Showing papers on "Dirty paper coding published in 2006"

On the optimality of multiantenna broadcast scheduling using zero-forcing beamforming

Abstract: Although the capacity of multiple-input/multiple-output (MIMO) broadcast channels (BCs) can be achieved by dirty paper coding (DPC), it is difficult to implement in practical systems. This paper investigates if, for a large number of users, simpler schemes can achieve the same performance. Specifically, we show that a zero-forcing beamforming (ZFBF) strategy, while generally suboptimal, can achieve the same asymptotic sum capacity as that of DPC, as the number of users goes to infinity. In proving this asymptotic result, we provide an algorithm for determining which users should be active under ZFBF. These users are semiorthogonal to one another and can be grouped for simultaneous transmission to enhance the throughput of scheduling algorithms. Based on the user grouping, we propose and compare two fair scheduling schemes in round-robin ZFBF and proportional-fair ZFBF. We provide numerical results to confirm the optimality of ZFBF and to compare the performance of ZFBF and proposed fair scheduling schemes with that of various MIMO BC strategies.

The Capacity Region of the Gaussian Multiple-Input Multiple-Output Broadcast Channel

Abstract: The Gaussian multiple-input multiple-output (MIMO) broadcast channel (BC) is considered. The dirty-paper coding (DPC) rate region is shown to coincide with the capacity region. To that end, a new notion of an enhanced broadcast channel is introduced and is used jointly with the entropy power inequality, to show that a superposition of Gaussian codes is optimal for the degraded vector broadcast channel and that DPC is optimal for the nondegraded case. Furthermore, the capacity region is characterized under a wide range of input constraints, accounting, as special cases, for the total power and the per-antenna power constraints

Achievable rates in cognitive radio channels

Abstract: Cognitive radio promises a low-cost, highly flexible alternative to the classic single-frequency band, single-protocol wireless device. By sensing and adapting to its environment, such a device is able to fill voids in the wireless spectrum and can dramatically increase spectral efficiency. In this paper, the cognitive radio channel is defined as a two-sender, two-receiver interference channel in which sender 2 obtains the encoded message sender 1 plans to transmit. We consider two cases: in the genie-aided cognitive radio channel, sender 2 is noncausally presented the data to be transmitted by sender 1 while in the causal cognitive radio channel, the data is obtained causally. The cognitive radio at sender 2 may then choose to transmit simultaneously over the same channel, as opposed to waiting for an idle channel as is traditional for a cognitive radio. Our main result is the development of an achievable region which combines Gel'fand-Pinkser coding with an achievable region construction for the interference channel. In the additive Gaussian noise case, this resembles dirty-paper coding, a technique used in the computation of the capacity of the Gaussian multiple-input multiple-output (MIMO) broadcast channel. Numerical evaluation of the region in the Gaussian noise case is performed, and compared to an inner bound, the interference channel, and an outer bound, a modified Gaussian MIMO broadcast channel. Results are also extended to the case in which the message is causally obtained.

Coordinating multiple antenna cellular networks to achieve enormous spectral efficiency

Abstract: Intercell interference limits the capacity of wireless networks. To mitigate this interference we explore coherently coordinated transmission (CCT) from multiple base stations to each user. To treat users fairly, we explore equal rate (ER) networks. We evaluate the downlink network efficiency of CCT as compared to serving each user with single base transmission (SBT) with a separate base uniquely assigned to each user. Efficiency of ER networks is measured as total network throughput relative to the number of network antennas at 10% user outage. Efficiency is compared relative to the baseline of single base transmission with power control, (ER-SBT), where base antenna transmissions are not coordinated and apart from power control and the assignment of 10% of the users to outage, nothing is done to mitigate interference. We control the transmit power of ER systems to maximise the common rate for ER-SBT, ER-CCT based on zero forcing, and ER-CCT employing dirty paper coding. We do so for (no. of transmit antennas per base, no. of receive antennas per user) equal to (1,1), (2,2) and (4,4). We observe that CCT mutes intercell interference enough, so that enormous spectral efficiency improvement associated with using multiple antennas in isolated communication links occurs as well for the base-to-user links in a cellular network.

