Showing papers on "Dirty paper coding published in 2009"

Performance of Orthogonal Beamforming for SDMA With Limited Feedback

Abstract: On the multiantenna broadcast channel, the spatial degrees of freedom support simultaneous transmission to multiple users. The optimal multiuser transmission, which is known as dirty paper coding, is not directly realizable. Moreover, close-to-optimal solutions such as Tomlinson-Harashima precoding are sensitive to channel state information (CSI) inaccuracy. This paper considers a more practical design called per user unitary and rate control (PU2RC), which has been proposed for emerging cellular standards. PU2RC supports multiuser simultaneous transmission, enables limited feedback, and is capable of exploiting multiuser diversity. Its key feature is an orthogonal beamforming (or precoding) constraint, where each user selects a beamformer (or precoder) from a codebook of multiple orthonormal bases. In this paper, the asymptotic throughput scaling laws for PU2RC with a large user pool are derived for different regimes of the signal-to-noise ratio (SNR). In the multiuser interference-limited regime, the throughput of PU2RC is shown to logarithmically scale with the number of users. In the normal SNR and noise-limited regimes, the throughput is found to scale double logarithmically with the number of users and linearly with the number of antennas at the base station. In addition, numerical results show that PU2RC achieves higher throughput and is more robust against CSI quantization errors than the popular alternative of zero-forcing beamforming if the number of users is sufficiently large.

Lattices are everywhere

Abstract: As bees and crystals (and people selling oranges in the market) know it for many years, lattices provide efficient structures for packing, covering, quantization and channel coding In the recent years, interesting links were found between lattices and coding schemes for multi-terminal networks This tutorial paper covers close to 20 years of my research in the area; of enjoying the beauty of lattice codes, and discovering their power in dithered quantization, dirty paper coding, Wyner-Ziv DPCM, modulo-lattice modulation, distributed interference cancelation, and more

On the Loss of Single-Letter Characterization: The Dirty Multiple Access Channel

Abstract: For general memoryless systems, the existing information-theoretic solutions have a ldquosingle-letterrdquo form. This reflects the fact that optimum performance can be approached by a random code (or a random binning scheme), generated using independent and identically distributed copies of some scalar distribution. Is that the form of the solution of any (information-theoretic) problem? In fact, some counter examples are known. The most famous one is the ldquotwo help onerdquo problem: Korner and Marton showed that if we want to decode the modulo-two sum of two correlated binary sources from their independent encodings, then linear coding is better than random coding. In this paper we provide another counter example, the ldquodoubly-dirtyrdquo multiple-access channel (MAC). Like the Korner-Marton problem, this is a multiterminal scenario where side information is distributed among several terminals; each transmitter knows part of the channel interference while the receiver only observes the channel output. We give an explicit solution for the capacity region of the binary doubly-dirty MAC, demonstrate how this region can be approached using a linear coding scheme, and prove that the ldquobest known single-letter regionrdquo is strictly contained in it. We also state a conjecture regarding the capacity loss of single-letter characterization in the Gaussian case.

