arXiv subjects

B. Sundar Rajan

Publications and source records attributed to B. Sundar Rajan.

At least 217 records · Page 12Linked to original sources

arXiv2008

Square Complex Orthogonal Designs with no Zero Entry for any $2^m$ Antennas

Space-time block codes from square complex orthogonal designs (SCOD) have been extensively studied and most of the existing SCODs contain large number of zeros. The zeros in the designs result in high peak-to-average power ratio and also impose a severe constraint on hardware implementation of the code while turning off some of the transmitting antennas whenever a zero is transmitted. Recently, SCODs with no zero entry have been constructed for $2^a$ transmit antennas whenever $a+1$ is a power of 2. Though there exists codes for 4 and 16 transmit antennas with no zero entry, there is no general method of construction which gives codes for any number of transmit antennas. In this paper, we construct SCODs for any power of 2 number of transmit antennas having all its entries non-zero. Simulation results show that the codes constructed in this paper outperform the existing codes for the same number of antennas under peak power constraint while performing the same under average power constraint.

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arXiv2008

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 $\frac{2}{N}$ when the relays do not have CSI to 1/2, which is independent of N.

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arXiv2008

Multi-group ML Decodable Collocated and Distributed Space Time Block Codes

In this paper, collocated and distributed space-time block codes (DSTBCs) which admit multi-group maximum likelihood (ML) decoding are studied. First the collocated case is considered and the problem of constructing space-time block codes (STBCs) which optimally tradeoff rate and ML decoding complexity is posed. Recently, sufficient conditions for multi-group ML decodability have been provided in the literature and codes meeting these sufficient conditions were called Clifford Unitary Weight (CUW) STBCs. An algebraic framework based on extended Clifford algebras is proposed to study CUW STBCs and using this framework, the optimal tradeoff between rate and ML decoding complexity of CUW STBCs is obtained for few specific cases. Code constructions meeting this tradeoff optimally are also provided. The paper then focuses on multi-group ML decodable DSTBCs for application in synchronous wireless relay networks and three constructions of four-group ML decodable DSTBCs are provided. Finally, the OFDM based Alamouti space-time coded scheme proposed by Li-Xia for a 2 relay asynchronous relay network is extended to a more general transmission scheme that can achieve full asynchronous cooperative diversity for arbitrary number of relays. It is then shown how differential encoding at the source can be combined with the proposed transmission scheme to arrive at a new transmission scheme that can achieve full cooperative diversity in asynchronous wireless relay networks with no channel information and also no timing error knowledge at the destination node. Four-group decodable DSTBCs applicable in the proposed OFDM based transmission scheme are also given.

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arXiv2008

Leveraging Coherent Distributed Space-Time Codes for Noncoherent Communication in Relay Networks via Training

For point to point multiple input multiple output systems, Dayal-Brehler-Varanasi have proved that training codes achieve the same diversity order as that of the underlying coherent space time block code (STBC) if a simple minimum mean squared error estimate of the channel formed using the training part is employed for coherent detection of the underlying STBC. In this letter, a similar strategy involving a combination of training, channel estimation and detection in conjunction with existing coherent distributed STBCs is proposed for noncoherent communication in AF relay networks. Simulation results show that the proposed simple strategy outperforms distributed differential space-time coding for AF relay networks. Finally, the proposed strategy is extended to asynchronous relay networks using orthogonal frequency division multiplexing.

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arXiv2008

Low ML-Decoding Complexity, Large Coding Gain, Full-Rate, Full-Diversity STBCs for 2 X 2 and 4 X 2 MIMO Systems

