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 non-clustered). 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 is 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 idealistic assumption of full-duplex relays and a clustered network, this virtual multi-input multi-output (MIMO) system can never fully mimic a real MIMO DMT. For cooperative systems with multiple sources and multiple destinations the same limitation remains to be in effect.
When multiple single antenna relays are present, the papers @cite_12 @cite_9 @cite_49 @cite_27 @cite_32 @cite_22 @cite_30 show that diversity gains similar to multi-input single-output ( ) or single-input multi-output ( ) systems are achievable for Rayleigh fading channels. Similarly, @cite_3 @cite_48 @cite_18 @cite_29 upper bound the system behavior by or if all links have Rayleigh fading. In other words, relay systems behave similar to either transmit or receive antenna arrays. is first analyzed in @cite_2 in terms of achievable rates only, where the authors compare a two-source two-destination cooperative system with a @math and show that the former is multiplexing gain limited by 1, whereas the latter has maximum multiplexing gain of 2.
@cite_30 @cite_18 @cite_22 @cite_48 @cite_9 @cite_29 @cite_32 @cite_3 @cite_27 @cite_49 @cite_2 @cite_12
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We examine a network consisting of one source, one destination and two amplifying and forwarding relays and consider a scenario in which destination and relays can have various processing limitations. For all possible diversity combining schemes at the relays and at the destination, we find diversity order results analytically and confirm our findings through numerical calculations of bit error rate (BER) versus signal-to-noise-ratio (SNR) curves. We compare our results with direct transmission, well known transmit diversity methods and traditional multihop transmission and conclude that diversity reception in multihop networks provides the lowest error rate. We consider a wireless network with multiple terminals (m spl ges 2) as well as multiple receive antennas at the destination (N spl ges 1) and obtain diversity multiplexing tradeoff upper bounds for some recently proposed cooperative diversity protocols. The results obtained show that irrespective of the coding scheme employed none of these protocols can yield a diversity order greater than N+m-1. Further, the tradeoff bounds indicate that the protocol yielding the best diversity order may change with the multiplexing gain. Using these bounds we propose a switching strategy that yields the best tradeoff bound which also significantly outperforms the optimal tradeoff curve for the baseline noncooperative system at all possible multiplexing gains. We investigate reliability exchange schemes that allow a group of radios to act as a distributed antenna array in which radio links are used to exchange information between the various radios. We consider a scenario in which multiple nodes receive independent copies of the same message. Each node independently decodes its message and then participates in a process of "smart" information exchange with the other nodes. Each node transmits its estimates of the a posteriori probabilities of some set of bits, and these estimates are used as a priori information by other receivers. The a priori information is used to perform maximum a posteriori decoding on the received sequence. This process of decoding and information exchange can be repeated several times. Simulation results show that the performance can be significantly improved by careful selection of the bits for which information is exchanged. We propose novel cooperative transmission protocols for delay-limited coherent fading channels consisting of N (half-duplex and single-antenna) partners and one cell site. In our work, we differentiate between the relay, cooperative broadcast (down-link), and cooperative multiple-access (CMA) (up-link) channels. The proposed protocols are evaluated using Zheng-Tse diversity-multiplexing tradeoff. For the relay channel, we investigate two classes of cooperation schemes; namely, amplify and forward (AF) protocols and decode and forward (DF) protocols. For the first class, we establish an upper bound on the achievable diversity-multiplexing tradeoff with a single relay. We then construct a new AF protocol that achieves this upper bound. The proposed algorithm is then extended to the general case with (N-1) relays where it is shown to outperform the space-time coded protocol of Laneman and Wornell without requiring decoding encoding at the relays. For the class of DF protocols, we develop a dynamic decode and forward (DDF) protocol that achieves the optimal tradeoff for multiplexing gains 0lesrles1 N. Furthermore, with a single relay, the DDF protocol is shown to dominate the class of AF protocols for all multiplexing gains. The superiority of the DDF protocol is shown to be more significant in the cooperative broadcast channel. The situation is reversed in the CMA channel where we propose a new AF protocol that achieves the optimal tradeoff for all multiplexing gains. A distinguishing feature of the proposed protocols in the three scenarios is that they do not rely on orthogonal subspaces, allowing for a more efficient use of resources. In fact, using our results one can argue that the suboptimality of previously proposed protocols stems from their use of orthogonal subspaces rather than the half-duplex constraint. Closed form expressions for the statistics of the harmonic mean of two independent exponential variates are presented. These statistical results are then applied to study the performance of wireless communication systems with non-regenerative relays over flat Rayleigh fading channels. It is shown that these results can either be exact or tight lower bounds on the performance of these systems depending on the choice of the relay gain. More specifically, outage probability formulas for noise limited systems are obtained. Furthermore, outage capacity and bit error rate (BER) expressions for binary differential phase shift keying are derived. Finally, comparisons between regenerative and non-regenerative systems are presented. Numerical results show that the former systems clearly outperform the latter ones for low average