Statistical CSI based zero-forcing beamforming for cooperative two-cell downlink transmission

This paper proposes a statistical-eigenmode space-division multiple-access (SE-SDMA) transmission approach for a two-user downlink system where two transmit antennas are deployed at the base station and each mobile user has only one receive antenna, assuming that only statistical channel state information (SCSI) is available at the transmitter. By maximizing a lower bound of the ergodic signal-to-leakage-and-noise ratio (SLNR), the proposed SE-SDMA approach selects two users with orthogonal principal statistical eigen-directions and then transmits to each user along the corresponding eigenmode. For this approach, we derive an exact expression of the achievable ergodic rate, and compare it with the zero-forcing beamforming (ZFBF) system exploiting instantaneous CSI. We show that SE-SDMA can achieve the maximum ergodic sum-rate of the two selected users, and provide significant user selection gains. For comparison with ZFBF, we show that the rate gap between SE-SDMA and ZFBF with perfect CSI at the transmitter (CSIT) tends to zero in highly correlated channels. Further, when ZFBF is implemented with inaccurate CSIT, the operating regions of SE-SDMA and ZFBF are investigated for different ranges of signal-to-noise ratio (SNR), instantaneous CSIT accuracy levels, and spatial correlation levels. Numerical results confirm the analytically derived conclusions, and physical insights are provided.

This paper investigates the zero-forcing (ZF) beamforming transmit strategy in the multiple-antenna multiuser downlink systems. We consider the case of mobile users equipped with multiple antennas. Although the capacity of such systems can be achieved by dirty paper coding (DPC), DPC is extremely difficult and challenging to implement. Thus, simple but suboptimal linear beamforming techniques like ZF beamforming can be deployed. However, the number of users that can be served using this strategy is limited by the number of transmit antennas at the base station. The solution for this limitation is user selection (scheduling), which also exploits multiuser diversity. Therefore, user selection can be used to enhance the throughput of the system. Recently, it has been shown that ZF beamforming strategy with user selection is asymptotically optimal for a large number of users. In this paper, a semi-orthogonal user selection (SUS) algorithm is extended to the system with multiple-antenna mobile users. This algorithm aims to select users, which are semi-orthogonal. The optimal ZF beamforming matrices are obtained and it is shown that the optimal ZF beamforming throughput is related to the eigenvalues of the user channels. Therefore, SUS is aimed to select the proper group of users based on maximizing the channel eigenvalues and therefore improving the optimal ZF beamforming throughput of the system.

In this paper, a comprehensive design and analysis of multiple-input multiple-output (MIMO) full-duplex (FD) relaying systems in a multi-cell environment is investigated, where a multi-antenna amplify-and-forward FD relay station serves multiple half-duplex (HD) multi-antenna users. The pivotal obstacles of loopback self-interference (LI) and multiple co-channel interferers (CCI) at the relay and destination when employing FD relaying in cellular networks are addressed. In contrast to the HD relaying mode, the CCI in the FD relaying mode is predicted to double since the uplink and downlink communications are simultaneously scheduled via the same channel. In this paper, the optimal layout of transmit (receive) precoding (decoding) weight vectors which maximizes the overall signal-to-interference-plus-noise ratio is constructed by a suitable optimization problem, and then a closed-form sub-optimal formula based on null space projection is presented. The proposed hop-by-hop rank-1 zero-forcing (ZF) beamforming vectors are based on added ZF constraints used to suppress the LI and CCI channels at the relay and destination, i.e., the source and relay perform transmit ZF beamforming, while the relay and destination employ receive ZF combining. To this end, unified accurate expressions for the outage probability and ergodic capacity are derived in closed form. In addition, simpler tight lower bound formulas for the outage probability and ergodic capacity are presented. Moreover, the asymptotic approximations for outage probability are considered to gain insights into system behavior in terms of the diversity order and array gain. Numerical and simulation results show the accuracy of the presented exact analytical expressions and the tightness of the lower bound expressions. The case of hop-by-hop maximum-ratio transmission/maximal-ratio combining beamforming is included for comparison purposes. Furthermore, our results show that while multi-antenna terminals improve the system performance, the detrimental effect of CCI on FD relaying is clearly seen. Therefore, our findings unveil that MIMO FD relaying could significantly improve the system performance compared to its conventional MIMO HD relaying counterpart.

