Fig 6 - uploaded by Jingya Li
Content may be subject to copyright.
BS activation probability vs. target spectral efficiency per user (R k ). 

BS activation probability vs. target spectral efficiency per user (R k ). 

Source publication
Article
Full-text available
This paper considers a downlink heterogeneous network, where different types of multi-antenna base stations (BSs) communicate with a number of single-antenna users. Multiple BSs can serve the users by spatial multiflow transmission techniques. Assuming imperfect channel state information at both BSs and users, the precoding, load balancing, and BS...

Context in source publication

Context 1
... different joint precoding and load balancing schemes are compared in the scenario depicted in Fig. 2. We name these three schemes as "Optimal", "Heuristic" and "All Active" respectively. The "Optimal" scheme obtains the global optimal solution as described in Theorem 1, by an exhaustive search over all 2 5 possible BS mode combinations. The "Heuristic" scheme follows the algorithm proposed in Section IV, and the value of the soft threshold δ is set to 10 −4 . The "All Active" scheme is used as our performance baseline, which solves the optimization problem (9) by assuming that all BSs are active, i.e., the BS mode indicator z v = 1 for all BSs v ∈ V. For each scheme, the performance is averaged over 1000 independent user drops that provide feasible solutions for our optimization problem (9). For each user drop, the algorithms are evaluated over 50 independent channel realizations. The weights a v are set to 1 for all BSs. Define the dynamic part of total power consumption as the total RF power ( ∑ M v=1 a v ∆ v P trans,v ), and the remaining part of the total power consumption as the circuit power Figs. 3 and 4 demonstrate the total RF power and the total power con- sumption as a function of target spectral efficiency per user, respectively. As expected, the total power consumption and the RF power increase as the target spectral efficiency increases. Fig. 3 shows that the RF power for the "All Active" scheme is less than that of the "Heuristic" and "Optimal" schemes. This is expected since all BSs are active in the "All Active" scheme, whileas for the "Heuristic" and "Optimal" schemes, some BSs are put into sleep mode. With more BSs being active, the "All Active" scheme provides better energy-focusing and less propagation losses between the users and the transmitters, and will therefore reduce the total RF power. However, as can be seen from Fig. 4, compared to the "All Active" scheme, the "Heuristic" and "Optimal" schemes can substantially reduce the total power consumption, especially when the target QoS is small. This is because the circuit power consumption under the sleep mode is much lower compared to the one under the active mode, i.e., P sleep,v ≪ P active,v . For the "All Active" scheme, the increase in the circuit part from the extra power consumed by activating BSs clearly outweighs the decrease in the dynamic part. This implies that putting a BS into sleep mode by proper load balancing is an important solution for energy savings in heterogeneous networks. Fig. 5 plots the cumulative distribution function (CDF) of the total power consumption for the considered three schemes. The target spectral efficiency per user R k is 4 bit/s/Hz. We observe that compared to the "All Active" scheme, 20% of the total power consumption can be saved by the "Optimal" scheme with 70% probability and by the "Heuristic" scheme with 55% probability. For some user drops, the energy con- sumption can be reduced by 30% for both the "Optimal" and "Heuristic" schemes. Fig. 6 demonstrates the BS activation probability versus the target spectral efficiency per user. Here, the activation probability of the SBS is averaged over the probabilities of the four SBSs depicted in Fig. 2. We see that for the "All Active" scheme, the activation probabilities of the MBS and SBS are always one, since all BSs are always active in this scheme. Moreover, as anticipated, for both the "Heuristic" and "Optimal" schemes, the BS activation probabilities of the MBS and SBS increase as the target spectral efficiency per user increases. This is because in order to satisfy the raised QoS expectations of all users, the probability that a BS becomes active should increase so as to provide better energy- focusing and less propagation losses. Over the considered range of target spectral efficiency per user, the "Optimal" scheme has lower activation probability for the MBS and higher activation probability for the SBS as compared to the "Heuristic" scheme. Note that the circuit power consumed under the active mode P active,v for the MBS is much higher than that of the SBSs. Thus, as shown in Fig. 4, the "Optimal" scheme results in better energy saving as compared to the "Heuristic" ...

