Joint Downlink Beamforming and Discrete Resource Allocation Using Mixed-Integer Programming

Multi-antenna processing is widely adopted as one of the key enabling technologies for current and future cellular networks. Particularly, multiuser downlink beamforming (also known as space-division multiple access), in which multiple users are simultaneously served with spatial transmit beams in the same time and frequency resource, achieves high spectral efficiency with reduced energy consumption. To harvest the potential of multiuser downlink beamforming in practical systems, optimal beamformer design shall be carried out jointly with network resource allocation. Due to the specifications of cellular standards and/or implementation constraints, resource allocation in practice naturally necessitates discrete decision makings, e.g., base station (BS) association, user scheduling and admission control, adaptive modulation and coding, and codebook-based beamforming (precoding). This dissertation focuses on the joint optimization of multiuser downlink beamforming and discrete resource allocation in modern cellular networks. The problems studied in this thesis involve both continuous and discrete decision variables and are thus formulated as mixed-integer programs (MIPs). A systematic MIP framework is developed to address the problems. The MIP framework consists of four components: (i) MIP formulations that support the commercial solver based approach for computing the optimal solutions, (ii) analytic comparisons of the MIP formulations, (iii) customizing techniques for speeding up the MIP solvers, and (iv) low-complexity heuristic algorithms for practical applications. We consider first joint network topology optimization and multi-cell downlink beamforming (JNOB) for coordinated multi-point transmission. The objective is to minimize the overall power consumption of all BSs while guaranteeing the quality-of-service (QoS) requirements of the mobile stations (MSs). A standard mixed-integer second-order cone program (MISOCP) formulation and an extended MISOCP formulation are developed, both of which support the branch-and-cut (BnC) method. Analysis shows that the extended formulation admits tighter continuous relaxations (and hence less computational complexity) than that of the standard formulation. Effective strategies are proposed to customize the BnC method in the MIP solver CPLEX when applying it to the JNOB problem. Low-complexity inflation and deflation procedures are devised for large-scale applications. The simulations show that our design results in sparse network topologies and partial BS cooperation. We study next the joint optimization of discrete rate adaptation and downlink beamforming (DRAB), in which rate adaptation is carried out via modulation and coding scheme (MCS) assignment and admission control is embedded in the MCS assignment procedure. The objective is to achieve the maximum sum-rate with the minimum transmitted BS power. As in the JNOB problem, a standard and an extended MISOCP formulations are developed, and analytic comparisons of the two formulations are carried out. The analysis also leads to efficient customizing strategies for the BnC method in CPLEX. We also develop fast inflation and deflation procedures for applications in large-scale networks. Our numerical results show that the heuristic algorithms yield sum-rates that are very close to the optimal ones. We then turn our attention to codebook-based downlink beamforming. Codebook-based beamforming is employed in the latest cellular standards, e.g., in long-term evolution advanced (LTE-A), to simplify the signaling procedure of beamformers with reduced signaling overhead. We consider first the standard codebook-based downlink beamforming (SCBF) problem, in which precoding vector assignment and power allocation are jointly optimized. The objective is to minimize the total transmitted BS power while ensuring the prescribed QoS targets of the MSs. We introduce a virtual uplink (VUL) problem, which is proved to be equivalent to the SCBF problem. A customized power iteration method is developed to solve optimally the VUL problem and hence the SCBF problem. To improve the performance of codebook-based downlink beamforming, we propose a channel predistortion mechanism that does not introduce any additional signalling overhead or require modification of the mobile receivers. The joint codebook-based downlink beamforming and channel predistortion (CBCP) problem represents a non-convex MIP. An alternating optimization algorithm and an alternating feasibility search algorithm are devised to approximately solve the CBCP problem. The simulation results confirm the efficiency of the channel predistortion scheme, e.g., achieving significant reductions of the total transmitted BS power. We study finally the worst-case robust codebook-based downlink beamforming when only estimated channel covariance matrices are available at the BS. Similar to the DRAB problem, user admission control is embedded in the precoding vector assignment procedure. In the robust codebook-based downlink beamforming and admission control (RCBA) problem, the objective is to achieve the maximum number of admitted MSs with the minimum transmitted BS power. We develop a conservative mixed-integer linear program (MILP) approximation and an exact MISOCP formulation of the RCBA problem. We further propose a low-complexity inflation procedure. Our simulations show that the three approaches yield almost the same average number of admitted MSs, while the MILP based approach requires much more transmitted BS power than the other two to support the admitted MSs. The MIP framework developed in this thesis can be applied to address various discrete resource allocation problems in interference limited cellular networks. Both optimal solutions, i.e., performance benchmarks, and low-complexity practical algorithms are considered in our MIP framework. Conventional approaches often did not adopt the exact discrete models and approximated the discrete variables by (quantized) continuous ones, which could lead to highly suboptimal solutions or infeasible problem instances

