysis and show that IRS can significantly enhance the security of system.

Joint Transmit Beamforming and Receive Filters Design for Coordinated Two-Cell Interfering Dual-Functional Radar-Communication Networks

Dual-functional radar-communication (DFRC) has been viewed as a promising component in future networks. The considered two-cell interfering DFRC network involves two multi-antenna base stations (BSs), and each BS serves multiple single-antenna users and receives echo signals to detect the target. An optimization framework for the joint transmit beamforming and receive filters design of a coordinated two-cell network is formulated. Specifically, we minimize the transmit power at two BSs subject to the signal-to-interference-and-noise ratio constraints. To solve the formulated non-convex optimization problem, an alternating optimization-based method is invoked. For the transmit beamforming design, a locally optimal successive inner convex approximation (SICA)-based method with fast convergence is firstly proposed. To further reduce the computational complexity, we also provide three zero-forcing (ZF)-based sub-optimal methods for practical consideration. For the receive filters design, a power iterations-based method is proposed. Simulation results validate the effectiveness of our proposed SICA-based locally optimal and ZF-based sub-optimal schemes.

On the Deployment of Small Cells in 3D HetNets With Multi-Antenna Base Stations

With the dense deployment of small cells, the impact of height difference between base stations (BSs) and user equipment (UE) on the performance of heterogeneous networks (HetNets) becomes significant. The traditional two-dimensional models are no longer sufficient to capture the three-dimensional (3D) features of dense HetNets. On the other hand, deploying multiple antennas on BSs is a promising approach to improve network capacity. In this paper, we propose a 3D model for a <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"> <tex-math notation="LaTeX">$K$ </tex-math></inline-formula> -tier HetNet with multi-antenna BSs, where different tiers share the same frequency band but may differ in BS height, BS density, number of antennas per BS, BS transmit power, association bias, and path loss exponent. We analytically derive the per-tier association probability under both the strongest received signal and the closest BS cell-association strategies. Based on that, we derive the expressions for the downlink ergodic rate, area spectral efficiency (ASE) and energy efficiency. The numerical results reveal that in the presence of macrocell BSs, for low to medium small-cell BS (SBS) densities, the closest BS cell-association strategy leads to low ergodic rate, ASE and energy efficiency regardless of the SBS height; while at very high SBS densities, under both cell-association strategies, SBSs should be deployed at the same height as UE to achieve high ergodic rate, ASE and energy efficiency. Moreover, we find that for a given SBS height, there exists an optimal combination of SBS density and number of antennas per SBS that maximizes the system energy efficiency.