Robust Beamforming Design for RIS-Aided Cell-Free Systems With CSI Uncertainties and Capacity-Limited Backhaul
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Abstract:
In this paper, we consider the robust beamforming design in a reconfigurable intelligent surface (RIS)-aided cell-free (CF) system considering the channel state information (CSI) uncertainties of both the direct channels and cascaded channels at the transmitter with capacity-limited backhaul. We jointly optimize the precoding at the access points (APs) and the phase shifts at multiple RISs to maximize the worst-case sum rate of the CF system subject to the constraints of maximum transmit power of APs, unit-modulus phase shifts, limited backhaul capacity, and bounded CSI errors. By applying a series of transformations, the non-smoothness and semi-infinite constraints are tackled in a low-complexity manner that facilitates the design of an alternating optimization (AO)-based iterative algorithm. The proposed algorithm divides the considered problem into two subproblems. For the RIS phase shifts optimization subproblem, we exploit the penalty convex-concave procedure (P-CCP) to obtain a stationary solution and achieve effective initialization. For precoding optimization subproblem, successive convex approximation (SCA) is adopted with a convergence guarantee to a Karush-Kuhn-Tucker (KKT) solution. Numerical results demonstrate the effectiveness of the proposed robust beamforming design, which achieves superior performance with low complexity. Moreover, the importance of RIS phase shift optimization for robustness and the advantages of distributed RISs in the CF system are further highlighted.Keywords:
Karush–Kuhn–Tucker conditions
Robustness
Initialization
Backhaul (telecommunications)
Channel state information
Zero-forcing precoding
Robust Optimization
In this paper, an SLNR based cascaded interference align precoding algorithm is proposed according to the study on interference suppression in downlink coordinated multipoint transmission system. In this algorithm, cascaded precoding is adopted rather than delivering channel state information (CSI) among cells to deal with inter and inner cell interference stage by stage. In the first stage, interferences from different cells are aligned to the orthogonal space of receiving matrix of the expected cell, so that interference to the expected cell can be avoided. In the second stage, SLNR precoding is adopted to suppress the interferences among users within a cell. Simulation results indicate that the proposed algorithm improves the system capacity, reduces the bit error rate, and overcomes the limitation that the amount of online users within a cell.
Zero-forcing precoding
Interference Alignment
Channel state information
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Downlink closed loop transmission schemes for multi user MIMO systems are usually sensitive to delays in the feedback of channel state information (CSI). We present a novel and simple transmit precoding scheme which exploits the delayed interference state information (INTSI) and the concept of interference alignment (IA). We design the precoding such that the inter-cell interference subspace from the previous transmission is aligned at the desired receiver with the intra-cell interference subspace of the current transmission. Although the alignment is not perfect for the current transmission, we show that with the help of proper receiver design, one can minimize the leakage interference caused by outdated information and still achieve good performance. We evaluate our scheme with the help of extensive system level simulations and provide a comparison with state of the art MU-MIMO transmit precoding schemes in terms of mean user rates. The simulation results show that our proposed scheme provides considerable gains over the other transmission schemes.
Zero-forcing precoding
Channel state information
Interference Alignment
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In this paper, the design of precoding method for multi-gateway multi-beam satellite system is considered. A two-stage precoding framework is proposed, which composed of the on-ground precoding in feeder link and the on-board precoding in user link. We first propose the on-board precoding method based on successive interference cancellation (SIC), which the precoding sub-matrix is designed in sequence. Then based on the long-term statistics of the effective channel, the on-ground precoding can be obtained to maximize signal to leakage plus noise ratio (SLNR). The performance of the proposed schemes through simulations is demonstrated.
Zero-forcing precoding
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This paper considers coordinated precoding design in multi-cell scenarios where transmitters and receivers are both equipped with multiple antennas. To suppress the co-channel interference, much channel state information (CSI) should be sent back to the transmitters. Most previous work in the area has assumed that transmitters have common knowledge of both data symbols of all users and full or local CSI. Herein, we propose coordinated precoding scheme with interference CSI only. Note that interference CSI denotes the channel state information from the transmitter to the interference user particularly. "Zero-Forcing" (ZF) method can be easily adopted to minimize the co-channel interference. However, coordinated ZF precoding imposes a condition that each BS should have more antennas than receive antennas combined by all users. Therefore, a coordinated precoding scheme is presented by minimizing leakage-plus-noise (MLN) which is similar to maximizing signal-to-leakage-plus-noise ratio (SLNR) criterion. Simulation results show that the proposed precoding scheme endures an acceptable performance loss compared to traditional schemes while much feedback overload is reduced.
