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In this paper, we study how to maintain the communication quality for high-speed users by utilizing array processing techniques. In conventional phase-array approaches, the phase lags among array antennas need to be updated frequently to tune the array transmission direction, thereby rendering considerable operational costs. To alleviate this, we develop a novel frequency diverse array (FDA) approach. The key point is introducing small frequency offsets across array antennas to generate a time-variant beampattern, making it possible that the FDA beampattern peak automatically accompanies the quickly-moving user without the need of refreshing the frequency offsets, which is referred to as a user-centric beampattern. In this work, we consider two cases of interests: 1) one base station (BS) equipped with an FDA serves a user moving quickly along a relatively short track; 2) multiple BSs cooperatively serve the user along a much longer track. In the single-BS case, we optimize the frequency offsets such that the beampattern peak maximally accompanies the user. In the multi-BS case, we further incorporate BS activation to well balance the service quality and the BS maintenance cost. Two low-complexity algorithms are designed to iteratively solve the two problems with stationary convergence guarantee. Simulations confirm that with the same implementation complexity, the FDA approach serves the high-speed user better than the phase-array approach.

Admission control is an effective solution to managing a wireless network with a large user set. It dynamically rejects users in bad conditions, and thereby guarantees high quality-of-service (QoS) for the others. Unfortunately, a frequently-varying admissible user set requests remarkable power to continually re-establish the transmission link. Hence, we explore the stability of admissible user set, and formulate a joint long-term admission control and beamforming problem for a network with one multi-antenna base station (BS) and multiple single-antenna users. We consider the downlink transmission in a time period containing multiple time slices. By jointly optimizing the admissible users and the BS transmit beamformers in different time slices, we aim to minimize the total power cost, including not only the power for QoS guarantee, but also the power for user status switching. Due to the NP-hardness of the problem, we develop two (offline and online) algorithms to find some efficient suboptimal solutions. The offline algorithm requires all channel state information (CSI), and solves the admissible users and beamformers in different time slices in one shot, based on successive upper-bound minimization (SUM). To support real-time data transmission, we further design an alternating direction method of multipliers (ADMM)-based online algorithm, which outputs the admissible users and beamformers in different time slices successively, utilizing the previous admissible user set, the actual value of current CSI, and the distribution of future CSI. Simulations validate the performance of the two algorithms, and show that the online algorithm is an efficient practical alternative to the offline algorithm., Comment: 12 pages, 13 figure

Direction-of-arrival (DOA) estimation is an important task in many unmanned aerial vehicle (UAV) applications. However, the complicated electromagnetic wave propagation in urban environments substantially deteriorates the performance of many conventional model-driven DOA estimation approaches. To alleviate this, a deep learning based DOA estimation approach is proposed in this paper. Specifically, a complex-valued convolutional neural network (CCNN) is designed to fit the electromagnetic UAV signal with complex envelope better. In the CCNN design, we construct some mapping functions using quantum probabilities, and further analyze some factors which may impact the convergence of complex-valued neural networks. Numerical simulations show that the proposed CCNN converges faster than the real convolutional neural network, and the DOA estimation result is more accurate and robust.

Consider multicell heterogeneous networks (HetNets), where each cell consists of a number of small (micro/pico) base stations (SBSs) and the SBSs perform coordinated multipoint (CoMP) transmission/reception to serve a number of downlink/uplink (DL/UL) users over the same frequency band. The SBSs work in full-duplex (FD) mode and the DL/UL users are half-duplex (HD). Due to co-channel transmissions, the DL and the UL are mutually interfered. This motivates us to consider a joint DL/UL beamformer design for maximizing the system sum rate. Different from the conventional sum rate maximization (SRM), where the user's rate is allowed to be any nonnegative real number, herein we focus on the discrete-rate case — each user's rate is constrained to a prescribed discrete-rate set. This discrete-rate constraint is motivated by the fact that practical communication systems are designed for a finite number of transmission rates, owing to the finite number of modulation and coding schemes (MCS). In view of this, our SRM problem is coined as discrete SRM (DSRM). The DSRM problem is essentially a mixed-integer nonlinear program, and NP-hard. To tackle it, two different approaches are proposed. The first approach is built upon the simplex reformulation of the discrete rate and the mirror descent (MD) algorithm. The second approach exploits the correspondence between the rate and minimum mean-square error (MMSE), and employs the block-coordinate descent (BCD) method to find an approximate solution. Simulation results demonstrate the superior rate performance of the proposed designs as compared with the weighted MMSE (WMMSE) design with naive rate quantization.