Advances in Multiuser Detection

Abstract: Preface. Contributors. 1 Overview of Multiuser Detection ( Michael L. Honig). 1.1 Introduction. 1.2 Matrix Channel Model. 1.3 Optimal Multiuser Detection. 1.4 Linear Detectors. 1.5 Reduced-Rank Estimation. 1.6 Decision-Feedback Detection. 1.7 Interference Mitigation at the Transmitter. 1.8 Overview of Remaining Chapters. References. 2 Iterative Techniques ( Alex Grant and Lars K. Rasmussen). 2.1 Introduction. 2.2 Iterative Joint Detection for Uncoded Data. 2.3 Iterative Joint Decoding for Coded Data. 2.4 Concluding Remarks. References. 3 Blind Multiuser Detection in Fading Channels ( Daryl Reynolds, H. Vincent Poor, and Xiaodong Wang). 3.1 Introduction. 3.2 Signal Models and Blind Multiuser Detectors for Fading Channels. 3.3 Performance of Blind Multiuser Detectors. 3.4 Bayesian Multiuser Detection for Long-Code CDMA. 3.5 Multiuser Detection for Long-Code CDMA in Fast-Fading Channels. 3.6 Transmitter-Based Multiuser Precoding for Fading Channels. 3.7 Conclusion. References. 4 Performance with Random Signatures ( Matthew J. M. Peacock, Iain B. Collings, and Michael L. Honig). 4.1 Random Signatures and Large System Analysis. 4.2 System Models. 4.3 Large System Limit. 4.4 Random Matrix Terminology. 4.5 Incremental Matrix Expansion. 4.6 Analysis of Downlink Model. 4.7 Spectral Efficiency. 4.8 Adaptive Linear Receivers. 4.9 Other Models and Extensions. 4.10 Bibliographical Notes. References. 5 Generic Multiuser Detection and Statistical Physics < Dongning Guo and Toshiyuki Tanaka). 5.1 Introduction. 5.2 Generic Multiuser Detection. 5.3 Main Results: Single-User Characterization. 5.4 The Replica Analysis of Generic Multiuser Detection. 5.5 Further Discussion. 5.6 Statistical Physics and the Replica Method. 5.7 Interference Cancellation. 5.8 Concluding Remarks. 5.9 Acknowledgments. References. 6 Joint Detection for Multi-Antenna Channels ( Antonia Tulino, Matthew R. McKay, Jeffrey G. Andrews,. Iain B. Collings, and Robert W. Heath, Jr.). 6.1 Introduction. 6.2 Wireless Channels: The Multi-Antenna Realm. 6.3 Definitions and Preliminaries. 6.4 Multi-Antenna Capacity: Ergodic Regime. 6.5 Multi-Antenna Capacity: Non-Ergodic Regime. 6.6 Receiver Architectures and Performance. 6.7 Multiuser Multi-Antenna Systems. 6.8 Diversity-Multiplexing Tradeoffs and Spatial Adaptation. 6.9 Conclusions. References. 7 Interference Avoidance for CDMA Systems ( Dimitrie C. Popescu, Sennur Ulukus, Christopher Rose, and Roy Yates). 7.1 Introduction. 7.2 Interference Avoidance Basics. 7.3 Interference Avoidance over Time-Invariant Channels. 7.4 Interference Avoidance in Fading Channels. 7.5 Interference Avoidance in Asynchronous Systems. 7.6 Feedback Requirements for Interference Avoidance. 7.7 Recent Results on Interference Avoidance. 7.8 Summary and Conclusions. References. 8 Capacity-Approaching Multiuser Communications Over Multiple Input/Multiple Output Broadcast Channels ( Uri Erez and Stephan ten Brink). 8.1 Introduction. 8.2 Many-to-One Multiple Access versus One-to-Many Scalar Broadcast Channels. 8.3 Alternative Approach: Dirty Paper Coding. 8.4 A Simple 2 x 2 Example. 8.5 General Gaussian MIMO Broadcast Channels. 8.6 Coding with Side Information at the Transmitter. 8.7 Summary. References. Index.

Network Coordinated Beamforming for Cell-Boundary Users: Linear and Nonlinear Approaches

Abstract: In this paper, low-complexity linear and nonlinear network coordinated beamforming (N-CBF) algorithms are proposed for the multi-cell downlink channel. We consider a downlink scenario with three base stations (BSs) equipped with one transmit antenna each and three mobile users, each of which has more than one receive antenna and is located on the cell-boundary. A single data stream is transmitted to all three cell-boundary users where each user receives his/her own independent data stream (called full broadcast channel), or where two users receive the same data stream while the third user receives a different data stream (called clustered broadcast channel). For full and clustered broadcast channel scenarios, we propose low-complexity linear N-CBF algorithms approaching the sum capacity realized by multi-cell dirty paper coding. We also propose low complexity nonlinear N-CBF algorithms that avoid power enhancement and maximize the effective channel gain for enhancing the bit error rate (BER). The impact of the number of receive antennas on the behavior of the proposed system is also discussed. Monte Carlo simulations are carried out to verify the sum rate and BER performances of the proposed algorithms.

How much does transmit correlation affect the sum-rate scaling of MIMO gaussian broadcast channels?

