Dirty Paper Research Articles

Zero-forcing dirty paper coding aided physical-layer network coding for MIMO two-way relaying channels with multiple users

This article considers the two-way multiple-input multiple-output (MIMO) relaying channels with multiple users, in which multiple users are served simultaneously by the base station (BS) with the assistance of the relay. The transmission consists of only two phases, doubling the system throughout over traditional one-way half-duplex transmission. A zero-forcing dirty paper coding (ZFDPC) aided physical-layer network coding (PNC) scheme is proposed in this article and the achievable capacity of the ZFDPC aided PNC scheme is derived. Simulation results show that the proposed scheme outperforms the previous decode-and-forward (DF) and zero-forcing beamforming (ZFBF) aided PNC scheme due to more degrees of freedoms and the advantage of PNC. Moreover, we analyze the effect of the imperfect channel state information (CSI) from RS to users at BS side to show the robustness of the proposed ZFDPC aided PNC scheme.

Toward a Practical Scheme for Binary Broadcast Channels with Varying Channel Quality Using Dirty Paper Coding

We consider practical schemes for binary dirty-paper channels and broadcast channels (BCs) with two receivers and varying channel quality. With the BC application in mind, this paper proposes a new design for binary dirty paper coding (DPC). By exploiting the concept of coset binning, the complexity of the system is greatly reduced when compared to the existing works. Some design challenges of the coset binning approach are identified and addressed. The proposed binary DPC system achieves similar performance to the state-of-the-art, superposition-coding-based system while demonstrating significant advantages in terms of complexity and flexibility of system design. For binary BCs, achieving the capacity generally requires the superposition of a normal channel code and a carefully designed channel code with non-uniform bit distribution. The non-uniform bit distribution is chosen according to the channel conditions. Therefore, to achieve the capacity for binary BCs with varying channel quality, it is necessary to use quantization codes of different rates, which significantly increases the implementation complexity. In this paper, we also propose a broadcast scheme that generalizes the concept of binary DPC, which we term soft DPC. By combining soft DPC with time sharing, we achieve a large percentage of the capacity for a wide range of channel quality with little complexity overhead. Our scheme uses only one fixed pair of codes for users 1 and 2, and a single quantization code, which possesses many practical advantages over traditional time sharing and superposition coding solutions and provides strictly better performance.

DPC Rates and Multiplexing Gains for MIMO Broadcast Systems with Multi-Dimensional Space-Time Modulation

This paper considers multiple-antenna broadcast channels (BCs) with multi-dimensional space-time modulation schemes, created by various allocations of signal dimensions to transmit antennas. The signal dimensions are divided into disjoint subsets, where one is shared between all users, and each of the others are assigned to different users. This model encompasses several practical single point to multi-point wireless communication systems employing multiple antennas. Assuming space and time dispersive channels, we consider the transmission rates that are achieved by applying dirty paper coding (DPC) at the transmitter, present inner and outer bounds for the DPC rate region, and study the effects of space-time modulation formats. At high SNR, we consider the limit form of these bounds, derive an achievable multiplexing gain region, and study the effects of sharing signal dimensions between users.

An Empirical Study of the Achievable Rates of Several Indoor Network-MIMO Techniques

This paper presents an empirical study of the achievable data rates of network multiple-input multiple-output (MIMO) techniques including zero-forcing (ZF), zero-forcing dirty paper coding (ZF-DPC) and dirty paper coding (DPC) using actual 4-by-4 indoor wireless channel measurements at 3.5 GHz. Their performances are contrasted with those of conventional techniques, in which either the base stations are not coordinated (NC), or their interference is avoided using frequency division (FD) multiplexing. The measurements were taken in aisle-to-office and large unobstructed hall scenarios. The study of these results reveals that, at high signal-to-noise ratios (SNRs), DPC and ZF-DPC can yield more than a three-fold increase in attainable data rates when compared to NC and FD. The gains obtained using ZF are smaller, but still significant. At low SNRs the system is noise-(rather than interference-) limited, and only DPC exhibits gains. The evaluations in this paper also show that collaborative systems such as DPC can benefit from interference-prone environments to yield increased transmission capacity. With regard to the propagation channel, the classical log-normal plus Rayleigh/Ricean fading model, with parameters fitted to the scenario type, was found to be good at predicting the statistics of the achievable data rates of all the strategies considered.