In this paper, we focus on downlink zero forcing (ZF) beamforming design scheme for multiuser (MU) spatial multiplexing (SM) multiple-input multiple-output (MIMO) systems. Based on the minimum average probability of symbol error (PSE), we give the optimal design method of the beamforming weight matrices. Furthermore, we derive the upper bound PSEs to evaluate the impact of channel feedback errors on the system performance. Comparison of the upper bounds of the average PSE for several schemes shows that the downlink ZF beamforming for multiuser spatial multiplexing MIMO schemes provide almost the same performance as the SU beamforming scheme.

For a multiple-input single-output (MISO) downlink channel with M transmit antennas, it has been recently proved that zero-forcing beamforming (ZFBF) to a subset of (at most) M "semi-orthogonal" users is optimal in terms of the sum-rate, asymptotically with the number of users. However, determining the subset of users for transmission is a complex optimization problem. Adopting the ZFBF scheme in a cooperative multi-cell scenario renders the selection process even more difficult since more users are involved. In this paper, we consider a multi-cell cooperative ZFBF scheme combined with a simple sub-optimal users selection procedure for the Wyner downlink channel setup. According to this sub-optimal procedure, the user with the "best" local channel is selected for transmission in each cell. It is shown that under an overall power constraint, a distributed multi-cell ZFBF to this sub-optimal subset of users achieves the same sum-rate growth rate as an optimal scheme deploying joint multi-cell dirty-paper coding (DPC) techniques, asymptotically with the number of users per cell. Moreover, the overall power constraint is shown to ensure in probability, equal per-cell power constraints when the number of users per-cell increases.

In this paper, we develop a statistical group sparse beamforming framework to minimize the network power consumption for green cloud radio access networks (Cloud-RANs). It will promote group sparsity structures in the beamforming vectors, which will provide a good indicator for remote radio head (RRH) ordering to enable adaptive RRH selection for power saving. In contrast to the previous works that depend heavily on instantaneous channel state information (CSI), the proposed algorithm only depends on the long-term channel state attenuation for RRH ordering, which does not require frequent update, thereby significantly reducing the computation overhead. This is achieved by developing a smoothed l p -minimization approach to induce group sparsity in beamforming vectors, followed by an iterative reweighted-l 2 algorithm via the principles of the majorization-minimization (MM) algorithm and the Lagrangian duality theory. With the well-structured closed-form solutions at each iteration, we further leverage the large-dimensional random matrix theory to derive deterministic approximations for the squared l 2 -norm of the induced group sparse beamforming vectors in the large system regimes. The deterministic approximation results only depend on statistical CSI and will guide the RRH ordering. Simulation results demonstrate the near-optimal performance of the proposed algorithm, even in finite systems.

We propose two closed form zero-forcing beamformers (ZFBF) for the full-duplex (FD) two way relay network, which efficiently suppress the self-interferences at the involved nodes so that the two way relaying can be implemented in a single time phase. We assume a large portion of the self-interferences are suppressed by analog circuit parts and the proposed digital domain beamforming remove the remaining interference. By repetitive applications of projection onto the orthogonal space combined with the geometric geodesic beamforming, the two schemes allow us to characterize the rate pair curves of the FD two way relay network by simply varying the angles forming the geodesic beamforming vectors. Two optimization approaches can be applied to find the angle parameters and the better ZFBF design.

This paper studies the optimal joint beamforming and power control strategy for device-to-device (D2D) communication underlaying multiuser multiple-input multiple-output cellular networks. We consider multiple antennas at the base station (BS) and a single antenna at each cellular user (CU), D2D transmitter (DT), and D2D receiver (DR). We aim to minimize the total transmission power of the system by jointly designing the transmit beamforming at the BS and the transmit powers for both BS and DTs, while satisfying the signal-to-interference-plus-noise ratio based quality-of-service constraints for both CUs and DRs. Due to the nonconvex nature of the problem, we apply the semidefinite relaxation technique to find the optimal solution, which always satisfies the rank-one constraint. We also investigate three suboptimal fixed beamforming schemes: zero-forcing (ZF), regularized ZF, and hybrid maximum ratio transmission-ZF, where the focus is to minimize the total transmission power while reducing complexity. When perfect channel information is not available, we propose a robust transmit power minimization strategy with ZF beamforming that only requires limited feedback based channel direction information at the BS. Finally, computer simulation results are presented to demonstrate the effectiveness of the proposed schemes.

