Optimal throughput-delay scaling in wireless networks - part I: the fluid model

Gupta and Kumar (2000) introduced a random model to study throughput scaling in a wireless network with static nodes, and showed that the throughput per source-destination pair is /spl Theta/(1//spl radic/(nlogn)). Grossglauser and Tse (2001) showed that when nodes are mobile it is possible to have a constant throughput scaling per source-destination pair. In most applications, delay is also a key metric of network performance. It is expected that high throughput is achieved at the cost of high delay and that one can be improved at the cost of the other. The focus of this paper is on studying this tradeoff for wireless networks in a general framework. Optimal throughput-delay scaling laws for static and mobile wireless networks are established. For static networks, it is shown that the optimal throughput-delay tradeoff is given by D(n)=/spl Theta/(nT(n)), where T(n) and D(n) are the throughput and delay scaling, respectively. For mobile networks, a simple proof of the throughput scaling of /spl Theta/(1) for the Grossglauser-Tse scheme is given and the associated delay scaling is shown to be /spl Theta/(nlogn). The optimal throughput-delay tradeoff for mobile networks is also established. To capture physical movement in the real world, a random-walk (RW) model for node mobility is assumed. It is shown that for throughput of /spl Oscr/(1//spl radic/(nlogn)), which can also be achieved in static networks, the throughput-delay tradeoff is the same as in static networks, i.e., D(n)=/spl Theta/(nT(n)). Surprisingly, for almost any throughput of a higher order, the delay is shown to be /spl Theta/(nlogn), which is the delay for throughput of /spl Theta/(1). Our result, thus, suggests that the use of mobility to increase throughput, even slightly, in real-world networks would necessitate an abrupt and very large increase in delay.     

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.      

带有广义反馈的多址接入中继信道的可达速率区域的研究

多址接入中继信道是含有多个接入节点、1个中继节点和1个目的接收节点的无线多用户信道,同时考虑接入节点之间能够接收彼此含噪的广义反馈信息,此种模型存在于接入节点之间协作通信能力较差的多跳无线网络和无线传感器网络。论文给出了带有此种广义反馈的离散无记忆多址接入中继信道的可达速率区域,并将这一结果推广到高斯信道。提出一个新的编码方案,主要基于速率划分和译码前传策略,并通过采用分组Markov叠加编码建立各接入源节点之间以及源节点和中继节点之间的协作通信,在可达性证明中还采用规则编码和反向译码策略。结果表明,在离散无记忆信道环境下可达速率区域相比较以往结果更具一般性,在高斯信道环境下可达速率区域被扩展。     

Superposition turbo TCM for multirate broadcast

Bergmans and Cover identified the capacity region of the Gaussian degraded broadcast channel, where different receivers observe the transmitted signal with different signal-to-noise ratios. This letter presents a superposition turbo-coding scheme that performs within 1 dB of the capacity region boundary of the degraded broadcast channel at a bit-error rate of 10/sup -5/.     

Compound Multiple-Access Channels With Partial Cooperation

A two-user discrete memoryless compound multiple-access channel (MAC) with a common message and conferencing decoders is considered. The capacity region is characterized in the special cases of physically degraded channels and unidirectional cooperation, and achievable rate regions are provided for the general case. The results are then extended to the corresponding Gaussian model. In the Gaussian setup, the provided achievable rates are shown to lie within some constant number of bits from the boundary of the capacity region in several special cases. An alternative model, in which the encoders are connected by conferencing links rather than having a common message, is studied as well, and the capacity region for this model is also determined for the cases of physically degraded channels and unidirectional cooperation. Numerical results are also provided to obtain insights about the potential gains of conferencing at the decoders and encoders.      

Towards the Secrecy Capacity of the Gaussian MIMO Wire-Tap Channel: The 2-2-1 Channel

We find the secrecy capacity of the 2-2-1 Gaussian MIMO wiretap channel, which consists of a transmitter and a receiver with two antennas each, and an eavesdropper with a single antenna. We determine the secrecy capacity of this channel by proposing an achievable scheme and then developing a tight upper bound that meets the proposed achievable secrecy rate. We show that, for this channel, Gaussian signalling in the form of beam-forming is optimal, and no pre-processing of information is necessary.      

