223 research outputs found
Lattice-Based Precoding And Decoding in MIMO Fading Systems
In this thesis, different aspects of lattice-based precoding and decoding for the transmission of digital and analog data over MIMO fading channels are investigated:
1) Lattice-based precoding in MIMO broadcast systems:
A new viewpoint for adopting the lattice reduction in communication over MIMO broadcast channels is introduced. Lattice basis reduction helps us to reduce the average transmitted energy by modifying the region which includes the constellation points. The new viewpoint helps us to generalize the idea of lattice-reduction-aided precoding for the case of unequal-rate transmission, and obtain analytic results for the asymptotic behavior of the symbol-error-rate for the lattice-reduction-aided precoding and the perturbation technique. Also, the outage probability for both cases of fixed-rate users and fixed sum-rate is analyzed. It is shown that the lattice-reduction-aided method, using LLL algorithm, achieves the optimum asymptotic slope of symbol-error-rate (called the precoding diversity).
2) Lattice-based decoding in MIMO multiaccess systems and MIMO point-to-point systems:
Diversity order and diversity-multiplexing tradeoff are two important measures for the performance of communication systems over MIMO fading channels. For the case of MIMO multiaccess systems (with single-antenna transmitters) or MIMO point-to-point systems with V-BLAST transmission scheme, it is proved that lattice-reduction-aided decoding achieves the maximum receive diversity (which is equal to the number of receive antennas). Also, it is proved that the naive lattice decoding (which discards the out-of-region decoded points) achieves the maximum diversity in V-BLAST systems. On the other hand, the inherent drawbacks of the naive lattice decoding for general MIMO fading systems is investigated. It is shown that using the naive lattice decoding for MIMO systems has considerable deficiencies in terms of the diversity-multiplexing tradeoff. Unlike the case of maximum-likelihood decoding, in this case, even the perfect lattice space-time codes which have the non-vanishing determinant property can not achieve the optimal diversity-multiplexing tradeoff.
3) Lattice-based analog transmission over MIMO fading channels:
The problem of finding a delay-limited schemes for sending an analog source over MIMO fading channels is investigated in this part. First, the problem of robust joint source-channel coding over an additive white Gaussian noise channel is investigated. A new scheme is proposed which achieves the optimal slope for the signal-to-distortion-ratio (SDR) curve (unlike the previous known coding schemes). Then, this idea is extended to MIMO channels to construct lattice-based codes for joint source-channel coding over MIMO channels. Also, similar to the diversity-multiplexing tradeoff, the asymptotic performance of MIMO joint source-channel coding schemes is characterized, and a concept called diversity-fidelity tradeoff is introduced in this thesis
Integer-Forcing MIMO Linear Receivers Based on Lattice Reduction
A new architecture called integer-forcing (IF) linear receiver has been
recently proposed for multiple-input multiple-output (MIMO) fading channels,
wherein an appropriate integer linear combination of the received symbols has
to be computed as a part of the decoding process. In this paper, we propose a
method based on Hermite-Korkine-Zolotareff (HKZ) and Minkowski lattice basis
reduction algorithms to obtain the integer coefficients for the IF receiver. We
show that the proposed method provides a lower bound on the ergodic rate, and
achieves the full receive diversity. Suitability of complex
Lenstra-Lenstra-Lovasz (LLL) lattice reduction algorithm (CLLL) to solve the
problem is also investigated. Furthermore, we establish the connection between
the proposed IF linear receivers and lattice reduction-aided MIMO detectors
(with equivalent complexity), and point out the advantages of the former class
of receivers over the latter. For the and MIMO
channels, we compare the coded-block error rate and bit error rate of the
proposed approach with that of other linear receivers. Simulation results show
that the proposed approach outperforms the zero-forcing (ZF) receiver, minimum
mean square error (MMSE) receiver, and the lattice reduction-aided MIMO
detectors.Comment: 9 figures and 11 pages. Modified the title, abstract and some parts
of the paper. Major change from v1: Added new results on applicability of the
CLLL reductio
On the Proximity Factors of Lattice Reduction-Aided Decoding
Lattice reduction-aided decoding features reduced decoding complexity and
near-optimum performance in multi-input multi-output communications. In this
paper, a quantitative analysis of lattice reduction-aided decoding is
presented. To this aim, the proximity factors are defined to measure the
worst-case losses in distances relative to closest point search (in an infinite
lattice). Upper bounds on the proximity factors are derived, which are
functions of the dimension of the lattice alone. The study is then extended
