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109
On optimal quasiorthogonal spacetime block codes with minimum decoding complexity
 IEEE ISIT
, 2005
"... Orthogonal spacetime block codes (OSTBC) from orthogonal designs have both advantages of complex symbolwise maximumlikelihood (ML) decoding and full diversity. However, their symbol rates are upper bounded by 3/4 for more than 2 antennas for complex symbols. To increase the symbol rates, they hav ..."
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Cited by 31 (6 self)
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Orthogonal spacetime block codes (OSTBC) from orthogonal designs have both advantages of complex symbolwise maximumlikelihood (ML) decoding and full diversity. However, their symbol rates are upper bounded by 3/4 for more than 2 antennas for complex symbols. To increase the symbol rates, they have been generalized to quasiorthogonal spacetime block codes (QOSTBC) by Jafarkhani, TirkkonenBoarinHottinen, and PapadiasFoschini but the diversity order is reduced by half and the complex symbolwise ML decoding is significantly increased to complex symbol pairwise (pair of complex symbols) ML decoding. The QOSTBC has been lately modified by rotating half of the complex symbols for achieving the full diversity while maintaining the complex symbol pairwise ML decoding. The optimal rotation angles for any signal constellation of any finite symbols located on both square lattices and equalliteral triangular lattices have been found by SuXia, where the optimality means the optimal diversity product (or product distance). Most recently, QOSTBC has also been modified by YuenGuanTjhung by rotating information symbols in another way such that it has full diversity and in the meantime it has real symbol pairwise ML decoding (the same complexity as complex symbolwise
Superquasiorthogonal spacetime trellis codes for four transmit antennas
 IEEE Trans. on Wireless Comm
, 2005
"... Abstract—We introduce a new family of space–time trellis codes that extends the powerful characteristics of superorthogonal space–time trellis codes to four transmit antennas. We consider a family of quasiorthogonal space–time block codes as building blocks in our new trellis codes. These codes co ..."
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Cited by 20 (6 self)
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Abstract—We introduce a new family of space–time trellis codes that extends the powerful characteristics of superorthogonal space–time trellis codes to four transmit antennas. We consider a family of quasiorthogonal space–time block codes as building blocks in our new trellis codes. These codes combine set partitioning and a super set of quasiorthogonal space–time block codes in a systematic way to provide full diversity and improved coding gain. The result is a powerful code that provides full rate, full diversity, and high coding gain. It is also possible to maintain a tradeoff between coding gain and rate. Simulation results demonstrate the good performance of our new superquasiorthogonal space–time trellis codes. Index Terms—Quasiorthogonal designs, set partitioning, space–time codes, superorthogonal codes, transmitter diversity, trellis codes. I.
Rectangular Coordinate Interleaved Orthogonal Designs
 Elect. Commun. Eng., Indian Inst. Sci., Bangalore, India, IIScDRDO Rep
, 2003
"... SpaceTime block codes (STBC) from Orthogonal Designs (OD), QuasiOrthogonal Designs (QOD) and Coordinate Interleaved Orthogonal Designs (CIOD) have been attracting wider attention due to their amenability for fast (singlesymbol decoding for OD, CIOD and doublesymbol decoding for QOD) ML decoding ..."
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Cited by 18 (6 self)
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SpaceTime block codes (STBC) from Orthogonal Designs (OD), QuasiOrthogonal Designs (QOD) and Coordinate Interleaved Orthogonal Designs (CIOD) have been attracting wider attention due to their amenability for fast (singlesymbol decoding for OD, CIOD and doublesymbol decoding for QOD) ML decoding, and rateone with fullrank over quasistatic fading channels [1][13]. The importance of CIOD is due to the fact that, rateone, fullrank, square ODs for arbitrary complex constellations exist only for 2 transmit antennas while such a CIOD exists for 2,3 and 4 transmit antennas with a slight restriction on the complex constellations [12], [13]. These limitations motivate study of rectangular (nonsquare) designs. One way of obtaining rectangular designs is by deleting columns from square or nonsquare ODs or CIODs. In this paper, we present a new construction of rectangular singlesymbol decodable designs that have higher maximum mutual information than those obtained by deleting columns of CIODs and has lower peak to average power ratio (PAPR). Simulation results are presented for three and five transmit antennas and compared with that of OD, QODs, CIODs to demonstrate the superiority of the proposed rectangular designs.
On Full Diversity SpaceTime Block Codes with Partial Interference Cancellation Group Decoding
"... In this paper, we propose a partial interference cancellation (PIC) group decoding strategy/scheme for linear dispersive spacetime block codes (STBC) and a design criterion for the codes to achieve full diversity when the PIC group decoding is used at the receiver. A PIC group decoding decodes the ..."
