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334
A VectorPerturbation technique for NearCapacity . . .
 IEEE TRANS. COMMUN
, 2005
"... Recent theoretical results describing the sum capacity when using multiple antennas to communicate with multiple users in a known rich scattering environment have not yet been followed with practical transmission schemes that achieve this capacity. We introduce a simple encoding algorithm that achi ..."
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Cited by 323 (10 self)
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Recent theoretical results describing the sum capacity when using multiple antennas to communicate with multiple users in a known rich scattering environment have not yet been followed with practical transmission schemes that achieve this capacity. We introduce a simple encoding algorithm that achieves nearcapacity at sum rates of tens of bits/channel use. The algorithm is a variation on channel inversion that regularizes the inverse and uses a “sphere encoder ” to perturb the data to reduce the power of the transmitted signal. This paper is comprised of two parts. In this first part, we show that while the sum capacity grows linearly with the minimum of the number of antennas and users, the sum rate of channel inversion does not. This poor performance is due to the large spread in the singular values of the channel matrix. We introduce regularization to improve the condition of the inverse and maximize the signaltointerferenceplusnoise ratio at the receivers. Regularization enables linear growth and works especially well at low signaltonoise ratios (SNRs), but as we show in the second part, an additional step is needed to achieve nearcapacity performance at all SNRs.
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 273 (9 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.
On the Complexity of Sphere Decoding in Digital Communications
 IN DIGITAL COMMUNICATIONS,” IEEE TRANSACTIONS ON SIGNAL PROCESSING, TO APPEAR
, 2005
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Algorithm and implementation of the KBest sphere decoding for MIMO detection
 IEEE Journal on Selected Areas in Communications
, 2006
"... Abstract—Kbest Schnorr–Euchner (KSE) decoding algorithm is proposed in this paper to approach nearmaximumlikelihood (ML) performance for multipleinput–multipleoutput (MIMO) detection. As a low complexity MIMO decoding algorithm, the KSE is shown to be suitable for very large scale integration ( ..."
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Cited by 88 (1 self)
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Abstract—Kbest Schnorr–Euchner (KSE) decoding algorithm is proposed in this paper to approach nearmaximumlikelihood (ML) performance for multipleinput–multipleoutput (MIMO) detection. As a low complexity MIMO decoding algorithm, the KSE is shown to be suitable for very large scale integration (VLSI) implementations and be capable of supporting soft outputs. Modified KSE (MKSE) decoding algorithm is further proposed to improve the performance of the softoutput KSE with minor modifications. Moreover, a VLSI architecture is proposed for both algorithms. There are several low complexity and lowpower features incorporated in the proposed algorithms and the VLSI architecture. The proposed hardoutput KSE decoder and the softoutput MKSE decoder is implemented for 4 4 16quadrature amplitude modulation (QAM) MIMO detection in a 0.35 m and a 0.13 m CMOS technology, respectively. The implemented hardoutput KSE chip core is 5.76 mm2 with 91 K gates. The KSE decoding throughput is up to 53.3 Mb/s with a core power consumption of 626 mW at 100 MHz clock frequency and 2.8 V supply. The implemented softoutput MKSE chip can achieve a decoding throughput of more than 100 Mb/s with a 0.56 mm2 core area and 97 K gates. The implementation results show that it is feasible to achieve nearML performance and high detection throughput for a 4 4 16QAM MIMO system using the proposed algorithms and the VLSI architecture with reasonable complexity. Index Terms—Multipleinput–multipleoutput (MIMO), Schnorr–Euchner algorithm, sphere decoder, very large scale integration (VLSI). I.
LowComplexity NearMaximumLikelihood Detection and Precoding for MIMO Systems using Lattice Reduction
 IEEE Information Theory Workshop 2003
, 2003
"... Abstract — We consider the latticereductionaided detection scheme for 2×2 channels recently proposed by Yao and Wornell [11]. Using an equivalent realvalued substitute MIMO channel model their lattice reduction algorithm can be replaced by the wellknown LLL algorithm, which enables the applicati ..."
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Cited by 82 (12 self)
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Abstract — We consider the latticereductionaided detection scheme for 2×2 channels recently proposed by Yao and Wornell [11]. Using an equivalent realvalued substitute MIMO channel model their lattice reduction algorithm can be replaced by the wellknown LLL algorithm, which enables the application to MIMO systems with arbitrary numbers of dimensions. We show how lattice reduction can also be favourably applied in systems that use precoding and give simulation results that underline the usefulness of this approach. I.