to the dual-basis reduction. It is found that the bounds for dual basis
reduction may be smaller. Reasonably good bounds are derived in many cases. The
constant bounds on proximity factors not only imply the same diversity order in
fading channels, but also relate the error probabilities of (infinite) lattice
decoding and lattice reduction-aided decoding.Comment: remove redundant figure
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
Integer-Forcing Linear Receivers
Linear receivers are often used to reduce the implementation complexity of
multiple-antenna systems. In a traditional linear receiver architecture, the
receive antennas are used to separate out the codewords sent by each transmit
antenna, which can then be decoded individually. Although easy to implement,
this approach can be highly suboptimal when the channel matrix is near
singular. This paper develops a new linear receiver architecture that uses the
receive antennas to create an effective channel matrix with integer-valued
entries. Rather than attempting to recover transmitted codewords directly, the
decoder recovers integer combinations of the codewords according to the entries
of the effective channel matrix. The codewords are all generated using the same
linear code which guarantees that these integer combinations are themselves
codewords. Provided that the effective channel is full rank, these integer
combinations can then be digitally solved for the original codewords. This
paper focuses on the special case where there is no coding across transmit
antennas and no channel state information at the transmitter(s), which
corresponds either to a multi-user uplink scenario or to single-user V-BLAST
encoding. In this setting, the proposed integer-forcing linear receiver
significantly outperforms conventional linear architectures such as the
zero-forcing and linear MMSE receiver. In the high SNR regime, the proposed
receiver attains the optimal diversity-multiplexing tradeoff for the standard
MIMO channel with no coding across transmit antennas. It is further shown that
in an extended MIMO model with interference, the integer-forcing linear
receiver achieves the optimal generalized degrees-of-freedom.Comment: 40 pages, 16 figures, to appear in the IEEE Transactions on
Information Theor
DMT Optimality of LR-Aided Linear Decoders for a General Class of Channels, Lattice Designs, and System Models
The work identifies the first general, explicit, and non-random MIMO
encoder-decoder structures that guarantee optimality with respect to the
diversity-multiplexing tradeoff (DMT), without employing a computationally
expensive maximum-likelihood (ML) receiver. Specifically, the work establishes
the DMT optimality of a class of regularized lattice decoders, and more
importantly the DMT optimality of their lattice-reduction (LR)-aided linear
counterparts. The results hold for all channel statistics, for all channel
dimensions, and most interestingly, irrespective of the particular lattice-code
applied. As a special case, it is established that the LLL-based LR-aided
linear implementation of the MMSE-GDFE lattice decoder facilitates DMT optimal
decoding of any lattice code at a worst-case 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 quasi-static MIMO, MIMO-OFDM, ISI,
cooperative-relaying, and MIMO-ARQ channels, in all of which the DMT optimality
of the LR-aided 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.Comment: 16 pages, 1 figure (3 subfigures), submitted to the IEEE Transactions
on Information Theor
Decoding by Sampling: A Randomized Lattice Algorithm for Bounded Distance Decoding
Despite its reduced complexity, lattice reduction-aided decoding exhibits a
widening gap to maximum-likelihood (ML) performance as the dimension increases.
To improve its performance, this paper presents randomized lattice decoding
based on Klein's sampling technique, which is a randomized version of Babai's
nearest plane algorithm (i.e., successive interference cancelation (SIC)). To
find the closest lattice point, Klein's algorithm is used to sample some
lattice points and the closest among those samples is chosen. Lattice reduction
increases the probability of finding the closest lattice point, and only needs
to be run once during pre-processing. Further, the sampling can operate very
efficiently in parallel. The technical contribution of this paper is two-fold:
we analyze and optimize the decoding radius of sampling decoding resulting in
better error performance than Klein's original algorithm, and propose a very
efficient implementation of random rounding. Of particular interest is that a
fixed gain in the decoding radius compared to Babai's decoding can be achieved
at polynomial complexity. The proposed decoder is useful for moderate
dimensions where sphere decoding becomes computationally intensive, while
lattice reduction-aided decoding starts to suffer considerable loss. Simulation
results demonstrate near-ML performance is achieved by a moderate number of
samples, even if the dimension is as high as 32
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