Zero-forcing Dirty Paper Coding Research Articles

Optimal Sum Rate-Fairness Tradeoff for MIMO Downlink Communications Employing Successive Zero Forcing Dirty Paper Coding

New power allocation schemes taking both sum-rate and fairness into account for MIMO downlink communications employing successive zero-forcing dirty paper coding are presented in this letter. Specifically, using a revised $\ell _{1}$ -norm fairness measure that allows for a more comprehensive consideration when users have an unequal number of receive antennas, the optimal tradeoff between sum-rate and fairness for MIMO downlink communications with arbitrary channel statistics is completely characterized. A novel stochastic power allocation scheme capable of achieving this optimal tradeoff is also given. To put the optimal tradeoff into practical use, an explicit rule for selecting operating sum-rate from the tradeoff is then proposed. Simulation results show that the new scheme can yield higher sum-rate and better fairness at the same time.

Programmable ASIPs for Multimode MIMO Transceiver

Application specific instruction-set processors (ASIP) are a programmable and flexible alternative of traditional finite state machine (FSM) controlled register-transfer level (RTL) designs for multimode basedband systems. In this paper, we present two ASIPs for small scale multiple-input multiple-output (MIMO) wireless communication systems that demonstrate the soundness and effectiveness of ASIPs for this type of applications. The first ASIP is programmed with multiple MIMO symbol detection algorithms for 4 × 4 systems. The supported detection algorithms are minimum mean-square error (MMSE), two variants of the selective spanning with fast enumeration (SSFE) and K-best list sphere detection (LSD). The second ASIP supports MMSE and zero-forcing dirty paper coding (ZF-DPC) algorithms for a base station (BS) with 4 antennas and for 4 users. Both ASIPs are based on transport triggered architecture (TTA) and are programmed with a retargetable compiler with high level language to meet the time-to-market requirements. The detection and precoding algorithms can be switched in the respective ASIPs based on the error-rate requirements. Depending on the algorithms, MIMO detection ASIP delivers 6.16–66.66 Mbps throughput at a clock frequency of 200 MHz on 90 nm technology. The precoder ASIP provides a throughput of 52.17 and 51.95 Mbps for MMSE and ZF-DPC precoding respectively at a clock frequency of 210 MHz on 90 nm technology.

Dirty-Paper Coding Based Secure Transmission for Multiuser Downlink in Cellular Communication Systems

This paper studies the secure transmission in a multiuser broadcast channel where only the statistical channel state information of the eavesdropper is available. We propose to apply secret dirty-paper coding (S-DPC) in this scenario to support the secure transmission of one user and the normal (unclassified) transmission of the other users. By adopting the S-DPC and encoding the secret message in the first place, all the information-bearing signals of the normal transmission are treated as noise by potential eavesdroppers and thus provide secrecy for the secure transmission. In this way, the proposed approach exploits the intrinsic secrecy of multiuser broadcasting and can serve as an energy-efficient alternative to the traditional artificial noise (AN) scheme. To evaluate the secrecy performance of this approach and compare it with the AN scheme, we propose two S-DPC-based secure transmission schemes for maximizing the secrecy rate under constraints on the secrecy outage probability (SOP) and the normal transmission rates. The first scheme directly optimizes the covariance matrices of the transmit signals, and a novel approximation of the intractable SOP constraint is derived to facilitate the optimization. The second scheme combines zero-forcing dirty-paper coding and AN, and the optimization involves only power allocation. We establish efficient numerical algorithms to solve the optimization problems for both schemes. Theoretical and simulation results confirm that, in addition to supporting the normal transmission, the achievable secrecy rates of the proposed schemes can be close to that of the traditional AN scheme, which supports only the secure transmission of one user.