Similar publications

Article
Full-text available
In this paper, we consider the problem of power control and load balancing in uplink of cell-free (CF) multi-user (MU) Massive MIMO system. The power control problem is solved using three different criteria: power minimization, maximize min quality of service (QoS) and maximize sum spectral efficiency (SE) under imperfect channel state information...

Citations

... To further explore the potential of cell-free mMIMO system with limited fronthauls, another candidate serving mode, i.e., non-coherent joint transmission (NCJT), attracts attention recently [10], [11]. In the NCJT serving mode, since each AP that serves a particular UE transmit different part of the data [12], [13], the total fronthaul consumption of one specific UE equals to its data rate. ...
Preprint
With a great potential of improving the service fairness and quality for user equipments (UEs), cell-free massive multiple-input multiple-output (mMIMO) has been regarded as an emerging candidate for 6G network architectures. Under ideal assumptions, the coherent joint transmission (CJT) serving mode has been considered as an optimal option for cell-free mMIMO systems, since it can achieve coherent cooperation gain among the access points. However, when considering the limited fronthaul constraint in practice, the non-coherent joint transmission (NCJT) serving mode is likely to outperform CJT, since the former requires much lower fronthaul resources. In other words, the performance excellence and worseness of single serving mode (CJT or NCJT) depends on the fronthaul capacity, and any single transmission mode cannot perfectly adapt the capacity limited fronthaul. To explore the performance potential of the cell-free mMIMO system with limited fronthauls by harnessing the merits of CJT and NCJT, we propose a CJT-NCJT hybrid serving mode framework, in which UEs are allocated to operate on CJT or NCJT serving mode. To improve the sum-rate of the system with low complexity, we first propose a probability-based random serving mode allocation scheme. With a given serving mode, a successive convex approximation-based power allocation algorithm is proposed to maximize the system's sum-rate. Simulation results demonstrate the superiority of the proposed scheme.
... It is noted that, different from the power minimization problem, applying MRT for a WSR maximizing scheme does not lead to a tractable problem. Noncoherent JT design for minimizing weighted power consumption with imperfect channel state information was considered in [22]. A heuristic beamforming design for maximizing the WSR under the limited fronthaul capacity for CRAN networks was proposed in [23], which showed that noncoherent JT might outperform coherent JT in the regime of low fronthaul capacity. ...
Preprint
Full-text available
We investigate the coordinated multi-point noncoherent joint transmission (JT) in dense small cell networks. The goal is to design beamforming vectors for macro cell and small cell base stations (BSs) such that the weighted sum rate of the system is maximized, subject to a total transmit power at individual BSs. The optimization problem is inherently nonconvex and intractable, making it difficult to explore the full potential performance of the scheme. To this end, we first propose an algorithm to find a globally optimal solution based on the generic monotonic branch reduce and bound optimization framework. Then, for a more computationally efficient method, we adopt the inner approximation (InAp) technique to efficiently derive a locally optimal solution, which is numerically shown to achieve near-optimal performance. In addition, for decentralized networks such as those comprising of multi-access edge computing servers, we develop an algorithm based on the alternating direction method of multipliers, which distributively implements the InAp-based solution. Our main conclusion is that the noncoherent JT is a promising transmission scheme for dense small cell networks, since it can exploit the densitification gain, outperforms the coordinated beamforming, and is amenable to distributed implementation.
... To achieve spatial multiplexing and cooperative transmissions, a user k is assumed to be able to receive useful signals from multiple BSs, where the data symbols x k,m from different BSs are assumed to be mutually independent [26], [34]. In this way, the user k implements successive interference cancellation to decode the data streams sequentially. ...
... To satisfy a minimum spectral efficiency τ k , (26) can be reformed to the following quadratic inequalities by using the cyclic property of the trace operation: ...
... Problem P 3 is a convex semidefinite problem if we apply the semidefinite relaxation by replacing the constraint rank (D k ) = 1 with D k ≥ 0. Then, it can be solved efficiently using convex optimization tools and a rank-1 solution always exists given that the solution is feasible [26]. ...
