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51
On MaximumLikelihood Detection and the Search for the Closest Lattice Point
 IEEE TRANS. INFORM. THEORY
, 2003
"... Maximumlikelihood (ML) decoding algorithms for Gaussian multipleinput multipleoutput (MIMO) linear channels are considered. Linearity over the field of real numbers facilitates the design of ML decoders using numbertheoretic tools for searching the closest lattice point. These decoders are colle ..."
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Cited by 266 (7 self)
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Maximumlikelihood (ML) decoding algorithms for Gaussian multipleinput multipleoutput (MIMO) linear channels are considered. Linearity over the field of real numbers facilitates the design of ML decoders using numbertheoretic tools for searching the closest lattice point. These decoders are collectively referred to as sphere decoders in the literature. In this paper, a fresh look at this class of decoding algorithms is taken. In particular, two novel algorithms are developed. The first algorithm is inspired by the Pohst enumeration strategy and is shown to offer a significant reduction in complexity compared to the ViterboBoutros sphere decoder. The connection between the proposed algorithm and the stack sequential decoding algorithm is then established. This connection is utilized to construct the second algorithm which can also be viewed as an application of the SchnorrEuchner strategy to ML decoding. Aided with a detailed study of preprocessing algorithms, a variant of the second algorithm is developed and shown to offer significant reductions in the computational complexity compared to all previously proposed sphere decoders with a nearML detection performance. This claim is supported by intuitive arguments and simulation results in many relevant scenarios.
Improved Linear SoftInput SoftOutput Detection via Soft Feedback Successive Interference Cancellation
"... Abstract—We propose an improved minimum mean square error (MMSE) vertical Bell Labs layered spacetime (VBLAST) detection technique, called a soft input, soft output, and soft feedback (SIOF) VBLAST detector, for turbo multiinput multioutput (TurboMIMO) systems. We derive a symbol estimator by m ..."
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Cited by 19 (1 self)
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Abstract—We propose an improved minimum mean square error (MMSE) vertical Bell Labs layered spacetime (VBLAST) detection technique, called a soft input, soft output, and soft feedback (SIOF) VBLAST detector, for turbo multiinput multioutput (TurboMIMO) systems. We derive a symbol estimator by minimizing the power of the interference plus noise, given apriori probabilities of undetected layer symbols and a posteriori probabilities for past detected layer symbols. For a lowcomplexity implementation, an approximate SIOF algorithm is presented, which allows for a timeinvariant realization of the symbol ordering and an MMSE filtering process. Another implementation, referred to as the iterative SIOF algorithm is introduced, which decides on symbol detection order based on a posteriori symbol probabilities to improve the detection performance. Simulations performed on a spacetime bitinterleaved coded modulation (STBICM) architecture over quasistatic MIMO fading channels demonstrate that the SIOF VBLAST detector provides performance gains over previous TurboBLAST detectors, most notably when more transmit antennas are used.
SoftInput SoftOutput Single TreeSearch Sphere Decoding
, 2009
"... Softinput softoutput (SISO) detection algorithms form the basis for iterative decoding. The computational complexity of SISO detection often poses significant challenges for practical receiver implementations, in particular in the context of multipleinput multipleoutput (MIMO) wireless communica ..."
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Cited by 18 (5 self)
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Softinput softoutput (SISO) detection algorithms form the basis for iterative decoding. The computational complexity of SISO detection often poses significant challenges for practical receiver implementations, in particular in the context of multipleinput multipleoutput (MIMO) wireless communication systems. In this paper, we present a lowcomplexity SISO spheredecoding algorithm, based on the single treesearch paradigm proposed originally for softoutput MIMO detection in Studer, et al., IEEE JSAC, 2008. The new algorithm incorporates clipping of the extrinsic loglikelihood ratios (LLRs) into the treesearch, which results in significant complexity savings and allows to cover a large performance/complexity tradeoff region by adjusting a single parameter. Furthermore, we propose a new method for correcting approximate LLRs —resulting from suboptimal detectors — which (often significantly) improves detection performance at low additional computational complexity. Index Terms Multipleinput multipleoutput (MIMO) communication, softinput softoutput detection, sphere decoding, iterative MIMO decoding
BitInterleaved Coded Modulation
 Foundations and Trends on Communications and Information Theory, Now Publishers
"... The principle of coding in the signal space follows directly from Shannon’s analysis of waveform Gaussian channels subject to an input constraint. The early design of communication systems focused separately on modulation, namely signal design and detection, and error correcting codes, which deal ..."
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Cited by 13 (4 self)
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The principle of coding in the signal space follows directly from Shannon’s analysis of waveform Gaussian channels subject to an input constraint. The early design of communication systems focused separately on modulation, namely signal design and detection, and error correcting codes, which deal with errors introduced at the demodulator of the underlying waveform channel. The correct perspective of signalspace coding, although never out of sight of information theorists, was brought back into the focus of coding theorists and system designers by Imai’s and Ungerböck’s pioneering works on coded modulation. More recently, powerful families of binary codes with a good tradeoff between performance and decoding complexity have been (re)discovered. BitInterleaved Coded Modulation (BICM) is a pragmatic approach combining the best out of both worlds: it takes advantage of the signalspace coding perspective, whilst allowing for the use
Approaching MIMO capacity using bitwise Markov chain Monte Carlo detection
 IEEE Trans. Commun
, 2010
"... Abstract—This paper examines near capacity performance of Markov Chain Monte Carlo (MCMC) detectors for multipleinput and multipleoutput (MIMO) channels. The proposed MCMC detector (LogMAPtb bMCMC) operates in a strictly bitwise fashion and adopts LogMAP algorithm with table lookup. When con ..."
