Statistical group sparse beamforming for green Cloud-RAN via large system analysis

In this paper, we investigate the network power minimization problem for the multicast cloud radio access network (Cloud-RAN) with imperfect channel state information (CSI). The key observation is that network power minimization can be achieved by adaptively selecting active remote radio heads (RRHs) via controlling the group-sparsity structure of the beamforming vector. However, this yields a non-convex combinatorial optimization problem, for which we propose a three-stage robust group sparse beamforming algorithm. In the first stage, a quadratic variational formulation of the weighted mixed l1/l2-norm is proposed to induce the group-sparsity structure in the aggregated beamforming vector, which indicates those RRHs that can be switched off. A perturbed alternating optimization algorithm is then proposed to solve the resultant non-convex group-sparsity inducing optimization problem by exploiting its convex substructures. In the second stage, we propose a PhaseLift technique based algorithm to solve the feasibility problem with a given active RRH set, which helps determine the active RRHs. Finally, the semidefinite relaxation (SDR) technique is adopted to determine the robust multicast beamformers. Simulation results will demonstrate the convergence of the perturbed alternating optimization algorithm, as well as, the effectiveness of the proposed algorithm to minimize the network power consumption for multicast Cloud-RAN.

In centralized massive multiple-input multiple-output (MIMO) systems, the channel hardening phenomenon can occur, in which the channel behaves as almost fully deterministic as the number of antennas increases. Nevertheless, in a cell-free massive MIMO system, the channel is less deterministic. In this paper, we propose using instantaneous channel state information (CSI) instead of statistical CSI to obtain the power control coefficient in cell-free massive MIMO. Access points (APs) and user equipment (UE) have sufficient time to obtain instantaneous CSI in a slowly time-varying channel environment. We derive the achievable downlink rate under instantaneous CSI for frequency division duplex (FDD) cell-free massive MIMO systems and apply the results to the power control coefficients. For FDD systems, quantized channel coefficients are proposed to reduce feedback overhead. The simulation results show that the spectral efficiency performance when using instantaneous CSI is approximately three times higher than that achieved using statistical CSI.

In this paper we present a local channel correlation based zero-forcing (ZF) beamforming framework for the cell edge users. Without the instantaneous CSI (ICSI) assisting, we derive the exact expression of the averaged pairwise error probability (PEP) upper bounds at both of the receivers. According to the derived PEP bounds, an multi-objective optimization problem is formulated to get the elaborate power allocation and ZF beamforming design with the knowledge of local statistical channel state information (SCSI) at the transmitter side. By factorizing each beamforming matrix as the multiplication of two matrices, we can avoid inter-user interference through column orthogonal matrix design. Moreover, the original complicated optimization problem can be further decoupled into four simple sub-optimization problems. Then utilizing the Lagrange multiplying method, we finally achieve the feasible distributed statistical ZF beamforming design, which only involves the distributed computations based on the local channel correlations. Both theoretical analysis and simulation results confirm that the multi-cell spatial diversity gain can be fully exploited with only local SCSI. For comparison, the traditional perfect ICSI based ZF beamforming is analyzed and discussed. It is shown that in the high regime of signal-to-noise ratio (SNR), the diversity gain of the proposed statistical ZF beamforming is even better than that achieved by the conventional ICSI-aided ZF beamforming.

