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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.
Asymptotic Performance of Linear Receivers in MIMO Fading Channels
 IEEE TRANS. ON INFO THEORY
, 2009
"... Linear receivers are an attractive lowcomplexity alternative to optimal processing for multiantenna MIMO communications. In this paper we characterize the informationtheoretic performance of MIMO linear receivers in two different asymptotic regimes. For fixed number of antennas, we investigate th ..."
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Cited by 31 (0 self)
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Linear receivers are an attractive lowcomplexity alternative to optimal processing for multiantenna MIMO communications. In this paper we characterize the informationtheoretic performance of MIMO linear receivers in two different asymptotic regimes. For fixed number of antennas, we investigate the limit of error probability in the highSNR regime in terms of the DiversityMultiplexing Tradeoff (DMT). Following this, we characterize the error probability for fixed SNR in the regime of large (but finite) number of antennas. As far as the DMT is concerned, we report a negative result: we show that both linear ZeroForcing (ZF) and linear Minimum MeanSquare Error (MMSE) receivers achieve the same DMT, which is largely suboptimal even in the case where outer coding and decoding is performed across the antennas. We also provide an approximate quantitative analysis of the markedly different behavior of the MMSE and ZF receivers at finite rate and nonasymptotic SNR, and show that while the ZF receiver achieves poor diversity at any finite rate, the MMSE receiver error curve slope flattens out progressively, as the coding rate increases. When SNR is fixed and the number of antennas becomes large, we show that the mutual information
On the Proximity Factors of Lattice ReductionAided Decoding
"... Lattice reductionaided decoding enables significant complexity saving and nearoptimum performance in multiinput multioutput (MIMO) communications. However, its remarkable performance largely remains a mystery to date. In this paper, a first step is taken towards a quantitative understanding of ..."
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Cited by 22 (7 self)
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Lattice reductionaided decoding enables significant complexity saving and nearoptimum performance in multiinput multioutput (MIMO) communications. However, its remarkable performance largely remains a mystery to date. In this paper, a first step is taken towards a quantitative understanding of its performance limit. To this aim, the proximity factors are defined to measure the worstcase gap to maximumlikelihood (ML) decoding in terms of the signaltonoise ratio (SNR) for given error rate. The proximity factors are derived analytically and found to be bounded above by a function of the dimension of the lattice alone. As a direct consequence, it follows that lattice reductionaided decoding can always achieve full receive diversity of MIMO fading channels. The study is then extended to the dualbasis reduction. It is found that in some cases reducing the dual can result in smaller proximity factors than reducing the primal basis. The theoretic bounds on the proximity factors are further compared with numerical results.
Multiuser MIMO Downlink Made Practical: Achievable Rates with Simple Channel State Estimation and Feedback Schemes
"... We consider a MIMO fading broadcast channel and compute achievable ergodic rates when channel state information is acquired at the receivers via downlink training and explicit channel feedback is performed to provide transmitter channel state information (CSIT). Both “analog” and quantized (digital) ..."
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Cited by 22 (6 self)
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We consider a MIMO fading broadcast channel and compute achievable ergodic rates when channel state information is acquired at the receivers via downlink training and explicit channel feedback is performed to provide transmitter channel state information (CSIT). Both “analog” and quantized (digital) channel feedback are analyzed, and digital feedback is shown to be potentially superior when the feedback channel uses per channel coefficient is larger than 1. Also, we show that by proper design of the digital feedback link, errors in the feedback have a relatively minor effect even if simple uncoded modulation is used on the feedback channel. We extend our analysis to the case of fading MIMO Multiaccess Channel (MIMOMAC) in the feedback link, as well as to the case of a timevarying channel and feedback delay. We show that by exploiting the MIMOMAC nature of the uplink channel, a fully scalable system with both downlink multiplexing gain and feedback redundancy proportional to the number of base station antennas can be achieved. Furthermore, the feedback strategy is optimized by a nontrivial combination of timedivision and spacedivision multipleaccess. For the case of delayed feedback, we show that in the realistic case where the fading process has (normalized) maximum Doppler frequency shift 0 ≤ F < 1/2, a fraction 1 − 2F of the optimal multiplexing gain is achievable. The general conclusion of this work is that very significant downlink throughput is achievable with simple and efficient channel state feedback, provided that the feedback link is properly designed.
Lattice Reduction  A survey with applications in wireless communications
, 2011
"... Lattice reduction is a powerful concept for solving diverse problems involving point lattices. Signal processing applications where lattice reduction has been successfully used include global positioning system (GPS), frequency estimation, color space estimation in JPEG pictures, and particularly da ..."
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Cited by 19 (0 self)
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Lattice reduction is a powerful concept for solving diverse problems involving point lattices. Signal processing applications where lattice reduction has been successfully used include global positioning system (GPS), frequency estimation, color space estimation in JPEG pictures, and particularly data detection and precoding in wireless communication systems. In this article, we first provide some background on point lattices and then give a tutorialstyle introduction to the theoretical and practical aspects of lattice reduction. We describe the most important lattice reduction algorithms and comment on their performance and computational complexity. Finally, we discuss the application of lattice reduction in wireless communications and statistical signal processing. Throughout the article, we point out open problems and interesting questions for future research.