Abstract: This paper considers the effect of spatial correlation between transmit antennas on the sum-rate capacity of the MIMO Gaussian broadcast channel (i.e., downlink of a cellular system). Specifically, for a system with a large number of users n, we analyze the scaling laws of the sum-rate for the dirty paper coding and for different types of beamforming transmission schemes. When the channel is i.i.d., it has been shown that for large n, the sum rate is equal to M log log n + M log P/M + o(1) where M is the number of transmit antennas, P is the average signal to noise ratio, and o(1) refers to terms that go to zero as n rarr infin. When the channel exhibits some spatial correlation with a covariance matrix R (non-singular with tr(R) = M), we prove that the sum rate of dirty paper coding is M log log n + M log P/M + log det(R) + o(1). We further show that the sum-rate of various beamforming schemes achieves M log log n + M log P/M + M log c + o(1) where c les 1 depends on the type of beamforming. We can in fact compute c for random beamforming proposed in and more generally, for random beamforming with preceding in which beams are pre-multiplied by a fixed matrix. Simulation results are presented at the end of the paper.

Joint Wyner–Ziv/Dirty-Paper Coding by Modulo-Lattice Modulation

Abstract: The combination of source coding with decoder side information (the Wyner-Ziv problem) and channel coding with encoder side information (the Gel'fand-Pinsker problem) can be optimally solved using the separation principle. In this work, we show an alternative scheme for the quadratic-Gaussian case, which merges source and channel coding. This scheme achieves the optimal performance by applying a modulo-lattice modulation to the analog source. Thus, it saves the complexity of quantization and channel decoding, and remains with the task of ldquoshapingrdquo only. Furthermore, for high signal-to-noise ratio (SNR), the scheme approaches the optimal performance using an SNR-independent encoder, thus it proves for this special case the feasibility of universal joint source-channel coding.

Capacity of channels with action-dependent states

Abstract: We consider channels with action-dependent states: Given the message to be communicated, the transmitter chooses an action sequence that affects the formation of the channel states, and then creates the channel input sequence based on the state sequence. We characterize the capacity of such a channel both for the case where the channel inputs are allowed to depend non-causally on the state sequence and the case where they are restricted to causal dependence. Our setting covers previously considered scenarios involving transmission over channels with states known at the encoder, as well as various new coding scenarios for channels with a ‘rewrite’ option that may arise naturally in storage for computer memories with defects or in magnetic recoding. A few examples are worked out in detail.

The Secrecy Capacity Region of the Gaussian MIMO Broadcast Channel

Abstract: In this paper, we consider a scenario where a source node wishes to broadcast two confidential messages for two respective receivers via a Gaussian MIMO broadcast channel. A wire-tapper also receives the transmitted signal via another MIMO channel. First we assumed that the channels are degraded and the wire-tapper has the worst channel. We establish the capacity region of this scenario. Our achievability scheme is a combination of the superposition of Gaussian codes and randomization within the layers which we will refer to as Secret Superposition Coding. For the outerbound, we use the notion of enhanced channel to show that the secret superposition of Gaussian codes is optimal. We show that we only need to enhance the channels of the legitimate receivers, and the channel of the eavesdropper remains unchanged. Then we extend the result of the degraded case to non-degraded case. We show that the secret superposition of Gaussian codes along with successive decoding cannot work when the channels are not degraded. we develop a Secret Dirty Paper Coding (SDPC) scheme and show that SDPC is optimal for this channel. Finally, we investigate practical characterizations for the specific scenario in which the transmitter and the eavesdropper have multiple antennas, while both intended receivers have a single antenna. We characterize the secrecy capacity region in terms of generalized eigenvalues of the receivers channel and the eavesdropper channel. We refer to this configuration as the MISOME case. In high SNR we show that the capacity region is a convex closure of two rectangular regions.