Performance of Orthogonal Beamforming for SDMA with Limited Feedback

Abstract: On the multi-antenna broadcast channel, the spatial degrees of freedom support simultaneous transmission to multiple users. The optimal multiuser transmission, known as dirty paper coding, is not directly realizable. Moreover, close-to-optimal solutions such as Tomlinson-Harashima precoding are sensitive to 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 scale logarithmically 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 also 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.

On the Maximum Common Rate Achievable in a Coordinated Network

Abstract: We quantify the ultimate performance limits of inter-cell coordinatation in a cellular downlink network. The goal is to achieve fairness by maximizing the minimum rate in the network subject to per base power constraints. We first solve the max-min rate problem for a particular zero-forcing dirty paper coding scheme so as to obtain an achievable max-min rate, which serves as a lower bound on the ultimate limit. We then obtain a simple upper bound on the max-min rate of any scheme, and show that the rate achievable by the zero-forcing dirty paper coding scheme is close to this upper bound. We also extend our analysis to coordinated networks with multiple antennas.

Zero-Forcing Precoding for the MIMO Broadcast Channel under Per-Antenna Power Constraints

Abstract: We consider the downlink transmission of a wireless communication system where M antennas transmit independent information to a subset of K users, each equipped with a single antenna. The Shannon capacity of this MIMO broadcast channel (MIMO-BC) can be achieved using a non-linear preceding technique known as dirty paper coding (DPC) which is difficult to implement in practice. Motivated to study simpler transmission techniques, we focus on a linear precoding technique based on the zero-forcing (ZF) algorithm. In contrast to the typical sum power constraint (SPC), we consider a per-antenna power constraint (PAPC) motivated both by current antenna array designs where each antenna is powered by a separate amplifier and by future wireless networks where spatially separated antennas transmit cooperatively to users. We show that the problem of power allocation for maximizing the weighted sum rate under ZF with PAPC is a constrained convex optimization problem that can be solved using conventional numerical optimization techniques. For the special case of two users, we find an analytic solution based on waterfilling techniques. For the case where the number of users increases without bound, we show that ZF with PAPC is asymptotically optimal in the sense that the ratio of the expected sum-rate capacities between ZF with PAPC and DPC with SPC approaches one. We also show how the results can be generalized for multiple frequency bands and for a hybrid power constraint. Finally, we provide numerical results that show ZF with PAPC achieves a significant fraction of the optimum DPC sum-rate capacity in practical cases where K is bounded

Sum Capacity of Multiuser MIMO Broadcast Channels with Block Diagonalization

Abstract: The sum capacity of a Gaussian broadcast MIMO channel can be achieved with Dirty Paper Coding (DPC). Deploying DPC in real-time systems is, however, impractical. Block Diagonalization (BD) is an alternative precoding technique for downlink multiuser MIMO systems, which can eliminate inter-user interference at each receiver, at the expense of suboptimal sum capacity vs. DPC. In this paper, we study the sum capacity loss of BD for a fixed channel. We show that 1) if the user channels are orthogonal to each other, then BD achieves the complete sum capacity; and 2) if the user channels lie in a common row vector space, then the gain of DPC over BD can be bounded by the minimum of the number of transmit and receive antennas and the number of users. We also compare the ergodic sum capacity of DPC with that of BD in a Rayleigh fading channel. Simulations show that BD can achieve a significant part of the total throughput of DPC. An upper bound on the ergodic sum capacity gain of DPC over BD is derived, which can be evaluated with a few numerical integrations. With this bound, we can easily estimate how far away BD is from being optimal in terms of ergodic sum capacity, which is useful in directing practical system designs.

