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22
Multipleantenna cooperative wireless systems: A diversity multiplexing tradeoff perspective
, 2007
"... We consider a general multipleantenna 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 (halfduplex o ..."
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Cited by 70 (3 self)
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We consider a general multipleantenna 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 (halfduplex or fullduplex), and the network geometry (clustered or nonclustered). We first study the multipleantenna relay channel with a fullduplex 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 decodeandforward (DF), and compressandforward (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 multipleantenna relay channel with a halfduplex relay. We show that the halfduplex DMT behavior can significantly be different from the fullduplex case. We find that CF is DMT optimal for halfduplex relaying as well, and is the first protocol known to achieve the halfduplex relay DMT. We next study the multipleaccess 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 fullduplex relays and a clustered network, this virtual multipleinput multipleoutput (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.
DMT optimality of LRaided linear decoders for a general class of channels, lattice designs, and system models
 IEEE TRANS. INFOM. THEORY
, 2010
"... The work identifies the first general, explicit, and nonrandom MIMO encoderdecoder structures that guarantee optimality with respect to the diversitymultiplexing tradeoff (DMT), without employing a computationally expensive maximumlikelihood (ML) receiver. Specifically, the work establishes the ..."
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Cited by 33 (4 self)
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The work identifies the first general, explicit, and nonrandom MIMO encoderdecoder structures that guarantee optimality with respect to the diversitymultiplexing tradeoff (DMT), without employing a computationally expensive maximumlikelihood (ML) receiver. Specifically, the work establishes the DMT optimality of a class of regularized lattice decoders, and more importantly the DMT optimality of their latticereduction (LR)aided linear counterparts. The results hold for all channel statistics, for all channel dimensions, and most interestingly, irrespective of the particular latticecode applied. As a special case, it is established that the LLLbased LRaided linear implementation of the MMSEGDFE lattice decoder facilitates DMT optimal decoding of any lattice code at a worstcase complexity that grows at most linearly in the data rate. This represents a fundamental reduction in the decoding complexity when compared to ML decoding whose complexity is generally exponential in rate. The results’ generality lends them applicable to a plethora of pertinent communication scenarios such as quasistatic MIMO, MIMOOFDM, ISI, cooperativerelaying, and MIMOARQ channels, in all of which the DMT optimality of the LRaided linear decoder is guaranteed. The adopted approach yields insight, and motivates further study, into joint transceiver designs with an improved SNR gap to ML decoding.
Multiantenna cooperative wireless systems: A diversity multiplexing tradeoff perspective
 IEEE Trans. Inform. Theory
, 2007
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FiniteSNR DiversityMultiplexing Tradeoff via Asymptotic Analysis of Large MIMO Systems
, 2010
"... Diversitymultiplexing tradeoff (DMT) was characterized asymptotically (SNR> infinity) for i.i.d. Rayleigh fading channel by Zheng and Tse [1]. The SNRasymptotic DMT overestimates the finiteSNR one [2]. This paper outlines a number of additional limitations and difficulties of the DMT framewo ..."
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Cited by 15 (9 self)
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Diversitymultiplexing tradeoff (DMT) was characterized asymptotically (SNR> infinity) for i.i.d. Rayleigh fading channel by Zheng and Tse [1]. The SNRasymptotic DMT overestimates the finiteSNR one [2]. This paper outlines a number of additional limitations and difficulties of the DMT framework and discusses their implications. Using the recent results on the sizeasymptotic (in the number of antennas) outage capacity distribution, the finiteSNR, sizeasymptotic DMT is derived for a broad class of fading distributions. The SNR range over which the finiteSNR DMT is accurately approximated by the SNRasymptotic one is characterized. The multiplexing gain definition is shown to affect critically this range and thus should be carefully selected, so that the SNRasymptotic DMT is an accurate approximation at realistic SNR values and thus has operational significance to be used as a design criterion. The finiteSNR diversity gain is shown to decrease with correlation and power imbalance in a broad class of fading channels, and such an effect is described in a compact, closed form. Complete characterization of the outage probability (or outage capacity) requires not only the finiteSNR DMT, but also the SNR offset, which is introduced and investigated as well. This offset, which is not accounted for in the DMT framework, is shown to have a significant impact on the outage probability for a broad class of fading channels, especially when the multiplexing gain is small. The analytical results and conclusions are validated via extensive Monte Carlo simulations. Overall, the sizeasymptotic DMT represents a valuable alternative to the SNRasymptotic one.
