1,133 research outputs found
Nonintersecting Subspaces Based on Finite Alphabets
Two subspaces of a vector space are here called ``nonintersecting'' if they
meet only in the zero vector. The following problem arises in the design of
noncoherent multiple-antenna communications systems. How many pairwise
nonintersecting M_t-dimensional subspaces of an m-dimensional vector space V
over a field F can be found, if the generator matrices for the subspaces may
contain only symbols from a given finite alphabet A subseteq F? The most
important case is when F is the field of complex numbers C; then M_t is the
number of antennas. If A = F = GF(q) it is shown that the number of
nonintersecting subspaces is at most (q^m-1)/(q^{M_t}-1), and that this bound
can be attained if and only if m is divisible by M_t. Furthermore these
subspaces remain nonintersecting when ``lifted'' to the complex field. Thus the
finite field case is essentially completely solved. In the case when F = C only
the case M_t=2 is considered. It is shown that if A is a PSK-configuration,
consisting of the 2^r complex roots of unity, the number of nonintersecting
planes is at least 2^{r(m-2)} and at most 2^{r(m-1)-1} (the lower bound may in
fact be the best that can be achieved).Comment: 14 page
Complementary Sets, Generalized Reed-Muller Codes, and Power Control for OFDM
The use of error-correcting codes for tight control of the peak-to-mean
envelope power ratio (PMEPR) in orthogonal frequency-division multiplexing
(OFDM) transmission is considered in this correspondence. By generalizing a
result by Paterson, it is shown that each q-phase (q is even) sequence of
length 2^m lies in a complementary set of size 2^{k+1}, where k is a
nonnegative integer that can be easily determined from the generalized Boolean
function associated with the sequence. For small k this result provides a
reasonably tight bound for the PMEPR of q-phase sequences of length 2^m. A new
2^h-ary generalization of the classical Reed-Muller code is then used together
with the result on complementary sets to derive flexible OFDM coding schemes
with low PMEPR. These codes include the codes developed by Davis and Jedwab as
a special case. In certain situations the codes in the present correspondence
are similar to Paterson's code constructions and often outperform them
Code Design for Non-Coherent Detection of Frame Headers in Precoded Satellite Systems
In this paper we propose a simple method for generating short-length
rate-compatible codes over that are robust to non-coherent
detection for -PSK constellations. First, a greedy algorithm is used to
construct a family of rotationally invariant codes for a given constellation.
Then, by properly modifying such codes we obtain codes that are robust to
non-coherent detection. We briefly discuss the optimality of the constructed
codes for special cases of BPSK and QPSK constellations. Our method provides an
upper bound for the length of optimal codes with a given desired non-coherent
distance. We also derive a simple asymptotic upper bound on the frame error
rate (FER) of such codes and provide the simulation results for a selected set
of proposed codes. Finally, we briefly discuss the problem of designing binary
codes that are robust to non-coherent detection for QPSK constellation.Comment: 11 pages, 5 figure
Low Correlation Sequences over the QAM Constellation
This paper presents the first concerted look at low correlation sequence
families over QAM constellations of size M^2=4^m and their potential
applicability as spreading sequences in a CDMA setting.
Five constructions are presented, and it is shown how such sequence families
have the ability to transport a larger amount of data as well as enable
variable-rate signalling on the reverse link.
Canonical family CQ has period N, normalized maximum-correlation parameter
theta_max bounded above by A sqrt(N), where 'A' ranges from 1.8 in the 16-QAM
case to 3.0 for large M. In a CDMA setting, each user is enabled to transfer 2m
bits of data per period of the spreading sequence which can be increased to 3m
bits of data by halving the size of the sequence family. The technique used to
construct CQ is easily extended to produce larger sequence families and an
example is provided.
Selected family SQ has a lower value of theta_max but permits only (m+1)-bit
data modulation. The interleaved 16-QAM sequence family IQ has theta_max <=
sqrt(2) sqrt(N) and supports 3-bit data modulation.
The remaining two families are over a quadrature-PAM (Q-PAM) subset of size
2M of the M^2-QAM constellation. Family P has a lower value of theta_max in
comparison with Family SQ, while still permitting (m+1)-bit data modulation.
