474 research outputs found
Full Diversity Unitary Precoded Integer-Forcing
We consider a point-to-point flat-fading MIMO channel with channel state
information known both at transmitter and receiver. At the transmitter side, a
lattice coding scheme is employed at each antenna to map information symbols to
independent lattice codewords drawn from the same codebook. Each lattice
codeword is then multiplied by a unitary precoding matrix and sent
through the channel. At the receiver side, an integer-forcing (IF) linear
receiver is employed. We denote this scheme as unitary precoded integer-forcing
(UPIF). We show that UPIF can achieve full-diversity under a constraint based
on the shortest vector of a lattice generated by the precoding matrix . This constraint and a simpler version of that provide design criteria for
two types of full-diversity UPIF. Type I uses a unitary precoder that adapts at
each channel realization. Type II uses a unitary precoder, which remains fixed
for all channel realizations. We then verify our results by computer
simulations in , and MIMO using different QAM
constellations. We finally show that the proposed Type II UPIF outperform the
MIMO precoding X-codes at high data rates.Comment: 12 pages, 8 figures, to appear in IEEE-TW
Full-Rate, Full-Diversity, Finite Feedback Space-Time Schemes with Minimum Feedback and Transmission Duration
In this paper a MIMO quasi static block fading channel with finite N-ary
delay-free, noise-free feedback is considered. The transmitter uses a set of N
Space-Time Block Codes (STBCs), one corresponding to each of the N possible
feedback values, to encode and transmit information. The feedback function used
at the receiver and the N component STBCs used at the transmitter together
constitute a Finite Feedback Scheme (FFS). Although a number of FFSs are
available in the literature that provably achieve full-diversity, there is no
known universal criterion to determine whether a given arbitrary FFS achieves
full-diversity or not. Further, all known full-diversity FFSs for T<N_t where
N_t is the number of transmit antennas, have rate at the most 1. In this paper
a universal necessary condition for any FFS to achieve full-diversity is given,
using which the notion of Feedback-Transmission duration optimal (FT-Optimal)
FFSs - schemes that use minimum amount of feedback N given the transmission
duration T, and minimum transmission duration given the amount of feedback to
achieve full-diversity - is introduced. When there is no feedback (N=1) an
FT-optimal scheme consists of a single STBC with T=N_t, and the universal
necessary condition reduces to the well known necessary and sufficient
condition for an STBC to achieve full-diversity: every non-zero codeword
difference matrix of the STBC must be of rank N_t. Also, a sufficient condition
for full-diversity is given for the FFSs in which the component STBC with the
largest minimum Euclidean distance is chosen. Using this sufficient condition
full-rate (rate N_t) full-diversity FT-Optimal schemes are constructed for all
(N_t,T,N) with NT=N_t. These are the first full-rate full-diversity FFSs
reported in the literature for T<N_t. Simulation results show that the new
schemes have the best error performance among all known FFSs.Comment: 12 pages, 5 figures, 1 tabl
Space-time coding techniques with bit-interleaved coded modulations for MIMO block-fading channels
The space-time bit-interleaved coded modulation (ST-BICM) is an efficient
technique to obtain high diversity and coding gain on a block-fading MIMO
channel. Its maximum-likelihood (ML) performance is computed under ideal
interleaving conditions, which enables a global optimization taking into
account channel coding. Thanks to a diversity upperbound derived from the
Singleton bound, an appropriate choice of the time dimension of the space-time
coding is possible, which maximizes diversity while minimizing complexity.
Based on the analysis, an optimized interleaver and a set of linear precoders,
called dispersive nucleo algebraic (DNA) precoders are proposed. The proposed
precoders have good performance with respect to the state of the art and exist
for any number of transmit antennas and any time dimension. With turbo codes,
they exhibit a frame error rate which does not increase with frame length.Comment: Submitted to IEEE Trans. on Information Theory, Submission: January
2006 - First review: June 200
Achieving a vanishing SNR-gap to exact lattice decoding at a subexponential complexity
The work identifies the first lattice decoding solution that achieves, in the
general outage-limited MIMO setting and in the high-rate and high-SNR limit,
both a vanishing gap to the error-performance of the (DMT optimal) exact
solution of preprocessed lattice decoding, as well as a computational
complexity that is subexponential in the number of codeword bits. The proposed
solution employs lattice reduction (LR)-aided regularized (lattice) sphere
decoding and proper timeout policies. These performance and complexity
guarantees hold for most MIMO scenarios, all reasonable fading statistics, all
channel dimensions and all full-rate lattice codes.