Near-Capacity Dirty-Paper Code Design: A Source-Channel Coding Approach

Abstract: This paper examines near-capacity dirty-paper code designs based on source-channel coding. We first point out that the performance loss in signal-to-noise ratio (SNR) in our code designs can be broken into the sum of the packing loss from channel coding and a modulo loss, which is a function of the granular loss from source coding and the target dirty-paper coding rate (or SNR). We then examine practical designs by combining trellis-coded quantization (TCQ) with both systematic and nonsystematic irregular repeat-accumulate (IRA) codes. Like previous approaches, we exploit the extrinsic information transfer (EXIT) chart technique for capacity-approaching IRA code design; but unlike previous approaches, we emphasize the role of strong source coding to achieve as much granular gain as possible using TCQ. Instead of systematic doping, we employ two relatively shifted TCQ codebooks, where the shift is optimized (via tuning the EXIT charts) to facilitate the IRA code design. Our designs synergistically combine TCQ with IRA codes so that they work together as well as they do individually. By bringing together TCQ (the best quantizer from the source coding community) and EXIT chart-based IRA code designs (the best from the channel coding community), we are able to approach the theoretical limit of dirty-paper coding. For example, at 0.25 bit per symbol (b/s), our best code design (with 2048-state TCQ) performs only 0.630 dB away from the Shannon capacity.

Lower bounds on the capacity of the relay channel with states at the source

Abstract: We consider a state-dependent three-terminal full-duplex relay channel with the channel states noncausally available at only the source, that is, neither at the relay nor at the destination. This model has application to cooperation over certain wireless channels with asymmetric cognition capabilities and cognitive interference relay channels. We establish lower bounds on the channel capacity for both discrete memoryless (DM) and Gaussian cases. For the DM case, the coding scheme for the lower bound uses techniques of rate-splitting at the source, decode-and-forward (DF) relaying, and a Gel'fand-Pinsker-like binning scheme. In this coding scheme, the relay decodes only partially the information sent by the source. Due to the rate-splitting, this lower bound is better than the one obtained by assuming that the relay decodes all the information from the source, that is, full-DF. For the Gaussian case, we consider channel models in which each of the relay node and the destination node experiences on its link an additive Gaussian outside interference. We first focus on the case in which the links to the relay and to the destination are corrupted by the same interference; and then we focus on the case of independent interferences. We also discuss a model with correlated interferences. For each of the first two models, we establish a lower bound on the channel capacity. The coding schemes for the lower bounds use techniques of dirty paper coding or carbon copying onto dirty paper, interference reduction at the source and decode-and-forward relaying. The results reveal that, by opposition to carbon copying onto dirty paper and its root Costa's initial dirty paper coding (DPC), it may be beneficial in our setup that the informed source uses a part of its power to partially cancel the effect of the interference so that the uninformed relay benefits from this cancellation, and so the source benefits in turn.

Low-Complexity Linear Zero-Forcing for the MIMO Broadcast Channel

Abstract: Maximizing the sum capacity in the multiple-input multiple-output (MIMO) broadcast channel requires the use of dirty paper coding (DPC). However, practical implementations of DPC which are nearly optimum exhibit high computational complexity. As an alternative to DPC linear zero-forcing can be used where the multiuser interference is completely canceled by linear beamforming. Determining the optimum user allocation, transmit and receive filters thereby constitutes a combinatorial and nonconvex optimization problem. To circumvent its direct solution and therefore reduce complexity, we propose an algorithm that successively allocates data streams to users and, in contrast to state-of-the-art approaches, includes the receive filters into the optimization. We then show several steps that reduce the complexity of the algorithm at marginal performance losses. Thus, performance of state-of-the-art approaches can be maintained while the computational complexity is reduced considerably, as it is shown by a detailed complexity analysis and simulation results.

Dirty Paper Coding for Fading Channels with Partial Transmitter Side Information

Abstract: The problem of Dirty Paper Coding (DPC) over the Fading Dirty Paper Channel (FDPC) Y = H(X + S)+Z, a more general version of Costa's channel, is studied for the case in which there is partial and perfect knowledge of the fading process H at the transmitter (CSIT) and the receiver (CSIR), respectively. A key step in this problem is to determine the optimal inflation factor (under Costa's choice of auxiliary random variable) when there is only partial CSIT. Towards this end, two iterative numerical algorithms are proposed. Both of these algorithms are seen to yield a good choice for the inflation factor. Finally, the high-SNR (signal-to-noise ratio) behavior of the achievable rate over the FDPC is dealt with. It is proved that FDPC (with t transmit and r receive antennas) achieves the largest possible scaling factor of min(t,r) log SNR even with no CSIT. Furthermore, in the high SNR regime, the optimality of Costa's choice of auxiliary random variable is established even when there is partial (or no) CSIT in the special case of FDPC with t <= r. Using the high-SNR scaling-law result of the FDPC (mentioned before), it is shown that a DPC-based multi-user transmission strategy, unlike other beamforming-based multi-user strategies, can achieve a single-user sum-rate scaling factor over the multiple-input multiple-output Gaussian Broadcast Channel with partial (or no) CSIT.