MIMO广播信道中联合多用户速率和延迟约束调度的研究

该文给出了一种多入多出高斯广播信道中具有延迟约束的多用户无线数据包的传输方案。首先,在信道的QR分解及脏纸编码基础上,通过贪婪算法获取多用户分集与包延迟约束之间的有效结合。其次,将包到达速率、可达服务速率、用户数以及传输天线数构成一优化问题,得到最佳的用户组合及调度周期。最后,在不同用户数及发射天线数情况下对该方案进行了性能仿真,仿真结果表明:在满足包传递最小延迟等待要求的同时,得到了传输容量的最大化。     

User Cooperation in the Absence of Phase Information at the Transmitters

In this paper, a multiuser communication system in which wireless users cooperate to transmit information to a base station is considered. The proposed scheme can significantly enlarge the achievable rate region, provided that the wireless connections between pairs of cooperating users are stronger than the connection from every user to the base station. The gains in transmission rate remain substantial even when the channel phase information is only available at the receivers, not at the transmitters. In the proposed scheme, a transmission period is divided into two time intervals. During the first time interval, wireless users send data to the base station and to the neighboring users simultaneously using a broadcast channel paradigm. During the second time interval, the users cooperate to transmit information to the base station. The achievable rate region corresponding to this paradigm is characterized under a random phase channel model for a two-user system. Results are then generalized to a multiple-user scenario. For fixed system parameters, the achievable rate region is strictly larger than that of the traditional multiple-access channel, thereby allowing a fair distribution of the wireless resources among users. Numerical analysis suggests that cooperating with a single partner is enough to achieve most of the benefits associated with cooperation.      

Communication Via Decentralized Processing

The problem of a nomadic terminal sending information to a remote destination via agents with lossless connections to the destination is investigated. Such a setting suits, e.g., access points of a wireless network where each access point is connected by a wire to a wireline-based network. The Gaussian codebook capacity for the case where the agents do not have any decoding ability is characterized for the Gaussian channel. This restriction is demonstrated to be severe, and allowing the nomadic transmitter to use other signaling improves the rate. For both general and degraded discrete memoryless channels, lower and upper bounds on the capacity are derived. An achievable rate with unrestricted agents, which are capable of decoding, is also given and then used to characterize the capacity for the deterministic channel.      

On degraded Gaussian two-user channels (Corresp.)

Several bounds to the capacity region of a degraded Gaussian channel are studied. An outer bound utilizing the capacity region of the corresponding broadcast channel is obtained. Two achievable regions obtained previously are compared, and a region including both is introduced by using frequency division multiplexing.     

A dynamic resource allocation scheme for delay-constrained multimedia services in CDMA 1/spl times/EV-DV forward link

CDMA2000 1/spl times/EV-DV has been proposed as one of the global standards of third-generation (3G) networks, which adopts TDM/CDM and adaptive modulation and coding (AMC) techniques to enhance the data rate. The current CDMA2000 1/spl times/EV-DV standard specifies all possible combinations of system parameters, but there is no any further specification in the standard on how to dynamically change the system parameters to support the quality-of-service (QoS) requirements imposed by the upper-layer applications. In the meantime, one of the major deficiencies of previous research work done in this area is that they all are based on the channel models of physical layer such as Rayleigh model, which is unable to capture the link-layer QoS parameters such as queueing delay. Since the dynamic resource allocation usually resides in the data link layer, a wireless channel model at the link layer would be desirable to handle the QoS requirements. In this paper, we develop a dynamic resource allocation scheme using the effective capacity link model to support delay-bounded multimedia services in CDMA2000 1/spl times/EV-DV networks. Extensive simulations have been set up and the simulation results show that the proposed dynamic resource allocation scheme significantly improves the delay and throughput performance for all types of application traffic with various QoS requirements.     

Capacity of interference-limited ad hoc networks with infrastructure support

In this letter, we consider the capacity of ad hoc networks with infrastructure support. Although Grossglauser-Tse mobile network model enables /spl Theta/(1) per-node throughput scaling, the mobility assumption may be too unrealistic to be accepted in some practical situations. One of the key observations we acquired is that the infrastructure support plays the same role played by the mobility in the Grossglauser-Tse model. We show that nodes can utilize the randomly located infrastructure support instead of mobility when nodes are nearly static. In this case, we show that the per-node throughput of /spl Theta/(1) is still achievable when the number of access points grows linearly with respect to the number of nodes.     

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.      

A general coding scheme for the two-way channel

A general coding scheme for the nonrestricted memoryless discrete two-way channel is presented based on the introduction of auxiliary random variables forming a stationary Markov process. The coding scheme yields an achievable rate region which exceeds the inner bound of Shannon in the general case. A finite cardinality bound for the auxiliary random variables is given, showing that the region is computable. Finally, the capacity region for the memoryless Gaussian two-way channel is established.     

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.     

