Multiple-Antenna Cooperative Wireless Systems: A Diversity–Multiplexing Tradeoff Perspective

We consider a general multiple-antenna network with multiple sources, multiple destinations, and multiple relays in terms of the diversity-multiplexing tradeoff (DMT). We examine several subcases of this most general problem taking into account the processing capability of the relays (half-duplex or full-duplex), and the network geometry (clustered or nonclustered). We first study the multiple-antenna relay channel with a full-duplex relay to understand the effect of increased degrees of freedom in the direct link. We find DMT upper bounds and investigate the achievable performance of decode-and-forward (DF), and compress-and-forward (CF) protocols. Our results suggest that while DF is DMT optimal when all terminals have one antenna each, it may not maintain its good performance when the degrees of freedom in the direct link are increased, whereas CF continues to perform optimally. We also study the multiple-antenna relay channel with a half-duplex relay. We show that the half-duplex DMT behavior can significantly be different from the full-duplex case. We find that CF is DMT optimal for half-duplex relaying as well, and is the first protocol known to achieve the half-duplex relay DMT. We next study the multiple-access relay channel (MARC) DMT. Finally, we investigate a system with a single source-destination pair and multiple relays, each node with a single antenna, and show that even under the ideal assumption of full-duplex relays and a clustered network, this virtual multiple-input multiple-output (MIMO) system can never fully mimic a real MIMO DMT. For cooperative systems with multiple sources and multiple destinations the same limitation remains in effect.     

Diversity–Multiplexing Tradeoff in ISI Channels

The optimal diversity–multiplexing tradeoff curve for the intersymbol interference (ISI) channel is computed and various equalizers are analyzed using this performance metric. Maximum-likelihood signal decoding (MLSD) and decision feedback equalization (DFE) equalizers achieve the optimal tradeoff without coding, but zero forcing (ZF) and minimum mean-square-error (MMSE) equalizers do not. However if each transmission block is ended with a period of silence lasting the coherence time of the channel, both ZF and MMSE equalizers become diversity-multiplexing optimal. This suggests that the bulk of the performance gain obtained by replacing linear decoders with computationally intensive ones such as orthogonal frequency-division multiplexing (OFDM) or Viterbi, can be realized in much simpler fashion—with a small modification to the transmit scheme.      

On the Diversity–Multiplexing Tradeoff in Multiple-Relay Network

This paper studies the setup of a multiple-relay network in which $K$ half-duplex multiple-antenna relays assist in the transmission between either one or several multiple-antenna transmitter(s) and a multiple-antenna receiver. Each two nodes are assumed to be either connected through a quasi-static Rayleigh-fading channel, or disconnected. We propose a new scheme, which we call random sequential (RS), based on the amplify-and-forward relaying. We prove that for general multiple-antenna multiple-relay networks, the proposed scheme achieves the maximum diversity gain. Furthermore, we derive diversity–multiplexing tradeoff (DMT) of the proposed RS scheme for general single-antenna multiple-relay networks. It is shown that for single-antenna two-hop multiple-access multiple-relay $(K > 1)$ networks (without direct link between the transmitter(s) and the receiver), the proposed RS scheme achieves the optimum DMT. However, for the case of multiple-access single-relay setup, we show that the RS scheme reduces to the naive amplify-and-forward (AF) relaying and is not optimum in terms of DMT, while the dynamic decode-and-forward (DF) scheme is shown to be optimum for this scenario.      

Diversity–Multiplexing Tradeoff and Outage Performance for Rician MIMO Channels

In this paper, we analyze the diversity–multiplexing tradeoff (DMT), originally introduced by Zheng and Tse, and outage performance for Rician multiple-input–multiple-output (MIMO) channels. The DMT characteristics of Rayleigh and Rician channels are shown to be identical. In a high signal-to-noise ratio (SNR) regime, the log–log plot of outage probability versus SNR curve for a Rician channel is a shifted version of that for the corresponding Rayleigh channel. The SNR gap between the outage curves of the Rayleigh and Rician channels is derived. The DMT and outage performance are also analyzed for Rician multiple-input–single-output (MISO)/single-input–multiple-output (SIMO) channels over a finite SNR regime. A closed-form expression for the outage probability is derived and the finite SNR DMT characteristic is analyzed. It is observed that the maximum diversity gain can be achieved at some finite SNR–the maximum gain tends to increase linearly with the Rician factor. The finite SNR diversity gain is shown to be a linear function of the finite SNR multiplexing gain. The consistency between the DMTs for finite and infinite SNRs is also shown.      

