Rate-splitting Scheme Research Articles

Performance Analysis of Rate Splitting in K-User Interference Channel Under Imperfect CSIT: Average Sum Rate, Outage Probability and SER

Interference alignment (IA) and rate splitting (RS) are two promising interference processing techniques to handle the interference problems in the multi-input multi-output (MIMO) multi-cell cooperation scenario. However, under the imperfect channel state information (CSIT) in the practical systems, the poor robustness of IA has become a bottleneck of its performance gain. On the other hand, RS can provide a robust solution, yet its outage performance is limited by its SIC decoding process. To make up these two schemes’ shortcomings and achieve the robust and reliable multi-cell cooperation, in this paper, we propose a novel transmission scheme, signal and interference alignment based rate splitting (SIA-RS), and provide comprehensively analyze the performance under CSIT quantization error. Closed-from expressions are derived for the average sum rate, outage probability and symbol error rate (SER) and their asymptotic versions in high signal-to-noise ratio (SNR) region. Due to signal alignment and common message, there exists certain correlation between the key variables. The nested finite weighted sum of independent and correlated Erlang random variables is used to approximate the exact expressions of performance. The relationship between “splitting” and “alignment” is revealed via the analytical derivation and numerical simulation. The simulation results show that the proposed SIA-RS achieves the best average sum rate compared with conventional IA and RS schemes, indicate that alignment would further reduce the outage probability, and suggest to the separate modulation schemes for common and private messages in terms of SER.

Achievable Secure Degrees of Freedom of ${K}$ -User MISO Broadcast Channel With Imperfect CSIT

In this letter, we derive the achievable secure degrees of freedom (SDoF) of ${K}$ -user multiple-input single-output broadcast channel with imperfect channel state information (CSI) at the transmitter. With the help of an $N_{j}$ -antenna external jammer, we propose a jamming rate splitting (J-RS) scheme to ensure the security of two wiretap models: 1) broadcast channel with confidential messages and 2) broadcast channel with an $N_{e}$ -antenna external eavesdropper, where each legal node has no CSI of wiretap channels. Our converse is based on the degrees of freedom (DoF) of the network with secrecy constraints, and the achievability is based on J-RS. By numerical analysis, it indicates that the proposed scheme can achieve more SDoF than the traditional rate splitting scheme, zero forcing scheme, and jamming scheme, which can reach to the DoF of the network.

Approximate Capacity of Fast Fading Interference Channels With no Instantaneous CSIT

We develop a characterization of fading models, which assigns a number called logarithmic Jensen’s gap to a given fading model. We show that as a consequence of a finite logarithmic Jensen’s gap, an approximate capacity region can be obtained for fast fading interference channels (FF-ICs) for several scenarios. We illustrate three instances where a constant capacity gap can be obtained as a function of the logarithmic Jensen’s gap. First, for an FF-IC with neither feedback nor instantaneous channel state information at transmitter (CSIT), if the fading distribution has finite logarithmic Jensen’s gap, we show that a rate-splitting scheme based on the average interference-to-noise ratio can achieve its approximate capacity. Second, we show that a similar scheme can achieve the approximate capacity of FF-IC with feedback and delayed CSIT, if the fading distribution has finite logarithmic Jensen’s gap. Third, when this condition holds, we show that point-to-point codes can achieve approximate capacity for a class of FF-ICs with feedback. We prove that the logarithmic Jensen’s gap is finite for common fading models, including Rayleigh and Nakagami fading, thereby obtaining the approximate capacity region of FF-IC with these fading models.