A unified framework for tree search decoding: rediscovering the sequential decoder,”
 IEEE Transactions on Information Theory,
, 2006
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Nearmaximumlikelihood detection of MIMO systems using MMSEbased latticereduction
 IEEE Conf. on Commun
, 2004
"... Abstract — In recent publications the use of latticereduction for signal detection in multiple antenna systems has been proposed. In this paper, we adopt these latticereductionaided schemes to the MMSE criterion. We show that an obvious way to do this is infeasible and propose an alternative meth ..."
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Cited by 69 (3 self)
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Abstract — In recent publications the use of latticereduction for signal detection in multiple antenna systems has been proposed. In this paper, we adopt these latticereductionaided schemes to the MMSE criterion. We show that an obvious way to do this is infeasible and propose an alternative method based on an extended system model, which in conjunction with simple successive interference cancellation nearly reaches the performance of maximumlikelihood detection. Furthermore, we demonstrate that a sorted QR decomposition can significantly reduce the computational effort associated with latticereduction. Thus, the new algorithm clearly outperforms existing methods with comparable complexity.
Softoutput sphere decoding: Algorithms and VLSI implementation
 IEEE Journal on Selected Areas in Communications
, 2008
"... Multipleinput multipleoutput (MIMO) detection algorithms providing soft information for a subsequent channel decoder pose significant implementation challenges due to their high computational complexity. In this paper, we show how sphere decoding can be used as an efficient tool to implement soft ..."
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Cited by 68 (13 self)
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Multipleinput multipleoutput (MIMO) detection algorithms providing soft information for a subsequent channel decoder pose significant implementation challenges due to their high computational complexity. In this paper, we show how sphere decoding can be used as an efficient tool to implement softoutput MIMO detection with flexible tradeoffs between computational complexity and (error rate) performance. In particular, we provide VLSI implementation results which demonstrate that single treesearch, sorted QRdecomposition, channel matrix regularization, loglikelihood ratio clipping, and imposing runtime constraints are the key ingredients for realizing softoutput MIMO detectors with near maxlog performance at a chip area that is only 50 % higher than that of the bestknown hardoutput sphere decoder VLSI implementation. tion.
A deterministic single exponential time algorithm for most lattice problems based on Voronoi cell computations.
 In STOC,
, 2010
"... ABSTRACT We give deterministicÕ(2 2n+o(n) )time algorithms to solve all the most important computational problems on point lattices in NP, including the Shortest Vector Problem (SVP), Closest Vector Problem (CVP), and Shortest Independent Vectors Problem (SIVP). This improves the n O(n) running ti ..."
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Cited by 62 (3 self)
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ABSTRACT We give deterministicÕ(2 2n+o(n) )time algorithms to solve all the most important computational problems on point lattices in NP, including the Shortest Vector Problem (SVP), Closest Vector Problem (CVP), and Shortest Independent Vectors Problem (SIVP). This improves the n O(n) running time of the best previously known algorithms for CVP (Kannan, Math. Operation Research 12(3): 1987) and SIVP (Micciancio, Proc. of SODA, 2008), and gives a deterministic and asymptotically faster alternative to the 2 O(n) time (and space) randomized algorithm for SVP of (Ajtai, Kumar and Sivakumar, STOC 2001). The core of our algorithm is a new method to solve the closest vector problem with preprocessing (CVPP) that uses the Voronoi cell of the lattice (described as intersection of halfspaces) as the result of the preprocessing function. In the process, we also give algorithms for several other lattice problems, including computing the kissing number of a lattice, and computing the set of all Voronoi relevant vectors. All our algorithms are deterministic, and have 2 O(n) time and space complexity.
Complex lattice reduction algorithms for lowcomplexity MIMO detection
 IN IEEE GLOBAL TELECOMMN. CONF. (GLOBECOM
, 2006
"... Recently, latticereductionaided detectors have been proposed for multipleinput multipleoutput (MIMO) systems to give performance with full diversity like maximum likelihood receiver, and yet with complexity similar to linear receivers. However, these latticereductionaided detectors are based ..."
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Cited by 59 (7 self)
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Recently, latticereductionaided detectors have been proposed for multipleinput multipleoutput (MIMO) systems to give performance with full diversity like maximum likelihood receiver, and yet with complexity similar to linear receivers. However, these latticereductionaided detectors are based on the traditional LLL reduction algorithm that was originally introduced for reducing real lattice bases, in spite of the fact that the channel matrices are inherently complexvalued. In this paper, we introduce the complex LLL algorithm for direct application to reduce the basis of a complex lattice which is naturally defined by a complexvalued channel matrix. We prove that complex LLL reductionaided detection can also achieve full diversity. Our analysis reveals that the new complex LLL algorithm can achieve a reduction in complexity of nearly 50 % over the traditional LLL algorithm, and this is confirmed by simulation. It is noteworthy that the complex LLL algorithm aforementioned has nearly the same biterrorrate performance as the traditional LLL algorithm.