New Diversity Combining Receivers for Cooperative Multiplexing in Wireless Multiuser Relay Networks

We propose two new diversity combining receivers that support cooperative multiplexing in two-hop wireless multiuser relay networks. Cooperative multiplexing has the potential to double the achievable throughput by allowing the base station (BS) and the relay station (RS) to transmit to different users at the same time in the second time slot of the half time division duplexed (TDD) relay transmission. This throughput improvement comes at a cost of performance degradation due to inter-user interference between the BS and the RS. To overcome this degradation, we propose two new receivers for the relay-link users: (1) cooperative multiplexing optimum combining (CMOC) and (2) cooperative multiplexing selection combining (CMSC). The proposed CMOC receiver combines the signals in the first and second time slot of the half TDD transmission such that the output signal-to-interference-plus-noise ratio (SINR) is maximized. The proposed CMSC receiver allows the relay-link user terminal to be active in only one of the two half TDD time slots. As such, CMSC offers power savings relative to CMOC. New insights are drawn from our exact closed-form expressions that we derive for the moment generation function, probability density function, and the cumulative distribution function of the output SINR. Based on these, we present new analytical expressions for the outage probability, symbol error rate, and achievable throughput. Our results show a 3.5 times improvement in the achievable throughput relative to the standard single-channel receiver in the high interference regime.     

End-to-End Energy–Bandwidth Tradeoff in Multihop Wireless Networks

In this paper, energy-constrained wireless multihop networks with a single source-destination pair are considered. A network model that incorporates both the energy radiated by the transmitter and the energy consumed by the circuits that process the received signals is proposed. The rate of communication is the number of information bits transmitted (end-to-end) per coded symbol transmitted by any node in the network that is forwarding the data. The tradeoff between the total energy consumption and the end-to-end rate of communication is analyzed. The performance (either energy or rate) depends on the transmission strategy of each node, the location of the relay nodes, and the data rate used by each node. Communication strategies include the rate of transmission on each link, the scheduling of links, and the power used for each link. Strategies that minimize the total energy consumption for a given rate are found. Two communication strategies that capture the inherent constraints of some practical networks are also considered and compared with the optimum strategies. In the case of equispaced relays, analytical results for the tradeoff between the energy and the end-to-end data rate are provided. The minimum energy over all possible data rates is also obtained. Low rates incur a significant penalty because the receiver is on for a long time period while high rates require high transmission energy. At high rates routes with fewer hops minimize the energy consumption while at lower rates more hops minimize the energy consumption.      

Optimal Diversity‐Multiplexing Tradeoff of MIMO Multi‐way Relay Channel

A MIMO multi‐way relay channel with full data exchange in which K users exchange messages with each other via the help of a single relay is considered. For the case in which each link is quasi‐static Rayleigh fading and the relay is full‐duplex, the fundamental diversity‐multiplexing tradeoff (DMT) is investigated, and we show that a compress‐and‐forward relay protocol can achieve the optimal DMT.     

Diversity and Multiplexing Tradeoff in General Fading Channels

The optimal tradeoff between diversity gain and multiplexing gain for multiple-inputmultiple-output (MIMO) channels has been studied recently under the independent and identically distributed (i.i.d.) Rayleigh-fading assumption. In this correspondence, this result is extended and the optimal tradeoff performance is derived for generalized fading channel conditions, including different fading types, nonidentical fading distributions, spatial correlation, and nonzero channel means. Our results include many known models as special cases and shed light on the effects of different channel parameters on the optimal tradeoff performance     

Diversity and Multiplexing Tradeoff of Spatial Multiplexing MIMO Systems With CSI

Following the seminal work of Zheng and Tse, this paper investigates the fundamental diversity and multiplexing tradeoff of multiple-input-multiple-output (MIMO) systems in which knowledge of the channel state at both sides of the link is employed to transmit independent data streams through the channel eigenmodes. First, the fundamental diversity and multiplexing tradeoff of each of the individual substreams is obtained and this result is then used to derive a tradeoff optimal scheme for rate allocation along channel eigenmodes. The tradeoff of spatial multiplexing is finally compared to the fundamental tradeoff of the MIMO channel and to the one of both space only codes and V-BLAST which do not require channel state information (CSI) at the transmit side.     