Zero-forcing precoding
Channel state information
Interference Alignment
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Focusing on the problem that the co-frequency interference of the downlink channels in multi-cell of multi-out multi-input (MIMO) systems, this paper used the adaptive network precoding based on the SJNR to reduce the inter-cell interference. First of all, the adaptive precoding design based on the SJNR criteria is given. In this design, each base station use independent precoding approach to suppress adjacent inter-cell interference. And then in order to decrease the handing complex by the active way, the adaptive network precoding is attained respectively in the urban and suburb area environments, two adaptive network precoding based on SJNR are obtained respectively. Simulation results show that the inter-cell interference was obviously restrained and the system performance was improved after using the active network precoding basing on the SJNR, but also reduced processing algorithms of system.
Zero-forcing precoding
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We present a simple transmit precoding scheme which exploits the delayed interference state information (INTSI) and the concept of interference alignment (IA). We design the precoding such that the inter-cell interference subspace from the previous transmission is aligned at the desired receiver with the intra-cell interference subspace of current transmission. Due to this fact, the alignment is not perfect for current transmission and causes leakage interference in the desired signal space. However, we show that with the help of proper receiver design, we can minimize this leakage interference and get substantial gains. We also consider the practical limitations of the current receivers and provide a modified solution to overcome these limits. With the help of extensive system level simulations we compare our scheme with other baseline MU-MIMO transmit precoding schemes in terms of mean user rates. The simulation results show that our proposed scheme provides considerable gains over the baseline transmission schemes.
Zero-forcing precoding
Interference Alignment
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This reported work considers multiple-input-multiple-output (MIMO) interference channels, and a decentralised precoding scheme based on maximising the signal to weighted generated interference plus noise ratio is proposed with only locally available channel state information at each transmitter. By weighted suppression of the generated interference, each transmitter effectively achieves a balance between desired signal maximisation and weighted generated interference minimisation. Simulation results confirm that proposed precoding scheme offers significant sum rate enhancement in MIMO interference channels.
Zero-forcing precoding
Interference Alignment
Channel state information
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This paper addresses distributed precoding design for MIMO interference networks, where multiple MIMO links share the same bandwidth. In our proposed design, the precoding matrix for an individual link is given as the product of two matrices obtained in two sequential steps. In particular, the first matrix is derived by maximizing the desired signal power given the leakage power as a penalty and the second matrix is obtained by suppressing the interference among data streams belonging to one link (inter-stream interference). Comparing to the naive precoding design, where each transmitter selfishly employs waterfilling transmission scheme, the achievable rate achieved by our proposed two-step precoding design increases as the SNR increases. Moreover, the performance gain of our proposed precoding design over the naive design depends on the available spatial degrees-of-freedom.
Zero-forcing precoding
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Cell densification is a key driver to increase area spectral efficiencies in multi-antenna cellular systems. As increasing the densities of base stations (BSs) and users that share the same spectrum, however, both inter-user-interference (IUI) and inter-cell interference (ICI) problems give rise to a significant loss in spectral efficiencies in such systems. To resolve this problem under the constraint of local channel state information per BS, in this paper, we present a novel noncooperative multi-user multiple-input multiple-output (MIMO) precoding technique, called signal-to-interference-plus-leakage-plus-noise-ratio (SILNR) maximization precoding. The key innovation of our distributed precoding method is to maximize the product of SILNRs of users per cell using local channel state information at the transmitter (CSIT). We show that our precoding technique only using local CSIT can asymptotically achieve the multi-cell cooperative bound attained by cooperative precoding using global CSIT in some cases. We also present a precoding algorithm that is robust to CSIT errors in multi-cell scenarios. By multi-cell system-level simulations, we demonstrate that our distributed precoding technique outperforms all existing noncooperative precoding methods considerably and can also achieve the multi-cell bound very tightly even with not-so-many antennas at BSs.
Zero-forcing precoding
Channel state information
Spectral Efficiency
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We present a novel downlink transmit precoding scheme for multi user MIMO cellular system where each cell schedules two users on the same resource. Our approach is to exploit the delayed interference state information (INTSI) and the concept of interference alignment (IA). We design the precoding such that the inter-cell interference subspace from the previous transmission is aligned at the intended receiver with the intra-cell interference subspace of the current transmission. Due to this outdated alignment we expect leakage interference in the desired signal space. However, we show that with the help of proper receiver design, we can suppress the interference and minimize the residual leakage interference and get substantial gains even with outdated alignment. We also address the practical issues and limitations related to the receiver design and provide a modified precoding scheme to overcome these limitations. We also present a comparison with other state of the art multiuser MIMO transmit precoding schemes with the help of extensive system level simulations. The simulation results show that our proposed scheme provides considerable gains over the other transmission schemes with ideal as well as practical considerations.
Zero-forcing precoding
Interference Alignment
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