Dirty Paper Coding for the MIMO Cognitive Radio Channel with Imperfect CSIT

Abstract: A Dirty Paper Coding (DPC) based transmission scheme for the Gaussian multiple-input multiple-output (MIMO) cognitive radio channel (CRC) is studied when there is imperfect and perfect channel knowledge at the transmitters (CSIT) and the receivers, respectively. In particular, the problem of optimizing the sum-rate of the MIMO CRC over the transmit covariance matrices is dealt with. Such an optimization, under the DPC-based transmission strategy, needs to be performed jointly with an optimization over the inflation factor. To this end, first the problem of determination of inflation factor over the MIMO channel $Y=H_1 X + H_2 S + Z$ with imperfect CSIT is investigated. For this problem, two iterative algorithms, which generalize the corresponding algorithms proposed for the channel $Y=H(X+S)+Z$, are developed. Later, the necessary conditions for maximizing the sum-rate of the MIMO CRC over the transmit covariances for a given choice of inflation factor are derived. Using these necessary conditions and the algorithms for the determination of the inflation factor, an iterative, numerical algorithm for the joint optimization is proposed. Some interesting observations are made from the numerical results obtained from the algorithm. Furthermore, the high-SNR sum-rate scaling factor achievable over the CRC with imperfect CSIT is obtained.

Reduced feedback and random beamforming for OFDM MIMO broadcast channels

Abstract: It has been shown that random beamforming using partial channel state information (CSI) achieves the same throughput scaling as obtained from dirty paper coding for a broadcast (downlink) channel with M transmit antennas and K users where K is large. In this paper, we apply this scheme to wideband MIMO broadcast channels. By using OFDM, an L-tap wideband channel can be decomposed to N parallel narrowband channels (subcarriers), where N > L . Neighboring subcarriers are highly correlated. Therefore, we consider neighboring subcarriers as a cluster and find the closed form solution for the joint characteristic function of SINR values at two subcarriers in a cluster. We show numerically how the knowledge of the quality of the center subcarrier sheds light about the quality of other subcarriers in the same cluster, and address the issue of cluster size. In addition, through complex and asymptotic analysis, we show that for cluster size of order N/L?(log K) (for large K), users need only feedback the best SINR at the center subcarrier of each cluster in order for the transmitter to perform opportunistic beamforming and maintain the same throughput scaling as when full CSI is available. Using simulation results, we verify our analytical result and show that even fewer feedback can be tolerated, and larger clusters (N/2L) can be implemented for a small throughput hit.

Opportunistic Beamforming Communication With Throughput Analysis Using Asymptotic Approach

Abstract: The opportunistic beamforming system (OBS) is currently receiving much attention in the field of downlink beamforming due to its simple random beamforming, low feedback complexity, and same throughput scaling obtained with perfect channel-state information using dirty paper coding at the transmitter. In this paper, we focus on its closed-form throughput evaluation over Rayleigh fading channels, based on the asymptotic theory of extreme order statistics. First, the throughput of a single-beam OBS is investigated, and an analytical solution tighter than the previously reported one is derived. Then, the asymptotic throughput bounds on a multibeam OBS are presented, and also, our analytical expression is shown to be very tight with the simulation results even with fewer users. After that, we argue that the reported conclusion that the single-beam OBS is much preferable to the multibeam OBS in the high-signal-to-noise-ratio (SNR) regime is inaccurate, but that, instead, it is satisfied only when the number of users is very small, due to its limited multiuser diversity gain. Finally, we show that four transmit beams is the most preferable in the multibeam OBS with a large number of users and moderate SNR, which arrives at the tradeoff between increasing spatial multiplexing gain and disappearing multiuser diversity gain.