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Cited by 9 (2 self)
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Abstract—This paper examines near capacity performance of Markov Chain Monte Carlo (MCMC) detectors for multipleinput and multipleoutput (MIMO) channels. The proposed MCMC detector (LogMAPtb bMCMC) operates in a strictly bitwise fashion and adopts LogMAP algorithm with table lookup. When concatenated with an optimized lowdensity paritycheck (LDPC) code, LogMAPtb bMCMC can operate within 1.21.8 dB of the capacity of MIMO systems with 8 transmit/receive antennas at spectral efficiencies up to
Efficient Soft Demodulation of MIMO QPSK via Semidefinite Relaxation
, 2008
"... We develop a computationally efficient and memory efficient approach to (near) maximum a posteriori probability demodulation for MIMO systems with QPSK signalling, based on semidefinite relaxation. Existing approaches to this problem require either storage of a large list of candidate bitvectors, o ..."
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Cited by 7 (1 self)
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We develop a computationally efficient and memory efficient approach to (near) maximum a posteriori probability demodulation for MIMO systems with QPSK signalling, based on semidefinite relaxation. Existing approaches to this problem require either storage of a large list of candidate bitvectors, or the solution of multiple binary quadratic problems. In contrast, the proposed demodulator does not require the storage of a candidate list, and involves the solution of a single (efficiently solvable) semidefinite program per channel use. Our simulation results show that the resulting computational and memory efficiencies are obtained without incurring a significant degradation in performance.
A branch and bound approach to speed up the sphere decoder
"... It is well known that maximumlikelihooddecoding in many communications applications reduces to solving an integer leastsquares problem which is NP hard in the worstcase. On the other hand, it has recently been shown that, over a wide range of dimensions and SNRs, the sphere decoder can be used to ..."
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Cited by 6 (3 self)
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It is well known that maximumlikelihooddecoding in many communications applications reduces to solving an integer leastsquares problem which is NP hard in the worstcase. On the other hand, it has recently been shown that, over a wide range of dimensions and SNRs, the sphere decoder can be used to find the exact solution with an expected complexity that is roughly cubic in the dimension of the problem. However, the computational complexity becomes prohibitive if the SNR is too low and/or if the dimension of the problem is too large. In this paper, we target these two regimes and attempt to find faster algorithms by pruning the search tree beyond what is done in the standard sphere decoder. The search tree is pruned by computing lower bounds on the possible optimal solution as we proceed to go down the tree. We observe a tradeoff between the computational complexity required to compute the lower bound and the size of the pruned tree: the more effort we spend in computing a tight lower bound, the more branches that can be eliminated in the tree. Thus, even though it is possible to prune the search tree (and hence the number of points visited) by several orders of magnitude, this may be offset by the computations required to perform the pruning. All of which suggests the need for computationallyefficient tight lower bounds. We present three different lower bounds based on sphericalrelaxation, on polytoperelaxation and on duality, simulate their performances and discuss their relative merits. 1.
Markov Chain Monte Carlo: Applications to MIMO detection and channel equalization
"... Abstract — In this paper, we present an overview of recent work ..."
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Cited by 4 (0 self)
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Abstract — In this paper, we present an overview of recent work
On joint detection and decoding of linear block codes on Gaussian vector channels
"... Abstract—Optimal receivers recovering signals transmitted across noisy communication channels employ a maximumlikelihood (ML) criterion to minimize the probability of error. The problem of finding the most likely transmitted symbol is often equivalent to finding the closest lattice point to a given ..."
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Abstract—Optimal receivers recovering signals transmitted across noisy communication channels employ a maximumlikelihood (ML) criterion to minimize the probability of error. The problem of finding the most likely transmitted symbol is often equivalent to finding the closest lattice point to a given point and is known to be NPhard. In systems that employ errorcorrecting coding for data protection, the symbol space forms a sparse lattice, where the sparsity structure is determined by the code. In such systems, ML data recovery may be geometrically interpreted as a search for the closest point in the sparse lattice. In this paper, motivated by the idea of the “sphere decoding ” algorithm of Fincke and Pohst, we propose an algorithm that finds the closest point in the sparse lattice to the given vector. This given vector is not arbitrary, but rather is an unknown sparse lattice point that has been perturbed by an additive noise vector whose statistical properties are known. The complexity of the proposed algorithm is thus a random variable. We study its expected value, averaged over the noise and over the lattice. For binary linear block codes, we find the expected complexity in closed form. Simulation results indicate significant performance gains over systems employing separate detection and decoding, yet are obtained at a complexity that is practically feasible over a wide range of system parameters. Index Terms—Expected complexity, integer least squares, joint detection and decoding, lattice problems, multiantenna systems, NP hard, sphere decoding (SD), wireless communications. I.
PeaktoAverage Power Ratio (PAR) Reduction in OFDM Based on Lattice Decoding
"... Abstract — A new method for PAR reduction in OFDM is introduced. It is based on periodically extending the signal constellations (modulocongruent points) in each carrier and the application of a lattice decoder to find the best representative in each carrier. Main advantages of this scheme are that ..."
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Abstract — A new method for PAR reduction in OFDM is introduced. It is based on periodically extending the signal constellations (modulocongruent points) in each carrier and the application of a lattice decoder to find the best representative in each carrier. Main advantages of this scheme are that no side information has to be communicated to the receiver and, without changing operation, any (square) signal constellation can be used. Numerical simulations cover the performance of PAR reduction in OFDM based on lattice decoding. I. INTRODUCTION AND PAR REDUCTION Main point in orthogonal frequencydivision multiplexing (OFDM) systems is the transmission of a data stream by modulating a (usually large) number of carriers individually. Due to the superposition of the individual signal