Massive MIMO attains high spectral and power efficiency transmission by leveraging a large number of transmit antennas. However, to capture the benefits of massive MIMO, each antenna should be accompanied with a dedicated RF chain, and consequently, the hardware costs would scale up tremendously with the increase of the antennas. Cheap implementations of massive MIMO have recently gained considerable attention, and constant modulus (CM) signaling is seen as a promising solution, owing to its low peak-to-average power ratio (PAPR). This paper investigates the physical-layer (PHY) security in massive MIMO with an emphasis on the CM signaling. In particular, we consider a transmitter with massive antennas broadcast common confidential information to a group of legitimate receivers, and a number of eavesdroppers overhear the transmission and attempt to intercept the information. Our goal is to design the CM beamforming at the transmitter so that the multicast secrecy rate is maximized. This secrecy rate maximization (SRM) problem is generally NP-hard. To tackle it, two tractable approaches are developed. The first one employs the semidefinite relaxation (SDR) technique and the Charnes–Copper transformation to obtain a convex relaxation of the SRM problem. However, due to the dimension lifting of SDR, this approach is feasible only for small to medium antenna sizes. The second approach leverages the Dinkelbach method to work directly over the beamformer domain; a custom-build nonconvex alternating direction method of multipliers (ADMM) algorithm is proposed to efficiently perform each Dinkelbach update. Simulation results demonstrate that the second approach is computationally more efficient and can achieve nearly optimal performance when the number of antennas is large.

The max–min fairness (MMF) strategy has been widely employed to manage wireless networks since it guarantees fairness among users. However, with a large number of users awaiting service, the network tends to be congested and the quality-of-service (QoS) will degrade substantially. This motivates us to study the MMF problem jointly with the consideration of admission control. Specifically, the authors consider a downlink network consisting of a multi-antenna base station (BS) and multiple single-antenna users. By jointly optimising the admissible users and the BS transmit beamformers, they aim to maximise the minimum signal-to-interference-plus-noise-ratio of the admissible users, such that high QoS and fairness can be guaranteed simultaneously for them. This problem is essentially NP-hard, and hence they pursue an efficient approximate solution to it. To this end, they first reformulate this problem from the perspective of sparse optimisation, and then develop a low-complexity algorithm to iteratively solve the approximate problem. Moreover, to facilitate the algorithm's implementation, they further recast the subproblem in each iteration, such that it fits into the framework of the alternating direction methods of multipliers. Finally, an efficient distributed algorithm is designed, with each step being simply computed in a closed form.

Consider a network consisting of one multi-antenna base station (BS) and multiple pairs of multi-antenna user equipment’s (UEs). For each UE pair, the communication between transmitter and receiver is established either through BS or via device-to-device (D2D) link. We assume that the D2D transmission and cellular transmission are equally prioritized and share the same resources. To improve the network throughput, we maximize the sum rate by jointly optimizing the transmission mode of each UE pair and the associated transceivers. Due to the NP-hardness of this problem, we first perform some efficient approximation to it and then design an iterative algorithm, which is guaranteed to converge to a stationary solution by solving a series of weighted minimum mean square error (WMMSE) problems. The proposed algorithm has two distinguishing features. First, it only solves the WMMSE problem inexactly in each iteration, which thereby has a simplified algorithm structure and accelerated convergence behavior than the classical one. Second, we further fit the WMMSE problem into the alternating direction method of multipliers (ADMM) framework, making it amenable to parallel and distributed computation. Finally, the approximated problem is solved efficiently and distributively, with simple closed-form solutions in each step.

In most existing robust array beam pattern synthesis studies, the bounded-sphere model is used to describe the steering vector (SV) uncertainties. In this letter, instead of bounding the norm of SV perturbations as a whole, we explore the amplitude and phase perturbations of each SV element separately, thereby obtaining a tighter SV uncertainty model. Based on this model, we formulate the robust array pattern synthesis problem from the perspective of the min-max optimization, which aims to minimize the maximum side lobe response, while preserving the main lobe response. However, this problem is difficult due to the infinitely many non-convex constraints. As a remedy, we employ the worst-case criterion and recast the problem as a convex second-order cone program (SOCP). To solve the SOCP, we further develop an alternating direction method of multipliers (ADMM)-based algorithm, which is computationally efficient with each step being computed in closed form. Numerical simulations demonstrate the efficacy and efficiency of the proposed algorithm., Comment: 6 pages, 2 figures