一种在宽带无线网络环境下的协作分集方法

协作通信可以使单天线的移动终端共享它们的天线而产生虚拟多发射天线阵列以获得发射分集。提出了一种在频率选择性衰落信道条件下的协作分集方法,信宿不仅利用转接节点转发的信号而且还利用了信源直接传来的信号来进行解码。通过计算机仿真,比较了考虑信源到信宿的直接传输的协作方法和未考虑信源到信宿的直接传输的协作方法的误比特率性能。结果表明,考虑信源到信宿的直接传输可提高系统的协作分集增益。     

Energy-Spectral-Efficiency Tradeoff in Interference-Limited Wireless Networks

Spectral efficiency (SE) is an important metric in traditional wireless network design. However, as the development of high-data rate services and rapid increase of energy consumption, energy efficiency (EE) has received more and more attention. In this paper, we investigate the EE–SE tradeoff problem in interference-limited wireless networks. Different from previous researches, we try to optimize EE and SE simultaneously. Firstly, the problem is formulated as a multi-objective optimization problem (MOP), with the constraint of transmit power limit. Then, we convert the MOP to a single-objective optimization problem by the weighted linear sum method. We present an algorithm utilizing difference between two convex functions programming (DCP) to handle with SE optimization problem (SD). EE optimization problem can be solved by an algorithm (EFD) consists of fractional programming embedded with DCP. While for EE–SE tradeoff problem, a particle swarm optimization algorithm is proposed (ESTP) to deal with it. Simulation results validate that the proposed algorithm can efficiently balance EE and SE by adjusting the value of weighted coefficient, which could be used to design a flexible energy efficient network in the future.

     

Maximizing Cooperative Diversity Energy Gain for Wireless Networks

We are concerned with optimally grouping active mobile users in a two-user-based cooperative diversity system to maximize the cooperative diversity energy gain in a radio cell. The optimization problem is formulated as a non-bipartite weighted-matching problem in a static network setting. The weighted-matching problem can be solved using maximum weighted (MW) matching algorithm in polynomial time O(n³). To reduce the implementation and computational complexity, we develop a Worst-Link-First (WLF) matching algorithm, which gives the user with the worse channel condition and the higher energy consumption rate a higher priority to choose its partner. The computational complexity of the proposed WLF algorithm is O(n) while the achieved average energy gain is only slightly lower than that of the optimal maximum weighted- matching algorithm and similar to that of the 1/2-approximation Greedy matching algorithm (with computational complexity of O(n² log n)) for a static-user network. We further investigate the optimal matching problem in mobile networks. By intelligently applying user mobility information in the matching algorithm, high cooperative diversity energy gain with moderate overhead is possible. In mobile networks, the proposed WLF matching algorithm, being less complex than the MW and the Greedy matching algorithms, yields performance characteristics close to those of the MW matching algorithm and better than the Greedy matching algorithm.     

Decode-and-Forward Cooperative Diversity with Power Allocation in Wireless Networks

We study power allocation for the decode-and-forward cooperative diversity protocol in a wireless network under the assumption that only mean channel gains are available at the transmitters. In a Rayleigh fading channel with uniformly distributed node locations, we aim to find the power allocation that minimizes the outage probability under a short-term power constraint, wherein the total power for all nodes is less than a prescribed value during each two-stage transmission. Due to the computational and implementation complexity of the optimal solution, we derived a simple near-optimal solution. In this near-optimal scheme, a fixed fraction of the total power is allocated to the source node in stage I. In stage II, the remaining power is split equally among a set of selected nodes if the selected set is not empty, and otherwise is allocated to the source node. A node is selected if it can decode the message from the source and its mean channel gain to the destination is above a threshold. In this scheme, each node only needs to know its own mean channel gain to the destination and the number of selected nodes. Simulation results show that the proposed scheme achieves an outage probability close to that for the optimal scheme obtained by numerical search, and achieves significant performance gain over other schemes in the literature     

MIMO系统中分集增益和空间复用增益的折衷关系

论文导出了分集增益与空间复用增益间的最佳折衷关系式。该关系式为阶梯递减右连续函数,阶梯数等于接收天线数目。分集增益的取值与分组长度有关,只有当分组长度不小于发射天线数目时才能获得满分集增益。折衷关系表明,采用合适的空时编码可以同时获得分集增益和空间复用增益,但是两种增益不能同时达到最大。由最佳折衷关系可以推测一定空间复用增益时可得到的最大分集增益,以及一定分集增益时能获得的最大空间复用增益。     

Capacity of Multiuser Diversity with Cooperative Relaying in Wireless Networks

This letter provides an analysis of the interaction between cooperative diversity and multiuser diversity in downlink channels. Through an approximation of the signal-to-noise ratio (SNR) distribution of each cooperative link using gamma distribution, we can derive an analytic expression for the average throughput of a single-cell wireless system with multiple cooperative diversity links combined with a fair-access scheduler. The proposed analytic approach is verified through comparisons with simulated results and shows that cooperative diversity has a detrimental impact on multiuser diversity.     