On Linearly Precoded Rate Splitting for Gaussian MIMO Broadcast Channels

In this paper, we consider a general K-user Gaussian multiple-input multiple-output (MIMO) broadcast channel (BC). We assume that the channel state is deterministic and known to all the nodes. While the private-message capacity region is well known to be achievable with dirty paper coding (DPC), we are interested in the simpler linearly precoded transmission schemes. In particular, we focus on linear precoding schemes combined with rate-splitting (RS). First, we derive an achievable rate region with minimum mean square error (MMSE) precoding at the transmitter and joint decoding of the sub-messages at the receivers. Then, we study the achievable sum rate of this scheme and obtain two findings: 1) an analytically tractable upper bound on the sum rate that is shown numerically to be a close approximation, and 2) how to reduce the number of active streams -- crucial to the overall complexity -- while preserving the sum rate to within a constant loss. The latter results in two practical algorithms: a stream elimination algorithm and a stream ordering algorithm. Finally, we investigate the constant-gap optimality of linearly precoded RS with respect to the capacity. Our result reveals that, while the achievable rate of linear precoding alone can be arbitrarily far from the capacity, the introduction of RS can help achieve the capacity region to within a constant gap in the two-user case. Nevertheless, we prove that the RS scheme's constant-gap optimality does not extend to the three-user case. Specifically, we show, through a pathological example, that the gap between the sum rate and the sum capacity can be unbounded.

Achievable DoF Regions of MIMO Networks With Imperfect CSIT

We focus on a two-receiver Multiple-Input-Multiple-Output (MIMO) Broadcast Channel (BC) and Interference Channel (IC) with an arbitrary number of antennas at each node. We assume an imperfect knowledge of local Channel State Information at the Transmitters (CSIT), whose error decays with the Signal-to-Noise-Ratio. With such configuration, we characterize the achievable Degrees-of-Freedom (DoF) regions in both BC and IC, by proposing a Rate-Splitting approach, which divides each receiver's message into a common part and a private part. Compared to the RS scheme designed for the symmetric MIMO case, this scheme is suitable for the general asymmetric deployment with an arbitrary number of antennas at each node. In BC, the proposed block 1) employs an unequal power allocation to the private messages of the two receivers, 2) exploits the benefit of having an extra spatial dimension at one receiver, and 3) is carried out with a Space-Time transmission. These features enable the scheme to yield a greater DoF region than trivially extending the scheme designed for the symmetric case. In IC, we modify the scheme proposed for the BC case by applying a linear transformation to the channel matrices. Such a linear transformation allows us to identify the signal space where the two transmitted signals interfere with each other and propose a proper power allocation policy. The achievable DoF regions are shown to be optimal for some antenna configurations.

Robust Transmission in Downlink Multiuser MISO Systems: A Rate-Splitting Approach

We consider a downlink multiuser MISO system with bounded errors in the Channel State Information at the Transmitter (CSIT). We first look at the robust design problem of achieving max-min fairness amongst users (in the worst-case sense). Contrary to the conventional approach adopted in literature, we propose a rather unorthodox design based on a Rate-Splitting (RS) strategy. Each user's message is split into two parts, a common part and a private part. All common parts are packed into one super common message encoded using a public codebook, while private parts are independently encoded. The resulting symbol streams are linearly precoded and simultaneously transmitted, and each receiver retrieves its intended message by decoding both the common stream and its corresponding private stream. For CSIT uncertainty regions that scale with SNR (e.g. by scaling the number of feedback bits), we prove that a RS-based design achieves higher max-min (symmetric) Degrees of Freedom (DoF) compared to conventional designs (NoRS). For the special case of non-scaling CSIT (e.g. fixed number of feedback bits), and contrary to NoRS, RS can achieve a non-saturating max-min rate. We propose a robust algorithm based on the cutting-set method coupled with the Weighted Minimum Mean Square Error (WMMSE) approach, and we demonstrate its performance gains over state-of-the art designs. Finally, we extend the RS strategy to address the Quality of Service (QoS) constrained power minimization problem, and we demonstrate significant gains over NoRS-based designs.

Sum-Rate Maximization for Linearly Precoded Downlink Multiuser MISO Systems With Partial CSIT: A Rate-Splitting Approach

This paper considers the sum-rate (SR) maximization problem in downlink multi-user multiple input simgle output (MU-MISO) systems under imperfect channel state information at the transmitter (CSIT). Contrary to existing works, we consider a rather unorthodox transmission scheme. In particular, the message intended to one of the users is split into two parts: a common part which can be recovered by all users, and a private part recovered by the corresponding user. On the other hand, the rest of users receive their information through private messages. This rate-splitting (RS) approach was shown to boost the achievable degrees of freedom when CSIT errors decay with increased SNR. In this paper, the RS strategy is married with linear precoder design and optimization techniques to achieve a maximized ergodic SR (ESR) performance over the entire range of SNRs. Precoders are designed based on partial CSIT knowledge by solving a stochastic rate optimization problem using means of sample average approximation coupled with the weighted minimum mean square error approach. Numerical results show that in addition to the ESR gains, the benefits of RS also include relaxed CSIT quality requirements and enhanced achievable rate regions compared with conventional transmission with no rate-splitting.

