17 research outputs found
STBCs from Representation of Extended Clifford Algebras
A set of sufficient conditions to construct -real symbol Maximum
Likelihood (ML) decodable STBCs have recently been provided by Karmakar et al.
STBCs satisfying these sufficient conditions were named as Clifford Unitary
Weight (CUW) codes. In this paper, the maximal rate (as measured in complex
symbols per channel use) of CUW codes for is
obtained using tools from representation theory. Two algebraic constructions of
codes achieving this maximal rate are also provided. One of the constructions
is obtained using linear representation of finite groups whereas the other
construction is based on the concept of right module algebra over
non-commutative rings. To the knowledge of the authors, this is the first paper
in which matrices over non-commutative rings is used to construct STBCs. An
algebraic explanation is provided for the 'ABBA' construction first proposed by
Tirkkonen et al and the tensor product construction proposed by Karmakar et al.
Furthermore, it is established that the 4 transmit antenna STBC originally
proposed by Tirkkonen et al based on the ABBA construction is actually a single
complex symbol ML decodable code if the design variables are permuted and
signal sets of appropriate dimensions are chosen.Comment: 5 pages, no figures, To appear in Proceedings of IEEE ISIT 2007,
Nice, Franc
Algebraic Distributed Space-Time Codes with Low ML Decoding Complexity
"Extended Clifford algebras" are introduced as a means to obtain low ML
decoding complexity space-time block codes. Using left regular matrix
representations of two specific classes of extended Clifford algebras, two
systematic algebraic constructions of full diversity Distributed Space-Time
Codes (DSTCs) are provided for any power of two number of relays. The left
regular matrix representation has been shown to naturally result in space-time
codes meeting the additional constraints required for DSTCs. The DSTCs so
constructed have the salient feature of reduced Maximum Likelihood (ML)
decoding complexity. In particular, the ML decoding of these codes can be
performed by applying the lattice decoder algorithm on a lattice of four times
lesser dimension than what is required in general. Moreover these codes have a
uniform distribution of power among the relays and in time, thus leading to a
low Peak to Average Power Ratio at the relays.Comment: 5 pages, no figures. To appear in Proceedings of IEEE ISIT 2007,
Nice, Franc
A Novel Construction of Multi-group Decodable Space-Time Block Codes
Complex Orthogonal Design (COD) codes are known to have the lowest detection
complexity among Space-Time Block Codes (STBCs). However, the rate of square
COD codes decreases exponentially with the number of transmit antennas. The
Quasi-Orthogonal Design (QOD) codes emerged to provide a compromise between
rate and complexity as they offer higher rates compared to COD codes at the
expense of an increase of decoding complexity through partially relaxing the
orthogonality conditions. The QOD codes were then generalized with the so
called g-symbol and g-group decodable STBCs where the number of orthogonal
groups of symbols is no longer restricted to two as in the QOD case. However,
the adopted approach for the construction of such codes is based on sufficient
but not necessary conditions which may limit the achievable rates for any
number of orthogonal groups. In this paper, we limit ourselves to the case of
Unitary Weight (UW)-g-group decodable STBCs for 2^a transmit antennas where the
weight matrices are required to be single thread matrices with non-zero entries
in {1,-1,j,-j} and address the problem of finding the highest achievable rate
for any number of orthogonal groups. This special type of weight matrices
guarantees full symbol-wise diversity and subsumes a wide range of existing
codes in the literature. We show that in this case an exhaustive search can be
applied to find the maximum achievable rates for UW-g-group decodable STBCs
with g>1. For this purpose, we extend our previously proposed approach for
constructing UW-2-group decodable STBCs based on necessary and sufficient
conditions to the case of UW-g-group decodable STBCs in a recursive manner.Comment: 12 pages, and 5 tables, accepted for publication in IEEE transactions
on communication
Algebraic Distributed Differential Space-Time Codes with Low Decoding Complexity
The differential encoding/decoding setup introduced by Kiran et al,
Oggier-Hassibi and Jing-Jafarkhani for wireless relay networks that use
codebooks consisting of unitary matrices is extended to allow codebooks
consisting of scaled unitary matrices. For such codebooks to be usable in the
Jing-Hassibi protocol for cooperative diversity, the conditions involving the
relay matrices and the codebook that need to be satisfied are identified. Using
the algebraic framework of extended Clifford algebras, a new class of
Distributed Differential Space-Time Codes satisfying these conditions for power
of two number of relays and also achieving full cooperative diversity with a
low complexity sub-optimal receiver is proposed. Simulation results indicate