Effective Transmit Weight Design for DPC with Maximum Beam in Multiuser MIMO OFDM Downlink

In this paper, we consider the signal processing algorithm on each subcarrier for the downlink of Multi-User Multiple-Input Multiple-Output Orthogonal Frequency Division Multiplexing (MU-MIMO OFDM) system. A novel transmit scheme is proposed for the cancellation of Inter-User Interference (IUI) at the Base Station (BS). The improved performance of each user is obtained by optimizing the transmit scheme on each subcarrier, where the Particle Swarm Optimization (PSO) algorithm is employed to solve the constrained nonlinear optimization problem. Compared with the conventional Zero Forcing Dirty Paper Coding (ZF-DPC) having only single receive antenna at each Mobile Station (MS), the proposed scheme also applies the principle of DPC to cancel the IUI, but the MS users can be equipped with multiple receive antennas producing their increased receive SNR's. With the Channel State Information (CSI) being known at the BS and the MS, the eigenvalues for all the user channels are calculated first and then the user with the maximum eigenvalue is selected as the 1-st user. The remaining users are ordered and sequentially processed, where the transmit weights are generated from the previously selected users by the Particle Swarm Optimization (PSO) algorithm which ensures the transmit gain for each user as large as possible. The computational complexity analysis, BER performance and achievable sum-rate analysis of system verify the effectiveness of the proposed scheme.

Optimal Symbol-by-Symbol Costa Precoding for a Relay-Aided Downlink Channel

In this article, we consider practical approaches to Costa precoding (also known as dirty paper coding). Specifically, we propose a symbol-by-symbol scheme for cancellation of interference known at the transmitter in a relay-aided downlink channel. For finite-alphabet signaling and interference, we derive the optimal (in terms of maximum mutual information) modulator under a given power constraint. A sub-optimal modulator is also proposed by formulating an optimization problem that maximizes the minimum distance of the signal constellation, and this non-convex optimization problem is approximately solved by semi-definite relaxation. For the case of binary signaling with binary interference, we obtain a closed-form solution for the sub-optimal modulator, which only suffers little performance degradation compared to the optimal modulator in the region of interest. For more general signal constellations and more general interference distributions, we propose an optimized Tomlinson-Harashima precoder (THP), which uniformly outperforms conventional THP with heuristic parameters. Bit-level simulation shows that the optimal and sub-optimal modulators can achieve significant gains over the THP benchmark as well as over non-Costa reference schemes, especially when the power of the interference is larger than the power of the noise.

Linear Precoding in Cooperative MIMO Cellular Networks with Limited Coordination Clusters

In a cooperative multiple-antenna downlink cellular network, maximization of a concave function of user rates is considered. A new linear precoding technique called soft interference nulling (SIN) is proposed, which performs at least as well as zero-forcing (ZF) beamforming. All base stations share channel state information, but each user's message is only routed to those that participate in the user's coordination cluster. SIN precoding is particularly useful when clusters of limited sizes overlap in the network, in which case traditional techniques such as dirty paper coding or ZF do not directly apply. The SIN precoder is computed by solving a sequence of convex optimization problems. SIN under partial network coordination can outperform ZF under full network coordination at moderate SNRs. Under overlapping coordination clusters, SIN precoding achieves considerably higher throughput compared to myopic ZF, especially when the clusters are large.

Opportunistic Random Beamforming with Optimal Precoding for Spatially Correlated Channels

It has been shown recently that dirty paper coding (DPC) achieves optimum sum-rate capacity in a multi-antenna broadcast channel with full channel state (CSI) information at the transmitter. With only partial feedback, random beamforming (RBF) is able to match the sumrate of DPC for large number of users. However, in the presence of spatial correlation, RBF incurs an SNR hit as compared to DPC. In this letter, we explore precoding techniques to reduce the effect of correlation on RBF. We thus derive the optimum precoding matrix that minimizes the rate gap between DPC and RBF. Given the numerical complexity involved in calculating the optimum precoder, we derive approximate precoding matrices that are simple to calculate and close in performance to the optimum precoder.