Group Sparse Precoding for Cloud-RAN with Multiple User Antennas

Cloud radio access network (C-RAN) has become a promising network architecture to support the massive data traffic in the next generation cellular networks. In a C-RAN, a massive number of low-cost remote antenna ports (RAPs) are connected to a single baseband unit (BBU) pool via high-speed low-latency fronthaul links, which enables efficient resource allocation and interference management. As the RAPs are geographically distributed, the group sparse beamforming schemes attracts extensive studies, where a subset of RAPs is assigned to be active and a high spectral efficiency can be achieved. However, most studies assumes that each user is equipped with a single antenna. How to design the group sparse precoder for the multiple antenna users remains little understood, as it requires the joint optimization of the mutual coupling transmit and receive beamformers. This paper formulates an optimal joint RAP selection and precoding design problem in a C-RAN with multiple antennas at each user. Specifically, we assume a fixed transmit power constraint for each RAP, and investigate the optimal tradeoff between the sum rate and the number of active RAPs. Motivated by the compressive sensing theory, this paper formulates the group sparse precoding problem by inducing the $\ell_0$-norm as a penalty and then uses the reweighted $\ell_1$ heuristic to find a solution. By adopting the idea of block diagonalization precoding, the problem can be formulated as a convex optimization, and an efficient algorithm is proposed based on its Lagrangian dual. Simulation results verify that our proposed algorithm can achieve almost the same sum rate as that obtained from exhaustive search

Fast converging robust beamforming for downlink massive MIMO systems in heterogenous networks

Massive multiple-input multiple-output (MIMO) is an emerging technology, which is an enabler for future broadband wireless networks that support high speed connection of densely populated areas. Application of massive MIMO at the macrocell base stations in heterogeneous networks (HetNets) offers an increase in throughput without increasing the bandwidth, but with reduced power consumption. This research investigated the optimisation problem of signal-to-interference-plus-noise ratio (SINR) balancing for macrocell users in a typical HetNet scenario with massive MIMO at the base station. The aim was to present an efficient beamforming solution that would enhance inter-tier interference mitigation in heterogeneous networks. The system model considered the case of perfect channel state information (CSI) acquisition at the transmitter, as well as the case of imperfect CSI at the transmitter. A fast converging beamforming solution, which is applicable to both channel models, is presented. The proposed beamforming solution method applies the matrix stuffing technique and the alternative direction method of multipliers, in a two-stage fashion, to give a modestly accurate and efficient solution. In the first stage, the original optimisation problem is transformed into standard second-order conic program (SOCP) form using the Smith form reformulation and applying the matrix stuffing technique for fast transformation. The second stage uses the alternative direction method of multipliers to solve the SOCP-based optimisation problem. Simulations to evaluate the SINR performance of the proposed solution method were carried out with supporting software-based simulations using relevant MATLAB toolboxes. The simulation results of a typical single cell in a HetNet show that the proposed solution gives performance with modest accuracy, while converging in an efficient manner, compared to optimal solutions achieved by state-of-the-art modelling languages and interior-point solvers. This is particularly for cases when the number of antennas at the base station increases to large values, for both models of perfect CSI and imperfect CSI. This makes the solution method attractive for practical implementation in heterogeneous networks with large scale antenna arrays at the macrocell base station.Dissertation (MEng)--University of Pretoria, 2018.Electrical, Electronic and Computer EngineeringMEngUnrestricte

Energy-Efficient and Robust Hybrid Analog-Digital Precoding for Massive MIMO Systems