This paper (Part of the content of this manuscript has been accepted for presentation in IEEE Globecom 2008, to be held in New Orleans) deals with low maximum likelihood (ML) decoding complexity, full-rate and full-diversity space-time block codes (STBCs), which also offer large coding gain, for the 2 transmit antenna, 2 receive antenna ($2\times 2$) and the 4 transmit antenna, 2 receive antenna ($4\times 2$) MIMO systems. Presently, the best known STBC for the $2\times2$ system is the Golden code and that for the $4\times2$ system is the DjABBA code. Following the approach by Biglieri, Hong and Viterbo, a new STBC is presented in this paper for the $2\times 2$ system. This code matches the Golden code in performance and ML-decoding complexity for square QAM constellations while it has lower ML-decoding complexity with the same performance for non-rectangular QAM constellations. This code is also shown to be \emph{information-lossless} and \emph{diversity-multiplexing gain} (DMG) tradeoff optimal. This design procedure is then extended to the $4\times 2$ system and a code, which outperforms the DjABBA code for QAM constellations with lower ML-decoding complexity, is presented. So far, the Golden code has been reported to have an ML-decoding complexity of the order of $M^4$ for square QAM of size $M$. In this paper, a scheme that reduces its ML-decoding complexity to $M^2\sqrt{M}$ is presented.

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arXiv2008

A Class of Maximal-Rate, Low-PAPR, Non-square Complex Orthogonal Designs

Space-time block codes (STBCs) from non-square complex orthogonal designs are bandwidth efficient when compared with those from square real/complex orthogonal designs. Though there exists rate-1 ROD for any number of transmit antennas, rate-1 complex orthogonal designs (COD) does not exist for more than 2 transmit antennas. Liang (IEEE Trans. Inform. Theory, 2003) and Lu et al (IEEE Trans. Inform. Theory, 2005) have constructed a class of maximal rate non-square CODs where the rate is ${1/2}+\frac{1}{n}$ if number of transmit antennas $n$ is even and ${1/2}+\frac{1}{n+1}$ if $n$ is odd. In this paper, we present a simple construction for maximal rate non-square CODs obtained from square CODs which resembles the construction of rate-1 non-square RODs from square RODs. These designs are shown to be amenable for construction of a class of generalized CODs (called Coordinate-Interleaved Scaled CODs) with low peak-to-average power ratio (PAPR) having the same parameters as the maximal rate codes. Simulation results indicate that these codes perform better than the existing maximal rate codes under peak power constraint while performing the same under average power constraint.

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arXiv2008

Co-ordinate Interleaved Distributed Space-Time Coding for Two-Antenna-Relays Networks

Distributed space time coding for wireless relay networks when the source, the destination and the relays have multiple antennas have been studied by Jing and Hassibi. In this set-up, the transmit and the receive signals at different antennas of the same relay are processed and designed independently, even though the antennas are colocated. In this paper, a wireless relay network with single antenna at the source and the destination and two antennas at each of the R relays is considered. A new class of distributed space time block codes called Co-ordinate Interleaved Distributed Space-Time Codes (CIDSTC) are introduced where, in the first phase, the source transmits a T-length complex vector to all the relays and in the second phase, at each relay, the in-phase and quadrature component vectors of the received complex vectors at the two antennas are interleaved and processed before forwarding them to the destination. Compared to the scheme proposed by Jing-Hassibi, for $T \geq 4R$, while providing the same asymptotic diversity order of 2R, CIDSTC scheme is shown to provide asymptotic coding gain with the cost of negligible increase in the processing complexity at the relays. However, for moderate and large values of P, CIDSTC scheme is shown to provide more diversity than that of the scheme proposed by Jing-Hassibi. CIDSTCs are shown to be fully diverse provided the information symbols take value from an appropriate multi-dimensional signal set.

