Precoder design for multi-antenna transmission in MU-MIMO with QoS requirements

Abstract. A multiple-input multiple-output (MIMO) interference broadcast channel (IBC) channel is considered. There are several base stations (BSs) transmitting useful information to their own users and unwanted interference to its neighboring BS users. Our main interest is to maximize the system throughput by designing transmit precoders with weighted sum rate maximization (WSRM) objective for a multi-user (MU)-MIMO transmission. In addition, we include the quality of service (QoS) requirement in terms of guaranteed minimum rate for the users in the system. Unfortunately, the problem considered is nonconvex and known to be non-deterministic polynomial (NP) hard. Therefore, to determine the transmit precoders, we first propose a centralized precoder design by considering two closely related approaches, namely, direct signal-to-interference-plus-noise-ratio (SINR) relaxation via sequential parametric convex approximation (SPCA), and mean squared error (MSE) reformulation. In both approaches, we adopt successive convex approximation (SCA) technique to solve the nonconvex optimization problem by solving a sequence of convex subproblems. Due to the huge signaling requirements in the centralized design, we propose two different distributed precoder designs, wherein each BS determines only the relevant set of transmit precoders by exchanging minimal information among the coordinating BSs. Initially, we consider designing precoders in a decentralized manner by using alternating directions method of multipliers (ADMM), wherein each BS relaxes inter-cell interference as an optimization variable by including it in the objective. Then, we also propose a distributed precoder design by solving the Karush-Kuhn-Tucker (KKT) expressions corresponding to the centralized problems. Numerical simulations are provided to compare different system configurations with QoS constraints for both centralized and distributed algorithms

Interference management via user clustering in two-stage precoder design

Abstract We consider a single cell downlink (DL) massive multiple-input multiple-output (MIMO) set-up with user clustering based on statistical information. The problem is to design a fully digital two-stage beamforming aiming to reduce the complexity involved in the conventional MIMO processing. The fully digital two-stage beamforming consists of a slow varying channel statistics based outer beamformer (OBF) and an inner beamformer (IBF) accounting for fast channel variations. Two different methods are presented to design the OBF matrix, so as to reduce the size of effective channel used for IBF design. A group specific two-stage optimization problem with weighted sum rate maximization (WSRM) objective is formulated to find the IBF for fixed OBF. We begin by proposing centralized IBF design were the optimization is carried out for all sub group jointly with user specific inter-group interference constraints. In order to further reduce the complexity, we also propose a group specific IBF design by fixing the inter group interference to a constant or by ignoring them from the problem altogether. In spite of incurring a small loss in performance, the computational complexity can be saved to a large extent with the group specific processing. Numerical experiments are used to demonstrate the performance of various proposed schemes by comparing the total sum rate of all users and the design complexity

Distributed two-stage multi-cell precoding

Abstract This paper proposes a distributed downlink precoding design for multi-cell massive multiple-input multiple-output systems. Two-stage precoding is adopted assuming that the user equipments (UEs) in each base station (BS) are grouped according to matching channel statistics. In this regard, the channel dimension is first reduced by means of statistical, group-specific processing. Subsequently, the UE-specific inner beamformers (IBFs) are optimized based on the resulting (lower-dimensional) effective channels, with sensibly reduced computational complexity. We begin by formulating a centralized IBF design that derives from iteratively solving the Karush-Kuhn-Tucker conditions of the weighted sum rate maximization problem. Then, we propose a distributed algorithm where inter-cell interference (ICI) terms and dual variables are periodically exchanged among neighboring BSs via backhaul signaling, whereas the inter-group interference (IGI) within each BS is handled locally. Furthermore, the ICI updates between the BSs are allowed to take place less frequently than the local IGI updates. Numerical results show that enabling backhaul signaling every 5—10 iterations of the algorithm yields a remarkably small performance loss with respect to the case with full information exchange between the BSs

Precoder design for MU-MISO transmission with guaranteed QoS constraints

Abstract We study the problem of designing transmit beamformer for maximizing the weight sum rate of a multi-user (MU)-multiple-input single-output (MISO) interference broadcast channel (IBC) with individual quality-of-service (QoS) constraints. The considered problem is known to be nonconvex and NP-hard indeed, and most of existing high-performance solutions are based on the centralized method. In this paper, we propose a distributed approach for the weighted sum rate maximization (WSRM) problem with QoS constraints by combining successive convex approximation (SCA) framework and the alternating directions method of multipliers (ADMM) technique. More specifically, the proposed algorithm extends a current centralized solution, where the SCA is used to arrive at an approximate convex problem at each step of the iterative procedure. The idea is that we apply the ADMM technique to solve the convex problem of the SCA based subproblem in a distributed manner. We also discuss some heuristic ways to accelerate the convergence rate of the proposed algorithm. Numerical simulations are provided to compare different models for both centralized and distributed algorithms

Minimum power based relay selection for orthogonal multiple access relay networks

Abstract We analyze the performance of a multi-source multi-helper transmission with lossy forward (LF) relaying. In LF, estimates at the relay are encoded and forwarded to the destination for improving the reliability of the received sequence transmitted from the multiple source nodes. Unlike the conventional decode-and-forward (DF) relaying, LF sends the data even in the case where decoding is not error-free. We extend the results of the channel with multiple sources and a single helper to perform relay selection by utilizing the union of rate regions. A power minimization problem is formulated using the above strategy and solved by exploiting the successive convex approximation (SCA) technique. Numerical results are presented to show that the proposed relay selection method achieves the same performance as the exhaustive search

