Achievable rate region for the multiple-access channel with multiple cognitive transmitters

A scenario where one ＇dumb＇ radio and multiple cognitive radios communicating simultaneously with a common receiver is considered. In this paper, we derive an achievable rate region of the multiple-user cognitive multiple-access channel （MUCMAC） under both additive white Gaussian noise （AWGN） channel and rayleigh fading channel, by using a combination of multiple user dirty paper coding （DPC） and superposition coding. Through cognition, it is assumed that the secondary users （SUs） are able to obtain the message of the primary user （PU） non-causally beforehand. Using this side information, the SUs can perform multiple user DPC to avoid the interference from the SU. Besides, the SUs can also allocate part of their transmit power to aid the PU, using superposition coding. Therefore, the capacity region of traditional multiple-access channel （MAC） can be enlarged. Moreover, some asymptotic results are shown as the number of SUs increases. In the AWGN case, it is illustrated that the maximum achievable rate of the PU grows logarithmically with the increase of the number of SUs, whereas in the Rayleigh case, we show that the cognitive gain will increase with the decreasing of the channel signal to noise ratio （SNR）.     

Interference Channels With Common Information

In this paper, the interference channel with common information (ICC), in which two senders need deliver not only private messages but also certain common messages to their corresponding receivers, is investigated. An achievable rate region for such a channel is obtained by applying a superposition coding scheme that consists of successive encoding and simultaneous decoding. It is shown that the derived achievable rate region includes or extends several existing results for the interference channels with or without common information. The rate region is then specialized to a class of ICCs in which one sender has no private information to transmit, and a class of deterministic interference channels with common information (DICCs). In particular, the derived rate region is found to be the capacity region for this class of DICCs. Last, the achievable rate region derived for the discrete memoryless ICC is extended to the Gaussian case, in which a numerical example is provided to illustrate the improvement of our rate region over an existing result.     

Practical Vector Dirty Paper Coding for MIMO Gaussian Broadcast Channels

Recently, the vector dirty paper coding (DPC) achievable rate region has been shown to be the capacity region of a multiple-input multiple-output Gaussian broadcast channel (MIMO GBC). With DPC, the multiuser interference noncausally known at the transmitter can be completely removed. In this paper, we present a vector DPC structure for MIMO GBC. It is a generalization of the single antenna superposition dirty paper coding for the scalar Gaussian dirty paper problem proposed by Bennatan et al. In a theoretical random code setting, this construction is shown to be able to achieve the promised rate performance of the MIMO GBC. We also implement it with existing vector quantizer and capacity-achieving channel coding. Combined with iterative decoding, a design example validates the effectiveness of our methods.     

On the Achievable Rate Regions for Interference Channels With Degraded Message Sets

The interference channel with degraded message sets (IC-DMS) refers to a communication model, in which two senders attempt to communicate with their respective receivers simultaneously through a common medium, and one sender has complete and a priori (noncausal) knowledge about the message being transmitted by the other. A coding scheme that collectively has advantages of cooperative coding, collaborative coding, and dirty paper coding, is developed for such a channel. With resorting to this coding scheme, achievable rate regions of the IC-DMS in both discrete memoryless and Gaussian cases are derived. The derived achievable rate regions generally include several previously known rate regions as special cases. A numerical example for the Gaussian case further demonstrates that the derived achievable rate region offers considerable improvements over these existing results in the high-interference-gain regime.      

Secrecy Capacity Region of a Multiple-Antenna Gaussian Broadcast Channel With Confidential Messages

Wireless communication is particularly susceptible to eavesdropping due to its broadcast nature. Security and privacy systems have become critical for wireless providers and enterprise networks. This paper considers the problem of secret communication over the Gaussian broadcast channel, where a multiple-antenna transmitter wishes to send independent confidential messages to two users with information-theoretic secrecy. That is, each user would like to obtain its own confidential message in a reliable and safe manner. This communication model is referred to as the multiple-antenna Gaussian broadcast channel with confidential messages (MGBC-CM). Under this communication scenario, a secret dirty-paper coding scheme and the corresponding achievable secrecy rate region are first developed based on Gaussian codebooks. Next, a computable Sato-type outer bound on the secrecy capacity region is provided for the MGBC-CM. Furthermore, the Sato-type outer bound proves to be consistent with the boundary of the secret dirty-paper coding achievable rate region, and hence, the secrecy capacity region of the MGBC-CM is established. Finally, two numerical examples demonstrate that both users can achieve positive rates simultaneously under the information-theoretic secrecy requirement.      