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arXiv2008

Low-delay, Low-PAPR, High-rate Non-square Complex Orthogonal Designs

The maximal rate for non-square Complex Orthogonal Designs (CODs) with $n$ transmit antennas is ${1/2}+\frac{1}{n}$ if $n$ is even and ${1/2}+\frac{1}{n+1}$ if $n$ is odd, which are close to 1/2 for large values of $n.$ A class of maximal rate non-square CODs have been constructed by Liang (IEEE Trans. Inform. Theory, 2003) and Lu et. al. (IEEE Trans. Inform. Theory, 2005) have shown that the decoding delay of the codes given by Liang, can be reduced by 50% when number of transmit antennas is a multiple of 4. Adams et. al. (IEEE Trans. Inform. Theory, 2007) have shown that the designs of Liang are of minimal-delay for $n$ equal to 1 and 3 modulo 4 and that of Lu et.al. are of minimal delay when $n$ is a multiple of $4.$ However, these minimal delays are large compared to the delays of the rate 1/2 non-square CODs constructed by Tarokh et al (IEEE Trans. Inform. Theory, 1999) from rate-1 real orthogonal designs (RODs). In this paper, we construct a class of rate-1/2 non-square CODs for any $n$ with the decoding delay equal to 50% of that of the delay of the rate-1/2 codes given by Tarokh et al. This is achieved by giving first a general construction of rate-1 square Real Orthogonal Designs (RODs) which includes as special cases the well known constructions of Adams, Lax and Phillips and Geramita and Pullman, and then making use of it to obtain the desired rate-1/2 non-square COD. For the case of 9 transmit antennas, our rate-1/2 COD is shown to be of minimal-delay. The proposed construction results in designs with zero entries which may have high Peak-to-Average Power Ratio (PAPR) and it is shown that by appropriate postmultiplication, a design with no zero entries can be obtained with no change in the code parameters.

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arXiv2008

Square Complex Orthogonal Designs with Low PAPR and Signaling Complexity

Space-Time Block Codes from square complex orthogonal designs (SCOD) have been extensively studied and most of the existing SCODs contain large number of zero. The zeros in the designs result in high peak-to-average power ratio (PAPR) and also impose a severe constraint on hardware implementation of the code when turning off some of the transmitting antennas whenever a zero is transmitted. Recently, rate 1/2 SCODs with no zero entry have been reported for 8 transmit antennas. In this paper, SCODs with no zero entry for $2^a$ transmit antennas whenever $a+1$ is a power of 2, are constructed which includes the 8 transmit antennas case as a special case. More generally, for arbitrary values of $a$, explicit construction of $2^a\times 2^a$ rate $\frac{a+1}{2^a}$ SCODs with the ratio of number of zero entries to the total number of entries equal to $1-\frac{a+1}{2^a}2^{\lfloor log_2(\frac{2^a}{a+1}) \rfloor}$ is reported, whereas for standard known constructions, the ratio is $1-\frac{a+1}{2^a}$. The codes presented do not result in increased signaling complexity. Simulation results show that the codes constructed in this paper outperform the codes using the standard construction under peak power constraint while performing the same under average power constraint.

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arXiv2008

A Non-differential Distributed Space-Time Coding for Partially-Coherent Cooperative Communication

In a distributed space-time coding scheme, based on the relay channel model, the relay nodes co-operate to linearly process the transmitted signal from the source and forward them to the destination such that the signal at the destination appears as a space time block code. Recently, a code design criteria for achieving full diversity in a partially-coherent environment have been proposed along with codes based on differential encoding and decoding techniques. For such a set up, in this paper, a non-differential encoding technique and construction of distributed space time block codes from unitary matrix groups at the source and a set of diagonal unitary matrices for the relays are proposed. It is shown that, the performance of our scheme is independent of the choice of unitary matrices at the relays. When the group is cyclic, a necessary and sufficient condition on the generator of the cyclic group to achieve full diversity and to minimize the pairwise error probability is proved. Various choices on the generator of cyclic group to reduce the ML decoding complexity at the destination is presented. It is also shown that, at the source, if non-cyclic abelian unitary matrix groups are used, then full-diversity can not be obtained. The presented scheme is also robust to failure of any subset of relay nodes.

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arXiv2008

A Low-decoding-complexity, Large coding Gain, Full-rate, Full-diversity STBC for 4 X 2 MIMO System

This paper proposes a low decoding complexity, full-diversity and full-rate space-time block code (STBC) for 4 transmit and 2 receive ($4\times 2$) multiple-input multiple-output (MIMO) systems. For such systems, the best code known is the DjABBA code and recently, Biglieri, Hong and Viterbo have proposed another STBC (BHV code) which has lower decoding complexity than DjABBA but does not have full-diversity like the DjABBA code. The code proposed in this paper has the same decoding complexity as the BHV code for square QAM constellations but has full-diversity as well. Compared to the best code in the DjABBA family of codes, our code has lower decoding complexity, a better coding gain and hence a better error performance as well. Simulation results confirming these are presented.