that the proposed codes outperform both the cyclic codes as well as the
circulant codes. Furthermore, these codes can also be applied as Differential
Space-Time codes for non-coherent communication in classical point to point
multiple antenna systems.Comment: To appear in IEEE Transactions on Wireless Communications. 10 pages,
5 figure
Training-Embedded, Single-Symbol ML-Decodable, Distributed STBCs for Relay Networks
Recently, a special class of complex designs called Training-Embedded Complex
Orthogonal Designs (TE-CODs) has been introduced to construct single-symbol
Maximum Likelihood (ML) decodable (SSD) distributed space-time block codes
(DSTBCs) for two-hop wireless relay networks using the amplify and forward
protocol. However, to implement DSTBCs from square TE-CODs, the overhead due to
the transmission of training symbols becomes prohibitively large as the number
of relays increase. In this paper, we propose TE-Coordinate Interleaved
Orthogonal Designs (TE-CIODs) to construct SSD DSTBCs. Exploiting the block
diagonal structure of TE-CIODs, we show that, the overhead due to the
transmission of training symbols to implement DSTBCs from TE-CIODs is smaller
than that for TE-CODs. We also show that DSTBCs from TE-CIODs offer higher rate
than those from TE-CODs for identical number of relays while maintaining the
SSD and full-diversity properties.Comment: 7 pages, 2 figure
Distributed space-time block codes for two-hop wireless relay networks
Recently, the idea of space-time coding has been applied to wireless relay networks wherein a set of geographically separated relay nodes cooperate to process the received signal from the source and forward them to the destination such that the signal received at the destination appears like a Space-Time Block Code (STBC). Such STBCs (referred to as Distributed Space-Time Block Codes (DSTBCs)) when appropriately designed are known to offer spatial diversity. It is known that different classes of DSTBCs can be designed primarily depending on (i) whether the Amplify and Forward (AF) protocol or the Decode and Forward (DF) protocol is employed at the relays and (ii) whether the relay nodes are synchronized or not. In this paper, we present a survey on the problems and results associated with the design of DSTBCs for the following classes of two-hop wireless relay networks: (i) synchronous relay networks with AF protocols, (ii) asynchronous relay networks with AF protocols (iii) synchronous relay networks with DF protocols and (iv) asynchronous relay Fig. 1. Co-located MIMO channel model networks with DF protocols
Noncoherent Low-Decoding-Complexity Space-Time Codes for Wireless Relay Networks
The differential encoding/decoding setup introduced by Kiran et al, Oggier et
al and Jing et al for wireless relay networks that use codebooks consisting of
unitary matrices is extended to allow codebooks consisting of scaled unitary
matrices. For such codebooks to be used in the Jing-Hassibi protocol for
cooperative diversity, the conditions that need to be satisfied by the relay
matrices and the codebook are identified. A class of previously known rate one,
full diversity, four-group encodable and four-group decodable Differential
Space-Time Codes (DSTCs) is proposed for use as Distributed DSTCs (DDSTCs) in
the proposed set up. To the best of our knowledge, this is the first known low
decoding complexity DDSTC scheme for cooperative wireless networks.Comment: 5 pages, no figures. To appear in Proceedings of IEEE ISIT 2007,
Nice, Franc
Single-Symbol ML Decodable Distributed STBCs for Partially-Coherent Cooperative Networks
Space-time block codes (STBCs) that are single-symbol decodable (SSD) in a
co-located multiple antenna setting need not be SSD in a distributed
cooperative communication setting. A relay network with N relays and a single
source-destination pair is called a partially-coherent relay channel (PCRC) if
the destination has perfect channel state information (CSI) of all the channels
and the relays have only the phase information of the source-to-relay channels.
In this paper, first, a new set of necessary and sufficient conditions for a
STBC to be SSD for co-located multiple antenna communication is obtained. Then,
this is extended to a set of necessary and sufficient conditions for a
distributed STBC (DSTBC) to be SSD for a PCRC, by identifying the additional
conditions. Using this, several SSD DSTBCs for PCRC are identified among the
known classes of STBCs. It is proved that even if a SSD STBC for a co-located
MIMO channel does not satisfy the additional conditions for the code to be SSD
for a PCRC, single-symbol decoding of it in a PCRC gives full-diversity and
only coding gain is lost. It is shown that when a DSTBC is SSD for a PCRC, then
arbitrary coordinate interleaving of the in-phase and quadrature-phase
components of the variables does not disturb its SSD property for PCRC.
Finally, it is shown that the possibility of {\em channel phase compensation}
operation at the relay nodes using partial CSI at the relays increases the
possible rate of SSD DSTBCs from when the relays do not have CSI
to 1/2, which is independent of N