On Downlink Transmission Without Transmit Channel State Information and With Outage Constraints

Abstract: This paper investigates downlink transmission over a quasi-static fading Gaussian broadcast channel (BC), to model delay-sensitive applications over slowly time-varying fading channels. System performance is characterized by the outage capacity region. In contrast to most previous work, here the problem is studied under the key assumption that the transmitter knows only the probability distributions of the fading coefficients, not their realizations. For scalar-input channels, two coding schemes are studied. The first scheme is called blind dirty paper coding (B-DPC), which utilizes a robustness property of dirty paper coding to perform precoding at the transmitter. The second scheme is called statistical superposition coding (S-SC), in which each receiver adaptively performs successive decoding with the process statistically governed by the realized fading. Both B-DPC and S-SC schemes achieve the outage capacity region, which dominates the outage rate region of time-sharing, irrespective of the particular fading distributions. The S-SC scheme can be extended to BCs with multiple transmit antennas.

A modified belief propagation algorithm for code word quantization

Abstract: Modern coding advances, including dirty paper coding and information hiding, require quantizing a given binary word to a code word. A 'good' solution would approach the rate-distortion bound in lossy source compression. Here we propose a simple variant on belief propagation which is observed to converge to a solution giving respectable rate-distortion performance. Comparisons with other recently proposed source quantization methods reveal that the proposed algorithm holds particular interest in short block-length applications, as encountered in packet-based communication systems.

Sensing in cognitive radio channels: A theoretical perspective

Abstract: The cognitive radio paradigm is based on the ability of sensing the radio environment in order to make informed decisions. This paper describes the effects of sensing on the cognitive radio channels capacity region. Sensing is modeled as a compression channel, which results in partial knowledge of the primary messages at the cognitive transmitter. This model enables to impose constraints on the sensing strategy. First, the dirty paper channel capacity is derived when the channel encoder knows partially the side information. Then, the capacity area of the Gaussian cognitive channel with partial information is derived. Finally, numerical results illustrate the capacity reduction associated with constrained sensing, in comparison to the capacity of the cognitive radio channel.

Fast Distributed Multi-Cell Scheduling with Delayed Limited-Capacity Backhaul Links

Abstract: Both fast scheduling and spatial signal processing have proven to be capacity-increasing methods in wireless communication systems. However, when applied in the downlink of a cellular network, the combination of both leads to non-stationary intercell interference. If the base stations do not cooperate, either they have to encode the data very conservatively to gain robustness or the non-stationary fluctuations of the interference powers lead to frequent outages, both of which strongly impair the average achievable throughput. On the other hand, base station cooperation increases complexity and delays, contradicting the desire for fast scheduling algorithms. In this paper, we propose a scheme that makes average channel state information available to all base stations via low-rate backhaul communication, whereas high-rate inter-base-station communication is limited to B ⌈log2 K⌉-bit integers, K being the number of users in each of the B cells. Simulations show that for slow fading channels, the proposed algorithm preserves most of the per cell sum-rate of other beamforming and dirty-paper coding approaches that have unlimited-capacity backhaul links. Furthermore, when out-of-cell information is outdated the proposed algorithm even outperforms those.

On transmit antenna selection for multiuser MIMO systems with dirty paper coding

Abstract: In this paper, we address the transmit antenna selection in multi-user MIMO systems with precoding. The optimum and reduced complexity sub-optimum antenna selection algorithms are introduced. QR-decomposition (QRD) based antenna selection is investigated and the reason behind its sub-optimality is analytically derived. We introduce the conventional QRD-based algorithm and propose an efficient QRD-based transmit antenna scheme (maxR) that is both implementation and performance efficient. Moreover, we derive explicit formulae for the computational complexities of the aforementioned algorithms. Simulation results and analysis demonstrate that the proposed maxR algorithm requires only 1% of the computational efforts required by the optimal algorithm for a degradation of 1dB and 0.1dB in the case of linear zero-forcing and Tomlinson-Harashima precoding schemes, respectively.