The technology of specific emitter identification (SEI) has important military significance in electronic warfare. However, it is hard to obtain sufficient signal samples from the specific emitter in the electromagnetic environment of the battlefield. Therefore, it is a challenging issue to learn from a handful of samples to accurately identify complex and changeable emitter. A small sample identification method based on adversarial embedded networks is proposed to solve this problem. This method combines the improved generative adversarial networks (GAN) and the Convolutional neural networks (CNN) for classification. In the context of a handful of samples, high-quality simulation samples are generated by the generator in the generative adversarial networks to expand the available feature quantities of the model, thereby improving the recognition efficiency and accuracy. Through the training and testing of a small number of radar emitter data and communication station emitter data, the results show that the method just needs a small amount of data to achieve higher recognition accuracy.

Transmit beamforming and artificial noise-based methods have been widely employed to achieve physical-layer (PHY) security. However, these approaches may fail to provide satisfactory secure performance if the channels of legitimate user (LU) and eavesdropper (Eve) are highly correlated, which usually occurs in the case of close-located LU and Eve. The goal of this paper is to address the PHY security problem for proximal LU and Eve in millimeter-wave transmissions. To this end, we propose a novel frequency diverse array (FDA) beamforming approach, which intentionally introduces some frequency offsets across array antennas to decouple the highly correlated channels of LU and Eve. By exploiting this decoupling capability, the FDA beamforming can degrade Eve’s reception and thus enhance PHY security. Leveraging FDA beamforming, we aim to maximize the secrecy rate by jointly optimizing the frequency offsets and the transmit beamformer. This secrecy rate maximization problem is difficult due to the tightly coupled variables. However, we show that it can be reformulated into a form only depending on the frequency offsets. Building upon this reformulation, we further employ the block successive upper-bound minimization method to iteratively obtain a solution with stationary convergence guarantee. Numerical results demonstrate that FDA beamforming can provide higher secrecy rate than conventional beamforming, especially for proximal LU and Eve.

Consider a multicell downlink network, where the base stations (BSs) in different cells cooperate in the precoder level, while those in the same cell are coordinated for joint processing (JP). To achieve green communication, we optimize the network power consumption under some quality-of-service (QoS) constraints. Different from the conventional approaches based on BS activation and beamforming, we further integrate user admission control into network management, and thus minimize the power consumption by jointly optimizing the active BSs, the admissible users and the transmit beamformers. This strategy has two advantages. First, it ensures that the network still works even when some users cannot achieve the QoS requirements. Second, it helps select a subset of users whose QoS requirements can be satisfied with relatively low power cost, thereby improving the power efficiency. However, this problem is challenging due to the mixed-integer programming. To pursue some efficient approximate solution, we first reformulate it as a convex sparse optimization problem and then develop a distributed algorithm to iteratively solve the problem, utilizing the alternating direction method of multipliers (ADMM). The proposed algorithm has very low complexity since each step can be computed in closed form. Its efficacy and efficiency are demonstrated by numerical simulations.

Consider a full-duplex (FD) bidirectional secure communication system, where two communication nodes, named Alice and Bob, simultaneously transmit and receive confidential information from each other, and an eavesdropper, named Eve, overhears the transmissions. Our goal is to maximize the sum secrecy rate (SSR) of the bidirectional transmissions by optimizing the transmit covariance matrices at Alice and Bob. To tackle this SSR maximization (SSRM) problem, we develop an alternating difference-of-concave (ADC) programming approach to alternately optimize the transmit covariance matrices at Alice and Bob. We show that the ADC iteration has a semi-closed-form beamforming solution, and is guaranteed to converge to a stationary solution of the SSRM problem. Besides the SSRM design, this paper also deals with a robust SSRM transmit design under a moment-based random channel state information (CSI) model, where only some roughly estimated first and second-order statistics of Eve's CSI are available, but the exact distribution or other high-order statistics is not known. This moment-based error model is new and different from the widely used bounded-sphere error model and the Gaussian random error model. Under the consider CSI error model, the robust SSRM is formulated as an outage probability-constrained SSRM problem. By leveraging the Lagrangian duality theory and DC programming, a tractable safe solution to the robust SSRM problem is derived. The effectiveness and the robustness of the proposed designs are demonstrated through simulations., Comment: Accepted by IEEE Transactions Signal Procesing, 14 pages, 10 figures

