Adaptive Multicell 3-D Beamforming in Multiantenna Cellular Networks

The impacts of channel estimation errors, inter-cell interference, phase adjustment cost, and computation cost on an intelligent reflecting surface (IRS)-assisted system are severe in practice but have been ignored for simplicity in most existing works. In this paper, we investigate a multi-antenna base station (BS) serving a single-antenna user with the help of a multi-element IRS in the presence of channel estimation errors and inter-cell interference. We consider imperfect channel state information (CSI) at the BS, i.e., imperfect CSIT, and focus on the robust optimization of the BS's instantaneous CSI-adaptive beamforming and the IRS's quasi-static phase shifts. First, we formulate the robust optimization of the BS's instantaneous channel state information (CSI)-adaptive beamforming and IRS's quasi-static phase shifts for the ergodic rate maximization as a very challenging two-timescale stochastic non-convex problem. Then, we obtain a closed-form beamformer for any given phase shifts and a more tractable single-timescale stochastic non-convex problem only for phase shifts. Next, we propose a low-complexity stochastic algorithm to obtain quasi-static phase shifts which correspond to a KKT point of the single-timescale stochastic problem. It is worth noting that the proposed method offers a closed-form robust instantaneous CSI-adaptive beamforming design that can promptly adapt to rapid CSI changes over slots and a robust quasi-static phase shift design of low computation and phase adjustment costs in the presence of channel estimation errors and inter-cell interference. Finally, numerical results demonstrate the notable gains of the proposed robust joint design over existing ones and reveal the practical values of the proposed solutions.

SUMMARY To mitigate the inter-cell interference in mul-ticell downlink systems, this letter consider the robust precoderdesign for multicell cooperation where the knowledge of chan-nel state available at the base station is imperfect. Assumingthat imperfect channel state information (CSI) can be exchangedamong cells but with no data sharing, we investigate the worst-case performance optimization problem with bounded CSI error.Our objective is to minimize the weighted sum mean-square-error(MSE) subject to per-base-station power constraints. A dis-tributed solution is obtained by reformulating the upper bound ofMSE and exploiting the Lagrangian method for the optimal prob-lem. Simulation results demonstrate that the proposed algorithmis robust to guarantee the worst-case sum rate performance andhas lower computational complexity than the SINR-based design. key words: Multi-cell cooperation, robust precoder, upper boundof MSE, weighted sum MSE minimization. 1. IntroductionMulticell cooperation communication between base sta-tions (BSs) has emerged as a promising approach toimprove the performance of systems and reduce the in-tercell interference with universal frequency reuse. De-pending on the BS coordinated level, it can be per-formed by two mode[1],[2]. In the first mode, the BSsshare both data and channel state information (CSI),where the system is termed as “network multiple inputmultiple output (MIMO)” or “joint processing (JP)”.In the second mode, the cooperative BSs exchange CSIonly, and the system is called “multicell system” or “co-ordinated beamforming (CBF)”. In this paper, we focuson the latter.One crucial processing for the cooperative multi-cell system is how to optimize the cooperation trans-mission between the cells. Without data sharing, [3]consider the sum-power minimization problem subjectto signal-to-interference plus noise ratio (SINR) con-straint. In [4], the weighted sum-rate maximizationproblem is solved through virtual SINR maximization,but the distributed solution is only suitable for highsignal-to-noise ratio (SNR) regime. To achieve a fair-ness basedrate optimality, [5] proposeda distributedal-gorithm to approach the performance of the centralized

Bit error rate evaluation of relay-aided cooperative NOMA with energy harvesting under imperfect SIC and CSI

Base station cooperation is an attractive technique to increase the spectral efficiency of multi-cell systems. One of the challenges in multi-cell systems is obtaining accurate channel state information (CSI) at the base station. One source of CSI inaccuracy is the delay incurred in obtaining CSI and exchanging it among base stations. The presence of delay is inevitable when CSI is exchanged over the back-haul. In addition, CSI is commonly obtained using limited feedback techniques which further contribute to its inaccuracy. In this paper, we re-visit the comparison between competitive (egoistic) and cooperative (altruistic) beamforming strategies in the presence of imperfect CSI. The impact of CSI inaccuracy due to delay and finite codebook size on the achieved sum rate is analyzed. Closed-form expressions for a lower bound and a first-order approximation of the average sum rates achieved by these beamforming strategies are derived. Using the closed-form expressions, a mode switching criterion is proposed to switch between competitive and cooperative beamforming based on the signal-to-noise ratio (SNR), delay, Doppler frequency and codebook size. It is shown that competitive beamforming is preferred in the limit of low SNR irrespective of the quality of CSI, while cooperative beamforming is preferred only at high SNR and low Doppler frequencies, confirming that base station cooperation is not always advantageous.