The Cost of Uncorrelation and Noncooperation in MIMO Channels

We investigate the capacity loss for using uncorrelated Gaussian input over a multiple-input multiple-output (MIMO) linear additive-noise channel. We upper-bound the capacity loss by a universal constant C* which is independent of the channel matrix and the noise distribution. For a single-user MIMO channel with n_t inputs and n_r outputs C* = min [ 1/2, n_r/n_t log₂ (1+n_t/n_r) ] bit per input dimension (or 2C* bit per transmit antenna per second per hertz), under both total and per-input power constraints. If we restrict attention to (colored) Gaussian noise, then the capacity loss is upper-bounded by a smaller constant C_G = n_r/2n_r log₂ (n_t/n_r) for n_r ges n_t/e, and C_G = 0.265 otherwise, and this bound is tight for certain cases of channel matrix and noise covariance. We also derive similar bounds for the sum-capacity loss in multiuser MIMO channels. This includes in particular uncorrelated Gaussian transmission in a MIMO multiple-access channel (MAC), and "flat" Gaussian dirty-paper coding (DPC) in a MIMO broadcast channel. In the context of wireless communication, our results imply that the benefit of beamforming and spatial water-filling over simple isotropic transmission is limited. Moreover, the excess capacity of a point-to-point MIMO channel over the same MIMO channel in a multiuser configuration is bounded by a universal constant.     

A broadcast approach for a single-user slowly fading MIMO channel

A broadcast transmission strategy for the slowly fading Gaussian multiple-input multiple-output (MIMO) channel is introduced. This broadcast strategy is an extension of the single-input single-output (SISO) broadcast approach. Perfect channel state information (CSI) is assumed known at the receiver end only. This strategy facilitates to adapt the reliably decoded rate to the actual channel state without having any feedback link to the transmitter. Transmission of layered coded information is motivated by the theory of majorization. We derive the basic equations characterizing achievable rates of the strategy. Several ad hoc approximations to the achievable region are considered and their performance is compared with the SISO setting and the ergodic capacity. It has been demonstrated that a single-layer outage approach is reasonably efficient in the MIMO setting in terms of the average reliably decoded rate. A multiple-access channel (MAC) broadcast approach is also applied for the MIMO case, and demonstrated to be relatively efficient.     

认知无线信道及其可达速率域的研究

认知无线信道是基于认知无线电理论的一种新的无线通信网络模型。到目前为止,已经有一些针对认知无线信道的可达速率域和速率域外界的结果给出,但是还不能得到认知信道的确切的容量域。文中主要研究了认知无线信道模型,以及实现其可达容量域所用到的编码方法,并给出了一些速率域的结果。     

Slepian-Wolf coding over broadcast channels

We discuss reliable transmission of a discrete memoryless source over a discrete memoryless broadcast channel, where each receiver has side information (of arbitrary quality) about the source unknown to the sender. When there are K=2 receivers, the optimum coding strategy using separate and stand-alone source and channel codes is to build two independent binning structures and send bin indices using degraded message sets through the channel, yielding a full characterization of achievable rates. However, as we show with an example, generalization of this technique to multiple binning schemes does not fully resolve the K>2 case. Joint source-channel coding, on the other hand, allows for a much simpler strategy (i.e., with no explicit binning) yielding a successful single-letter characterization of achievable rates for any Kges2. This characterization, which utilizes a trivial outer bound to the capacity region of general broadcast channels, is in terms of marginal source and channel distributions rather than a joint source-channel distribution. This contrasts with existing results for other multiterminal scenarios and implies that optimal schemes achieve "operational separation." On the other hand, it is shown with an example that an optimal joint source-channel coding strategy is strictly advantageous over the combination of stand-alone source and channel codes, and thus "informational separation" does not hold     

Code Design for MIMO Broadcast Channels

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.     

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

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     

Suboptimality of TDMA in the low-power regime

We consider multiaccess, broadcast, and interference channels with additive Gaussian noise. Although the set of rate pairs achievable by time-division multiple access (TDMA) is not equal to the capacity region, the TDMA achievable region converges to the capacity region as the power decreases. Furthermore, TDMA achieves the optimum minimum energy per bit. Despite those features, this paper shows that the growth of TDMA-achievable rates with the energy per bit is suboptimal in the low-power regime except in special cases: multiaccess channels where the users' energy per bit are identical and broadcast channels where the receivers have identical signal-to-noise ratios. For the additive Gaussian noise interference channel, we identify a small region of interference parameters outside of which TDMA is also shown to be suboptimal. The effect of fading (known to the receiver) on the suboptimality of TDMA is also explored.     

Discrete Memoryless Interference and Broadcast Channels With Confidential Messages: Secrecy Rate Regions

We study information-theoretic security for discrete memoryless interference and broadcast channels with independent confidential messages sent to two receivers. Confidential messages are transmitted to their respective receivers while ensuring mutual information-theoretic secrecy. That is, each receiver is kept in total ignorance with respect to the message intended for the other receiver. The secrecy level is measured by the equivocation rate at the eavesdropping receiver. In this paper, we present inner and outer bounds on secrecy capacity regions for these two communication systems. The derived outer bounds have an identical mutual information expression that applies to both channel models. The difference is in the input distributions over which the expression is optimized. The inner bound rate regions are achieved by random binning techniques. For the broadcast channel, a double-binning coding scheme allows for both joint encoding and preserving of confidentiality. Furthermore, we show that, for a special case of the interference channel, referred to as the switch channel, derived bounds meet. Finally, we describe several transmission schemes for Gaussian interference channels and derive their achievable rate regions while ensuring mutual information-theoretic secrecy. An encoding scheme in which transmitters dedicate some of their power to create artificial noise is proposed and shown to outperform both time-sharing and simple multiplexed transmission of the confidential messages.     