Energy Harvesting for Internet of Things with Heterogeneous Users

We study the energy harvesting problem in the Internet of Things with heterogeneous users, where there are three types of single-antenna users: ID users that only receive information, EH users that can only receive energy, and ID/EH users that receive information and energy simultaneously from a multiantenna base station via power splitting. We aim to maximize the minimum signal-to-interference-plus-noise ratio (SINR) of the ID users and ID/EH users by jointly designing the power allocation at the transmitter and the power splitting strategy at the ID/EH receivers under the maximum transmit power and the minimum energy harvesting constraints. Specifically, we first apply the semidefinite relaxation (SDR), zero-forcing (ZF), and maximum ratio transmission (MRT) techniques to solve the nonconvex problems. We then apply the zero-forcing dirty paper coding (ZF-DPC) technique to eliminate the multiuser interference and derive the closed-form optimal solution. Numerical results show that ZF-DPC provides higher achievable minimum SINR than SDR and ZF in most cases.

Cognitive interference channel: achievable rate region and power allocation

In this study, the authors consider a state-dependent two user interference channel. The two users sharing the spectrum are assumed to be cognitive and each user has a non-causal access to the signal from the other user. For this channel model, an achievable rate region is established for both discrete memoryless model and Gaussian channel. In particular, the achievable rate region is obtained by combining Han–Kobayashi rate splitting coding scheme, superposition coding, Gelfand–Pinsker coding scheme and zero-forcing dirty paper coding. Furthermore, the sum rate maximisation and the associated power allocation problem are studied, numerically and theoretically. The corresponding numerical examples show that the proposed combined coding scheme outperforms the existing schemes in the sense of achievable rate region. Moreover, the effectiveness of the optimal power allocation between the two cognitive nodes is also shown.

Efficient beamforming method for downlink MU-MIMO broadcast channels

The sum rate maximization in multiuser MIMO broadcast channels is investigated in this paper. Due to the high computational complexity of non-linear dirty paper coding (DPC), zero-forcing dirty paper coding (ZF-DPC) is proposed as an alternative suboptimal approach. However, traditional ZF-DPC method requires that the number of total receive antennas is less than or equal to the number of transmit antennas. In this paper, we consider the scenario where the sum number of receive antennas may be more than the number of transmit antennas. It is shown that the optimal data stream allocation needs exhaustive search over all possibilities, and the complexity is significantly high. We propose a greedy transmit data allocation scheme that allocates one data stream at each step, the corresponding transmit beamforming vector and receive combining vector are designed to avoid interfering with the previous allocated data streams, and the pre-equalization Tomlinson–Harashima Precoder (THP) technique is adopted to pre-cancel the non-causally known interference caused by the previous allocated data streams. The proposed method is computationally efficient thanks to the low complexity. Simulation results show that this novel method outperforms the methods in the literature.

Beamformer Designs for MISO Broadcast Channels with Zero-Forcing Dirty Paper Coding

We consider the beamformer design for multiple-input multiple-output (MISO) broadcast channels (MISO BCs) using zero-forcing dirty paper coding (ZF-DPC). Assuming a sum power constraint (SPC), most previously proposed beamformer designs are based on the QR decomposition (QRD), which is a natural choice to satisfy the ZF constraints. However, the optimality of the QRD-based design for ZF-DPC has remained unknown. In this paper, first, we analytically establish that the QRD-based design is indeed optimal for any performance measure under a SPC. Then, we propose an optimal beamformer design method for ZF-DPC with per-antenna power constraints (PAPCs), using a convex optimization framework. The beamformer design is first formulated as a rank-1-constrained optimization problem. Exploiting the special structure of the ZF-DPC scheme, we prove that the rank constraint can be relaxed and still provide the same solution. In addition, we propose a fast converging algorithm to the beamformer design problem, under the duality framework between the BCs and multiple access channels (MACs). More specifically, we show that a BC with ZF-DPC has the dual MAC with ZF-based successive interference cancellation (ZF-SIC). In this way, the beamformer design for ZF-DPC is transformed into a power allocation problem for ZF-SIC, which can be solved more efficiently.