Preprint
Full-text available
In this paper, we study the performance of cooperative millimeter wave (mmWave) networks using various precoding schemes. In our proposed method, multiple base stations (BSs) can jointly serve users and the BSs associated with no users are put into sleep mode to reduce the power consumption. Considering both the hardware power and the RF transmit power of the BSs, we propose a hybrid precoding scheme which minimizes the sum power consumption of the BSs subject to per-user spectral efficiency constraints as well as the per BS peak power constraints. In order to obtain tractable and near-optimal hybrid precoding solutions, we reformulate the analog precoding part as an equal-gain transmission problem and the digital precoding part as a relaxed convex semidefinite program. We present the results for both fully- and partially-connected hybrid precoding (FHP and PHP, respectively) schemes and show that, depending on the parameter settings, the power consumption of the PHP may be dominated by the RF transmit power and it may result in a larger power consumption than the FHP. For the cases with 2 BSs and 4 users, implementation of the FHP and the PHP in cooperative networks reduces the required RF transmit power, compared to the case in a non-cooperative network, by 71% and 65%, respectively.
... However, assuming that the signal from the second group, x (dp) 2,k , is detected first by treating x (dp) 1,k as noise, then one can subtract an estimated value of IoG (dp) 1,q from the received signal of the first group. This successive cancellation has been investigated in [36] and [37] and shown to significantly improve the minimal SINR value of users. ...
... where λ (tp) req is the required SINR, which is equivalent to a predetermined value of QoS as defined in (36). This optimization problem is a GP, and hence can be solved in polynomial time. ...
... req calculated in (36). Calculate the required R (dp) req as in (42) and solve (40). ...
Article
Full-text available
This paper proposes time-offset pilots for a single-cell multiuser massive multiple-input multiple-output (MIMO) system and studies its performance under the minimum mean-squared error channel estimator and successive interference cancellation. With the proposed time-offset pilots, users are divided into two groups and the uplink pilots from one group are transmitted simultaneously with the uplink data of the other group, which allows the system to accommodate more users for a given number of pilots. Successive interference cancellation is developed to ease the effect of pilot contamination and enhance data detection. Closed-form expressions for lower bounds of the uplink spectral efficiencies in both the training and data phases are derived when the maximum-ratio combining receiver is used at the base station. The power control problem is formulated with the objective of either maximizing the quality of service that can be equally provided to all users, or minimizing the total transmit power. Since the original power control problems are NP-hard, we also propose algorithms based on the bisection method to solve the problems separately in training and data phases. Analysis and numerical results show that the effect of pilot contamination can be mitigated by successive interference cancellation and proper power control.
... can be rewritten as in (27) at the top of the next page, where B π k j+1 ,k is given by ...
... By substituting the above beam-vectors into the data rate expression (27), we can obtain the data ratesr π k j ,k , ∀j = 1, · · · , |I k | , k ∈ U. Then, check whether the beam-vectors in (43) satisfy the per-link capacity constraints or not. ...
Article
Full-text available
The weighted sum rate maximization problem of ultra-dense cloud radio access networks (C-RANs) is considered, where realistic fronthaul capacity constraints are incorporated. To reduce the training overhead, pilot reuse is adopted and the transmit-beamforming used is designed to be robust to the channel estimation errors. In contrast to the conventional C-RAN where the remote radio heads (RRHs) coherently transmit their data symbols to the user, we consider their non-coherent transmission, where no strict phase-synchronization is required. By exploiting the classic successive interference cancellation (SIC) technique, we first derive the closed-form expressions of the individual data rates from each serving RRH to the user and the overall data rate for each user that is not related to their decoding order. Then, we adopt the reweighted l1-norm technique to approximate the l0-norm in the fronthaul capacity constraints as the weighted power constraints. A low-complexity algorithm based on a novel sequential convex approximation (SCA) algorithm is developed to solve the resultant optimization problem with convergence guarantee. A beneficial initialization method is proposed to find the initial points of the SCA algorithm. Our simulation results show that in the high fronthaul capacity regime, the coherent transmission is superior to the non-coherent one in terms of its weighted sum rate. However, significant performance gains can be achieved by the non-coherent transmission over the non-coherent one in the low fronthaul capacity regime, which is the case in ultra-dense C-RANs, where mmWave fronthaul links with stringent capacity requirements are employed. Index Terms-Ultra-dense networks (UDN), C-RAN, fronthaul capacity, pilot reuse, robust design.