In sharp contrast to the above manageable complexity, the complexity of other
standard preprocessed lattice decoding solutions is shown here to be extremely
high. Specifically the work is first to quantify the complexity of these
lattice (sphere) decoding solutions and to prove the surprising result that the
complexity required to achieve a certain rate-reliability performance, is
exponential in the lattice dimensionality and in the number of codeword bits,
and it in fact matches, in common scenarios, the complexity of ML-based
solutions. Through this sharp contrast, the work was able to, for the first
time, rigorously quantify the pivotal role of lattice reduction as a special
complexity reducing ingredient.
Finally the work analytically refines transceiver DMT analysis which
generally fails to address potentially massive gaps between theory and
practice. Instead the adopted vanishing gap condition guarantees that the
decoder's error curve is arbitrarily close, given a sufficiently high SNR, to
the optimal error curve of exact solutions, which is a much stronger condition
than DMT optimality which only guarantees an error gap that is subpolynomial in
SNR, and can thus be unbounded and generally unacceptable in practical
settings.Comment: 16 pages - submission for IEEE Trans. Inform. Theor
Bound-intersection detection for multiple-symbol differential unitary space-time modulation
This paper considers multiple-symbol differential detection (MSD) of differential unitary space-time modulation (DUSTM) over multiple-antenna systems. We derive a novel exact maximum-likelihood (ML) detector, called the bound-intersection detector (BID), using the extended Euclidean algorithm for single-symbol detection of diagonal constellations. While the ML search complexity is exponential in the number of transmit antennas and the data rate, our algorithm, particularly in high signal-to-noise ratio, achieves significant computational savings over the naive ML algorithm and the previous detector based on lattice reduction. We also develop four BID variants for MSD. The first two are ML and use branch-and-bound, the third one is suboptimal, which first uses BID to generate a candidate subset and then exhaustively searches over the reduced space, and the last one generalizes decision-feedback differential detection. Simulation results show that the BID and its MSD variants perform nearly ML, but do so with significantly reduced complexity
Explicit Space-Time Codes Achieving The Diversity-Multiplexing Gain Tradeoff
A recent result of Zheng and Tse states that over a quasi-static channel,
there exists a fundamental tradeoff, referred to as the diversity-multiplexing
gain (D-MG) tradeoff, between the spatial multiplexing gain and the diversity
gain that can be simultaneously achieved by a space-time (ST) block code. This
tradeoff is precisely known in the case of i.i.d. Rayleigh-fading, for T>=
n_t+n_r-1 where T is the number of time slots over which coding takes place and
n_t,n_r are the number of transmit and receive antennas respectively. For T <
n_t+n_r-1, only upper and lower bounds on the D-MG tradeoff are available.
In this paper, we present a complete solution to the problem of explicitly
constructing D-MG optimal ST codes, i.e., codes that achieve the D-MG tradeoff
for any number of receive antennas. We do this by showing that for the square
minimum-delay case when T=n_t=n, cyclic-division-algebra (CDA) based ST codes
having the non-vanishing determinant property are D-MG optimal. While
constructions of such codes were previously known for restricted values of n,
we provide here a construction for such codes that is valid for all n.
For the rectangular, T > n_t case, we present two general techniques for
building D-MG-optimal rectangular ST codes from their square counterparts. A
byproduct of our results establishes that the D-MG tradeoff for all T>= n_t is
the same as that previously known to hold for T >= n_t + n_r -1.Comment: Revised submission to IEEE Transactions on Information Theor
Golden Coded Multiple Beamforming
The Golden Code is a full-rate full-diversity space-time code, which achieves
maximum coding gain for Multiple-Input Multiple-Output (MIMO) systems with two
transmit and two receive antennas. Since four information symbols taken from an
M-QAM constellation are selected to construct one Golden Code codeword, a
maximum likelihood decoder using sphere decoding has the worst-case complexity
of O(M^4), when the Channel State Information (CSI) is available at the
receiver. Previously, this worst-case complexity was reduced to O(M^(2.5))
without performance degradation. When the CSI is known by the transmitter as
well as the receiver, beamforming techniques that employ singular value
decomposition are commonly used in MIMO systems. In the absence of channel
coding, when a single symbol is transmitted, these systems achieve the full
diversity order provided by the channel. Whereas this property is lost when
multiple symbols are simultaneously transmitted. However, uncoded multiple
beamforming can achieve the full diversity order by adding a properly designed
constellation precoder. For 2 \times 2 Fully Precoded Multiple Beamforming
(FPMB), the general worst-case decoding complexity is O(M). In this paper,
Golden Coded Multiple Beamforming (GCMB) is proposed, which transmits the
Golden Code through 2 \times 2 multiple beamforming. GCMB achieves the full
diversity order and its performance is similar to general MIMO systems using
the Golden Code and FPMB, whereas the worst-case decoding complexity of
O(sqrt(M)) is much lower. The extension of GCMB to larger dimensions is also
discussed.Comment: accepted to conferenc
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
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