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Cited by 18 (6 self)
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In this paper, we propose a partial interference cancellation (PIC) group decoding strategy/scheme for linear dispersive spacetime block codes (STBC) and a design criterion for the codes to achieve full diversity when the PIC group decoding is used at the receiver. A PIC group decoding decodes the symbols embedded in an STBC by dividing them into several groups and decoding each group separately after a linear PIC operation is implemented. It can be viewed as an intermediate decoding between the maximum likelihood (ML) receiver that decodes all the embedded symbols together, i.e., all the embedded symbols are in a single group, and the zeroforcing (ZF) receiver that decodes all the embedded symbols separately and independently, i.e., each group has and only has one embedded symbol, after the ZF operation is implemented. The PIC group decoding provides a framework to adjust the complexityperformance tradeoff by choosing the sizes of the information symbol groups. Our proposed design criterion (group independence) for the PIC group decoding to achieve full diversity is an intermediate condition between the loosest ML full rank criterion of codewords and the strongest ZF linear independence condition of the column vectors in the equivalent channel matrix. We also propose asymptotic optimal (AO) group decoding algorithm which is an intermediate decoding between the MMSE decoding algorithm and the ML decoding algorithm. The design criterion for the PIC group decoding can be applied to the AO group decoding algorithm because of its asymptotic optimality. It is wellknown that the symbol rate for a full rank linear STBC can be full, i.e., nt, for nt transmit antennas. It has been recently shown that its rate is upper bounded by 1 if a code achieves full diversity with a linear receiver. The intermediate criterion proposed in this paper provides the possibility for codes of rates between nt and 1 that achieve full diversity with the PIC group decoding. This therefore provides a complexityperformancerate tradeoff. Some design examples are given.
Spacetime block codes achieving full diversity with linear receivers
 IEEE TRANS. INFORM. THEORY
, 2008
"... In most of the existing space–time code designs, achieving full diversity is based on maximumlikelihood (ML) decoding at the receiver that is usually computationally expensive and may not have soft outputs. Recently, Zhang–Liu–Wong introduced Toeplitz codes and showed that Toeplitz codes achieve f ..."
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Cited by 16 (5 self)
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In most of the existing space–time code designs, achieving full diversity is based on maximumlikelihood (ML) decoding at the receiver that is usually computationally expensive and may not have soft outputs. Recently, Zhang–Liu–Wong introduced Toeplitz codes and showed that Toeplitz codes achieve full diversity when a linear receiver, zeroforcing (ZF) or minimum mean square error (MMSE) receiver, is used. Motivated from Zhang–Liu–Wong’s results on Toeplitz codes, in this paper, we propose a design criterion for space–time block codes (STBC), in which information symbols and their complex conjugates are linearly embedded, to achieve full diversity when ZF or MMSE receiver is used. The (complex) orthogonal STBC (OSTBC) satisfy the criterion as one may expect. We also show that the symbol rates of STBC under this criterion are upper bounded by 1. Subsequently, we propose a novel family of STBC that satisfy the criterion and thus achieve full diversity with ZF or MMSE receiver. Our newly proposed STBC are constructed by overlapping the 2 2 2 Alamouti code and hence named overlapped Alamouti codes in this paper. The new codes are close to orthogonal and their symbol rates can approach 1 for any number of transmit antennas. Simulation results show that overlapped Alamouti codes significantly outperform Toeplitz codes for all numbers of transmit antennas and also outperform OSTBC when the number of transmit antennas is above 4.
MIMO diversity in the presence of double scattering
 IEEE Trans. Inform. Theory
"... Abstract—The potential benefits of multipleantenna systems may be limited by two types of channel degradations—rank deficiency and spatial fading correlation of the channel. In this paper, we assess the effects of these degradations on the diversity performance of multipleinput multipleoutput (MI ..."
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Cited by 16 (4 self)
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Abstract—The potential benefits of multipleantenna systems may be limited by two types of channel degradations—rank deficiency and spatial fading correlation of the channel. In this paper, we assess the effects of these degradations on the diversity performance of multipleinput multipleoutput (MIMO) systems, with an emphasis on orthogonal space–time block codes (OSTBC), in terms of the symbol error probability (SEP), the effective fading figure (EFF), and the capacity at low signaltonoise ratio (SNR). In particular, we consider a general family of MIMO channels known as doublescattering channels—i.e., Rayleigh product MIMO channels—which encompasses a variety of propagation environments from independent and identically distributed (i.i.d.) Rayleigh to degenerate keyhole or pinhole cases by embracing both rankdeficient and spatial correlation effects. It is shown that a MIMO system with transmit and receive antennas achieves the diversity of order
Highrate fulldiversity spacetimefrequency codes for MIMO multipath blockfading channels
 in Proc. of the 48th Annual IEEE Global Telecommunications Conference (Globecom
, 2007
"... Abstract—A systematic design of highrate fulldiversity space–time–frequency (STF) codes is proposed for multipleinput multipleoutput frequencyselective blockfading channels. It is shown that the proposed STF codes can achieve rate w � and fulldiversity w�w �w˜v, i.e., the product of the numbe ..."