Secret-Key Agreement With Channel State Information at the Transmitter

We study the capacity of secret-key agreement over a wiretap channel with state parameters. The transmitter communicates to the legitimate receiver and the eavesdropper over a discrete memoryless wiretap channel with a memoryless state sequence. The transmitter and the legitimate receiver generate a shared secret key, that remains secret from the eavesdropper. No public discussion channel is available. The state sequence is known noncausally to the transmitter. We derive lower and upper bounds on the secret-key capacity. The lower bound involves constructing a common state reconstruction sequence at the legitimate terminals and binning the set of reconstruction sequences to obtain the secret-key. For the special case of Gaussian channels with additive interference (secret-keys from dirty paper channel) our bounds differ by 0.5 bit/symbol and coincide in the high signal-to-noise-ratio and high interference-to-noise-ratio regimes. For the case when the legitimate receiver is also revealed the state sequence, we establish that our lower bound achieves the the secret-key capacity. In addition, for this special case, we also propose another scheme that attains the capacity and requires only causal side information at the transmitter and the receiver.

On the Convergence of Genetic Scheduling Algorithms for Downlink Transmission in Multi-User MIMO Systems

In a multi-user MIMO system using a successive precoding method such as dirty paper coding, it is combinatorially complex to determine the optimal set of users to schedule and the proper order to encode their signals in order to optimize a utility function in a scheduling algorithm. Genetic algorithms represent a fast suboptimal approach to reducing the complexity of the search. In this paper, we build upon prior work that implements scheduling via genetic algorithms. We examine the impact of parameter values within the adaptive mutation rate of the algorithm on its convergence time. We demonstrate that although there is a range of values for the parameters that yields similar near-minimum convergence times, it is nonetheless important to ensure that the parameters are tuned to be within that range. In one case, tuning the parameter values reduces the time of convergence to less than 30% compared to that achievable with the initial parameter values. We also demonstrate that the proper parameter values are dependent on both the number of transmit antennas and the number of users in the pool of users to be scheduled. A simple equation is proposed that is linear in the adaptive mutation parameters to tune the values for different numbers of transmit antennas and users.

Rate Enhancement for the Gaussian Z-Interference Channel with Transmitter Cooperation

We study a two-user Gaussian Z-interference channel in which only one-sided interference exists. We assume that there is a one-sided conferencing link from the interfering transmitter to the other, which can be used to mitigate the interference. We propose a cooperative transmission scheme that delivers a part of the interfering message through the conferencing link and then applies the dirty paper coding by regarding the delivered message as a known transmit side information. We characterize its achievable rate region for general channel coefficients and show that a finite-rate conferencing can improve both achievable rate region and its sum rate.

Transmitter cooperation by joint dirty paper coding in ad-hoc networks

In wireless ad-hoc networks, users cooperate to transmit each others' messages. To some extent terminals therefore collectively act as an antenna array and create a virtual or distributed multiple-input multiple-output (MIMO) system. In order to mitigate interference at receivers, the dirty paper coding (DPC) schemes for various relaying schemes have become very important. In contrast to the conventional scheme that designs the reconstructed signal using DPC technique for each terminal, respectively, we propose a new scheme called joint dirty paper coding for decode-and-forward (DF) cooperative networks. The transmitter forms the reconstructed signal sequence based on its own signal and its partner's signal in terms of DPC technique. The precoding functions of transmitters are considered together, and interference is canceled at the receiver during the superposition of two signal sequences from the transmitter and its partner. The corresponding numerical results prove that, the gap between our proposed scheme and the perfect system without interference can be quite small. The proposed scheme can lead to a superior performance in the sense of frame error rate (FER), which improves as the power allocation ratio increases.

