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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 269 (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.
Signal Space Diversity : A Power and Bandwidth Efficient Diversity Technique for the Rayleigh Fading Channel
 IEEE Trans. on Information Theory
, 1998
"... Abstract—The increasing need for high datarate transmissions over time or frequencyselective fading channels has drawn attention to modulation schemes with high spectral efficiency such as QAM. With the aim of increasing the “diversity order” of the signal set we consider multidimensional rotated ..."
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Cited by 187 (28 self)
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Abstract—The increasing need for high datarate transmissions over time or frequencyselective fading channels has drawn attention to modulation schemes with high spectral efficiency such as QAM. With the aim of increasing the “diversity order” of the signal set we consider multidimensional rotated QAM constellations. Very high diversity orders can be achieved and this results in an almost Gaussian performance over the fading channel. This multidimensional modulation scheme is essentially uncoded and enables one to trade diversity for system complexity, at no power or bandwidth expense. Index Terms—Diversity, fading, lattices, number fields, QAM modulation, rotation.
On FastDecodable SpaceTime Block Codes
, 2008
"... We focus on fullrate, fastdecodable space–time block codes (STBCs) for 2×2 and 4×2 multipleinput multipleoutput (MIMO) transmission. We first derive conditions and design criteria for reducedcomplexity maximumlikelihood decodable 2×2 STBCs, and we apply them to two families of codes that were r ..."
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Cited by 72 (3 self)
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We focus on fullrate, fastdecodable space–time block codes (STBCs) for 2×2 and 4×2 multipleinput multipleoutput (MIMO) transmission. We first derive conditions and design criteria for reducedcomplexity maximumlikelihood decodable 2×2 STBCs, and we apply them to two families of codes that were recently discovered. Next, we derive a novel reducedcomplexity 4×2 STBC, and show that it outperforms all previously known codes with certain constellations.
SoftInput SoftOutput Lattice Sphere Decoder for Linear Channels
 Proc. of the IEEE GLOBECOM’03
, 2003
"... Soft output detection for signals transmitted on linear channels is investigated. A particular emphasis is made for signal detection on multiple antenna channels. The a posteriori information at the detector output is evaluated from a shifted spherical list of point candidates. The spherical list is ..."
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Cited by 50 (11 self)
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Soft output detection for signals transmitted on linear channels is investigated. A particular emphasis is made for signal detection on multiple antenna channels. The a posteriori information at the detector output is evaluated from a shifted spherical list of point candidates. The spherical list is centered on the maximum likelihood point, which has the great advantage of stabilizing the list size. Thus, the sphere radius is selected in order to control the list size and to cope with the boundaries of the finite multiple antenna constellation. Our new soft output sphere decoder is then applied to the computation of constrained channel capacity and to the iterative detection of a coded transmission. For example, we achieved a signaltonoise ratio at 1.25dB from capacity limit on a 44 MIMO channel with 16QAM modulation and a 4state rate 1/2 parallel turbo code.
On Optimal Multilayer Cyclotomic Space–Time Code Designs
, 2005
"... High rate and large diversity product (or coding advantage, or coding gain, or determinant distance, or minimum product distance) are two of the most important criteria often used for good space–time code designs. In recent (linear) latticebased space–time code designs, more attention is paid to t ..."
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Cited by 22 (7 self)
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High rate and large diversity product (or coding advantage, or coding gain, or determinant distance, or minimum product distance) are two of the most important criteria often used for good space–time code designs. In recent (linear) latticebased space–time code designs, more attention is paid to the high rate criterion but less to the large diversity product criterion. In this paper, we consider these two criteria together for multilayer cyclotomic space–time code designs. In a previous paper, we recently proposed a systematic cyclotomic diagonal space–time code design over a general cyclotomic number ring that has infinitely many designs for a fixed number of transmit antennas, where diagonal codes correspond to singlelayer codes in this paper. In this paper, we first propose a general multilayer cyclotomic space–time codes. We present a general optimality theorem for these infinitely many cyclotomic diagonal (or singlelayer) space–time codes over general cyclotomic number rings for a general number of transmit antennas. We then present optimal multilayer (fullrate) cyclotomic space–time code designs for two and three transmit antennas. We also present an optimal twolayer cyclotomic space–time code design for three and four transmit antennas. The optimality here is in the sense that, for a fixed mean transmission signal power, its diversity product is maximized, or equivalently, for a fixed diversity product, its mean transmission signal power is minimized. It should be emphasized that all the optimal multilayer cyclotomic space–time codes presented in this paper have the nonvanishing determinant property.
Spacetime block codes achieving full diversity with linear receivers
 IEEE TRANS. INFORM. THEORY
, 2008
"... In most of the existing space–time code designs, achieving full diversity is based on maximumlikelihood (ML) decoding at the receiver that is usually computationally expensive and may not have soft outputs. Recently, Zhang–Liu–Wong introduced Toeplitz codes and showed that Toeplitz codes achieve f ..."