Admission control has been widely utilized to alleviate network congestion. However, most current studies choose the admissible users based on instantaneous channel information. Due to the time-varying characteristics of wireless channels, the admissible user set changes quickly, which complicates network management and renders heavy operational costs. This motivates us to take the stability of the admissible user set into account in admission control, thus leading to a long-term admission control problem. In this paper, we consider a joint long-term admission control and beamforming problem in a downlink network consisting of one multi-antenna base station (BS) and multiple single-antenna users. To maintain a relatively stable admissible user set and minimize the power cost for the admissible users to achieve their quality-of-service levels, we jointly optimize the admissible users, the BS transmit beamformers, and the switching frequency of each user's admissible status in a given time period. To handle this challenging non-convex problem, we first design a sequential convex approximation (SCA) algorithm to iteratively compute a stationary solution. To facilitate algorithm's implementation, we further employ the alternating direction method of multipliers to come up with an efficient, semi-closed-form update of each SCA problem.

In this paper, we consider how to maintain the communication quality for high-speed users in array transmission. Due to high user speed, the array transmission angle changes quickly. As a consequence, the phase shifters (beamformers) of traditional phase arrays need to be updated frequently to aim at the user, thus yielding high implementation cost. To alleviate this, we propose a novel frequency diverse array (FDA) approach, which intentionally introduces some frequency offsets across the array antennas to activate an angle-range-time dependent beampattern; i.e., the FDA beampattern peak automatically moves in space. This motivates us to carefully design FDA parameters such that the beampattern peak accompanies the quickly-moving users. To this end, we maximize the average beampattern gain along some given user trace by optimizing the frequency offsets. The block successive upper-bound minimization (BSUM) method is applied to obtain a stationary solution to this non-convex problem. Compared with phase array beamforming, the FDA approach maintains service quality for high-speed users by updating frequency offsets less frequently, thus reducing the implementation cost remarkably.

Different from the conventional phased-array, frequency diverse array (FDA) introduces a small frequency increment across the array element, thus yielding a range-and-time-dependent beampattern. This property motivates the application of FDA in radio frequency (RF) localization deception. In this paper, the sum and difference beams algorithm is used to test the effectiveness of the proposed method in FDA reconnaissance. Both theoretical analysis and simulation results show that the sum and difference algorithm cannot achieve FDA radar reconnaissance effectively and accurately. Therefore, compared to phased-array, FDA has a better RF localization deception performance.

This paper considers mobile computation offloading in fog-radio access networks (F-RAN), where multiple mobile users offload their computation tasks to the F-RAN through a number of fog nodes [a.k.a. enhanced remote radio heads (RRHs)]. In addition to communication capability, the fog nodes are also equipped with computational resources to provide computing services for users. Each user chooses one fog node to offload its task, while each fog node may simultaneously serve multiple users. Depending on computational burden at the fog nodes, the tasks may be completed at the fog nodes or further offloaded to the cloud via fronthaul links with limited capacities. To complete all the tasks as fast as possible, a joint optimization of radio and computational resources of F-RAN is proposed to minimize the maximum latency of all users. This problem is formulated as a mixed integer nonlinear program (MINP). We first show that the MINP can be reformulated as a continuous optimization problem with a difference-of-convex (DC) objective. Then, an inexact DC algorithm is proposed to handle the min-max problem with stationary convergence guarantee. Simulation results show that the proposed algorithm outperforms the minimum distance-based and the random-based offloading strategies.

The conventional physical-layer (PHY) security approaches, e.g., transmit beamforming and artificial noise (AN)-based design, may fail when the channels of legitimate user (LU) and eavesdropper (Eve) are close correlated. Due to the highly directional transmission feature of millimeter-wave (mmWave), this may occur in mmWave transmissions as the transmitter, Eve and LU are aligned in the same direction exactly. To handle the PHY security problem with directionally-aligned LU and Eve, we propose a novel frequency diverse array (FDA) beamforming approach to differentiating the LU and Eve. By intentionally introducing some frequency offsets across the antennas, the FDA beamforming generates an angle-range dependent beampattern. As a consequence, it can degrade the Eve's reception and thus achieve PHY security. In this paper, we maximize the secrecy rate by jointly optimizing the frequency offsets and the beamformer. This secrecy rate maximization (SRM) problem is hard to solve due to the tightly coupled variables. Nevertheless, we show that it can be reformulated into a form depending only on the frequency offsets. Building upon this reformulation, we identify some cases where the SRM problem can be optimally solved in closed form. Numerical results demonstrate the efficacy of FDA beamforming in achieving PHY security, even for aligned LU and Eve.