Final report of detailed optimisation algorithm and performance comparisons:ICT-619555 RESCUE D2.2.2 Version 1.0

Abstract This deliverable provides comprehensive theoretical and simulation results on the proposed power optimization algorithms with four toy scenarios identified in the project. The proposed algorithms mainly assume that the statistical channel knowledge and/or location information are available at each node, which aims to be in line with RESCUE “links-on-the-fly” concept. Specifically, the outage probability based joint power allocation and relay position for lossy-forwarding relaying scheme is firstly investigated in toy scenario one, and then the work is extended to a symbol-level selective transmission scheme. For toy scenario two, compared with our previous work in D2.2.1, the outage probability based power allocation is extended to multi-relay case, meanwhile, the power allocation from rate distortion perspective is also investigated. Furthermore, the outage probability based power allocation for toy scenario three is presented for the first time, and the orthogonal multiple access relay channel based power allocation is also illustrated for the case with more than two sources. Based on the provided results, the proposed algorithms exhibit improved performances by comparing with the conventional schemes, e.g., equal-power allocation.Executive summary Recall the Links-on-the-fly Technology for Robust, Efficient, and Smart Communication in Unpredictable Environments (RESCUE) concept that relays are allowed to decode-and-forward the received frames with specified level of errors, which aims to provide efficient and simple information transfer. In this case, the error propagation effects can be mitigated at destination with modified distributed turbo decoding by taking source-relay link correlation information into account. Alternatively, relays can also predict the positions of decoding errors in a frame and then null out them in order to mitigate the error propagation effects. Both of these strategies have a common assumption that channel feedback from reception node to transmission node is not allowed. Thus, the optimal power allocation cannot be based on the knowledge of instantaneous channel state information (CSI). However, we can still use statistical CSI and/or nodes’ location information obtained through long term observation and training. In this deliverable, a comprehensive review of the proposed power allocation algorithms with statistical channel knowledge and/or nodes’ location information for different identified toy scenarios is presented. Firstly, the joint optimization of power allocation (PA) and relay position (RP) for lossy-forwarding relaying is proposed, where the objective is to minimize the system outage probability of toy scenario one (TS1). With the closed-form expression of the outage probability, we investigate adaptive PA with fixed RP, adaptive RP with fixed PA ratio, and joint optimization of PA and RP under total transmit power constraint. It is found that the proposed three algorithms outperform the equal PA, midpoint RP, and semi-adaptive optimization algorithms, respectively. Moreover, we also consider the optimal PA and RP for a symbol-level selective transmission at relay scheme. In this case, the optimal power allocation is to maximize the average received signal-to-noise (SNR) ratio at destination, where the SNR expression includes the derived probability of correctly predicted/forwarded symbols per frame at relay. It is shown that, within four presented relay locations, relay closed to destination provides the best average SNR performance, and its optimal power allocation happens when the relay is allocated with more power. As investigated in D2.2.1, the power allocation in order to minimize the system outage for two relays based chief executive officer (CEO) problem provides better performance than the ones with equal power allocation. In this deliverable, we extend the work with three or more relays cases and propose a simple, yet effective power allocation scheme based on the Slepian-Wolf theorem. Moreover, we also assess the performance of the proposed power allocation for a practical joint decoding (JD) introduced in literature, and the improved performances in terms of average bit-error-rate (BER) can be observed. In addition, we also investigate the optimal power allocation for the lossy communication networks in toy scenario two (TS2). Specifically, we consider the power allocation from rate distortion perspective in order to achieve optimum distortion under total power constraints. The problem can be formulated as convex optimization framework and solved by using Karush-Kuhn-Tucker conditions. In this deliverable, we introduce the optimal power allocation in toy scenario three (TS3) for the first time. Based on the derived outage upper bound presented in deliverable D1.2.2, we design the power allocation strategy to minimize the outage upper bound subject to the total transmission power constraints. It is shown that the proposed power allocation strategy can be asymptotically optimal at high SNR range. Similar as the ones for TS2, we also assess the performance of the proposed power allocation strategy for a practical JD scheme. An improved performance in terms of frame-error-rate (FER) is also observed. Comparing with the work for toy scenario four (TS4) in D2.2.1, we generalize the power allocation problem of lossy forwarding based multiple access relay channel for two sources, single relay and common destination case to more than two sources case. Here, we propose a heuristic power allocation approach for fading channels with the average SNR of each link. The objective of the problem is to minimize the transmit power subject to rate constants, and the non-convex based power allocation problem can still be solved with successive convex approximation method. Numerical results show that the proposed method provides better performances than the conventional cyclic redundancy check based DF relaying in terms of power assumption and outage probability. To sum up, the above mentioned power allocation algorithms for different toy scenarios are implemented mainly based on statistical channel knowledge and/or nodes’ location information, which can be obtained from long terms observation and training. This is consistent with RESCUE “links-on-the-fly” concept, where the signalling to guarantee reliable transmission for a specific link is not allowed in unpredictable environments