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Cited by 16 (5 self)
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In most of the existing space–time code designs, achieving full diversity is based on maximumlikelihood (ML) decoding at the receiver that is usually computationally expensive and may not have soft outputs. Recently, Zhang–Liu–Wong introduced Toeplitz codes and showed that Toeplitz codes achieve full diversity when a linear receiver, zeroforcing (ZF) or minimum mean square error (MMSE) receiver, is used. Motivated from Zhang–Liu–Wong’s results on Toeplitz codes, in this paper, we propose a design criterion for space–time block codes (STBC), in which information symbols and their complex conjugates are linearly embedded, to achieve full diversity when ZF or MMSE receiver is used. The (complex) orthogonal STBC (OSTBC) satisfy the criterion as one may expect. We also show that the symbol rates of STBC under this criterion are upper bounded by 1. Subsequently, we propose a novel family of STBC that satisfy the criterion and thus achieve full diversity with ZF or MMSE receiver. Our newly proposed STBC are constructed by overlapping the 2 2 2 Alamouti code and hence named overlapped Alamouti codes in this paper. The new codes are close to orthogonal and their symbol rates can approach 1 for any number of transmit antennas. Simulation results show that overlapped Alamouti codes significantly outperform Toeplitz codes for all numbers of transmit antennas and also outperform OSTBC when the number of transmit antennas is above 4.
Lattice Decoding for Joint Detection in Direct Sequence CDMA Systems
 IEEE Trans. Inform. Theory
, 2000
"... A new joint detection method based on sphere packing lattice decoding is presented. The algorithm is suitable for both synchronous and asynchronous multiple access CDMADSSS systems, and it may jointly detect up to 32 users with a reasonable complexity. The detection complexity is independent of the ..."
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Cited by 13 (0 self)
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A new joint detection method based on sphere packing lattice decoding is presented. The algorithm is suitable for both synchronous and asynchronous multiple access CDMADSSS systems, and it may jointly detect up to 32 users with a reasonable complexity. The detection complexity is independent of the modulation size and large MPAM or MQAM constellations can be used. Further, a theoretical gain analysis is performed where the multiple access system's performance is derived from the lattice parameters. Key Words : Lattice Decoding, CDMA, Multiuser Detection. The material in this paper will be presented in part at the Information Theory Workshop, Kruger National Park, South Africa, June 1999. 1 Introduction A new low complexity joint detection algorithm for direct sequence multiple access systems is proposed. The algorithm is optimal (Maximum Likelihood) for synchronous CDMA systems. The receiver models the despreading output as a multidimensional lattice point (sphere packing) corr...
Solving boxconstrained integer least squares problems
 IEEE Trans. Wireless Comm
"... Abstract — A boxconstrained integer least squares problem (BILS) arises from several wireless communications applications. Solving a BILS problem usually has two stages: reduction (or preprocessing) and search. This paper presents a reduction algorithm and a search algorithm. Unlike the typical red ..."
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Cited by 13 (10 self)
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Abstract — A boxconstrained integer least squares problem (BILS) arises from several wireless communications applications. Solving a BILS problem usually has two stages: reduction (or preprocessing) and search. This paper presents a reduction algorithm and a search algorithm. Unlike the typical reduction algorithms, which use only the information of the lattice generator matrix, the new reduction algorithm also uses the information of the given input vector and the box constraint and is very effective for search. The new search algorithm overcomes some shortcomings of the existing search algorithms and gives some other improvement. Simulation results indicate the combination of the new reduction algorithm and the new search algorithm can be much more efficient than the existing algorithms, in particular when the least squares residual is large. Index Terms — Decoding, detection, integer least squares, lattice, MIMO channels, reduction, search.
New SpaceTime Coding Techniques with Bit Interleaved Coded Modulations
, 2004
"... This thesis report describes new designs for transmitters and receivers of bit interleaved coded modulations over multiple antenna channels. The objective is to achieve near Shannon capacity performance over ergodic channels and near outage probability performance over block fading channels. Iterati ..."
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Cited by 13 (7 self)
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This thesis report describes new designs for transmitters and receivers of bit interleaved coded modulations over multiple antenna channels. The objective is to achieve near Shannon capacity performance over ergodic channels and near outage probability performance over block fading channels. Iterative joint detection and decoding are applied in the aim of achieving near maximum likelihood performance. Design criteria are derived for each block optimization from the error performance expressions under the ideal interleaving assumption. First, we describe the binary mapping optimization for ergodic channels by introducing the new concept of multidimensional mapping that provides large amount of coding gain. We achieve near capacity performance either with turbocodes or with multidimensional mappings associated with a simple code. Then, we present the bit interleaved coded modulation with linear precoding as a SpaceTime code for multiple antenna block fading channels. We show that the channel interleaver is the fundamental part of the bit interleaved coded modulation calling the shots about the achieved diversity. We describe the linear precoding optimality condition and a class of quasioptimal linear precoders. The minimal linear precoder size providing full diversity is deduced from a modified singleton bound applied to the global Euclidean code. We show that full diversity and quasioptimal coding gains are observed for a given error correcting code. Finally, we achieve near outage capacity performance thanks to turbocodes. Next, iterative joint detection and decoding techniques are considered, we describe a near optimum softinput softoutput list sphere decoder which allows the computation of a posteriori probabilities for very high spectral efficiency transmitter schemes with reduced complexity.