... Therefore, optimizing EE performance for downlink transmission in HetNets has attracted a lot of research interest recently and mixed deployment of HetNets has been shown to have a higher EE. To save the HetNets energy, some actice/sleep regimes for conventional HetNets and massive MIMO HetNets were proposed in [3,4,28,51]. It is importantly noted that the maximizing EE performance does not try to minimize the beamformer power since EE merit is a ratio of the network sum-rate and the total power consumption. ...
Article
Full-text available
Resource allocation is one important mission in wireless communication systems. In 5G wireless networks, it is essential that the new systems be more dynamic and wiser to simultaneously satisfy various network demands, by using new wireless technologies and approaches. To this end, resource allocation is faced with many significant challenges such as interference alignment, security attacks, or green communication. On the other hand, as one serious problem in 5G networks, the issue of energy is aected directly by the allocated resources in the system, i.e., bandwidth allocation, power control, association allocation, and deployment strategies. Consequently, together with the enhancement of spectral eÿciency performance, an emerging trend of 5G wireless networks is to approach green communication via energy eÿciency (EE) (bits/Hz/Joule), whose most significant challenge is due to its belonging to the fractional programming in the optimization field, i.e., nonconvex programming. This leaves many diÿcult tasks for improving network EE performance. In this paper, we will tackle the critical EE in 5G wireless networks.
... where h mk is the estimation of the actual channelĥ mk at BBU pool. The estimation error vector e mk CN (0, E mk ) is assumed to have zero-mean and covariance matrix E mk ∈ C N×N [24]. Furthermore, we defineĥ ...
Article
Full-text available
User-centric and energy efficient are becoming two foremost design principles in the cloud radio access networks (Cloud-RAN). In this paper, we thus consider the problem of how to assign each user to several preferred remote radio heads (RRHs) and design the corresponding beamforming coefficients in a user-centric and energy efficient manner. We formulate this problem as a joint clustering and beamforming optimization problem, with the objective to maximize the energy efficiency (EE) while satisfying the users’ quality of service (QoS) requirement and respecting the RRHs’ transmit power limits. We first transform it into an equivalent parametric subtractive problem using the approach in fractional programming, and then it is cast into a tractable convex optimization problem by introducing a lower bound of the objective function. Finally, the structure of the optimal solution is derived and a two-tier iterative scheme is developed to find the clustering pattern and beamforming coefficients that maximize EE. Specially, we derive a RRH-user association threshold, based on which the RRH clustering pattern and the corresponding beamforming coefficients can be simultaneously determined. Through simulations, we show the superior performance of the proposed user-centric clustering and beamforming scheme in Cloud-RAN. © 2018 Springer Science+Business Media, LLC, part of Springer Nature
... In other works, [5]- [7], heuristic solutions are offered to the joint optimization problem. The authors in [8] study joint precoding and association optimization in a heterogeneous network, while making use of BS sleep modes. However, their work does not take into consideration backhaul (in C-RAN referred to as fronthaul) limitations. ...
Conference Paper
Full-text available
Joint optimization of associations and precoders in wireless communication networks has become a crucial problem, due to the growing density of network infrastructure and users. Furthermore , network operators continue to show interest in improved energy efficiency and less power consumption. Due to the non-convex structure of the joint optimization problem, current methods and solvers struggle to offer satisfactory solutions. In the present paper, we provide a novel approach for joint optimization of the precoders and associations in a cooperative network with limited fronthaul capacity links. The proposed joint optimization method provides an iterative approximation of the original problem in the form of a mixed integer quadratic program (MIQP), solved via off the shelf numerical solvers. The second contribution of our work is a distributed hybrid association strategy, which serves as an alternative to the joint optimization framework. The performance of both methods is evaluated, suggesting that the proposed joint optimization framework can be used as a benchmark for other heuristic methods, due to its better performance and higher complexity. Meanwhile, the hybrid association strategy is deemed suitable for a distributed implementation in less computationally advanced networks.