The fifth-generation (5G) and future cellular networks are expected to facilitate wireless communication among tens of billions of devices with enormously high data rate and ultra-high reliability. At the same time, these networks are required to embrace green technology by significantly improving the energy efficiency of wireless communication to reduce their carbon footprint. The massive multiple-input multiple-output (MIMO) systems, in which the base stations are equipped with hundreds of antenna elements, can provide immensely high data rates and support a large number of users by employing the precoding at the base stations. However, the conventional precoding techniques - which require a dedicated radio-frequency chain for each antenna element - become prohibitively expensive for massive MIMO systems. To address this shortcoming, the hybrid analog-digital precoding architecture is proposed, which requires fewer radio-frequency chains than the antenna elements. The reduced hardware costs in this novel architecture, however, comes at the expense of reduced degrees of freedom for the precoding, which deteriorates the energy efficiency of the network. In this thesis, we consider the design of energy-efficient hybrid precoding techniques in multiuser downlink massive MIMO systems. These systems are fundamentally interference limited. To mitigate the interference, we adopt two interference management strategies while designing the hybrid precoding schemes. They are, namely, interference suppression-based hybrid precoding, and interference exploitation-based hybrid precoding. The former approach results in a lower computational complexity - as the resulting precoders remain the same as long as the channel is unchanged when compared to the latter approach. On the other hand, the interference exploitation-based hybrid precoding is more energy efficient due to judicious use of transmit symbol information, as compared to the interference suppression-based hybrid precoding. In the hybrid analog-digital precoding, analog precoders are implemented in analog radio-frequency domain using a large number of phase shifters, which are relatively inexpensive. These phase shifters, however, typically suffer from artifacts; their actual values differ from their nominal values. These imperfect phase shifters can lead to symbol estimation errors at the users, which may not be tolerable in many applications of future cellular networks. To establish a high-reliable communication under the plight of imperfect phase shifters in the hybrid precoding architecture, in this thesis, we propose an energy-efficient, robust hybrid precoding technique. The designed scheme guarantees 100% robustness against the considered hardware artifacts. Moreover, the thesis demonstrates that the proposed technique can save up to 12% transmit power when compared to a conventional method. Another critically important requirement of the future cellular networks - apart from ultra-high reliability and energy efficiency - is ultra-low latency. Some envisioned extreme real-time applications of 5G, such as autonomous driving and remote surgery, demand an end-to-end latency smaller than one millisecond. To fulfill such a stringent demand, we devise an efficient implementation scheme for the proposed robust hybrid precoding technique to reduce the required computational time. The devised scheme exploits special structures present in the algorithm to reduce the computational complexity and can compute the precoders in a distributed manner on a parallel hardware architecture. The results show that the proposed implementation scheme can reduce the average computation time of the algorithm by 35% when compared to a state-of-the-art method. Finally, we consider the hybrid precoding in heterogeneous networks, where the cell edge users typically experience severe interference. We propose a coordinated hybrid precoding technique based on the interference exploitation approach. The numerical results reveal that the proposed coordinated hybrid precoding results in a significant transmit power savings when compared to the uncoordinated hybrid precoding