Opportunistic Relaying in Wireless Networks

Relay networks having n source-to-destination pairs and m half-duplex relays, all operating in the same frequency band and in the presence of block fading, are analyzed. This setup has attracted significant attention, and several relaying protocols have been reported in the literature. However, most of the proposed solutions require either centrally coordinated scheduling or detailed channel state information (CSI) at the transmitter side. Here, an opportunistic relaying scheme is proposed that alleviates these limitations, without sacrificing the system throughput scaling in the regime of large n. The scheme entails a two-hop communication protocol, in which sources communicate with destinations only through half-duplex relays. All nodes operate in a completely distributed fashion, with no cooperation. The key idea is to schedule at each hop only a subset of nodes that can benefit from multiuser diversity. To select the source and destination nodes for each hop, CSI is required at receivers (relays for the first hop, and destination nodes for the second hop), and an index-valued CSI feedback at the transmitters. For the case when n is large and m is fixed, it is shown that the proposed scheme achieves a system throughput of m/2 bits/s/Hz. In contrast, the information-theoretic upper bound of (m/2) log log n bits/s/Hz is achievable only with more demanding CSI assumptions and cooperation between the relays. Furthermore, it is shown that, under the condition that the product of block duration and system bandwidth scales faster than log n log log n, the achievable throughput of the proposed scheme scales as Theta (log n). Notably, this is proven to be the optimal throughput scaling even if centralized scheduling is allowed, thus proving the optimality of the proposed scheme in the scaling law sense. Simulation results indicate a rather fast convergence to the asymptotic limits with the system's size, demonstrating the practical importance of the scaling results.     

Capacity Theorems for the “Z” Channel

We consider the two-user "Z" channel (ZC), where there are two senders and two receivers. One of the senders transmits information to its intended receiver (without interfering with the unintended receiver), while the other sender transmits information to both receivers. The complete characterization of the discrete memoryless ZC remains unknown to date. For the Gaussian ZC, the capacity has only been established for a crossover link gain of 1. In this work, we study both the discrete memoryless ZC and the Gaussian ZC. We first establish achievable rates for the general discrete memoryless ZC. The coding strategy uses rate-splitting and superposition coding at the sender with information for both receivers. At the receivers, we use joint decoding. We then specialize the rates obtained to two different types of degraded discrete memoryless ZCs and also derive respective outer bounds to their capacity regions. We show that as long as a certain condition is satisfied, the achievable rate region is the capacity region for one type of degraded discrete memoryless ZC. The results are then extended to the two-user Gaussian ZC with different crossover link gains. We determine an outer bound to the capacity region of the Gaussian ZC with strong crossover link gain and establish the capacity region for moderately strong crossover link gain     

Achievable Rates Over Time-Varying Rayleigh Fading Channels

This paper investigates achievable rates for a wireless communication system when neither the transmitter nor the receiver has a priori knowledge of the channel state information (CSI). The dynamics of the flat fading channel are characterized by a known Doppler spectrum. Quantitative results are provided for independent and identically distributed (i.i.d.) Gaussian signals and long data blocks. Expressions for the achievable rates include a lower bound on mutual information, and the achievable rates of pilot-aided systems with optimized resource allocation. A simple, low-duty-cycle signaling scheme is proposed to improve the information rates in the low signal-to-noise ratio (SNR) regime, and the optimal duty cycle is expressed as a function of the fading rate and SNR. It is demonstrated that the resource allocation and duty cycle developed for Gaussian signals can also be applied to systems using other signaling formats.     

On the /spl theta/-coverage and connectivity of large random networks

Wireless planar networks have been used to model wireless networks in a tradition that dates back to 1961 to the work of E. N. Gilbert. Indeed, the study of connected components in wireless networks was the motivation for his pioneering work that spawned the modern field of continuum percolation theory. Given that node locations in wireless networks are not known, random planar modeling can be used to provide preliminary assessments of important quantities such as range, number of neighbors, power consumption, and connectivity, and issues such as spatial reuse and capacity. In this paper, the problem of connectivity based on nearest neighbors is addressed. The exact threshold function for /spl theta/-coverage is found for wireless networks modeled as n points uniformly distributed in a unit square, with every node connecting to its /spl phi//sub n/ nearest neighbors. A network is called /spl theta/-covered if every node, except those near the boundary, can find one of its /spl phi//sub n/ nearest neighbors in any sector of angle /spl theta/. For all /spl theta//spl isin/(0,2/spl pi/), if /spl phi//sub n/=(1+/spl delta/)log/sub 2/spl pi//2/spl pi/-/spl theta//n, it is shown that the probability of /spl theta/-coverage goes to one as n goes to infinity, for any /spl delta/>0; on the other hand, if /spl phi//sub n/=(1-/spl delta/)log/sub 2/spl pi//2/spl pi/-/spl theta//n, the probability of /spl theta/-coverage goes to zero. This sharp characterization of /spl theta/-coverage is used to show, via further geometric arguments, that the network will be connected with probability approaching one if /spl phi//sub n/=(1+/spl delta/)log/sub 2/n. Connections between these results and the performance analysis of wireless networks, especially for routing and topology control algorithms, are discussed.