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.

MIMO can enhance the performance of wireless system greatly. However, the limited battery life and terminal size of the UE in a cellular system put a constraint on the performance enhancement from MIMO. Especially when the transmitter has more antenna than the receiver in downlink, the conventional MIMO schemes can only exploit partial spatial multiplexing gain and diversity gain. For different users' independent locations lead to independent spatial fading one another, adaptive spatial and temporal scheduling can be developed to exploit the spatial multiuser diversity and achieve the tradeoff between multiplexing gain and spatial diversity gain available. In this paper, the enhanced MIMO schemes with greedy multiuser diversity are compared when Node B has more antenna than UE, e.g. zero forcing beamforming (ZFB), dual space time block coding (DSTBC), singular value decomposition (SVD) and vertical Bell labs layered spatial time code plus antenna selection (VBLAST-AS). From the simulation results, the ZFB has achieved the best spectrum efficiency, and the gain exceeds VBLATS-AS and DSTBC more than 50%

This paper presents a novel precoding approach for MIMO broadcast channels, in which is performed on both sides of the wireless link. The aim of the proposed approach is to avoid the same precoding vectors choice when all users use a common codebook. In the proposal approach, firstly, we focus on the brute codeword selection at the transmitter side, thus there is zero probability to choose the same vector for more than one user. However, this solution leads an exhaustive search, especially when the number of user and the codebook size increase. To overcome this issue, secondly, we adopt the genetic algorithm in order to reduce the codeword search complexity. Compared with zero-forcing beamforming (ZFBF), the conducted simulation results for the critical scenario of low SNR, show that our scheme is better than ZFBF with the assumption of both perfect and partial channel state information at the transmitter.

A simple line network model is proposed to study the downlink cellular network. Without base station cooperation, the system is interference-limited. The interference limitation is overcome when the base stations are allowed to jointly encode the user signals, but the capacity-achieving dirty paper coding scheme can be too complex for practical implementation. A new linear precoding technique called soft interference nulling (SIN) is proposed, which performs at least as well as zero-forcing (ZF) beamforming under full network coordination. Unlike ZF, SIN allows the possibility of but over-penalizes interference. The SIN precoder is computed by solving a convex optimization problem, and the formulation is extended to multiple-antenna channels. SIN can be applied when only a limited number of base stations cooperate; it is shown that SIN under partial network coordination can outperform full network coordination ZF at moderate SNRs.

Zero-forcing (ZF) beamforming, an efficient technique for multiuser MIMO systems, requires perfect channel state information to be available at the base station. This is achieved by quantizing the channel and feeding back the information with a limited number of bits. A challenge of this method is the large downlink signaling overhead, which is due to the large size of the codebook that can be used at the base station for ZF beamforming. In this paper, we first analyze this problem and then present a technique designing codebooks with reduced size and minimal performance degradation. We also define the associated procedures required for the system implementation. Simulation results show that the size of the eNodeB codebook can be substantially reduced with only a small (5%) penalty in performance.

Joint processing (JP) is a powerful mechanism in alleviating inter-cell interference (ICI) and maximizing data rate of cell-edge users. However, JP puts tremendous load on both feedback and backhaul overhead, thus partial JP was proposed to overcome high overhead signaling. Unlike linear techniques such as zero-forcing (ZF), achieving an equivalent backhaul reduction and presenting a totally free ICI system based on limited feedback channel state information can be done by designing and implementing a multi-start particle swarm optimization algorithm (MSPSOA) as a beamforming (BF) mechanism. The performance of the proposed MSPSOA and ZF BF is evaluated based on the acquired spectral efficiency and utility of internet application such as hard real-time, adaptive and elastic applications. The simulation results shows that, the proposed MSPSOA BF achieves spectral efficiency up to 69.5% compared to ZF BF, and it maintains total utility for high data rate requirements of three common internet traffic such as hard real-time, adaptive and elastic applications.

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.