2,579 research outputs found
Achieving Low-Complexity Maximum-Likelihood Detection for the 3D MIMO Code
The 3D MIMO code is a robust and efficient space-time block code (STBC) for
the distributed MIMO broadcasting but suffers from high maximum-likelihood (ML)
decoding complexity. In this paper, we first analyze some properties of the 3D
MIMO code to show that the 3D MIMO code is fast-decodable. It is proved that
the ML decoding performance can be achieved with a complexity of O(M^{4.5})
instead of O(M^8) in quasi static channel with M-ary square QAM modulations.
Consequently, we propose a simplified ML decoder exploiting the unique
properties of 3D MIMO code. Simulation results show that the proposed
simplified ML decoder can achieve much lower processing time latency compared
to the classical sphere decoder with Schnorr-Euchner enumeration
Reduced-complexity maximum-likelihood decoding for 3D MIMO code
The 3D MIMO code is a robust and efficient space-time coding scheme for the
distributed MIMO broadcasting. However, it suffers from the high computational
complexity if the optimal maximum-likelihood (ML) decoding is used. In this
paper we first investigate the unique properties of the 3D MIMO code and
consequently propose a simplified decoding algorithm without sacrificing the ML
optimality. Analysis shows that the decoding complexity is reduced from O(M^8)
to O(M^{4.5}) in quasi-static channels when M-ary square QAM constellation is
used. Moreover, we propose an efficient implementation of the simplified ML
decoder which achieves a much lower decoding time delay compared to the
classical sphere decoder with Schnorr-Euchner enumeration.Comment: IEEE Wireless Communications and Networking Conference (WCNC 2013),
Shanghai : China (2013
Dual-lattice ordering and partial lattice reduction for SIC-based MIMO detection
This is the author's accepted manuscript. The final published article is available from the link below. Copyright @ 2009 IEEE. Personal use of this material is permitted. Permission from IEEE must be obtained for all other users, including reprinting/ republishing this material for advertising or promotional purposes, creating new collective works for resale or redistribution to servers or lists, or reuse of any copyrighted components of this work in other works.In this paper, we propose low-complexity lattice detection algorithms for successive interference cancelation (SIC) in multi-input multi-output (MIMO) communications. First, we present a dual-lattice view of the vertical Bell Labs Layered Space-Time (V-BLAST) detection. We show that V-BLAST ordering is equivalent to applying sorted QR decomposition to the dual basis, or equivalently, applying sorted Cholesky decomposition to the associated Gram matrix. This new view results in lower detection complexity and allows simultaneous ordering and detection. Second, we propose a partial reduction algorithm that only performs lattice reduction for the last several, weak substreams, whose implementation is also facilitated by the dual-lattice view. By tuning the block size of the partial reduction (hence the complexity), it can achieve a variable diversity order, hence offering a graceful tradeoff between performance and complexity for SIC-based MIMO detection. Numerical results are presented to compare the computational costs and to verify the achieved diversity order
Decoding by Embedding: Correct Decoding Radius and DMT Optimality
The closest vector problem (CVP) and shortest (nonzero) vector problem (SVP)
are the core algorithmic problems on Euclidean lattices. They are central to
the applications of lattices in many problems of communications and
cryptography. Kannan's \emph{embedding technique} is a powerful technique for
solving the approximate CVP, yet its remarkable practical performance is not
well understood. In this paper, the embedding technique is analyzed from a
\emph{bounded distance decoding} (BDD) viewpoint. We present two complementary
analyses of the embedding technique: We establish a reduction from BDD to
Hermite SVP (via unique SVP), which can be used along with any Hermite SVP
solver (including, among others, the Lenstra, Lenstra and Lov\'asz (LLL)
algorithm), and show that, in the special case of LLL, it performs at least as
well as Babai's nearest plane algorithm (LLL-aided SIC). The former analysis
helps to explain the folklore practical observation that unique SVP is easier
than standard approximate SVP. It is proven that when the LLL algorithm is
employed, the embedding technique can solve the CVP provided that the noise
norm is smaller than a decoding radius , where
is the minimum distance of the lattice, and . This
substantially improves the previously best known correct decoding bound . Focusing on the applications of BDD to decoding of
multiple-input multiple-output (MIMO) systems, we also prove that BDD of the
regularized lattice is optimal in terms of the diversity-multiplexing gain
tradeoff (DMT), and propose practical variants of embedding decoding which
require no knowledge of the minimum distance of the lattice and/or further
improve the error performance.Comment: To appear in IEEE Transactions on Information Theor
On the sphere-decoding algorithm I. Expected complexity
The problem of finding the least-squares solution to a system of linear equations where the unknown vector is comprised of integers, but the matrix coefficient and given vector are comprised of real numbers, arises in many applications: communications, cryptography, GPS, to name a few. The problem is equivalent to finding the closest lattice point to a given point and is known to be NP-hard. In communications applications, however, the given vector is not arbitrary but rather is an unknown lattice point that has been perturbed by an additive noise vector whose statistical properties are known. Therefore, in this paper, rather than dwell on the worst-case complexity of the integer least-squares problem, we study its expected complexity, averaged over the noise and over the lattice. For the "sphere decoding" algorithm of Fincke and Pohst, we find a closed-form expression for the expected complexity, both for the infinite and finite lattice. It is demonstrated in the second part of this paper that, for a wide range of signal-to-noise ratios (SNRs) and numbers of antennas, the expected complexity is polynomial, in fact, often roughly cubic. Since many communications systems operate at noise levels for which the expected complexity turns out to be polynomial, this suggests that maximum-likelihood decoding, which was hitherto thought to be computationally intractable, can, in fact, be implemented in real time - a result with many practical implications
Comparative Study of SVD and QRS in Closed-Loop Beamforming Systems
We compare two closed-loop beamforming algorithms, one based on singular
value decomposition (SVD) and the other based on equal diagonal QR
decomposition (QRS). SVD has the advantage of parallelizing the MIMO channel,
but each of the sub-channels has different gain. QRS has the advantage of
having equal diagonal value for the decomposed channel, but the subchannels are
not fully parallelized, hence requiring successive interference cancellation or
other techniques to perform decoding. We consider a closed-loop system where
the feedback information is a unitary beamforming matrix. Due to the discrete
and limited modulation set, SVD may have inferior performance to QRS when no
modulation set selection is performed. However, if the selection of modulation
set is performed optimally, we show that SVD can outperform QRS.Comment: Milcom 200
Markov Chain Monte Carlo Algorithms for Lattice Gaussian Sampling
Sampling from a lattice Gaussian distribution is emerging as an important
problem in various areas such as coding and cryptography. The default sampling
algorithm --- Klein's algorithm yields a distribution close to the lattice
Gaussian only if the standard deviation is sufficiently large. In this paper,
we propose the Markov chain Monte Carlo (MCMC) method for lattice Gaussian
sampling when this condition is not satisfied. In particular, we present a
sampling algorithm based on Gibbs sampling, which converges to the target
lattice Gaussian distribution for any value of the standard deviation. To
improve the convergence rate, a more efficient algorithm referred to as
Gibbs-Klein sampling is proposed, which samples block by block using Klein's
algorithm. We show that Gibbs-Klein sampling yields a distribution close to the
target lattice Gaussian, under a less stringent condition than that of the
original Klein algorithm.Comment: 5 pages, 1 figure, IEEE International Symposium on Information
Theory(ISIT) 201
- …