Hybrid beamforming is known to be a cost-effective and wide-spread solution for a system with large-scale antenna arrays. This paper studies the optimization of the analog and digital components of the hybrid beamforming solution for remote radio heads (RRHs) in a downlink cloud radio access network architecture. Digital processing is carried out at a baseband processing unit (BBU) in the “cloud,” and the precoded baseband signals are quantized prior to transmission to the RRHs via finite-capacity fronthaul links. In this system, we consider two different channel state information (CSI) scenarios: 1) ideal CSI at the BBU and 2) imperfect effective CSI. The optimization of digital beamforming and fronthaul quantization strategies at the BBU as well as analog radio-frequency (RF) beamforming at the RRHs is a coupled problem since the effect of the quantization noise at the receiver depends on the precoding matrices. The resulting joint optimization problem is examined with the goal of maximizing the weighted downlink sum-rate and the network energy efficiency. Fronthaul capacity and per-RRH power constraints are enforced along with constant modulus constraint on the RF beamforming matrices. For the case of perfect CSI, a block coordinate descent scheme is proposed based on the weighted minimum-mean-square-error approach by relaxing the constant modulus constraint of the analog beamformer. Also, we present the impact of imperfect CSI on the weighted sum-rate and network energy efficiency performance, and the algorithm is extended by applying the sample average approximation. The numerical results confirm the effectiveness of the proposed scheme and show that the proposed algorithm is robust to estimation errors.

A cloud radio access network (cloud-RAN) is a promising cellular architecture to increase both network spectral efficiency and energy efficiency. In the downlink transmission of cloud-RAN, a fundamental trade-off exists between the sum-spectral efficiency and the network power consumption induced by the fronthual links. To optimize this trade-off, it is essential to jointly identify a set of active remote radio heads (RRHs) and the beamforming vectors used at the active RRHs. To resolve this problem, this paper presents a novel group-sparse beamforming algorithm inspired by sparse principal component analysis (sparse-PCA). The key idea of the proposed method is to reformulate the sum-spectral efficiency maximization problem under a group-sparsity constraint into a generalized sparse-PCA problem, which is a tractable non-convex optimization problem. Using this reformulated optimization problem, a computationally efficient algorithm is proposed, which finds the solution that guarantees the first-order necessary optimality condition of the non-convex optimization problem. Simulation results demonstrate significant advantage of the proposed group-sparse beamfroming method.

We consider downlink transmission in cloud radio access networks with multiple cochannel multicasting groups served by a group of remote radio heads (RRHs), which receive information from a base band unit via finite-capacity fronthaul links. Our aim is to jointly design RRH selection and beamforming vectors such that the minimum weighted data rate among users is maximized under the constraints of maximum transmit power and fronthaul capacity at each specific RRH. The problem is intractable due to the numerical difficulties of combination and nonconvex functions. Based on a semidefinite relaxation technique, bisection search, and a branch-and-bound method, we develop an upper bound, which is also the optimal solution to the original problem if the relaxation is tight. More importantly, we propose a heuristic low-complexity iterative procedure for practical applications based on the state-of-the-art sequential convex approximation. Subsequently, we modify the proposed methods for the uncertain channel state information case. To be specific, the upper bound and its suboptimal solution are altered based on the $\mathcal {S}$ -lemma while the low-complexity algorithm is tailored by using two different approximations of intractable robust counterpart. The validity of the proposed methods in the region of limited fronthaul capacity is confirmed by numerical results.

In this paper, we investigate robust energy efficiency design for multicast downlink cloud radio access network (C- RAN) for both data-sharing and compression strategies. The two strategies mainly differ in whether the baseband units pool compresses the user messages before transmitting them to remote radio heads (RRH). The performance of worst-case energy efficiency for both strategies is compared by formulating the robust energy efficiency maximization problem subjected to finite RRH power budgets, limited fronthaul link capacity, and minimum quality-of-service constraints when only imperfect channel state information (CSI) is available at the transmitter. To solve these problems, we cast them into semidefinite program problems and solve them iteratively. Simulation results demon- strate effectiveness of our proposed algorithms and two strategies are compared under imperfect CSI.