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arXiv2008

A Low-Complexity, Full-Rate, Full-Diversity 2 X 2 STBC with Golden Code's Coding Gain

This paper presents a low-ML-decoding-complexity, full-rate, full-diversity space-time block code (STBC) for a 2 transmit antenna, 2 receive antenna multiple-input multiple-output (MIMO) system, with coding gain equal to that of the best and well known Golden code for any QAM constellation. Recently, two codes have been proposed (by Paredes, Gershman and Alkhansari and by Sezginer and Sari), which enjoy a lower decoding complexity relative to the Golden code, but have lesser coding gain. The $2\times 2$ STBC presented in this paper has lesser decoding complexity for non-square QAM constellations, compared with that of the Golden code, while having the same decoding complexity for square QAM constellations. Compared with the Paredes-Gershman-Alkhansari and Sezginer-Sari codes, the proposed code has the same decoding complexity for non-rectangular QAM constellations. Simulation results, which compare the codeword error rate (CER) performance, are presented.

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arXiv2008

OFDM based Distributed Space Time Coding for Asynchronous Relay Networks

Recently Li and Xia have proposed a transmission scheme for wireless relay networks based on the Alamouti space time code and orthogonal frequency division multiplexing to combat the effect of timing errors at the relay nodes. This transmission scheme is amazingly simple and achieves a diversity order of two for any number of relays. Motivated by its simplicity, this scheme is extended to a more general transmission scheme that can achieve full cooperative diversity for any number of relays. The conditions on the distributed space time block code (DSTBC) structure that admit its application in the proposed transmission scheme are identified and it is pointed out that the recently proposed full diversity four group decodable DSTBCs from precoded co-ordinate interleaved orthogonal designs and extended Clifford algebras satisfy these conditions. It is then shown how differential encoding at the source can be combined with the proposed transmission scheme to arrive at a new transmission scheme that can achieve full cooperative diversity in asynchronous wireless relay networks with no channel information and also no timing error knowledge at the destination node. Finally, four group decodable distributed differential space time block codes applicable in this new transmission scheme for power of two number of relays are also provided.

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arXiv2008

Large MIMO Detection: A Low-Complexity Detector at High Spectral Efficiencies

We consider large MIMO systems, where by `{\em large}' we mean number of transmit and receive antennas of the order of tens to hundreds. Such large MIMO systems will be of immense interest because of the very high spectral efficiencies possible in such systems. We present a low-complexity detector which achieves uncoded near-exponential diversity performance for hundreds of antennas (i.e., achieves near SISO AWGN performance in a large MIMO fading environment) with an average per-bit complexity of just $O(N_tN_r)$, where $N_t$ and $N_r$ denote the number of transmit and receive antennas, respectively. With an outer turbo code, the proposed detector achieves good coded bit error performance as well. For example, in a 600 transmit and 600 receive antennas V-BLAST system with a high spectral efficiency of 200 bps/Hz (using BPSK and rate-1/3 turbo code), our simulation results show that the proposed detector performs close to within about 4.6 dB from theoretical capacity. We also adopt the proposed detector for the low-complexity decoding of high-rate non-orthogonal space-time block codes (STBC) from division algebras (DA). For example, we have decoded the $16\times 16$ full-rate non-orthogonal STBC from DA using the proposed detector and show that it performs close to within about 5.5 dB of the capacity using 4-QAM and rate-3/4 turbo code at a spectral efficiency of 24 bps/Hz. The practical feasibility of the proposed high-performance low-complexity detector could potentially trigger wide interest in the implementation of large MIMO systems. In large MC-CDMA systems with hundreds of users, the proposed detector is shown to achieve near single-user performance at an average per-bit complexity linear in number of users, which is quite appealing for its use in practical CDMA systems.