Base station cooperation improves the sum-rates that can be achieved in cellular systems. Conventional cooperation techniques require sharing large amounts of information over finite-capacity backhaul links and assume that base stations have full channel state information (CSI) of all the active users in the system. In this paper, a new limited feedback strategy is proposed for multicell beamforming where cooperation is restricted to sharing only the CSI of active users among base stations. The system setup considered is a linear array of cells based on the “soft hand-off model,” where each cell contains single-antenna users and multi-antenna base stations. Beamforming vectors are designed using a generalized eigenvector approach to maximize the sum-rate in a single-interferer scenario, at high signal to noise ratio. Users are assumed to feedback quantized CSI of the desired and interfering channels using a finite-bandwidth feedback link. An upper bound on the mean loss in sum rate due to random vector quantization is derived. A new feedback-bit allocation strategy, to partition the available bits between the desired and interfering channels, is developed to reduce the mean loss in sum-rate due to quantization for the soft hand-off model. The proposed feedback-bit partitioning algorithm is shown, using simulations, to yield sum-rates close to the those obtained using full CSI at base station.

Linear precoding for cooperative multi-cell transmission can provide substantial gains in user throughput, while channel state information (CSI) need to be available at the transmitter. Performance degradation due to imperfect CSI can be partially compensated by robust precoding techniques. For distributed precoding the pre-processing of the user data is performed locally at each base station (BS), while CSI of all participating users is needed. Hence, CSI need to be exchanged between BSs. However, in practice CSI sharing is affected by backhaul latency or limited backhaul capacity resulting in different CSI versions available at the BSs. In this paper, we present a novel robust sum rate maximizing precoding solution, which accounts for imperfect CSI sharing between BSs. Applying the proposed scheme, each BS optimizes its precoding matrix based on local knowledge and by assuming a certain precoding matrix is applied at the other BSs. The assumed precoding matrix results from degrading local knowledge to common but less accurate knowledge. We show that our solution can significantly boost the rate performance compared to existing precoding solutions.

The impacts of channel estimation errors, inter-cell interference, phase adjustment cost, and computation cost on an intelligent reflecting surface (IRS)-assisted system are severe in practice but have been ignored for simplicity in most existing works. In this paper, we investigate a multi-antenna base station (BS) serving a single-antenna user with the help of a multi-element IRS in a multi-cell network with inter-cell interference. We consider imperfect channel state information (CSI) at the BS, i.e., imperfect CSIT, and focus on the robust optimization of the BS’s instantaneous CSI-adaptive beamforming and the IRS’s quasi-static phase shifts in two scenarios. In the scenario of coding over many slots, we formulate a robust optimization problem to maximize the user’s ergodic rate. In the scenario of coding within each slot, we formulate a robust optimization problem to maximize the user’s average goodput under the successful transmission probability constraints. The robust optimization problems are challenging two-timescale stochastic non-convex problems. In both scenarios, we obtain closed-form robust beamforming designs for any given phase shifts and more tractable stochastic non-convex approximate problems only for the phase shifts. Besides, we propose an iterative algorithm to obtain a Karush-Kuhn-Tucker (KKT) point of each of the stochastic problems for the phase shifts. It is worth noting that the proposed methods offer closed-form robust instantaneous CSI-adaptive beamforming designs which can promptly adapt to rapid CSI changes over slots and robust quasi-static phase shift designs of low computation and phase adjustment costs in the presence of imperfect CSIT and inter-cell interference. Numerical results further demonstrate the notable gains of the proposed robust joint designs over existing ones and reveal the practical values of the proposed solutions.