Writing on Dirty Paper with Feedback

Abstract: "Writing on dirty paper" refers to the communication problem over a channel with both noise and interference, where the interference is known to the encoder non-causally and unknown to the decoder. This problem is regarded as a basic building block in communication, and it has been extensively investigated by Costa and other researchers. However, little is known in the case that the encoder can have access to feedback from the decoder. In this paper, we study the dirty paper coding problem for feedback Gaussian channels without or with memory. We provide the most power efficient coding schemes for this problem, i.e., the schemes achieve lossless interference cancellation. These schemes are based on the Kalman filtering algorithm, extend the Schalkwijk-Kailath feedback codes, have low complexity and a doubly exponential reliability function, and reveal the interconnections among information, control, and estimation over dirty paper channels with feedback. This research may be found useful to, for example, power-constrained sensor network communication

On compound channels with side information at the transmitter

Abstract: Costa has proved that for noncausally known Gaussian interference at a power constrained transmitter communicating over an additive white Gaussian noise channel there is no capacity loss when compared to a scenario where interference is not present. For the case of a transmitter communicating over a quasistatic (i.e., nonergodic) fading channel, his method does not apply. In this correspondence, we derive upper and lower bounds on the capacity of compound channels with side information at the transmitter, first for finite alphabet channels and then, based on this result, for channels on standard alphabets (this includes real alphabets). For the special case of a degenerate compound channel with only one possible realization, our bounds are equivalent to the well-known capacity with side-information formula of Gel'fand and Pinsker. For the quasistatic fading channel, when fading is Ricean, we suggest a scheme based on our lower bound for which the performance is found to be relatively good even for moderate K-factor. As K/spl rarr//spl infin/, the uncertainty on the channel vanishes and our scheme obtains the performance of dirty paper coding, namely that the interference is perfectly mitigated. As K/spl rarr/0, the proposed scheme treats the interferer as additional noise. These results may be of importance for the emerging field of cognitive radios where one user may be aware of another user's intended message to a common receiver, but is unaware of the channel path gains.

High SNR Analysis for MIMO Broadcast Channels: Dirty Paper Coding vs. Linear Precoding

Abstract: We study the MIMO broadcast channel and compare the achievable throughput for the optimal strategy of dirty paper coding to that achieved with sub-optimal and lower complexity linear precoding (e.g., zero-forcing and block diagonalization) transmission. Both strategies utilize all available spatial dimensions and therefore have the same multiplexing gain, but an absolute difference in terms of throughput does exist. The sum rate difference between the two strategies is analytically computed at asymptotically high SNR, and it is seen that this asymptotic statistic provides an accurate characterization at even moderate SNR levels. Furthermore, the difference is not affected by asymmetric channel behavior when each user a has different average SNR. Weighted sum rate maximization is also considered, and a similar quantification of the throughput difference between the two strategies is performed. In the process, it is shown that allocating user powers in direct proportion to user weights asymptotically maximizes weighted sum rate. For multiple antenna users, uniform power allocation across the receive antennas is applied after distributing power proportional to the user weight.

Dirty Paper Coding vs. Linear Precoding for MIMO Broadcast Channels

Abstract: We study the MIMO broadcast channel and compare the achievable throughput for the optimal strategy of dirty paper coding to that achieved with sub-optimal and lower complexity linear precoding (e.g., zero-forcing and block diagonalization) transmission. Both strategies utilize all available spatial dimensions and therefore have the same multiplexing gain, but an absolute difference in terms of throughput does exist. The sum rate difference between the two strategies is analytically computed at asymptotically high SNR, and it is seen that this asymptotic statistic provides an accurate characterization at even moderate SNR levels. Weighted sum rate maximization is also considered, and a similar quantification of the throughput difference between the two strategies is computed. In the process, it is shown that allocating user powers in direct proportion to user weights asymptotically maximizes weighted sum rate.