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arXiv2007

Maximum-rate, Minimum-Decoding-Complexity STBCs from Clifford Algebras

It is well known that Space-Time Block Codes (STBCs) from orthogonal designs (ODs) are single-symbol decodable/symbol-by-symbol decodable (SSD) and are obtainable from unitary matrix representations of Clifford algebras. However, SSD codes are obtainable from designs that are not orthogonal also. Recently, two such classes of SSD codes have been studied: (i) Coordinate Interleaved Orthogonal Designs (CIODs) and (ii) Minimum-Decoding-Complexity (MDC) STBCs from Quasi-ODs (QODs). Codes from ODs, CIODs and MDC-QODs are mutually non-intersecting classes of codes. The class of CIODs have {\it non-unitary weight matrices} when written as a Linear Dispersion Code (LDC) proposed by Hassibi and Hochwald, whereas several known SSD codes including CODs have {\it unitary weight matrices}. In this paper, we obtain SSD codes with unitary weight matrices (that are not CODs) called Clifford Unitary Weight SSDs (CUW-SSDs) from matrix representations of Clifford algebras. A main result of this paper is the derivation of an achievable upper bound on the rate of any unitary weight SSD code as $\frac{a}{2^{a-1}}$ for $2^a$ antennas which is larger than that of the CODs which is $\frac{a+1}{2^a}$. It is shown that several known classes of SSD codes are CUW-SSD codes and CUW-SSD codes meet this upper bound. Also, for the codes of this paper conditions on the signal sets which ensure full-diversity and expressions for the coding gain are presented. A large class of SSD codes with non-unitary weight matrices are obtained which include CIODs as a proper subclass.

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arXiv2007

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.

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arXiv2007

Distributed Space Time Codes with Low Decoding Complexity for Asynchronous Relay Networks

Recently Li and Xia have proposed a transmission scheme for wireless relay networks based on the Alamouti space time code and orthogonal frequency division multiplexing to combat the effect of timing errors at the relay nodes. This transmission scheme is amazingly simple and achieves a diversity order of two for any number of relays. Motivated by its simplicity, this scheme is extended to a more general transmission scheme that can achieve full cooperative diversity for any number of relays. The conditions on the distributed space time code (DSTC) structure that admit its application in the proposed transmission scheme are identified and it is pointed out that the recently proposed full diversity four group decodable DSTCs from precoded co-ordinate interleaved orthogonal designs and extended Clifford algebras satisfy these conditions. It is then shown how differential encoding at the source can be combined with the proposed transmission scheme to arrive at a new transmission scheme that can achieve full cooperative diversity in asynchronous wireless relay networks with no channel information and also no timing error knowledge at the destination node. Finally, four group decodable distributed differential space time codes applicable in this new transmission scheme for power of two number of relays are also provided.

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arXiv2007

High Rate Single-Symbol ML Decodable Precoded DSTBCs for Cooperative Networks

Distributed Orthogonal Space-Time Block Codes (DOSTBCs) achieving full diversity order and single-symbol ML decodability have been introduced recently by Yi and Kim for cooperative networks and an upperbound on the maximal rate of such codes along with code constructions has been presented. In this paper, we introduce a new class of Distributed STBCs called Semi-orthogonal Precoded Distributed Single-Symbol Decodable STBCs (S-PDSSDC) wherein, the source performs co-ordinate interleaving of information symbols appropriately before transmitting it to all the relays. It is shown that DOSTBCs are a special case of S-PDSSDCs. A special class of S-PDSSDCs having diagonal covariance matrix at the destination is studied and an upperbound on the maximal rate of such codes is derived. The bounds obtained are approximately twice larger than that of the DOSTBCs. A systematic construction of S-PDSSDCs is presented when the number of relays $K \geq 4$. The constructed codes are shown to achieve the upperbound on the rate when $K$ is of the form 0 or 3 modulo 4. For the rest of the values of $K$, the constructed codes are shown to have rates higher than that of DOSTBCs. It is shown that S-PDSSDCs cannot be constructed with any form of linear processing at the relays when the source doesn't perform co-ordinate interleaving of the information symbols. Simulation result shows that S-PDSSDCs have better probability of error performance than that of DOSTBCs.

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