Dirty Paper Coding for the MIMO cognitive radio channel with imperfect CSIT

Abstract: A Dirty Paper Coding (DPC) based transmission scheme for the Gaussian multiple-input multiple-output (MIMO) cognitive radio channel (CRC) is studied when there is imperfect and perfect channel knowledge at the transmitters (CSIT) and the receivers, respectively. In particular, the problem of optimizing the sum-rate of the MIMO CRC over the transmit covariance matrices is dealt with. Such an optimization, under the DPC-based transmission strategy, needs to be performed jointly with an optimization over the inflation factor. To this end, first the problem of determination of inflation factor over the MIMO channel Y = H 1 X +H 2 S +Z with imperfect CSIT is investigated. For this problem, two iterative algorithms, which generalize the corresponding algorithms proposed for the channel Y = H(X +S)+Z, are developed. Later, the necessary conditions for maximizing the sum-rate of the MIMO CRC over the transmit covariances for a given choice of inflation factor are derived. Using these necessary conditions and the algorithms for the determination of the inflation factor, an iterative, numerical algorithm for the joint optimization is proposed. Some interesting observations are made from the numerical results obtained from the algorithm. Furthermore, the high-SNR sum-rate scaling factor achievable over the CRC with imperfect CSIT is obtained.

On the achievable rate of the fading dirty paper channel with imperfect CSIT

Abstract: The problem of dirty paper coding (DPC) over the (multi-antenna) fading dirty paper channel (FDPC) Y = H(X + S) + Z is considered when there is imperfect knowledge of the channel state information H at the transmitter (CSIT). The case of FDPC with positive definite (p.d.) input covariance matrix was studied by the authors in a recent paper, and here the more general case of positive semi-definite (p.s.d.) input covariance is dealt with. Towards this end, the choice of auxiliary random variable is modified. The algorithms for determination of inflation factor proposed in the p.d. case are then generalized to the case of p.s.d. input covariance. Subsequently, the largest DPC-achievable high-SNR (signal-to-noise ratio) scaling factor over the no-CSIT FDPC with p.s.d. input covariance matrix is derived. This scaling factor is seen to be a non-trivial generalization of the one achieved for the p.d. case. Next, in the limit of low SNR, it is proved that the choice of all-zero inflation factor (thus treating interference as noise) is optimal in the ‘ratio’ sense, regardless of the covariance matrix used. Further, in the p.d. covariance case, the inflation factor optimal at high SNR is obtained when the number of transmit antennas is greater than the number of receive antennas, with the other case having been already considered in the earlier paper. Finally, the problem of joint optimization of the input covariance matrix and the inflation factor is dealt with, and an iterative numerical algorithm is developed.

Opportunistic Relay Selection in Cooperative Systems With Dirty-Paper Coding

Abstract: This paper investigates an optimization of the conventional relay selection for multirelay environments. In contrast with previously reported selection schemes, where a selected relay accesses the channel in a dedicated cooperative slot, the proposed scheme recovers the bandwidth loss of the half-duplex constraint by allowing two relays to simultaneously access the channels. Based on an appropriate dirty-paper coding (DPC) technique among relays, the proposed scheme enables a relay to establish communication with the destination at the same time that another relay forwards the data from the source. It is proven that the interplay between relay selection and the superposition DPC weight factor provides a tradeoff between relaying and new data performance. Hence, an appropriate codesign of the superposition DPC parameter and opportunistic relay selection can achieve efficient communication for the new data without affecting the relaying performance. The proposed scheme is compared with conventional relaying approaches, and its enhancements are provided through theoretical studies and numerical results.

Gaussian MIMO Multi-Receiver Wiretap Channel

Abstract: We consider the Gaussian multiple-input multiple-output (MIMO) multi-receiver wiretap channel, and derive the secrecy capacity region of this channel for the most general case. We first prove the secrecy capacity region of the degraded MIMO channel, in which all receivers have the same number of antennas, and the noise covariance matrices exhibit a positive semidefinite order. We then generalize this result to the aligned case, in which all receivers have the same number of antennas, however there is no order among the noise covariance matrices. We accomplish this task by using the channel enhancement technique. Finally, we find the secrecy capacity region of the general MIMO channel by using some limiting arguments on the secrecy capacity region of the aligned MIMO channel. We show that a variant of dirty-paper coding with Gaussian signals is optimal.