On Space–Time Trellis Codes Achieving Optimal Diversity Multiplexing Tradeoff

Multiple antennas can be used for increasing the amount of diversity (diversity gain) or increasing the data rate (the number of degrees of freedom or spatial multiplexing gain) in wireless communication. As quantified by Zheng and Tse, given a multiple-input-multiple-output (MIMO) channel, both gains can, in fact, be simultaneously obtained, but there is a fundamental tradeoff (called the Diversity-Multiplexing Gain (DM-G) tradeoff) between how much of each type of gain, any coding scheme can extract. Space-time codes (STCs) can be employed to make use of these advantages offered by multiple antennas. Space-Time Trellis Codes (STTCs) are known to have better bit error rate performance than Space-Time Block Codes (STBCs), but with a penalty in decoding complexity. Also, for STTCs, the frame length is assumed to be finite and hence zeros are forced towards the end of the frame (called the trailing zeros), inducing rate loss. In this correspondence, we derive an upper bound on the DM-G tradeoff of full-rate STTCs with nonvanishing determinant (NVD). Also, we show that the full-rate STTCs with NVD are optimal under the DM-G tradeoff for any number of transmit and receive antennas, neglecting the rate loss due to trailing zeros. Next, we give an explicit generalized full-rate STTC construction for any number of states of the trellis, which achieves the optimal DM-G tradeoff for any number of transmit and receive antennas, neglecting the rate loss due to trailing zeros     

Diversity Multiplexing Tradeoff in MIMO Frequency Selective Channels with Partial CSIT

In this letter, we derive the optimal diversity- multiplexing tradeoff for a frequency selective MIMO channel with resolution-constrained channel feedback. The additional degree of freedom provided by the channel multipaths is succinctly captured in the tradeoff characterization. For instance, in a L-path SISO channel, with K-level feedback, the maximum diversity increase is exponential in K.     

基于DSTBC-MC-CDMA的无线网络协同发射分集系统

协同分集(cooperative diversity)技术通过使网络中各单天线用户共享彼此天线,形成虚拟的多天线阵列来实现发射或接收分集,可以有效地提高系统性能。该文提出无线网络中频率选择性衰落信道环境下的一种基于分布式空时分组码(Distributed Space Time Block Code, DSTBC)和MC-CDMA的协同发射分集方案,并给出了系统实现。建立了误码模型,探讨了协同用户间的信道状态信息(CSI)对系统误码性能的影响,分析了误码性能的上限,并给出了仿真结果。结果表明,DSTBC-MC-CDMA系统相对于未协同的MC-CDMA系统,获得了明显的性能增益。     

无线传感网物理层协作分集的性能分析

该文针对无线传感网中的远距传输问题,研究了一种无需网络同步和正交信道的协作分集方法的性能,给出了在两种典型信道中当解码转发存在误差传播时远程目的节点的误码率及分集指数;分析了当转发节点间为白高斯信道时增加协作节点数能够提高目的节点性能的条件。研究结果表明,当转发节点间为白高斯信道时,只要转发节点处于正常工作点,增加节点数就能提高目的节点的性能;当转发节点间为瑞利平衰落信道时,只有当转发节点处于一定位置时,协作分集相对于直接发送或传统空间分集才有性能增益;当转发节点间为瑞利平衰落信道时增加跳数性能更好,为白高斯信道时增加分支数更有效;当转发节点间为瑞利平衰落信道时,误差传播将使目的节点的分集指数为1,但在较低信噪比条件下对分集性能影响很小。     

Performance Analysis of Cooperative Diversity Wireless Networks over Nakagami-m Fading Channel

This letter analyzes the performance of cooperative diversity wireless networks using amplify-and-forward relaying over independent, non-identical, Nakagami-m fading channels. The error rate and the outage probability are determined using the moment generating function (MGF) of the total signal-to-noise-ratio (SNR) at the destination. Since it is hard to find a closed form for the probability density function (PDF) of the total SNR, we use an approximate value instead. We first derive the PDF and the MGF of the approximate value of the total SNR. Then, the MGF is used to determine the error rate and the outage probability. We also use simulation to verify the analytical results. Results show that the derived error rate and outage probability are tight lower bounds particularly at medium and high SNR