Bits About the Channel: Multiround Protocols for Twoway Fading Channels
 In Preparation. May 19, 2009 DRAFT
"... Most communication systems use some form of feedback, often related to channel state information. In this paper, we study diversity multiplexing tradeoff for both FDD and TDD systems, when both receiver and transmitter knowledge about the channel is noisy and potentially mismatched. For FDD systems, ..."
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Cited by 6 (3 self)
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Most communication systems use some form of feedback, often related to channel state information. In this paper, we study diversity multiplexing tradeoff for both FDD and TDD systems, when both receiver and transmitter knowledge about the channel is noisy and potentially mismatched. For FDD systems, we first extend the achievable tradeoff region for 1.5 rounds of message passing to get higher diversity compared to the best known scheme, in the regime of higher multiplexing gains. We then break the mold of all current channel state based protocols by using multiple rounds of conferencing to extract more bits about the actual channel. This iterative refinement of the channel increases the diversity order with every round of communication. The protocols are ondemand in nature, using high powers for training and feedback only when the channel is in poor states. The key result is that the diversity multiplexing tradeoff with perfect training and K levels of perfect feedback can be achieved, even when there are errors in training the receiver and errors in the feedback link, with a multiround protocol which has K rounds of training and K − 1 rounds of binary feedback. The above result can be viewed as a generalization of Zheng and Tse, and Aggarwal and Sabharwal, where the result was shown to hold for K = 1 and K = 2 respectively. For TDD systems, we also develop new achievable strategies with multiple rounds of communication between the transmitter and the receiver, which use the reciprocity of the forward and the feedback channel. The multiround TDD protocol achieves a diversitymultiplexing tradeoff which uniformly dominates its FDD counterparts, where no channel reciprocity is available.
Cooperative fading regions for decode and forward relaying
 IEEE Trans. On Information Theory
, 2008
"... Abstract—Cooperative transmission protocols over fading channels are based on a number of relaying nodes to form virtual multiantenna transmissions. Diversity provided by these techniques has been widely analyzed for the Rayleigh fading case. However, short range or fixed wireless communications o ..."
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Cited by 5 (4 self)
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Abstract—Cooperative transmission protocols over fading channels are based on a number of relaying nodes to form virtual multiantenna transmissions. Diversity provided by these techniques has been widely analyzed for the Rayleigh fading case. However, short range or fixed wireless communications often experience propagation environments where the fading envelope distribution is meaningfully different from Rayleigh. The main focus in this paper is to investigate the impact of fading distribution on performances of collaborative communication. Cooperative protocols are compared to colocated multiantenna systems by introducing the concept of cooperative fading region. This is the collection of fading distributions for which relayed transmission can be regarded as a competitive option (in terms of performances) compared to multiantenna direct (noncooperative) transmission. The analysis is dealt with by adopting the information theoretic outage probability as the performance metric. Cooperative link performances at high SNR are conveniently expressed here in terms of diversity and coding gain as outage parameters that are provided by the fading statistics of the channels involved in collaborative transmission. Advantages of cooperative transmission compared to multiantenna are related to the propagation environment so that the analysis can be used in network design. Index Terms—Cooperative diversity, cooperative transmissions, decode and forward relaying, distributed spacetime coding, fading channels. I.
Diversitymultiplexing tradeoff and outage probability in MIMO relay channels
 IEEE International Symp. Inf. Theory
, 2010
"... Abstract MIMO singlerelay fading channels are studied, where the source and destination are equipped with multiple antennas and the relay has a single one. Compact closedform expressions are obtained for the outage probability under i.i.d. and correlated Rayleighfading links. Insightful highSNR ..."
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Cited by 4 (3 self)
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Abstract MIMO singlerelay fading channels are studied, where the source and destination are equipped with multiple antennas and the relay has a single one. Compact closedform expressions are obtained for the outage probability under i.i.d. and correlated Rayleighfading links. Insightful highSNR approximations are derived, which show the impact of the number of antennas, correlation, relay noise, relaying protocol, etc. Diversitymultiplexing tradeoff (DMT) is obtained for a broad class of fading distributions, including, as special cases, Rayleigh, Rice, Nakagami, Weibull, which may be nonidentical, spatially correlated and/or nonzero mean. The DMT is shown to depend not on a particular fading distribution, but rather on its polynomial behavior near zero. It turns out to be the same for the simple "amplifyandforward " protocol and more complicated "decodeandforward ” one with capacity achieving codes, i.e. the full processing capability at the relay does not help to improve the DMT. However, we also emphasize significant difference between the SNRasymptotic DMT and the finiteSNR outage performance: while the former is not improved by using an extra antenna on either side, the latter can be significantly improved and, in particular, an extra antenna can be tradedoff for a full processing capability at the relay. I.