Personal Communication
, 1995
"... Abstract – A new circuit design is proposed for generating gridscroll chaos in the phase plane by using a secondorder linear system with a control of doublehysteresis series. The doublehysteresis series is constructed in a systematic way by using the basic doublehysteresis building blocks. With ..."
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Cited by 15 (0 self)
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Abstract – A new circuit design is proposed for generating gridscroll chaos in the phase plane by using a secondorder linear system with a control of doublehysteresis series. The doublehysteresis series is constructed in a systematic way by using the basic doublehysteresis building blocks. With the proposed scheme, the number of scrolls can be arbitrarily assigned, and the multiscroll chaotic attractors can be placed anywhere and can cover any chosen area in the phase plane. The gridscroll chaotic attractor is applied to biometric (fingerprint image) authentication. In this application, a twodimensional (2D) discrete chaotic image is created from these gridscroll chaotic attractors. Some of the parameters of the 2D chaotic image are extracted from the stable global structure of fingerprint image, and used to derive the encryption key at a terminal. Decryption, minutiae extraction and matching are fulfilled at the central server. I.
LowComplexity Decoding via Reduced Dimension MaximumLikelihood Search
"... Abstract—In this paper, we consider a lowcomplexity detection technique referred to as a reduced dimension maximumlikelihood search (RDMLS). RDMLS is based on a partitioned search which approximates the maximumlikelihood (ML) estimate of symbols by searching a partitioned symbol vector space ra ..."
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Cited by 12 (0 self)
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Abstract—In this paper, we consider a lowcomplexity detection technique referred to as a reduced dimension maximumlikelihood search (RDMLS). RDMLS is based on a partitioned search which approximates the maximumlikelihood (ML) estimate of symbols by searching a partitioned symbol vector space rather than that spanned by the whole symbol vector. The inevitable performance loss due to a reduction in the search space is compensated by 1) the use of a list tree search, which is an extension of a single best searching algorithm called sphere decoding, and 2) the recomputation of a set of weak symbols, i.e., those ignored in the reduced dimension search, for each strong symbol candidate found during the list tree search. Through simulations onquadrature amplitude modulation (QAM) transmission in frequency nonselective multiinputmultioutput (MIMO) channels, we demonstrate that the RDMLS algorithm shows near constant complexity over a wide range of bit error rate (BER) (10 1 10 4), while limiting performance loss to within 1 dB from ML detection. Index Terms—Dimension reduction, list tree search, maximumlikelihood (ML) decoding, minimum mean square error (MMSE), multiple input multiple output (MIMO), sphere decoding, stack algorithm. I.
On the Complexity Distribution of Sphere Decoding
, 2011
"... We analyze the (computational) complexity distribution of sphere decoding (SD) for random infinite lattices. In particular, we show that under fairly general assumptions on the statistics of the lattice basis matrix, the tail behavior of the SD complexity distribution is fully determined by the inve ..."
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Cited by 11 (5 self)
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We analyze the (computational) complexity distribution of sphere decoding (SD) for random infinite lattices. In particular, we show that under fairly general assumptions on the statistics of the lattice basis matrix, the tail behavior of the SD complexity distribution is fully determined by the inverse volume of the fundamental regions of the underlying lattice. Particularizing this result to N ×M, N ≥ M, i.i.d. circularly symmetric complex Gaussian lattice basis matrices, we find that the corresponding complexity distribution is of Paretotype with tail exponent given by N −M + 1. A more refined analysis reveals that the corresponding average complexity of SD is infinite for N =M and finite for N> M. Finally, for i.i.d. circularly symmetric complex Gaussian lattice basis matrices, we analyze SD preprocessing techniques based on latticereduction (such as the LLL algorithm or layersorting according to the VBLAST algorithm) and regularization. In particular, we show that latticereduction does not improve the tail exponent of the complexity distribution while regularization results in a SD complexity distribution with tails that decrease faster than polynomial.
The Equivalence of Semidefinite Relaxation MIMO Detectors for HigherOrder QAM
, 809
"... In multiinputmultioutput (MIMO) detection, semidefinite relaxation (SDR) has been shown to be an efficient highperformance approach. Developed initially for BPSK and QPSK, SDR has been found to be capable of providing nearoptimal performance (for those constellations). This has stimulated a num ..."
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Cited by 10 (4 self)
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In multiinputmultioutput (MIMO) detection, semidefinite relaxation (SDR) has been shown to be an efficient highperformance approach. Developed initially for BPSK and QPSK, SDR has been found to be capable of providing nearoptimal performance (for those constellations). This has stimulated a number of recent research endeavors that aim to apply SDR to the highorder QAM cases. These independently developed SDRs are different in concept and structure, and presently no serious analysis has been given to compare these methods. This paper analyzes the relationship of three such SDR methods, namely the polynomialinspired SDR (PISDR) by Wiesel et al., the boundconstrained SDR (BCSDR) by Sidiropoulos and Luo, and the virtuallyantipodal SDR (VASDR) by Mao et al. The result that we have proven is somehow unexpected: the three SDRs are equivalent. Simply speaking, we show that solving any one SDR is equivalent to solving the other SDRs. This paper also discusses some implications arising from the SDR equivalence, and provides simulation results to verify our theoretical findings.