On the Fading Paper Achievable Region of the Fading MIMO Broadcast Channel

Abstract: We consider transmission over the ergodic fading multi-antenna broadcast (MIMO-BC) channel with partial channel state information at the transmitter and full information at the receiver. Over the equivalent {\it non}-fading channel, capacity has recently been shown to be achievable using transmission schemes that were designed for the ``dirty paper'' channel. We focus on a similar ``fading paper'' model. The evaluation of the fading paper capacity is difficult to obtain. We confine ourselves to the {\it linear-assignment} capacity, which we define, and use convex analysis methods to prove that its maximizing distribution is Gaussian. We compare our fading-paper transmission to an application of dirty paper coding that ignores the partial state information and assumes the channel is fixed at the average fade. We show that a gain is easily achieved by appropriately exploiting the information. We also consider a cooperative upper bound on the sum-rate capacity as suggested by Sato. We present a numeric example that indicates that our scheme is capable of realizing much of this upper bound.

On Achievable Sum Rates of A Multiuser MIMO Relay Channel

Abstract: In this paper, we investigate a multiple input multiple output (MIMO) multiuser relay channel, where a source with multiple antennas sends data to multiple users via a relay with multiple antennas. The relay applies linear processing to the received signal and forwards the processed signal to multiple users. In our system model, the direct links from the source to the users are neglected. We propose algorithms to compute achievable sum rates of this system based on dirty paper coding. An achievable sum rate defines a sum rate that can be achieved in the MIMO multiuser relay channel with zero error probability for any user, hence it is also a lower bound of the capacity of this channel. These algorithms also produce coefficients of the precoder at the source node and the coefficients of the linear processing unit at the relay. Simulations show that the proposed system architecture and algorithms achieve sum rate performance that is close to the derived performance upper bound.

Sum-Rate of MIMO Broadcast Channels with One Bit Feedback

Abstract: The sum-capacity of a multi-antenna broadcast Gaussian channel is known to be achieved by Dirty Paper Coding techniques, or, asymptotically in the number of users n, by beamforming methods, that require full channel state information at the base station. Based on the opportunistic beamforming principle, it has been recently shown that the optimal scaling law of the sum-rate with respect to n, for fixed signal to noise ratio and number of transmitting antennas M, (i.e., M log log n) can be achieved by employing a feedback of only one real and one integer number per user. Moreover, it was proved that a linear scaling with respect of M can be guaranteed only if M scales no faster than log n. In this paper, the optimal scaling law of the sum-rate with respect to n is proved to be achievable with only one bit of feedback per user. The proof builds on opportunistic beamforming and binary quantization of the signal to noise plus interference ratio. Moreover, the linear scaling of the sum-rate with M is demonstrated to hold for M growing no faster than log n even with such a reduced feedback. Finally, the results above are extended to the MIMO case, where each user is equipped with multiple antennas.

A Cross Layer Method for Interference Cancellation and Network Coding in Wireless Networks

Abstract: Multi-hop wireless networks are expected to play an important role in the next-generation wireless systems. One of the central problems in such networks is the network capacity. This paper presents a novel cross layer method for interference cancellation and network coding, which significantly increases the capacity of multi-hop wireless networks. We decompose the multi-hop network into a cell-like sub-network, which we refer to as a wireless switching network. In the proposed approach, multiple nodes, each with its self-information, can communicate via relay nodes. The nodes' self information can then be utilized to cancel the multiuser interference and enable network coding. We shall derive the capacity regions of two cross layer strategies, and show that they are larger than that of the traditional broadcast channel.