signal-to-noise-ratio (SNR). They also show that the two systems have similar performance at high average SNR. Cooperative diversity has been recently proposed as a way to form virtual antenna arrays that provide dramatic gains in slow fading wireless environments. However, most of the proposed solutions require distributed space-time coding algorithms, the careful design of which is left for future investigation if there is more than one cooperative relay. We propose a novel scheme that alleviates these problems and provides diversity gains on the order of the number of relays in the network. Our scheme first selects the best relay from a set of M available relays and then uses this "best" relay for cooperation between the source and the destination. We develop and analyze a distributed method to select the best relay that requires no topology information and is based on local measurements of the instantaneous channel conditions. This method also requires no explicit communication among the relays. The success (or failure) to select the best available path depends on the statistics of the wireless channel, and a methodology to evaluate performance for any kind of wireless channel statistics, is provided. Information theoretic analysis of outage probability shows that our scheme achieves the same diversity-multiplexing tradeoff as achieved by more complex protocols, where coordination and distributed space-time coding for M relay nodes is required, such as those proposed by Laneman and Wornell (2003). The simplicity of the technique allows for immediate implementation in existing radio hardware and its adoption could provide for improved flexibility, reliability, and efficiency in future 4G wireless systems. We develop and analyze low-complexity cooperative diversity protocols that combat fading induced by multipath propagation in wireless networks. The underlying techniques exploit space diversity available through cooperating terminals' relaying signals for one another. We outline several strategies employed by the cooperating radios, including fixed relaying schemes such as amplify-and-forward and decode-and-forward, selection relaying schemes that adapt based upon channel measurements between the cooperating terminals, and incremental relaying schemes that adapt based upon limited feedback from the destination terminal. We develop performance characterizations in terms of outage events and associated outage probabilities, which measure robustness of the transmissions to fading, focusing on the high signal-to-noise ratio (SNR) regime. Except for fixed decode-and-forward, all of our cooperative diversity protocols are efficient in the sense that they achieve full diversity (i.e., second-order diversity in the case of two terminals), and, moreover, are close to optimum (within 1.5 dB) in certain regimes. Thus, using distributed antennas, we can provide the powerful benefits of space diversity without need for physical arrays, though at a loss of spectral efficiency due to half-duplex operation and possibly at the cost of additional receive hardware. Applicable to any wireless setting, including cellular or ad hoc networks-wherever space constraints preclude the use of physical arrays-the performance characterizations reveal that large power or energy savings result from the use of these protocols. When mobiles cannot support multiple antennas due to size or other constraints, conventional space-time coding cannot be used to provide uplink transmit diversity. To address this limitation, the concept of cooperation diversity has been introduced, where mobiles achieve uplink transmit diversity by relaying each other's messages. A particularly powerful variation of this principle is coded cooperation. Instead of a simple repetition relay, coded cooperation partitions the codewords of each mobile and transmits portions of each codeword through independent fading channels. This paper presents two extensions to the coded cooperation framework. First, we increase the diversity of coded cooperation in the fast-fading scenario via ideas borrowed from space-time codes. We calculate bounds for the bit- and block-error rates to demonstrate the resulting gains. Second, since cooperative coding contains two code components, it is natural to apply turbo codes to this framework. We investigate the application of turbo codes in coded cooperation and demonstrate the resulting gains via error bounds and simulations. At high SNR the capacity of a point-to point MIMO system with N T transmit antenna and NR receive antenna is min N T, NR log(SNR) + O(1). The factor in front of the log is called the multiplexing gain. In this paper we consider a network with 2N nodes (N source destination pairs) that each have only a single antenna. These single antenna nodes could cooperate to form larger virtual arrays, usually called cooperative diversity, user cooperation, or coded cooperation. The question we ask is: how large a multiplexing gain is possible. We prove that for N = 2 the multiplexing gain is 1, and consider generalizations to larger networks This paper presents theoretical characterizations and analysis for the physical layer of multihop wireless communications channels. Four channel models are considered and developed: the decoded relaying multihop channel; the amplified relaying multihop channel; the decoded relaying multihop diversity channel; and the amplified relaying multihop diversity channel. Two classifications are discussed: decoded relaying versus amplified relaying, and multihop channels versus multihop diversity channels. The channel models are compared, through analysis and simulations, with the "singlehop" (direct transmission) reference channel on the basis of signal-to-noise ratio, probability of outage, probability of error, and optimal power allocation. Each of the four channel models is shown to outperform the singlehop reference channel under the condition that the set of intermediate relaying terminals is selected intelligently. Multihop diversity channels are shown to outperform multihop channels. Amplified relaying is shown to outperform decoded relaying despite noise propagation. This is attributed to the fact that amplified relaying does not suffer from the error propagation which limits the performance of decoded relaying channels to that of their weakest link.