On Wireless Downlink Scheduling of MIMO Systems With Homogeneous Users

We investigate the problem of downlink user scheduling in multiple-input multiple-output (MIMO) systems with <i xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">M</i> transmit antennas and <i xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">K</i> homogeneous multiantenna receiving users. We develop a simple algorithm to schedule a subset of <i xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">M</i> active users for data transmission. We first identify a set of <i xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">L</i> candidate users that should provide channel information feedback. We then select <i xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">M</i> active users among the <i xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">L</i> candidates based on joint consideration of their effective channel gains and directions. We derive an asymptotic upper bound for the sum rate gap between the maximum sum rate of the <i xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">M</i> selected active users, achieved by dirty paper coding, and the full sum capacity of the original MIMO broadcast channel. Utilizing the upper bound, we show that the sum rate gap can be reduced to meet user requirement by suitably choosing a large but still finite <i xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">L</i> . Furthermore, we also investigate the performance of the low complexity zero-forcing beamforming (ZFBF) for the <i xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">M</i> active users.

Eigen-Based Transceivers for the MIMO Broadcast Channel With Semi-Orthogonal User Selection

This paper studies the sum rate performance of two low complexity eigenmode-based transmission techniques for the MIMO broadcast channel, employing greedy semi-orthogonal user selection (SUS). The first approach, termed ZFDPC-SUS, is based on zero-forcing dirty paper coding; the second approach, termed ZFBF-SUS, is based on zero-forcing beamforming. We first employ new analytical methods to prove that as the number of users K grows large, the ZFDPC-SUS approach can achieve the optimal sum rate scaling of the MIMO broadcast channel. We also prove that the average sum rates of both techniques converge to the average sum capacity of the MIMO broadcast channel for large K. In addition to the asymptotic analysis, we investigate the sum rates achieved by ZFDPC-SUS and ZFBF-SUS for finite K, and show that ZFDPC-SUS has significant performance advantages. Our results also provide key insights into the benefit of multiple receive antennas, and the effect of the SUS algorithm. In particular, we show that whilst multiple receive antennas only improves the asymptotic sum rate scaling via the second-order behavior of the multi-user diversity gain; for finite K, the benefit can be very significant. We also show the interesting result that the semi-orthogonality constraint imposed by SUS, whilst facilitating a very low complexity user selection procedure, asymptotically does not reduce the multi-user diversity gain in either first (log K) or second-order (loglog K) terms.

Multiuser Diversity for Successive Zero-Forcing Dirty Paper Coding: Greedy Scheduling Algorithms and Asymptotic Performance Analysis

<para xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"> Dirty paper coding (DPC) scheme is the capacity achieving transmission technique in multiuser MIMO downlink channels. As a suboptimal solution to DPC, successive zero-forcing DPC (SZF-DPC) has been proposed recently. The zero-interference constraint in designing the precoding matrices limits the number of supportable users. In this correspondence, we propose three low-complexity suboptimal user scheduling algorithms to exploit the multiuser diversity gain in SZF-DPC as the number of users grows. The first algorithm greedily maximizes the true sum rate. The second algorithm is based on eigenvalues. The third algorithm relies on the diagonal elements of the effective channel matrix since eigenvalues and diagonal entries of a Hermitian matrix have a strong relationship. Simulation results show that the proposed scheduling algorithms can obtain a significant fraction of sum rate of the optimal solution. Furthermore, the performance analysis is provided to prove that the proposed user selection algorithms can achieve the same asymptotic sum rate as that of DPC. </para>

Relay Scheduling in the Half-Duplex Gaussian Parallel Relay Channel

This study investigates the problem of communication for a network composed of two half-duplex parallel relays with additive white Gaussian noise (AWGN). There is no direct link between the source and the destination. However, the relays can communicate with each other through the channel between them. Two protocols, i.e., simultaneous and successive relaying, associated with two possible relay schedulings are proposed. The simultaneous relaying protocol is based on the Broadcast-Multiaccess with Common Message (BCM) scheme considered in . For the successive relaying protocol: (i) a non-cooperative scheme based on the Dirty Paper Coding (DPC) and (ii) a cooperative scheme based on the Block Markov Encoding (BME) are considered. The composite scheme of employing BME in at most one relay and DPC in at least another one is also proposed. It is proved that this scheme achieves at least the same rate when compared to the cooperative and non-cooperative schemes for the Gaussian case. A Simultaneous-Successive Relaying based on Dirty Paper Coding scheme (SSRD) is also proposed. The optimum scheduling of the relays, and hence the capacity of the half-duplex Gaussian parallel relay channel in the low and high signal-to-noise ratio (SNR) scenarios, is derived. In the low SNR scenario, it is revealed that under certain conditions for the channel coefficients the ratio of the achievable rate of the simultaneous relaying based on BCM to the cut-set bound tends to be 1. On the other hand, as SNR goes to infinity it is proved that successive relaying, based on the DPC, asymptotically achieves the capacity of the network.