... Then, the following lemma can be easily proven. Lemma 2: Let ( X, q) denote the optimal solution for the optimization problem in (10). Then, we have ...
... holds for the constraint (10b) at equality. According to the above lemma, the optimal solution for the optimization problem in (10) can be used to check the feasibility of (6) (i.e., feasibility of the demand vector for the users). More specifically, for a user j with demand d j , if q j = 0, then d j is satisfied for that user; otherwise (i.e., if q j > 0), demand d j for user j is not satisfied. ...
... A similar approach is taken in [30] to define the feasibility problem corresponding to a different optimization problem. Hereinafter, we call the optimization problem in (10) and q j the admissibility checking optimization problem and inadmissibility indicator (IAI) for user j, respectively. ...
Article
Full-text available
To improve the spectral efficiency in Long-Term Evolution (LTE) systems, the resource blocks (RBs) are shared among different cells/base stations (BSs) resulting in interference among the cells/BSs on each RB although all the sub-carriers (SCs) in an RB may not be used in a cell. Defining the load of a given BS per RB as the fraction of the active SCs in that RB, in this paper, we present a generalized signal-to-interferenceand- noise-ratio (SINR) model for downlink users on a given RB. This model considers both the transmit powers of the BSs and the loads of the cells over that RB. Under this load-coupled SINR model, to study the feasibility of a given rate demand vector for users, we formulate an optimization problem of minimizing the total load of the BSs on the RBs. Then, for two different scenarios of feasible and infeasible demand vectors, respectively, we study the load management problem (i.e., minimizing the total load of the BSs on the RBs) and admission control problem (i.e., finding the sub-set of users with maximum cardinality whose demands can be concurrently satisfied), respectively. Our theoretical investigations, which provide guidelines for designing radio resource management methods for load-coupled OFDMA networks, are complemented through Monte Carlo simulations.
... The problem is treated as a weighted-base LB where the traffic of an UE is divided into subflows, each of which is transmitted via a different access network. Authors in [49] consider a relaxed problem formulation where each user can be associated with multiple cells and ...
... show that these problems can be solved by convex optimization. For a weight-based LB scheme, the performance of this latter is highly depended on the specific weight, which was heuristically obtained in [49]. Based on the concept of auction in game theory [50], authors in [46] propose a two-stage LB scheme for offloading macro-UEs to small-cell layer. ...
Thesis
High demands on mobile networks provide a fresh opportunity to migrate towardsmulti-tier deployments, denoted as heterogeneous network (HetNet), involving a mix of cell types and radio access technologies working together seamlessly. In this context, network optimisation functionalities such as load balancing have to be properly engineered so that HetNet benefit are fully exploited. This dissertation aims to develop tractable frameworks to model and analyze load balancing dynamics while incorporating the heterogeneous nature of cellular networks. In this context we investigate and analyze a class of load balancingstrategies, namely adaptive handover based load balancing strategies. These latter were firstly studied under the general heading of stochastic networks using independent and homogeneous Poisson point processes based network model. We propose a baseline model to characterize rate coverage and handover signalling in K-tier HetNet with a general maximum power based cell association and adaptive handover strategies. Tiers differ in terms of deployment density and cells characteristics (i.e. transmit power, bandwidth, and path loss exponent). One of the main outcomes is demonstrating the impact of offloading traffic from macro- to small-tier. This impact was studied in terms of rate coverage and HO signalling. Results show that enhancement in rate coverage is penalized by HO signalling overhead. Then appropriate algorithms of LB based adaptive HO are designed and their performance is evaluated by means of extensive system level simulations. These latter are conducted in 3GPP defined scenarios, including representation of mobility procedures in both connectedstate. Simulation results show that the proposed LB algorithms ensure performance enhancement in terms of network throughput, packet loss ratio, fairness and HO signalling.