A Unified Graphical Approach to Random Coding for Single-Hop Networks

A unified graphical approach to random coding for any memoryless, single-hop, $K$ -user channel with or without common information is defined through two steps. The first step is user virtualization. Each user is divided into multiple virtual sub-users according to a chosen rate-splitting strategy. This results in an enhanced channel with a possibly larger number of users for which more coding possibilities are available and for which common messages to any subset of users can be encoded. Following user virtualization, the message of each user in the enhanced model is coded using a chosen combination of coded time-sharing, superposition coding, and joint binning. A graph is used to represent the chosen coding strategies. Nodes in the graph represent codewords, while edges represent coding operations. This graph is used to construct a graphical Markov model, which illustrates the statistical dependence among codewords that can be introduced by the superposition coding or joint binning. Using this statistical representation of the overall codebook distribution, the error probability of the code is shown to vanish through a unified analysis. The rate bounds that define the achievable rate region are obtained by linking the error analysis to the properties of the graphical Markov model. This proposed framework makes it possible to numerically obtain an achievable rate region by specifying a user virtualization strategy and describing a set of coding operations. The union of these rate regions defines the maximum achievable rate region of our unified coding strategy. The achievable rates obtained based on this unified graphical approach to random coding encompass the best random coding achievable rates for all memoryless single-hop networks known to date, including broadcast, multiple access, interference, and cognitive radio channels, as well as new results for topologies not previously studied, as we illustrate with several examples.

Power Minimization of Cooperative Relay Transmission with Relay's Private Information

Power minimization of a cooperative decode-and-forward (DF) half-duplex relaying, where two users communicate with one destination node (D), is studied in this paper. Recognizing the difference in link qualities, one user not only transmits its own message to D but also acts as a relay node (R) for the other user. To achieve total network power minimization, we consider two strategies: (i) a rate splitting strategy (RSS) which splits the whole message into two sub-messages with one being transmitted via R and the other directly to D, (ii) a transmission power boosting strategy (TPBS) in the broadcast phase that allocates more power than needed to ensure correct decoding of the message at R. We first consider joint optimization of rate splitting, a time sharing factor (between the broadcast phase and cooperation phase), and transmission powers. We then consider the second scenario where the time sharing factor is fixed. We prove that TPBS is not required for the first scenario, but is necessary for the second scenario to minimize the total network power. We also obtain channel conditions for which the optimal solution is to employ a multiple access channel (MAC) strategy, i.e., without relaying. Finally we show through numerical results that significant power saving is achieved by our proposed strategies.

Multicell Interference Mitigation with Joint Beamforming and Common Message Decoding

Conventional wireless cellular systems treat out-of-cell interference as noise. This paper proposes methods and examines the benefit of designing decodable interference signals, whereby a transmitter may split its message into a common and a private part, and the common message may be decoded and subtracted by users in adjacent cells. This paper considers a downlink scenario, where the base-stations are equipped with multiple antennas, the mobile users are equipped with a single antenna, and multiple users are active simultaneously via spatial multiplexing. The network optimization problem consists of jointly determining the appropriate users in adjacent cells for rate splitting, the optimal transmit beamformers for common and private messages, and the optimal common-private rates to maximize the minimum achievable rate across the users. This paper shows that for fixed user selection and fixed common-private rate splitting, the optimization of transmit beamformers can be solved using a semidefinite programming (SDP) relaxation approach. Further, it is shown that for the case where the network consists of two message-splitting pairs, SDP relaxation is tight, i.e., beamforming is optimal. Finally, this paper proposes a heuristic user-selection and rate splitting strategy to characterize the performance improvement for cell-edge users due to common-message decoding.