In modern wireless networks, optimizing the association between base stations (BSs) and users effectively improves network performance. On the other hand, a frequently changing BS-user association renders considerable operational burden for network management, e.g., it consumes extra power to awaken the deactivated BSs and to support users' switching among BSs. This motivates us to balance the flexibility and stability of BS-user association, leading to a long-term BS association problem. In this paper, we address this by considering the green communication problem in a MISO network where multiple BSs cooperatively forward information to multiple users. We minimize total power consumption (including not only the transmit power and device maintenance power, but also the switching power consumed as the BS-user association changes) by joint long-term BS activation and beamforming, i.e., we jointly optimize the active BSs, the transmit beamformer and the user switching frequency among BSs. Due to the inherent causality constraints on channel state information (CSI), we develop an online algorithm for the optimization problem, utilizing the sample average approximation (SAA) method. To improve the algorithm's efficiency, we further fit the problem into the framework of alternating direction method of multipliers (ADMM), and finally design a low-complexity distributed online algorithm for the green communication problem.

Consider a network consisting of one multi-antenna base station (BS) and multiple single-antenna users. With a lot of users awaiting service, the network tends to be congested and the quality of service (QoS) degrades remarkably. This promotes the research on user admission control; i.e., to guarantee QoS, the network serves only a subset of users and rejects the rest. In this paper, we consider a max-min fairness (MMF) problem based on joint admission control and beamforming. In particular, by jointly optimizing the admissible users and the transmit beamformers, we maximize the minimum signal-to-interference-plus-noise-ratio (SINR) of admissible users, such that high QoS and fairness can be guaranteed for them. This problem is essentially NP-hard, and hence we develop a low-complexity iterative deflation algorithm to obtain some efficient approximate solution. In each iteration, we improve the users' SINRs and drop the user with the lowest SINR-to-power ratio, until the given user number is achieved. To facilitate the algorithm implementation, especially in large-scale networks, we further employ the alternating direction method of multipliers (ADMM) to perform per-user optimization. Finally, an efficient distributed algorithm is developed, with each step being solved in closed form.

This paper deals with the physical-layer (PHY) security problem for a full-duplex (FD) two-way relay system, where two FD sources exchange confidential information through an FD relay. Assuming imperfect channel state information (CSI) of the eavesdropper (Eve), we aim for a robust amplify-andforward (AF) relaying scheme that maximizes the sum secrecy rate of the two-way transmissions. Different from the widely used norm-bounded deterministic error model and the Gaussian random error model, we adopt a moment-based random error model to capture the imperfection of Eve's CSI. Specifically, the CSI error is assumed to be randomly distributed with given mean and covariance, but the exact distribution or other highorder statistics are not known. Under this moment-based error model, we formulate an outage-constrained sum secrecy rate maximization (OC-SRM) problem, which guarantees the outage sum secrecy rate is kept below certain threshold for arbitrary distributions fulfilling the mean and covariance. To tackle this OC-SRM problem, we first reexpress the outage probability into a more explicit form, and then develop a semidefinite relaxation (SDR)-based alternating difference-of-concave (DC) programming approach to computing a safe solution. Simulation results corroborate the robustness of the proposed design when varying the Eve's CSI error distribution.

The multi-input single-output multi-eavesdropper (MISOME) wiretap channel is one of the generic wiretap channels in physical layer security. In Khisti and Wornell's classical work [1], the optimal secure beamformer for MISOME has been derived under the total power constraint. In this work, we revisit the MISOME wiretap channel and focus on the large-scale transmit antenna regime and the constant modulus beamformer design. The former is motivated by the significant spectral efficiency gains provided by massive antennas, and the latter is due to the consideration of cheap hardware implementation of constant modulus beamforming. However, from an optimization point of view, the secrecy beamforming with constant modulus constraints is challenging, more specifically, NP-hard. In light of this, we propose two methods to tackle it, namely the semidefinite relaxation (SDR) method and the ADMM-Dinkelbach method. Simulation results demonstrate that the ADMM-Dinkelbach method outperforms the SDR method, and can attain nearly optimal secrecy performance for the large-scale antenna scenario.