In this paper, we analyze the ergodic sum rate in a multiuser multi-cell downlink. Coordinated beamforming is employed to mitigate the interference, including intra-cell and inter-cell interference. However, due to the limited capacity of the backhaul link, only partial channel state information (CSI) is obtained at the base stations (BSs), resulting in residual interference even with coordinated beamforming. By quantifying the impact of imperfect CSI, we derive closed-form ergodic sum rate results for a multiuser multi-cell downlink in terms of i. CSI accuracy, ii. transmit signal-to-noise ratio (SNR) and iii. channel condition. Furthermore, through asymptotic analysis of the performance loss induced by imperfect CSI, we obtain some clear insights on the performance. Finally, our theoretical claims are validated through extensive simulations.

Channel state information (CSI) is critical for the performance of multicell cooperative transmission. This paper compares two cooperative multicell precoding methods, namely, centralized precoding with global CSI and distributed precoding with local individual CSI. For both cases, the BSs have access to the data of all the users. The only difference is that in centralized precoding, the precoding is based on the global CSI shared in a central control unit, while in distributed precoding, each BS performs precoding based on its local CSI. The comparison is made under the framework of large dimension analysis based on random matrix theory. The performance gap between these two approaches can be revealed and quantified theoretically in closed form. The gap converges to a constant value in the large number of antennas regime, which we refer to as the price of local CSI. We can obtain some insights into the impact of limited CSI on the cooperative multicell transmission performance. Numerical results are provided to confirm the theoretical results and to show performance of cooperative multicell transmission with local CSI almost decrease linearly with the increased ditributedness.

Multi-cell cooperation is a promising approach for mitigating inter-cell interference in dense cellular networks. Quantifying the performance of multi-cell cooperation is challenging as it integrates physical-layer techniques and network topologies. For tractability, existing work typically relies on the over-simplified Wyner-type models. In this paper, we propose a new stochastic- geometry model for a cellular network with multi-cell cooperation, which accounts for practical factors including the irregular locations of base stations (BSs) and the resultant path-losses. In particular, the proposed network-topology model has three key features: i) the cells are modeled using a Poisson random tessellation generated by Poisson distributed BSs, ii) multi-antenna BSs are clustered using a hexagonal lattice and BSs in the same cluster mitigate mutual interference by spatial interference avoidance, iii) BSs near cluster edges access a different sub- channel from that by other BSs, shielding cluster-edge mobiles from strong interference. Using this model and assuming sparse scattering, we analyze the shapes of the outage probabilities of mobiles served by cluster-interior BSs as the average number K of BSs per cluster increases. The outage probability of a mobile near a cluster center is shown to be proportional to e -c(2-√ν)2K where ν is the fraction of BSs lying in the interior of clusters and c is a constant. Moreover, the outage probability of a typical mobile is proved to scale proportionally with e -c′(1-√ν)2K where c′ is a constant. © 2011 IEEE.

Non-orthogonal multiple access (NOMA) is one of the key technologies to serve in ultra-dense networks with massive connections which is crucial for Internet of Things. Besides, NOMA provides better spectral efficiency compared to orthogonal multiple access. However, NOMA systems have been mostly investigated only in terms of ergodic capacity (EC) and outage probability (OP) whereas error performances have not been well-studied. In addition, in those analysis, mostly perfect successive interference canceler (SIC) is assumed or the considered imperfect SIC model is not reasonable. Besides, channel state information (CSI) errors are also not considered in most studies. However, this is not the case for the practical scenarios, and these imperfect SIC and CSI effects limit the performance of NOMA involved systems. Moreover, the imperfect SIC causes unfairness between users. In this paper, we introduce reversed decode-forward relaying NOMA (R-DFNOMA) to improve user fairness compared to conventional DFNOMA (C-DFNOMA). In the analysis, we define imperfect SIC effect as dependant to channel fading and with this imperfect SIC and CSI errors, we derive exact expressions of EC and OP. We also provide upper bound for EC, and asymptotic and lower bound expressions for OP. Furthermore, we evaluate bit error performance of the proposed R-DFNOMA and derive exact bit error probability (BEP) in closed-form with imperfect CSI which is the first study analyzing error performances of decode-forward relaying NOMA with imperfect CSI. Then, we define user fairness index in terms of all key performance indicators (KPIs) (i.e., EC, OP and BEP). Based on extensive simulations, all derived expressions are validated, and it is proved that the proposed R-DFNOMA provides better user fairness than C-DFNOMA in terms of all KPIs. Finally, we discuss the effect of power allocations at both source and relay on the performance metrics and user fairness.