Multiuser Downlink Beamforming Techniques for Cognitive Radio Networks

Spectrum expansion and a significant network densification are key elements in meeting the ever increasing demands in data rates and traffic loads of future communication systems. In this context, cognitive radio (CR) techniques, which sense and opportunistically use spectrum resources, as well as beamforming methods, which increase spectral efficiency by exploiting spatial dimensions, are particularly promising. Thus, the scope of this thesis is to propose efficient downlink (DL) beamforming and power allocation schemes, in a CR framework. The methods developed here, can be further applied to various practical scenarios such as hierarchical multi-tier, heterogenous or dense networks. In this work, the particular CR underlay paradigm is considered, according to which, secondary users (SUs) opportunistically use the spectrum held by primary users (PUs), without disturbing the operation of the latter. Developing beamforming algorithms, in this scenario, requires that channel state information (CSI) from both SUs and PUs is required at the BS. Since in CR networks PUs have typically limited or no cooperation with the SUs, we particularly focus on designing beamforming schemes based on statistical CSI, which can be obtained with limited or no feedback. To further meet the energy efficiency requirements, the proposed beamforming designs aim to minimize the transmitted power at the BS, which serves SUs at their desired Quality-of-Service (QoS), in form of Signal-to-interference-plus-noise (SINR), while respecting the interference requirements of the primary network. In the first stage, this problem is considered under the assumption of perfect CSI of both SUs and PUs. The difficulty of this problem consists on one hand, in its non-convexity and, on the other hand, in the fact that the beamformers are coupled in all constraints. State-of-the-art approaches are based on convex approximations, given by semidefinite relaxation (SDR) methods, and suffer from large computational complexity per iteration, as well as the drawback that optimal beamformers cannot always be retrieved from the obtained solutions. The approach, proposed in this thesis, aims to overcome these limitations by exploiting the structure of the problem. We show that the original downlink problem can be equivalently represented in a so called ’virtual’ uplink domain (VUL), where the beamformers and powers are allocated, such that uplink SINR constraints of the SUs are satisfied, while both SUs and PUs transmit to the BS. The resulting VUL problem has a simpler structure than the original formulation, as the beamformers are decoupled in the SINR constraints. This allows us to develop algorithms, which solve the original problem, with significantly less computational complexity than the state-of-the-art methods. The rigurous analysis of the Lagrange duality, performed next, exposes scenarios, in which the equivalence between VUL and DL problems can be theroretically proven and shows the relation between the obtained powers in the VUL domain and the optimal Lagrange multipliers, corresponding to the original problem. We further use the duality results and the intuition of the VUL reformulation, in the extended problem of joint admission control and beamforming. The aim of this is to find a maximal set of SUs, which can be jointly served, as well as the corresponding beamforming and power allocation. Our approach uses Lagrange duality, to detect infeasible cases and the intuition of the VUL reformulation to decide upon the users, which have the largest contribution to the infeasibiity of the problem. With these elements, we construct a deflation based algorithm for the joint beamforming and admission control problem, which benefits from low complexity, yet close to optimal perfomance. To make the method also suitable for dense networks, with a large number of SUs and PUs, a cluster aided approach is further proposed and consists in grouping users, based on their long term spatial signatures. The information in the clusters serves as an initial indication of the SUs which cannot be simultaneously served and the PUs which pose similar interference constraints to the BS. Thus, the cluster information can be used to significantly reduce the dimension of the problem in scenarios with large number of SUs and PUs, and this fact is further validated by extensive simulations. In the second part of this thesis, the practical case of imperfect covariance based CSI, available at the transmitter, is considered. To account for the uncertainty in the channel knowledge, a worst case approach is taken, in which the SINR and the interference constraints are considered for all CSI mismatches in a predefined set One important factor, which influences the performance of the worst case beamforming approach is a proper choice of the the defined uncertainty set, to accurately model the possible uncertainties in the CSI. In this thesis, we show that recently derived Riemannian distances are better suited to measure the mismatches in the statistical CSI than the commonly used Frobenius norms, as they better capture the properties of the covariance matrices, than the latter. Therefore, we formulate a novel worst case robust beamforming problem, in which the uncertainty set is bounded based on these measures and for this, we derive a convex approximation, to which a solution can be efficiently found in polynomial time. Theoretical and numerical results confirm the significantly better performance of our proposed methods, as compared to the state-of-the-art methods, in which Frobenius norms are used to bound the mismatches. The consistently better results of the designs utilizing Riemannian distances also manifest in scenarios with large number of users, where admission control techniques must supplement the beamforming design with imperfect CSI. Both benchmark methods as well as low complexity techniques, developed in this thesis to solve this problem, show that designs based on Riemannian distance outperform their competitors, in both required transmit power as well as number of users, which can be simultaneously served

Interference Exploitation via Symbol-Level Precoding: Overview, State-of-the-Art and Future Directions