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Cited by 14 (1 self)
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Abstract—A systematic design of highrate fulldiversity space–time–frequency (STF) codes is proposed for multipleinput multipleoutput frequencyselective blockfading channels. It is shown that the proposed STF codes can achieve rate w � and fulldiversity w�w �w˜v, i.e., the product of the number of transmit antennas w�, receive antennas w�, fading blocks w˜, and channel taps v. The proposed STF codes are constructed from a layered algebraic design, where each layer of algebraic coded symbols are parsed into different transmit antennas, orthogonal frequencydivision multiplexing tones, and fading blocks without rate loss. Simulation results show that the proposed STF codes achieve higher diversity gain in blockfading channels than some typical space–frequency codes. Index Terms—Blockfading channels, multipleinput multipleoutput (MIMO) systems, signal space diversity, spacefrequency (SF) codes, space–time (ST) codes, space–time–frequency (STF) codes. I.
A systematic design of spacetime block codes achieving fulldiversity with partial interference cancelation group decoding
 Proc. Globecom 2009
"... A partial interference cancellation (PIC) group decoding based spacetime block code (STBC) design criterion was recently proposed by Guo and Xia, where the decoding complexity and the code rate tradeoff is dealt when the full diversity is achieved. In this paper, a systematic design of STBC is pro ..."
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Cited by 13 (2 self)
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A partial interference cancellation (PIC) group decoding based spacetime block code (STBC) design criterion was recently proposed by Guo and Xia, where the decoding complexity and the code rate tradeoff is dealt when the full diversity is achieved. In this paper, a systematic design of STBC is proposed for any number of transmit antennas that can obtain full diversity when a PIC group decoding (with a particular grouping scheme) is applied at receiver. The proposed STBC are designed from multiple diagonal layers and each layer is composed of a fixed number of coded symbols which are encoded from a cyclotomic lattice design. With the PIC group decoding and an appropriate grouping scheme for the decoding, the proposed STBC are shown to obtain the same diversity gain as the ML decoding, but have a much less decoding complexity compared to the ML decoding. Moreover, the code rate of the proposed STBC can be up to full, i.e., M symbols per channel use for an MIMO system with M transmit antennas when the codeword length is sufficiently large. Some code design examples are given from the systematic code design approach. Simulation results show that the newly proposed STBC can obtain full diversity over Rayleigh fading channels and outperform some existing codes given the same bandwidth efficiency.
Singlesymbol ML decodable distributed STBCs for partiallycoherent cooperative networks,” submitted to
 IEEE Trans. Inform. Theory
, 2007
"... Abstract—Spacetime block codes (STBCs) that are singlesymbol decodable (SSD) in a colocated multiple antenna setting need not be SSD in a distributed cooperative communication setting. A relay network with N relays and a single sourcedestination pair is called a partiallycoherent relay channel ..."
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Cited by 12 (10 self)
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Abstract—Spacetime block codes (STBCs) that are singlesymbol decodable (SSD) in a colocated multiple antenna setting need not be SSD in a distributed cooperative communication setting. A relay network with N relays and a single sourcedestination pair is called a partiallycoherent 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 sourcetorelay channels. In this paper, first, a new set of necessary and sufficient conditions for a STBC to be SSD for colocated 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 colocated MIMO channel does not satisfy the additional conditions for the code to be SSD for a PCRC, singlesymbol decoding of it in a PCRC gives fulldiversity and only coding gain is lost.
Systemetic and optimal cyclotomic lattices and diagonal spacetime block code designs
 IEEE Trans. Inform. Theory
, 2004
"... In this correspondence, a new and systematic design of cyclotomic lattices with full diversity is proposed by using some algebraic number theory. This design provides innitely many full diversity cyclotomic lattices for a given lattice size. Based on the packing theory and the concrete form of the ..."
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Cited by 11 (6 self)
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In this correspondence, a new and systematic design of cyclotomic lattices with full diversity is proposed by using some algebraic number theory. This design provides innitely many full diversity cyclotomic lattices for a given lattice size. Based on the packing theory and the concrete form of the design, optimal cyclotomic lattices are presented by minimizing the mean transmission signal power for a given minimum (diversity) product (or equivalently maximizing the minimum product for a given mean transmission signal power). The newly proposed cyclotomic lattices can be applied to both spacetime code designs for multiantenna systems and linear precode design for signal space diversity in single antenna systems over fast Rayleigh fading channels. Although there are some cyclotomic lattices/spacetime codes existed in the literature, most of them are not optimal.