This paper considers the physical-layer secrecy design for full-duplex (FD) bidirectional communications in the presence of an eavesdropper (Eve). The goal of this work is to maximize the sum secrecy rate (SSR) of the bidirectional transmissions via appropriately designing the transmit covariance matrices at the legitimate nodes. To this end, we propose an alternating difference-of-concave (ADC) approach to iteratively optimizing the transmit covariance matrices. We show that each ADC iteration can be carried out efficiently with a semi-closed- form solution, and that every limit point of ADC iterations is a stationary solution of the SSR maximization problem. Besides the SSR maximization, this paper also deals with a robust SSR maximization problem to account for imperfect CSI of Eve. Assuming a moment-based random CSI error model (i.e., only mean and covariance of the error are known, but the exact distribution is not known), robust transmit designs based on Markov's inequality and the robust conic reformulation are developed. The efficacy of the proposed designs is demonstrated through simulations.

Consider a network that consists of one multi-antenna base station (BS) and multiple pairs of multi-antenna user equipments (UEs). In each UE pair, the communication between transmitter and receiver is established either through BS or via device-to-device (D2D) link. All the D2D transmission and the uplink transmission of BS relaying share the same resources, while causing interference to each other. To improve the network throughput, we consider a sum-rate maximization problem by jointly optimizing the transmission mode of each UE pair and the corresponding transceivers. Due to the NP-hardness of the problem, we seek for some efficient approximate solutions to it. To this end, we first reformulate the problem by the weighted MMSE (WMMSE) approach, and then fit it into the alternating direction method of multipliers (ADMM) framework. Finally, an efficient distributed algorithm, which converges to a stationary solution, is developed. In particular, each step of the algorithm can be computed in closed form, thus giving it very low complexity.

We consider the green communication problem in a downlink cooperative MISO network consisting of multiple base stations (BSs) and multiple users. We employ power efficiency as the performance metric, defined as the ratio of total user rate to total power consumption. The total user rate is related to the number of active users, while the total power consumption includes the transmit power and the device maintenance power, determined by the beamformers and the number of active BSs, respectively. Motivated by this observation, we consider a power efficiency maximization problem by jointly optimizing the active BSs, the admissible users and the cooperative beamform-ers. This problem is challenging due to the fractional objective and the mixed-integer program. To seek for some efficient approximate solution, we first formulate it as a convex sparse problem balancing the transmit power, the number of active BSs and the number of admissible users. A two-stage algorithm is then developed to solve the approximate problem. Simulations demonstrate the effectiveness of the proposed algorithm.

In modern wireless networks, dynamically optimizing the association between base stations (BSs) and users is a promising solution for performance improvement. However, a frequently changing BS-user association introduces heavy burden for network management. In this paper, we seek for balancing the flexibility and stability of the BS-user association in a green downlink MISO network. In addition to minimizing the transmit power and controlling the number of active BSs, we further consider reducing the users' switching frequency among BSs. This problem is a nonlinear mixed-integer program, and challenging to solve. As a compromise, we see for some efficient approximate solution to it by reformulating it as a convex sparse problem. An efficient algorithm is then developed to enhance the sparse solution, based on the iterative reweighted l 1 technique. The effectiveness of the proposed algorithm was validated by numerical simulations.

A novel approach of robust adaptive beamforming (RABF) is presented in this paper, aiming at robustness against both finite-sample effects and steering vector mismatches. It belongs to the class of diagonal loading approaches with the loading level determined based on worst-case performance optimization. The proposed approach, however, is distinguished by two points. (1) It takes finite-sample effects into account and applies worst-case performance optimization to not only the constraints, but also the objective of the constrained quadratic equation, for which it is referred to as joint worst-case RABF (JW-RABF). (2) It suggests a simple closed-form solution to the optimal loading after some approximations, revealing how different factors affect the loading. Compared with many existing methods in this field, the proposed one achieves better robustness in the case of small sample data size as well as steering vector mismatches. Moreover, it is less computationally demanding for presenting a simple closed-form solution to the optimal loading. Numerical examples confirm the effectiveness of the proposed approach.

Consider the max-min problem for an uplink SIMO heterogeneous network, where the base stations (BS) are coordinated dynamically for joint reception under some backhaul overhead constraints. We formulate this problem in the perspective of joint power allocation, BS assignment and beamformer design, and develop an efficient algorithm based on alternating optimization. In particular, we transfer the joint BS assignment and beamformer design subproblem into a group LASSO problem by applying the alternating direction method of multipliers (ADMM). Consequently, the problem is solved in a partially distributed manner and in each iteration a simple closed-form solution is derived. Numerical simulations demonstrate the effectiveness and efficiency of the proposed algorithm.