Duality, achievable rates, and sum-rate capacity of Gaussian MIMO broadcast channels

We consider a multiuser multiple-input multiple- output (MIMO) Gaussian broadcast channel (BC), where the transmitter and receivers have multiple antennas. Since the MIMO BC is in general a nondegraded BC, its capacity region remains an unsolved problem. We establish a duality between what is termed the "dirty paper" achievable region (the Caire-Shamai (see Proc. IEEE Int. Symp. Information Theory, Washington, DC, June 2001, p.322) achievable region) for the MIMO BC and the capacity region of the MIMO multiple-access channel (MAC), which is easy to compute. Using this duality, we greatly reduce the computational complexity required for obtaining the dirty paper achievable region for the MIMO BC. We also show that the dirty paper achievable region achieves the sum-rate capacity of the MIMO BC by establishing that the maximum sum rate of this region equals an upper bound on the sum rate of the MIMO BC.     

Parameterization of the MISO IFC rate region: the case of partial channel state information

We study the achievable rate region of the multipleinput single-output (MISO) interference channel (IFC), under the assumption that all receivers treat the interference as additive Gaussian noise. We assume the case of two users, and that the channel state information (CSI) is only partially known at the transmitters. Our main result is a characterization of Paretooptimal transmit strategies, for channel matrices that satisfy a certain technical condition. Numerical examples are provided to illustrate the theoretical results.     

The capacity region of broadcast channels with intersymbolinterference and colored Gaussian noise

We derive the capacity region for a broadcast channel with intersymbol interference (ISI) and colored Gaussian noise under an input power constraint. The region is obtained by first defining a similar channel model, the circular broadcast channel, which can be decomposed into a set of parallel degraded broadcast channels. The capacity region for parallel degraded broadcast channels is known. We then show that the capacity region of the original broadcast channel equals that of the circular broadcast channel in the limit of infinite block length, and we obtain an explicit formula for the resulting capacity region. The coding strategy used to achieve each point on the convex hull of the capacity region uses superposition coding on some or all of the parallel channels and dedicated transmission on the others. The optimal power allocation for any point in the capacity region is obtained via a multilevel water-filling. We derive this optimal power allocation and the resulting capacity region for several broadcast channel models     

Optimized Transmission for Fading Multiple-Access and Broadcast Channels With Multiple Antennas

In mobile wireless networks, dynamic allocation of resources such as transmit powers, bit-rates, and antenna beams based on the channel state information of mobile users is known to be the general strategy to explore the time-varying nature of the mobile environment. This paper looks at the problem of optimal resource allocation in wireless networks from different information-theoretic points of view and under the assumption that the channel state is completely known at the transmitter and the receiver. In particular, the fading multiple-access channel (MAC) and the fading broadcast channel (BC) with additive Gaussian noise and multiple transmit and receive antennas are focused. The fading MAC is considered first and a complete characterization of its capacity region and power region are provided under various power and rate constraints. The derived results can be considered as nontrivial extensions of the work done by Tse and Hanly from the case of single transmit and receive antenna to the more general scenario with multiple transmit and receive antennas. Efficient numerical algorithms are proposed, which demonstrate the usefulness of the convex optimization techniques in characterizing the capacity and power regions. Analogous results are also obtained for the fading BC thanks to the duality theory between the Gaussian MAC and the Gaussian BC.     

MIMO系统的信道容量研究

多输入多输出技术能够有效提高信道容量和频谱效率,已成为下一代无线通信系统的关键技术之一。文中首先分析了空时信道的模型,在SVD分解的基础上得出了MIMO系统的信道等效于独立并行信道,即随着天线数目的增加,信道容量线性增长,然后针对高斯广播信道和多址接入信道,讨论了MIMO多天线系统的多维信道容量区域,并且着重分析了两者之间的对偶性关系。     

Downlink capacity evaluation of cellular networks with known-interference cancellation

Recently, the capacity region of a multiple-input multiple-output (MIMO) Gaussian broadcast channel, with Gaussian codebooks and known-interference cancellation through dirty paper coding, was shown to equal the union of the capacity regions of a collection of MIMO multiple-access channels. We use this duality result to evaluate the system capacity achievable in a cellular wireless network with multiple antennas at the base station and multiple antennas at each terminal. Some fundamental properties of the rate region are exhibited and algorithms for determining the optimal weighted rate sum and the optimal covariance matrices for achieving a given rate vector on the boundary of the rate region are presented. These algorithms are then used in a simulation study to determine potential capacity enhancements to a cellular system through known-interference cancellation. We study both the circuit data scenario in which each user requires a constant data rate in every frame and the packet data scenario in which users can be assigned a variable rate in each frame so as to maximize the long-term average throughput. In the case of circuit data, the outage probability as a function of the number of active users served at a given rate is determined through simulations. For the packet data case, long-term average throughputs that can be achieved using the proportionally fair scheduling algorithm are determined. We generalize the zero-forcing beamforming technique to the multiple receive antennas case and use this as the baseline for the packet data throughput evaluation.