Audio watermarking under desynchronization and additive noise attacks

Abstract: Digital watermarking is often modeled as the transmission of a message over a noisy channel denoted as "watermark channel". Distortions introduced by the watermark channel result mainly from attacks and may include interference from the original signal. One of the main differences with classical transmission situations stems from the fact that perceived distortions have to be taken into account. However, measuring the perceived impact an attack has on a watermarked signal is currently an unsolved problem. Possible means of circumventing this problem would be 1) to define the distortion in a so-called "perceived domain" and define an "ad hoc" equivalence between objective and perceived distortion or 2) to define an "equivalent distortion" by removing from the attack noise the part that is correlated to the host signal. This paper concentrates on the second approach and first shows that the resulting "equivalent" attack is a particular case of a thoroughly studied channel: filtering plus additive noise. However, the approach in this paper emphasizes the fact that the additive noise in the model has to be decorrelated with the signal. Then, the formalism is applied to (desynchronization plus noise) attacks on audio signals. In this context, this paper provides the corresponding capacities, as well as optimal "attack" and "defense" strategies in a game theory context.

On the Capacity of Gaussian Weak Interference Channels with Degraded Message sets

Abstract: This paper is motivated by a sensor network on a correlated field where nearby sensors share information, and can thus assist rather than interfere with one another. We consider a special class of two-user Gaussian interference channels (IFCs) where one of the two transmitters knows both the messages to be conveyed to the two receivers. Both achievability and converse arguments are provided for a channel with Gaussian inputs and Gaussian noise when the interference is weaker than the direct link (a so called weak IFC). In general, this region serves as an outer bound on the capacity of weak IFCs with no shared knowledge between transmitters.

On the Capacity Region of Multi-Antenna Gaussian Broadcast Channels with Estimation Error

Abstract: In this paper we consider the effect of channel estimation error on the capacity region of MIMO Gaussian broadcast channels. It is assumed that the receivers and the transmitter have (the same) estimates of the channel coefficients (i.e., the feedback channel is noiseless). We obtain an achievable rate region based on the dirty paper coding scheme. We show that this region is given by the capacity region of a dual multi-access channel with a noise covariance that depends on the transmit power. We explore this duality to give the asymptotic behavior of the sum-rate for a system with a large number of user, i.e., n rarr infin. It is shown that as long as the estimation error is of fixed (w.r.t n) variance, the sum-capacity is of order M log log n, where M is the number of antennas deployed at the transmitter. We further obtain the sum-rate loss due to the estimation error. Finally, we consider a training-based scheme for block fading MISO Gaussian broadcast channels. We find the optimum length of the training interval as well as the optimum power used for training in order to maximize the achievable sum-rate

Efficient Scheduling of Multi-User Multi-Antenna Systems

Abstract: The capacity region of the Gaussian multi-antenna broadcast channel was characterized recently in [19]. It was shown that a scheme based on Dirty Paper Coding [2] achieves the full capacity region when the transmitter has perfect channel state information. However, this scheme potentially involves considerable amounts of feedback and complex algorithms for coding and user selection. This has led to a quest for practical transmission schemes and ways to reduce the amount of channel state information required. In particular, it has been shown that when the total number of users is large, the sum capacity can be closely approached by transmitting to a small subset of near-orthogonal users. In order to further quantify the latter observation, we study a Gaussian broadcast channel with two transmit antennas and K statistically identical, independent users each with a single receive antenna. We obtain an exact asymptotic characterization of the gap between the full sum capacity and the rate that can be achieved by transmitting to a suitably selected pair of users. Specifically, we consider various simple schemes for user-pair selection that take into account the channel norms as well as the relative orientation of the channel vectors. We conclude that a scheme that picks the strongest user and selects a second user to form the best pair, is asymptotically optimal, while also being attractive in terms of feedback and operational complexity.