Diversitymultiplexing tradeoff in MIMO relay channels for a broad class of fading distributions
 IEEE Commun. Lett
, 2010
"... Abstract—Diversity multiplexing tradeoff (DMT) in MIMO relay channels, where the transmitter and receiver are equipped with multiple antennas and the relay with a single one, is derived for a broad class of fading distributions, including, as special cases, nonidentical, spatially correlated, and n ..."
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Abstract—Diversity multiplexing tradeoff (DMT) in MIMO relay channels, where the transmitter and receiver are equipped with multiple antennas and the relay with a single one, is derived for a broad class of fading distributions, including, as special cases, nonidentical, spatially correlated, and nonzero mean channels. It is shown that the DMT does not depend on a particular fading distribution, but rather on its polynomial behavior near zero. The DMT turns out to be the same for the simple “amplifyandforward ” mode and more complicated “decodeandforward ” relaying (with capacity achieving codes), i.e. the full processing capability at the relay does not help to improve the DMT. Index Terms—Multiantenna (MIMO) system, diversity multiplexing tradeoff. I.
PowerControlled Feedback and Training for Twoway MIMO Channels
"... Most communication systems use some form of feedback, often related to channel state information. The common models used in analyses either assume perfect channel state information at the receiver and/or noiseless state feedback links. However, in practical systems, neither is the channel estimate ..."
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Cited by 3 (1 self)
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Most communication systems use some form of feedback, often related to channel state information. The common models used in analyses either assume perfect channel state information at the receiver and/or noiseless state feedback links. However, in practical systems, neither is the channel estimate known perfectly at the receiver and nor is the feedback link perfect. In this paper, we study the achievable diversity multiplexing tradeoff using i.i.d. Gaussian codebooks, considering the errors in training the receiver and the errors in the feedback link for FDD systems, where the forward and the feedback are independent MIMO channels. Our key result is that the maximum diversity order with onebit of feedback information is identical to systems with more feedback bits. Thus, asymptotically in SNR, more than one bit of feedback does not improve the system performance at constant rates. Furthermore, the onebit diversitymultiplexing performance is identical to the system which has perfect channel state information at the receiver along with noiseless feedback link. This achievability uses novel concepts of power controlled feedback and training, which naturally surface when we consider imperfect channel estimation and noisy feedback links. In the process of evaluating the proposed training and feedback protocols, we find an asymptotic expression for the joint probability of the SNR exponents of eigenvalues of the actual channel and the estimated channel which may be of independent interest.
Nearest Neighbor Decoding in MIMO BlockFading Channels With Imperfect CSIR
"... Abstract—This paper studies communication outages in multipleinput multipleoutput (MIMO) blockfading channels with imperfect channel state information at the receiver (CSIR). Using mismatched decoding error exponents, we prove the achievability of the generalized outage probability, the probabil ..."
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Cited by 3 (2 self)
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Abstract—This paper studies communication outages in multipleinput multipleoutput (MIMO) blockfading channels with imperfect channel state information at the receiver (CSIR). Using mismatched decoding error exponents, we prove the achievability of the generalized outage probability, the probability that the generalized mutual information (GMI) is less than the data rate, and show that this probability is the fundamental limit for independent and identically distributed (i.i.d.) codebooks. Then, using nearest neighbor decoding, we study the generalized outage probability in the high signaltonoise ratio (SNR) regime for random codes with Gaussian and discrete signal constellations. In particular, we study the SNR exponent, which is defined as the highSNR slope of the error probability curve on a logarithmiclogarithmic scale. We show that the maximum achievable SNR exponent of the imperfect CSIR case is given by the SNR exponent of the perfect CSIR case times the minimum of one and the channel estimation error diversity. Random codes with Gaussian constellations achieve the optimal SNR exponent with finite block length as long as the block length is larger than a threshold. On the other hand, random codes with discrete constellations achieve the optimal SNR exponent with block length growing with the logarithm of the SNR. The results hold for many fading distributions, including Rayleigh, Rician, Nakagami, Nakagami and Weibull as well as for optical wireless scintillation distributions such as lognormalRice and gammagamma. Index Terms—Blockfading channels, channel state information, diversity, error exponent, generalized mutual information (GMI), imperfect channel state information, MIMO, multiple antenna, nearest neighbor decoding, outage probability, SNR exponent. I.