Interleaved family IP, over the 8-ary Q-PAM constellation, permits 3-bit data
modulation and interestingly, achieves the Welch lower bound on theta_max.Comment: 21 pages, 3 figures. To appear in IEEE Transactions on Information
Theory in February 200
Optimization of Fast-Decodable Full-Rate STBC with Non-Vanishing Determinants
Full-rate STBC (space-time block codes) with non-vanishing determinants
achieve the optimal diversity-multiplexing tradeoff but incur high decoding
complexity. To permit fast decoding, Sezginer, Sari and Biglieri proposed an
STBC structure with special QR decomposition characteristics. In this paper, we
adopt a simplified form of this fast-decodable code structure and present a new
way to optimize the code analytically. We show that the signal constellation
topology (such as QAM, APSK, or PSK) has a critical impact on the existence of
non-vanishing determinants of the full-rate STBC. In particular, we show for
the first time that, in order for APSK-STBC to achieve non-vanishing
determinant, an APSK constellation topology with constellation points lying on
square grid and ring radius \sqrt{m^2+n^2} (m,n\emph{\emph{integers}}) needs
to be used. For signal constellations with vanishing determinants, we present a
methodology to analytically optimize the full-rate STBC at specific
constellation dimension.Comment: Accepted by IEEE Transactions on Communication
Constellation Optimization in the Presence of Strong Phase Noise
In this paper, we address the problem of optimizing signal constellations for
strong phase noise. The problem is investigated by considering three
optimization formulations, which provide an analytical framework for
constellation design. In the first formulation, we seek to design
constellations that minimize the symbol error probability (SEP) for an
approximate ML detector in the presence of phase noise. In the second
formulation, we optimize constellations in terms of mutual information (MI) for
the effective discrete channel consisting of phase noise, additive white
Gaussian noise, and the approximate ML detector. To this end, we derive the MI
of this discrete channel. Finally, we optimize constellations in terms of the
MI for the phase noise channel. We give two analytical characterizations of the
MI of this channel, which are shown to be accurate for a wide range of
signal-to-noise ratios and phase noise variances. For each formulation, we
present a detailed analysis of the optimal constellations and their performance
in the presence of strong phase noise. We show that the optimal constellations
significantly outperform conventional constellations and those proposed in the
literature in terms of SEP, error floors, and MI.Comment: 10 page, 10 figures, Accepted to IEEE Trans. Commu
Design guidelines for spatial modulation
A new class of low-complexity, yet energyefficient Multiple-Input Multiple-Output (MIMO) transmission techniques, namely the family of Spatial Modulation (SM) aided MIMOs (SM-MIMO) has emerged. These systems are capable of exploiting the spatial dimensions (i.e. the antenna indices) as an additional dimension invoked for transmitting information, apart from the traditional Amplitude and Phase Modulation (APM). SM is capable of efficiently operating in diverse MIMO configurations in the context of future communication systems. It constitutes a promising transmission candidate for large-scale MIMO design and for the indoor optical wireless communication whilst relying on a single-Radio Frequency (RF) chain. Moreover, SM may also be viewed as an entirely new hybrid modulation scheme, which is still in its infancy. This paper aims for providing a general survey of the SM design framework as well as of its intrinsic limits. In particular, we focus our attention on the associated transceiver design, on spatial constellation optimization, on link adaptation techniques, on distributed/ cooperative protocol design issues, and on their meritorious variants
Low-Complexity LP Decoding of Nonbinary Linear Codes
Linear Programming (LP) decoding of Low-Density Parity-Check (LDPC) codes has
attracted much attention in the research community in the past few years. LP
decoding has been derived for binary and nonbinary linear codes. However, the
most important problem with LP decoding for both binary and nonbinary linear
codes is that the complexity of standard LP solvers such as the simplex
algorithm remains prohibitively large for codes of moderate to large block
length. To address this problem, two low-complexity LP (LCLP) decoding
algorithms for binary linear codes have been proposed by Vontobel and Koetter,
henceforth called the basic LCLP decoding algorithm and the subgradient LCLP
decoding algorithm.
In this paper, we generalize these LCLP decoding algorithms to nonbinary
linear codes. The computational complexity per iteration of the proposed
nonbinary LCLP decoding algorithms scales linearly with the block length of the
code. A modified BCJR algorithm for efficient check-node calculations in the
nonbinary basic LCLP decoding algorithm is also proposed, which has complexity
linear in the check node degree.
Several simulation results are presented for nonbinary LDPC codes defined
over Z_4, GF(4), and GF(8) using quaternary phase-shift keying and
8-phase-shift keying, respectively, over the AWGN channel. It is shown that for
some group-structured LDPC codes, the error-correcting performance of the
nonbinary LCLP decoding algorithms is similar to or better than that of the
min-sum decoding algorithm.Comment: To appear in IEEE Transactions on Communications, 201
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