The Capacity Gain from Base Station Cooperative Scheduling in a MIMO DPC Cellular System

Abstract: As an alternative to traditional static frequency reuse patterns, this paper investigates cooperatively scheduling among neighboring base stations in a cellular multiple antenna system, where each cell adopts dirty paper coding. It is shown that cooperatively scheduled transmission can achieve almost the same amount of interference reduction as conventional frequency reuse and achieve an extra capacity gain. We analytically quantify the capacity gain of cooperatively scheduled transmission over conventional frequency reuse in an Mt times Mr dirty paper coded MIMO system. The theoretical analysis of this paper also provides an altered view of multiuser diversity in the context of a multi-cell system. Because the positions of the users are important in a multi-cell system, we find that the gain is O(radiclog K), from selecting the maximum of a compound lognormal-exponential distribution, whereas multiuser diversity capacity gain has been previously known to grow as O(log log K), from selecting the maximum of K exponentially-distributed powers

Joint Beamforming and Scheduling for SDMA Systems with Limited Feedback

Abstract: On a multi-antenna broadcast channel, exploiting spatial degrees of freedom supports simultaneous transmission to multiple users in the same time and frequency slot. Unfortunately, the optimal approach for such multi-user transmission, namely dirty paper coding, requires non-causal channel state information (CSI) and is hence not directly realizable. Therefore, this paper proposes a practical joint beamforming and scheduling algorithm, which supports multi-user simultaneous transmission, relies on quantized CSI feedback, and furthermore is capable of exploiting multi-user diversity. Using this algorithm, each user quantizes CSI using a codebook comprised of multiple orthonormal vector sets and sends back quantized CSI to the base station. Next, using feedback CSI, the base station jointly performs beamforming and scheduling. For a large number of users, the proposed algorithm is shown to achieve the optimal sum capacity scaling, which scales double logarithmically with the number of users and linearly with the number of antennas at the base station. To constrain the capacity loss due to CSI quantization, the required quantizer codebook size is derived as a polynomial function of the signal-to-noise ratio (SNR). Moreover, fixing the codebook size is found to prevent the sum capacity from growing continuously with the SNR. Numerical results show that the proposed algorithm achieves higher throughput than the conventional algorithms for the same amount of CSI feedback.

Random Beamforming with Multi-beam Selection for MIMO Broadcast Channels

Abstract: Previous work has shown that the capacity region of the Gaussian MIMO broadcast channels is achieved by dirty paper coding (DPC). However, due to high computation complexity of DPC and infeasibility of perfect channel state information (CSI) at the transmitter in many applications, this paper focuses on a reduced complexity transmission scheme named orthonormal random beamforming (ORBF) [16], which only requires partial CSI feedback at the transmitter. Different from the previous work, we analyze the performance of ORBF with moderate number of users and total transmit power constraint. The analysis results show that ORBF scheme is efficient under low SNR. Then we propose a multi-beam selection (MBS) scheme, which selects only the best subset of all the beams to maximize the sum-rate capacity under low SNR. The simulation results show that the proposed MBS scheme achieves great performance improvement when the SNR is low and the number of users is not very large.

Code Designs for MIMO Broadcast Channels

Abstract: Recent information-theoretic results show the optimality of dirty-paper coding (DPC) in achieving the full capacity region of the Gaussian multiple-input multiple-output (MIMO) broadcast channel (BC). This paper presents a DPC based code design for BCs. We consider the case in which there is an individual rate/signal-to-interference-plus-noise ratio (SINR) constraint for each user. For a fixed transmitter power, we choose the linear transmit precoding matrix such that the SINRs at users are uniformly maximized, thus ensuring the best bit-error rate performance. We start with Cover's simplest two-user Gaussian BC and present a coding scheme that operates 1.44 dB from the boundary of the capacity region at the rate of one bit per real sample (b/s) for each user. We then extend the coding strategy to a two-user MIMO Gaussian BC with two transmit antennas at the base-station and develop the first limit-approaching code design using nested turbo codes for DPC. At the rate of 1 b/s for each user, our design operates 1.48 dB from the capacity region boundary. We also consider the performance of our scheme over a slow fading BC. For two transmit antennas, simulation results indicate a performance loss of only 1.4 dB, 1.64 dB and 1.99 dB from the theoretical limit in terms of the total transmission power for the two, three and four user case, respectively.