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

Abstract: 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-1), 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.

Efficient User Selection and Ordering Algorithms for Successive Zero-Forcing Precoding for Multiuser MIMO Downlink

Abstract: In this paper we consider user scheduling problem for linearly preceded multiuser multiple-input multiple-output (MIMO) downlink, where base station as well as the mobile receivers are equipped with multiple antennas. Optimal precoding involves dirty paper coding (DPC) technique, and it is highly nonlinear and complex. On the other hand, complete inter-user interference cancellation using linear zero-forcing or block diagonalization precoding are suboptimal. Hence, we consider successive zero-forcing precoding, which achieves improved system throughput compared to block diagonalization by allowing users to work under limited interference. Due to the dimensionality constraint of linear precoding techniques user scheduling is required. The optimal user scheduling involves exhaustive search, which becomes very complex for realistic numbers of users and transmit antennas. In addition, for successive zero-forcing precoding the order in which users are precoded successively is important for sum rate maximization, which further increases the complexity of exhaustive search. In this paper we develop a low complexity greedy user scheduling algorithm for successive zero-forcing precoding, which incorporates various user ordering techniques. Simplified heuristic scheduling metrics are proposed, which are shown to perform close to the exhaustive search method. A suboptimal user ordering technique that is similar to the order, in which the proposed greedy user selection selects users, is proposed. Further simplification of regular greedy scheduling algorithm is obtained with the proposed intermediate user grouping technique. The proposed algorithm is of low complexity, but provides performance close to the highly complex exhaustive search algorithm.

Cooperation-Multiuser Diversity Tradeoff in Wireless Cellular Networks

Abstract: We introduce a new multiuser diversity scheme for interference management in cellular networks. A base station with K antennas communicates with at most K out of M mobile stations. It is proven that, if K ≪ M, then K independent data streams can be transmitted to K mobile stations with no need for cooperative joint decoding by such stations. This result is based on a new multiuser diversity concept that allows parallel communication in the network without any cooperation among mobile stations. If the network does not have enough mobile stations, then some of the users need to jointly decode their corresponding data streams. The result suggests the existence of a tradeoff between multiuser diversity and cooperation in the downlink of cellular networks. Our interference management approach is based on a new multiuser diversity concept that achieves the capacity of dirty paper coding (DPC) asymptotically. Surprisingly, this gain is achieved without requiring full channel state information (CSI) and only K integers related to CSI are fed back from mobile stations to the base station. An additional advantage of this scheme is the fact that the encoding and decoding of signals for this distributed MIMO system is based on simple point-to-point communications.

Practical Dirty Paper Coding with Nested Binary LDGM-LDPC Codes

Abstract: The superior shaping performance of low-density generation matrix (LDGM) codes makes them important in the design of capacity-approaching dirty paper coding (DPC) schemes. One possible LDGM-based DPC scheme is the nested LDGM-LDPC code proposed by Wainwright and Martinian, which has been shown to be capacity-achieving under optimal encoding and decoding. In this paper, considering the Gaussian DPC problem limited to a binary alphabet, we propose practical encoding and decoding algorithms for the nested LDGM-LDPC code utilizing ideas from the fast LDPC encoding algorithm to satisfy the parity constraints, and optimize the degree distributions of the code through density evolution. Simulation results show that the proposed scheme can indeed closely approach the alphabet-constrained DPC capacity.

Linear network coordinated beamforming for cell-boundary users

Abstract: In this paper, low complexity linear network coordinated beamforming (N-CBF) algorithms under a zero inter-user interference constraint are proposed for the multi-cell downlink channel. We consider a downlink scenario with three base stations (BSs) equipped with one transmit antenna each and three mobile users, each of which has more than one receive antenna and is located on the cell-boundary. A single data stream is transmitted to all three cell-boundary users where each user receives his/her own independent data stream (called full broadcast channel), or where two users receive the same data stream while the third user receives a different data stream (called clustered broadcast channel). For the full and clustered broadcast channel scenarios, we propose low complexity linear N-CBF algorithms approaching the sum capacity realized by multi-cell dirty paper coding. Monte Carlo simulations are carried out to verify the proposed algorithms.