We design novel transmission strategies to maximize the energy efficiency (EE) of the uplink multi-user multiple-input and multiple-output relay channel. In this channel, $K$ multi-antenna users communicate with a multi-antenna base station (BS) through a multi-antenna relay. To achieve the goal of EE maximization, we propose new iterative algorithms to jointly optimize the multi-user precoder and the relay precoder under transmit power constraints for two cases. In the first case, the perfect global channel state information (CSI) is available, while in the second case, the CSI between the relay and the BS is imperfect. To surmount the non-convexity of our formulated EE optimization problems in both cases, we introduce the parameter subtractive function into the proposed algorithms. Then, the EE parameter in the parameter subtractive function is updated by Dinkelbach’s algorithm in the perfect CSI case, and by the bisection method in the imperfect CSI case. Moreover, in the perfect CSI case, the relay precoder is optimized by the diagonalization operation and the multi-user precoder is optimized based on the weighted minimum mean square error method. Differently, in the imperfect CSI case, we apply the sign-definiteness lemma to promote the semidefinite programming formulation of the EE optimization problem. Furthermore, we present the numerical results to demonstrate that our proposed iterative algorithms have a good convergence rate in both cases. In addition, we show that our proposed iterative algorithms achieve a higher EE performance than the existing algorithms in both CSI cases.

In wireless communications, interference is known as a major restriction in achieving system capacity. Recently, distributed antenna system (DAS) has received considerable attention due to its potential to mitigating interference and path-loss. In LTE-A system, a transmitter and a receiver are collaborated together to tackle the interference. To do so in the frequency division duplex system, channel state information (CSI) of the downlink channel must be shared amongst transceivers via a limited feedback technique. In this regard, this article evaluates and compares the performance of DAS and centralized antenna system (CAS) under imperfect downlink CSI, where practical system restrictions such as out-of-cell interference, path-loss, and small-scale fading are taken into account. The system performance is evaluated in term of cell throughput, where a LTE-A standard compliant simulator is utilized for simulation. The results reveal high dependency of system performance to the accuracy of CSI, where system throughput severely degrades under imperfect CSI. In contrast to CAS, DAS is more robust again imperfect CSI, where under imperfect CSI, DAS significantly outperforms CAS in term of cell-throughput.

A robust scheme is proposed to optimize the linear precoders/decoders for MIMO downlinks where the available channel state information (CSI) at base station (BS) is imperfect. The objective is to minimize the sum mean square error (SMSE) over all data sub-streams under a per-user transmit power constraint. By using an iterative procedure, the proposed scheme extends the existing optimization algorithm for the single-user MIMO system with perfect CSI to solve approximately the minimizing SMSE problem in the multiuser MIMO downlink with imperfect CSI at BS. Simulation results demonstrate that the proposed scheme can effectively mitigate the performance loss induced by the imperfect CSI and can provide largest possible diversity as well as increased throughput.

<p>In this thesis new robust methods for the efficient sharing of the radio spectrum for underlay cognitive radio (CR) systems are developed. These methods provide robustness against uncertainties in the channel state information (CSI) that is available to the cognitive radios. A stochastic approach is taken and the robust spectrum sharing methods are formulated as convex optimisation problems. Three efficient spectrum sharing methods; power control, cooperative beamforming and conventional beamforming are studied in detail. The CR power control problem is formulated as a sum rate maximisation problem and transformed into a convex optimisation problem. A robust power control method under the assumption of partial CSI is developed and also transformed into a convex optimisation problem. A novel method of detecting and removing infeasible constraints from the power allocation problem is presented that results in considerably improved performance. The performance of the proposed methods in Rayleigh fading channels is analysed by simulations. The concept of cooperative beamforming for spectrum sharing is applied to an underlay CR relay network. Distributed single antenna relay nodes are utilised to form a virtual antenna array that provides increased gains in capacity through cooperative beamforming. It is shown that the cooperative beamforming problems can be transformed into convex optimisation problems. New robust cooperative beamformers under the assumption of partial and imperfect CSI are developed and also transformed into convex optimisation problems. The performance of the proposed methods in Rayleigh fading channels is analysed by simulations. Conventional beamforming to allow efficient spectrum sharing in an underlay CR system is studied. The beamforming problems are formulated and transformed into convex optimisation problems. New robust beamformers under the assumption of partial and imperfect CSI are developed and also transformed into convex optimisation problems. The performance of the proposed methods in Rayleigh fading channels is analysed by simulations.</p>