Multiple Antenna Broadcast Channels With Limited Feedback

Abstract: In this paper, we study the limited feedback model for partial CSI at the basestation (BS) for multiple antenna broadcast channels: the BS has the knowledge of quantized CSI of each user. We first give a practical limited feedback scheme designed for multiple antenna broadcast channels. Then, we study the sum rate performance of zero-forcing dirty paper coding under the proposed limited feedback scheme. An upper bound is also derived to get some insight about the impact of the use of limited feedback. Interestingly, we find that the systems experience a ceiling effect on the sum rate for a fixed feedback rate.

Capacity Evaluation of Various Multiuser MIMO Schemes in Downlink Cellular Environments

Abstract: Presented in this paper is a study of the capacity evaluation of various multiuser MIMO schemes in cellular environments. The throughputs per user of the generalized zero-forcing with rank adaptation and vector perturbation schemes are compared with the capacity bound of the Gaussian MIMO broadcast channel, obtained by dirty paper coding under proportional fairness scheduling. The average cell throughputs of these schemes are also compared. From these comparisons, this study provides vital information for applying multiuser MIMO schemes in multicell environments.

How Much Does Transmit Correlation Affect the Sum-Rate of MIMO Downlink Channels?

Abstract: This paper considers the effect of spatial correlation between transmit antennas on the sum-rate capacity of the MIMO 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 M. Sharif et al. (2005) 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 Beamforming and Scheduling for a MIMO Downlink with Random Arrivals

Abstract: We study a number of downlink signaling strategies under perfect and non-perfect channel state information at the transmitter (CSIT) for the case of random packet arrivals. Under this setting, the relevant fairness criterion is the stabilization of all buffer queues which guarantees a bounded average delay for all users. In the case of perfect CSIT, different linear beamforming schemes are compared with the stability optimal policy based on dirty-paper coding (DPC). It is found that simple linear beamforming schemes with greedy user selection achieve near DPC performance in terms of the average delay. In the case of non-perfect CSIT due to a delayed feedback, we propose a novel greedy beamforming (heuristic) scheme together with "analog feedback" of CSI, where each user sends back its estimated channel vector without quantizing and coding. The proposed scheme outperforms the previously proposed schemes such as opportunistic beamforming and requires a similar feedback overhead.

Degrees of Freedom on the MIMO X Channel - the Optimality of the MMK Scheme

Abstract: We characterize the degrees of freedomX in a system with two multiple antenna transmitters and two multiple antenna receivers. With M antennas at all nodes we find ⌊ 4 M ⌋ ≤ �X ≤ 4 M. The MMK scheme proposed in (1) is seen to achieve the maximum multiplexing gain rounded down to the nearest integer and is exactly optimal when M is a multiple of 3. Compared to zero forcing that allows only M degrees of freedom, we show that the X channel allows a higher multiplexing gain by a factor of at most 4 . While spatial zero forcing is not optimal on the X channel, the combination of zero forcing, dirty paper coding and successive decoding proposed in the MMK scheme is optimal for the maximum multiplexing gain rounded down to the nearest integer value.

A Proof of the Converse for the Capacity of Gaussian MIMO Broadcast Channels

Abstract: The paper provides a proof of the converse for the capacity region of the Gaussian MIMO broadcast channel under total average transmit power constraint. The proof uses several ideas from earlier works on the problem including the recent converse proof by Weingarten, Steinberg and Shamai. First the duality between Gaussian multiple access and broadcast channels is employed to show that every point on the boundary of the dirty paper coding region can be represented as the optimal solution to a convex optimization problem. Using the optimality conditions for this convex problem, a degraded broadcast channel is constructed for each point. It is then shown that the capacity region for this degraded broadcast channel contains the capacity region of the original channel. Moreover, the same point lies on the boundary of the dirty paper coding region for this degraded channel. Finally, the standard entropy power inequality is used to show that this point lies on the boundary of the capacity region of the degraded channel as well and consequently it is on the boundary of the capacity region of the original channel.