Weighted Sum Rate Maximization for MIMO Broadcast Channels Using Dirty Paper Coding and Zero-forcing Methods

We consider precoder design for maximizing the weighted sum rate (WSR) of successive zero-forcing dirty paper coding (SZF-DPC). For this problem, the existing precoder designs often assume a sum power constraint (SPC) and rely on the singular value decomposition (SVD). The SVD-based designs are known to be optimal but require high complexity. We first propose a low-complexity optimal precoder design for SZF-DPC under SPC, using the QR decomposition. Then, we propose an efficient numerical algorithm to find the optimal precoders subject to per-antenna power constraints (PAPCs). To this end, the precoder design for PAPCs is formulated as an optimization problem with a rank constraint on the covariance matrices. A well-known approach to solve this problem is to relax the rank constraints and solve the relaxed problem. Interestingly, for SZF-DPC, we are able to prove that the rank relaxation is tight. Consequently, the optimal precoder design for PAPCs is computed by solving the relaxed problem, for which we propose a customized interior-point method that exhibits a superlinear convergence rate. Two suboptimal precoder designs are also presented and compared to the optimal ones. We also show that the proposed numerical method is applicable for finding the optimal precoders for block diagonalization scheme.

On the Achievable User Number of the Downlinks in Cellular-Based Machine-to-Machine Communications

In cellular-based machine-to-machine (M2M) networks, supporting large number of machine-type communications (MTC) users (devices) has become a critical challenge in both the uplink and downlink channels. In this paper, we focus on the downlink beamforming using zero-forcing dirty paper coding (DPC). In order to characterize the system's ability of user admission, we consider the achievable user number, which is defined as the number of users whose signal-to-interference plus-noise ratios exceed a target threshold. Due to the complexity of the optimal scheme, we propose two algorithms with random user scheduling and greedy user scheduling in maximizing the achievable user number by dynamical power assignment. Using the joint distribution of effective channel gains, we derive the achievable user number of both the scheduling schemes. An upper bound on the achievable user number of the greedy scheme is then derived which is shown to be tight when there are a large number of users. From numerical results, we show that both of the schemes enjoy a linear increase in the achievable user number as the number of transmitter antennas increases. The performance of the greedy scheduling scheme is close to the optimal scheduling scheme.

Bit Concatenation Based User Relaying in MIMO Broadcast Channels

A novel user relaying scheme based on bit concatenation is proposed for multiple-input multiple-output (MIMO) broadcast channels. In a broadcasting phase, a part of information for a destination user is concatenated to data for a relaying user and transmitted to the relaying user. The destination user receives the part of information via the relaying user in a relaying phase in addition to the data in the broadcasting phase. An achievable rate region for the proposed scheme is derived and an algorithm to characterize the boundary of the rate region is proposed. Our analysis shows that the proposed user relaying in a MIMO BC expands the achievable rate region for the zero-forcing dirty paper coding (ZF-DPC) in the MIMO BC without relaying. It is also shown that the proposed user relaying scheme always outperforms a superposition coding (SC) based user relaying scheme. Optimal and suboptimal user pair scheduling algorithms are investigated for a two-user MIMO BC and the proposed suboptimal user pair scheduling scheme is shown to approach the optimal scheduling when the relaying channel gain is large.

Enhancing ZF-DPC Performance with Receiver Processing

Multiuser multiple-input multiple-output (MU-MIMO) systems are known to achieve superior data rates compared to single user (SU-MIMO) systems in the downlink. The achievable rates of MU-MIMO systems are dependent on the precoder design at the transmitter. Dirty paper coding (DPC) is a well known non-linear algorithm to achieve MIMO broadcast channel (BC) capacity. Zero forcing DPC (ZF-DPC) is a sub-optimal way to achieve DPC by triagularizing the channel. In a recent work, it was shown that ZF-DPC with receiver beamforming can provide further improvements. In this paper, we propose an enhancement of ZF-DPC with receiver processing by utilizing the MAC/BC duality. The proposed algorithm is iterative in nature which provides a useful trade-off between complexity and desired performance. Simulation results show that the proposed ZF-DPC algorithm achieves considerable improvement over conventional ZF-DPC and is within 1% of MIMO BC capacity.