Physical layer (PHY) security is recently regarded as a promising technique to improve the security performance of wireless communication networks. Current developments in PHY security are often based on the assumption of perfect channel state information (CSI). In this paper, both security and reliability performance for the downlink cloud radio access network with optimal remote radio heads (RRHs) node selection are investigated in a practical scenario by considering channel estimation (CE) errors. In particular, a three-phase transmission scheme is proposed and the linear minimum mean-square error (MMSE) estimation method is utilized to obtain the CSI. Based on the CSI estimates and the statistics of CE errors, the outage probability and intercept probability are derived in closed-form expression to evaluate the security and reliability performance, respectively. In addition, two possible cases (with or without intercepting signals from baseband unit) are considered for the eavesdropper. It is found that the suggested optimal RRHs selection scheme outperforms the nonselection scheme, and that the increasing number of RRHs can lower the outage probability as well as the intercept probability. It is also shown that there exists an optimal training number to minimize the sum of the outage probability and intercept probability. Finally, simulation results are provided to corroborate our proposed studies.

The Cloud radio access network (Cloud-RAN) has great potentials to improve energy efficiency and increase capacity of wireless networks. In this paper, we investigate multicast beamforming design for network power minimization of Cloud-RAN, which is shown to be a highly intractable non-convex mixed integer non-linear programming problem. To provide an efficient solution to this highly complicated problem, we propose a three-stage algorithm based on the group-sparsity inducing norm, which minimizes network power by coordinated multicast beamforming and adaptively selecting active remote radio heads (RRHs). In particular, a novel quadratic variational weighted l 1 =l 2 -norm aided alternating algorithm is proposed to exploit the group-sparsity structure of the beamforming vector, thereby guiding the active RRH set selection. Given the selected RRH set, multicast beamforming is performed to minimize the network power consumption. Furthermore, to enhance the computation efficiency upon utilizing the shared computing resources in the cloud center, we employ the alternating direction method of multipliers (ADMM) algorithm to solve the resulting semidefinite programming problems in parallel. Extensive simulation results will demonstrate the effectiveness of the proposed multicast group sparse beamforming algorithm.

In this paper, a source communicates to the destination with the cooperation of a relay, in the presence of an eavesdropper. All the links undergo Rayleigh fading and perfect decoding at the relays is not considered. The secrecy outage probability expression is evaluated for a decode-and-forward (DF) dual-hop cooperative relay network, both with and without the presence of direct source to eavesdropper transmission link. The performance of the maximal ratio combining (MRC) and selection combining (SC) diversity at the eavesdropper is investigated. Asymptotic and diversity gain analysis for both the single relay and multi-relay system is obtained, when average SNRs of source-relay and relay-destination links are balanced or unbalanced. We have shown that the increase in target secrecy rate and eavesdropper channel quality significantly affects the outage performance of the system. We have investigated the outage probability of optimal relay selection scheme, when either full instantaneous channel state information (ICSI) or statistical channel state information (SCSI) of all the links is available and have shown that there is improvement in the secrecy performance with the increase in the number of relays.

Heterogeneous cloud radio access networks (HCRANs) are potential solutions to improve both spectral and energy efficiencies by embedding cloud computing into heterogeneous networks (HetNets). The interference among remote radio heads (RRHs) can be suppressed with centralized cooperative processing in the base band unit (BBU) pool, while the intertier interference between RRHs and macro base stations (MBSs) is still challenging in H-CRANs. In this paper, to mitigate this inter-tier interference, a contract-based interference coordination framework is proposed, where three scheduling schemes are involved, and the downlink transmission interval is divided into three phases accordingly. The core idea of the proposed framework is that the BBU pool covering all RRHs is selected as the principal that would offer a contract to the MBS, and the MBS as the agent decides whether to accept the contract or not according to an individual rational constraint. An optimal contract design that maximizes the rate-based utility is derived when perfect channel state information (CSI) is acquired at both principal and agent. Furthermore, contract optimization under the situation where only the partial CSI can be obtained from practical channel estimation is addressed as well. Monte Carlo simulations are provided to confirm the analysis, and simulation results show that the proposed framework can significantly increase the transmission data rates over baselines, thus demonstrating the effectiveness of the proposed contract-based solution.