On the robustness of dirty paper coding

A dirty-paper channel is considered, where the transmitter knows the interference sequence up to a constant multiplicative factor, known only to the receiver. Lower bounds on the achievable rate of communication are derived by proposing a coding scheme that partially compensates for the imprecise channel knowledge.We focus on a communication scenario where the signal-to-noise ratio is high. Our approach is based on analyzing the performance achievable using lattice-based coding schemes. When the power of the interference is finite, we show that the achievable rate of this lattice-based coding scheme may be improved by a judicious choice of the scaling parameter at the receiver. We further show that the communication rate may be improved, for finite as well as infinite interference power, by allowing randomized scaling at the transmitter.

Cooperative Relaying With State Available Noncausally at the Relay

In this paper, we consider a three-terminal state-dependent relay channel (RC) with the channel state noncausally available at only the relay. Such a model may be useful for designing cooperative wireless networks with some terminals equipped with cognition capabilities, i.e., the relay in our setup. In the discrete memoryless (DM) case, we establish lower and upper bounds on channel capacity. The lower bound is obtained by a coding scheme at the relay that uses a combination of codeword splitting, Gel'fand-Pinsker binning, and decode-and-forward (DF) relaying. The upper bound improves upon that obtained by assuming that the channel state is available at the source, the relay, and the destination. For the Gaussian case, we also derive lower and upper bounds on the capacity. The lower bound is obtained by a coding scheme at the relay that uses a combination of codeword splitting, generalized dirty paper coding (DPC), and DF relaying; the upper bound is also better than that obtained by assuming that the channel state is available at the source, the relay, and the destination. In the case of degraded Gaussian channels, the lower bound meets with the upper bound for some special cases, and, so, the capacity is obtained for these cases. Furthermore, in the Gaussian case, we also extend the results to the case in which the relay operates in a half-duplex mode.

Efficient Weighted Sum Rate Maximization With Linear Precoding

Achieving the boundary of the capacity region in the multiple-input multiple-output (MIMO) broadcast channel requires the use of dirty paper coding (DPC). As practical nearly optimum implementations of DPC are computationally complex, purely linear approaches are often used instead. However, in this case, the problem of maximizing a weighted sum rate constitutes a nonconvex and, in most cases, also a combinatorial optimization problem. In this paper, we present two heuristic nearly optimum algorithms with reduced computational complexity. For this purpose, a lower bound for the weighted sum rate under linear zero-forcing constraints is used. Based on this bound, both greedy algorithms successively allocate data streams to users. In each step, the user is determined that is given an additional data stream such that the increase in weighted sum rate becomes maximum. Thereby, the data stream allocations and filters obtained in the previous steps are kept fixed and only the filter corresponding to the additional data stream is optimized. The first algorithm determines the receive and transmit filters directly in the downlink. The other algorithm operates in the dual uplink, from which the downlink transmit and receive filters can be obtained via the general rate duality leading to nonzero-forcing in the downlink. Simulation results reveal marginal performance losses compared to more complex algorithms.

Wyner–Ziv Coding Over Broadcast Channels: Digital Schemes

This paper addresses lossy transmission of a common source over a broadcast channel when there is correlated side information at the receivers, with emphasis on the quadratic Gaussian and binary Hamming cases. A digital scheme that combines ideas from the lossless version of the problem, i.e., Slepian-Wolf coding over broadcast channels, and dirty paper coding, is presented and analyzed. This scheme uses layered coding where the common layer information is intended for both receivers and the refinement information is destined only for one receiver. For the quadratic Gaussian case, a quantity characterizing the combined quality of each receiver is identified in terms of channel and side information parameters. It is shown that it is more advantageous to send the refinement information to the receiver with ¿better¿ combined quality. In the case where all receivers have the same overall quality, the presented scheme becomes optimal. Unlike its lossless counterpart, however, the problem eludes a complete characterization.