On the achievable rates of multiple antenna broadcast channels with feedback-link capacity constraint

In this paper, we study a MIMO fading broadcast channel where each receiver has perfect channel state information while the channel state information at the transmitter is acquired by explicit channel feedback from each receiver through capacity-constrained feedback links. Two feedback schemes are considered, i.e., the analog and digital feedback. We analyze the achievable ergodic rates of zero-forcing dirty-paper coding (ZF-DPC), which is a nonlinear precoding scheme inherently superior to linear ZF beamforming. Closed-form lower and upper bounds on the achievable ergodic rates of ZF-DPC with Gaussian inputs and uniform power allocation are derived. Based on the closed-form rate bounds, sufficient and necessary conditions on the feedback channels to ensure nonzero and full downlink multiplexing gain are obtained. Specifically, for analog feedback in both AWGN and Rayleigh fading feedback channels, it is sufficient and necessary to scale the average feedback link SNR linearly with the downlink SNR in order to achieve the full multiplexing gain. While for the random vector quantization-based digital feedback with angle distortion measure in an error-free feedback link, it is sufficient and necessary to scale the number of feedback bits B per user as where M is the number of transmit antennas and is the average downlink SNR.

Efficient user selection algorithms for multiuser MIMO systems with zero-forcing dirty paper coding

This paper investigates the user selection problem of successive zero-forcing precoded multiuser multiple-input multiple-output (MU-MIMO) downlink systems, in which the base station and mobile receivers are equipped with multiple antennas. Assuming full knowledge of the channel state information at the transmitter, dirty paper coding (DPC) is an optimal precoding strategy, but practical implementation is difficult because of its excessive complexity. As a suboptimal DPC solution, successive zero-forcing DPC (SZF-DPC) was recently proposed; it employs partial interference cancellation at the transmitter with dirty paper encoding. Because of a dimensionality constraint, the base station may select a subset of users to serve in order to maximize the total throughput. The exhaustive search algorithm is optimal; however, its computational complexity is prohibitive. In this paper, we develop two low-complexity user scheduling algorithms to maximize the sum rate capacity of MU-MIMO systems with SZF-DPC. Both algorithms add one user at a time. The first algorithm selects the user with the maximum product of the maximum column norm and maximum eigenvalue. The second algorithm selects the user with the maximum product of the minimum column norm and minimum eigenvalue. Simulation results demonstrate that the second algorithm achieves a performance similar to that of a previously proposed capacity-based selection algorithm at a high signal-to-noise (SNR), and the first algorithm achieves performance very similar to that of a capacity-based algorithm at a low SNR, but both do so with much lower complexity.

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.

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.

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>

Sum-Rate Capacity with Fairness in Correlated MIMO Broadcast Channels

Although the maximum sum-rate capacity of multiple-input multiple output(MIMO) broadcast channels(BCs) can be achieved by dirty-paper coding(DPC), the results were obtained without fairness considerations in uncorrelated MIMO channels. In this paper, we propose new multiuser scheduling algorithms, which find a best user set for approaching the maximum sum-rate capacity while maintaining fairness among users. We analyze the performance of the proposed algorithms using zero-forcing dirty paper coding(ZF-DPC) in the correlated MIMO BCs for throughput and delay fairness, respectively. Numerical results demonstrate that a large time window can reduce the average throughput difference between users, but it increases head-of-line(HOL) delay jitters in the case of delay fairness.

An efficient greedy scheduler for zero-forcing dirty-paper coding

In this paper, an efficient greedy scheduler for zero-forcing dirty-paper coding (ZF-DPC), which can be incorporated in complex Householder QR factorization of the channel matrix, is proposed. The ratio of the complexity of the proposed scheduler to the complexity of the channel matrix factorization required by ZF-DPC is O(M <sup xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">-1</sup> ), while such ratio for the original greedy scheduler is O(M), where M is the number of transmitters. Therefore, the new scheduler reduces the overhead of scheduling from being the bottleneck of ZF-DPC to being negligible.