Interference is traditionally viewed as a performance limiting factor in wireless communication systems, which is to be minimized or mitigated. Nevertheless, a recent line of work has shown that by manipulating the interfering signals such that they add up constructively at the receiver side, known interference can be made beneficial and further improve the system performance in a variety of wireless scenarios, achieved by symbol-level precoding (SLP). This paper aims to provide a tutorial on interference exploitation techniques from the perspective of precoding design in a multi-antenna wireless communication system, by beginning with the classification of constructive interference (CI) and destructive interference (DI). The definition for CI is presented and the corresponding mathematical characterization is formulated for popular modulation types, based on which optimization-based precoding techniques are discussed. In addition, the extension of CI precoding to other application scenarios as well as for hardware efficiency is also described. Proof-of-concept testbeds are demonstrated for the potential practical implementation of CI precoding, and finally a list of open problems and practical challenges are presented to inspire and motivate further research directions in this area

RIS-Aided Cell-Free Massive MIMO Systems for 6G: Fundamentals, System Design, and Applications

An introduction of intelligent interconnectivity for people and things has posed higher demands and more challenges for sixth-generation (6G) networks, such as high spectral efficiency and energy efficiency, ultra-low latency, and ultra-high reliability. Cell-free (CF) massive multiple-input multiple-output (mMIMO) and reconfigurable intelligent surface (RIS), also called intelligent reflecting surface (IRS), are two promising technologies for coping with these unprecedented demands. Given their distinct capabilities, integrating the two technologies to further enhance wireless network performances has received great research and development attention. In this paper, we provide a comprehensive survey of research on RIS-aided CF mMIMO wireless communication systems. We first introduce system models focusing on system architecture and application scenarios, channel models, and communication protocols. Subsequently, we summarize the relevant studies on system operation and resource allocation, providing in-depth analyses and discussions. Following this, we present practical challenges faced by RIS-aided CF mMIMO systems, particularly those introduced by RIS, such as hardware impairments and electromagnetic interference. We summarize corresponding analyses and solutions to further facilitate the implementation of RIS-aided CF mMIMO systems. Furthermore, we explore an interplay between RIS-aided CF mMIMO and other emerging 6G technologies, such as next-generation multiple-access (NGMA), simultaneous wireless information and power transfer (SWIPT), and millimeter wave (mmWave). Finally, we outline several research directions for future RIS-aided CF mMIMO systems.Comment: 30 pages, 15 figure

Precoding Schemes for Millimeter Wave Massive MIMO Systems

In an effort to cut high cost and power consumption of radio frequency (RF) chains, millimeter wave (mmWave) multiple input multiple output (MIMO) deploys hybrid architecture in which precoding is implemented as a combination of digital precoding and analog precoding, accomplished by using a smaller number of RF chains and a network of phase shifters respectively. The mmWave MIMO, which usually suffers from blockages, needs to be supported by Reconfigurable Intelligent Surface (RIS) to make communication possible. Along with the hybrid precoding in mmWave MIMO, the passive precoding of Reconfigurable Intelligent Surface (RIS) is investigated in a downlink RIS-assisted mmWave MIMO. The hybrid precoding and passive precoding are challenged by the unit modulus constraints on the elements of analog precoding matrix and passive precoding vector. The coupling of analog and digital precoders further complicates the hybrid precoding. One of the approaches taken in proposed hybrid precoding algorithms is the use of alternating optimization in which analog precoder and digital precoder are optimized alternately keeping the other fixed. Analog precoder is determined by solving a semidefinite programming problem, and from the unconstrained least squares solution during each iteration. In another approach taken in the proposed methods, the hybrid precoding is split into separate analog and digital precoding subproblems. The analog precoding subproblems are simplified using some approximations, and solved by using iterative power method and employing a truncated singular value decomposition method in two different hybrid precoding algorithms. In the prooposed codebook-based precoder, analog precoder is constructed by choosing precoding vectors from a codebook to maximize signal-to-leakage-and-noise ratio (SLNR). The passive precoding at the RIS in a single user MIMO is designed to minimize mean square error between the transmit signal and the estimate of received signal by using an iterative algorithm that solves the joint optimization problem of precoding, passive precoding and combiner. The problem of designing energy efficient RIS is solved by maximizing energy efficiency which is a joint optimization problem involving precoder, passive precoding matrix and power allocation matrix. The proposed hybrid precoding and passive precoding algorithms deliver very good performances and prove to be computationally efficient