Since proposed, Cloud Radio Access Network (Cloud-RAN) gives a committed architecture suitable for fulfilling 5G networks' applications. Cloud-RAN can solve challenges related to ever-evolving networks' mobile operators and an ever-growing number of end-users. Cloud-RAN architecture maintains both profitability and quality of service (QoS) . In this paper, power consumption is jointly formulated as power minimization beamforming and RRHs selection problem. Using the conventional convex or heuristic optimization approaches to find optimal solutions is highly complex; hence, we introduce an Artificial Neural Network (ANN) - based optimization model that aims to optimize the active Remote Radio Heads (RRHs) numbers in remote network sites and the consumed power. The proposed model considers various signal to interference plus noise ratios per client and power consumption models. Specifically, the model uses an adopted Bi-Section Group Sparse Beamforming (GSBF) optimization algorithm to reach near optimum solutions. Obtained validated results encourage machine learning techniques to reduce both the complexity and power consumption in such an emerging area.

In this paper, we study the capacity-achieving input covariance matrices for the multiuser multiple-input multiple-output (MIMO) uplink channel under jointly-correlated Rician fading when perfect channel state information (CSI) is known at the receiver, or CSIR while only statistical CSI at the transmitter, or CSIT, is available. The jointly-correlated MIMO channel (or the Weichselberger model) accounts for the correlation at two link ends and is shown to be highly accurate to model real channels. Classically, numerical techniques together with Monte-Carlo methods (named stochastic programming) are used to resolve the problem concerned but at a high computational cost. To tackle this, we derive the asymptotic sum-rate of the multiuser (MU) MIMO uplink channel in the large-system regime where the numbers of antennas at the transmitters and the receiver go to infinity with constant ratios. Several insights are gained from the analytic asymptotic sum-rate expression, based on which an efficient optimization algorithm is further proposed to obtain the capacity-achieving input covariance matrices. Simulation results demonstrate that even for a moderate number of antennas at each link, the new approach provides indistinguishable results as those obtained by the complex stochastic programming approach.

In this paper, we focus on heterogeneous networks (HetNet) where low-power remote radio head (RRH) nodes are deployed within the coverage area of an existing macro network, aiming at offloading traffic from the macro cell to small cells. To improve the data rate both for users served by macro base stations (BSs) and those by RRH nodes, this paper proposes a joint selection interference control (JSIC) based scheme, where each user equipment (UE) in the cell feeds its channel state information back to the corresponding BS based on the best companion cluster (BCC) method. After sharing users' information through the high-speed backhaul, macro-BS and RRH node make beam and UE selection simultaneously in order to avoid too much interference. To compare with JSIC-based scheme, we also discuss a related work prioritized selection interference control (PSIC)-based scheme. Simulation results show that JSIC-based scheme has a better performance of total throughput than PSIC-based scheme, providing fairness between macro users and RRH-users.

This paper addresses the design of a multiuser relaying subnetwork within a cloud radio access network (C-RAN) from an energy-efficient perspective. In the relaying subnetwork, multiple source–destination pairs communicate with the assistance of multiple remote radio heads (RRHs) connected to the baseband unit pool. Exploiting the flexible centralized processing structure of C-RAN, where RRHs can be adaptively activated/deactivated, we formulate the problem as a quality-of-service (QoS) based network energy minimization problem via joint RRH selection and relaying matrix optimization. Since the resultant optimization problem is nonconvex and mathematically challenging, we propose an iterative solution based on the concept of the re-weighted $l_1$ norm, along with a block-coordinate descent type algorithm. The active RRHs are then determined in a single attempt by thresholding a group sparsity pattern associated with the set of all RRH relaying matrices. To circumvent a potentially undesirable condition, where the selected subset of RRHs fails to simultaneously satisfy all the destination users’ QoS levels, we conceive a UE admission control mechanism for overcoming the associated infeasibility problem. Our simulation results demonstrate the explicit benefits of the proposed design approach, which results in a significantly lower energy consumption of the relaying subnetwork than conventional cooperative relaying.