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Proceedings ArticleDOI

Low complexity essentially maximum likelihood decoding of perfect space-time block codes

TL;DR: A reduced complexity algorithm for 3 × 3 perfect STBC which gives essentially maximum likelihood (ML) performance and which can be extended to otherperfect STBCs.
Abstract: Perfect space-time block codes (STBCs) were first introduced by Oggier et al. to have full rate, full diversity and non-vanishing determinant. A maximum likelihood decoder based on the sphere decoder has been used for efficient decoding of perfect STBCs. However the worst-case complexity for the sphere decoder is an exhaustive search. In this paper we present a reduced complexity algorithm for 3 × 3 perfect STBC which gives essentially maximum likelihood (ML) performance and which can be extended to other perfect STBC. The algorithm is based on the conditional maximization of the likelihood function with respect to one of the set of signal points given another. There are a number of choices for which signal points to condition on and the underlying structure of the code guarantees that one of the choices is good with high probability. Furthermore, the approach can be integrated with the sphere decoding algorithm with worst case complexity corresponding exactly to that of our algorithm.
Citations
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Journal ArticleDOI
TL;DR: This paper presents a simple algorithm with quadratic complexity for decoding the Golden code that can be employed by mobile terminals with either one or two receive antennas, that is resilient to near singularity of the channel matrix, and that gives essentially maximum likelihood (ML) performance.
Abstract: The Golden code is a full-rate full-diversity space-time code which has been incorporated in the IEEE 802.16 (WiMAX) standard. The worst case complexity of a tree-based sphere decoder for a square QAM constellation is O(N3), where N is the size of the underlying QAM constellation; the worst case will dominate average decoding complexity on any channel with a significant line of sight component. In this paper, we present a simple algorithm with quadratic complexity for decoding the Golden code that can be employed by mobile terminals with either one or two receive antennas, that is resilient to near singularity of the channel matrix, and that gives essentially maximum likelihood (ML) performance. Dual use is an advantage, since there will likely be some IEEE 802.16 mobile terminals with one receive antenna and some with two antennas. The key to the quadratic algorithm is a maximization of the likelihood function with respect to one of the pair of signal points conditioned on the other. This choice is made by comparing the determinants of two covariance matrices, and the underlying geometry of the Golden code guarantees that one of these choices is good with high probability.

61 citations

Journal ArticleDOI
TL;DR: A new code is presented that tests commonly accepted design principles and for which decoding by conditional optimization is both fast and ML, and shows that it is possible to give up on cubic shaping without compromising code performance or decoding complexity.
Abstract: This paper focuses on conditional optimization as a decoding primitive for high rate space-time codes that are obtained by multiplexing in the spatial and code domains. The approach is a crystallization of the work of Hottinen which applies to space-time codes that are assisted by quasi-orthogonality. It is independent of implementation and is more general in that it can be applied to space-time codes such as the Golden Code and perfect space-time block codes, that are not assisted by quasi-orthogonality, to derive fast decoders with essentially maximum likelihood (ML) performance. The conditions under which conditional optimization leads to reduced complexity ML decoding are captured in terms of the induced channel at the receiver. These conditions are then translated back to the transmission domain leading to codes that are constructed by multiplexing orthogonal designs. The methods are applied to several block space-time codes obtained by multiplexing Alamouti blocks where it leads to ML decoding with complexity O(N 2) where N is the size of the underlying QAM signal constellation. A new code is presented that tests commonly accepted design principles and for which decoding by conditional optimization is both fast and ML. The two design principles for perfect space-time codes are nonvanishing determinant of pairwise differences and cubic shaping, and it is cubic shaping that restricts the possible multiplexing structures. The new code shows that it is possible to give up on cubic shaping without compromising code performance or decoding complexity.

56 citations

Journal ArticleDOI
TL;DR: This treatise proposes a novel family of asynchronous cooperative linear dispersion codes (ACLDCs), which is capable of maintaining full diversity in cooperative scenarios, even in the presence of asynchronous reception.
Abstract: In this treatise, we propose a novel family of asynchronous cooperative linear dispersion codes (ACLDCs), which is capable of maintaining full diversity in cooperative scenarios, even in the presence of asynchronous reception. The linear dispersion structure is employed to accommodate the dynamic topology of cooperative networks, as well as to achieve higher throughput than conventional space-time codes based on orthogonal designs. By introducing guard intervals and block encoding/decoding techniques, the interference signals caused by asynchronous reception can be exploited rather than discarded.

24 citations

Journal ArticleDOI
TL;DR: In this article, the authors introduced two new low complexity decoders for Space-Time Block Codes (STBCs)-the Adaptive Conditional Zero-Forcing (ACZF) decoder and the ACZF decoder with successive interference cancellation, which include as a special case the decoding technique of Sirianunpiboon, Howard and Calderbank.
Abstract: A low complexity, essentially-ML decoding technique for the Golden code and the three antenna Perfect code was introduced by Sirianunpiboon, Howard and Calderbank. Though no theoretical analysis of the decoder was given, the simulations showed that this decoding technique has almost maximum-likelihood (ML) performance. Inspired by this technique, in this paper we introduce two new low complexity decoders for Space-Time Block Codes (STBCs)-the Adaptive Conditional Zero-Forcing (ACZF) decoder and the ACZF decoder with successive interference cancellation (ACZF-SIC), which include as a special case the decoding technique of Sirianunpiboon We show that both ACZF and ACZF-SIC decoders are capable of achieving full-diversity, and we give a set of sufficient conditions for an STBC to give full-diversity with these decoders. We then show that the Golden code, the three and four antenna Perfect codes, the three antenna Threaded Algebraic Space-Time code and the four antenna rate 2 code of Srinath and Rajan are all full-diversity ACZF/ACZF-SIC decodable with complexity strictly less than that of their ML decoders. Simulations show that the proposed decoding method performs identical to ML decoding for all these five codes. These STBCs along with the proposed decoding algorithm have the least decoding complexity and best error performance among all known codes for Nt ≤ 4 transmit antennas. We further provide a lower bound on the complexity of full-diversity ACZF/ACZF-SIC decoding. All the five codes listed above achieve this lower bound and hence are optimal in terms of minimizing the ACZF/ACZF-SIC decoding complexity. Both ACZF and ACZF-SIC decoders are amenable to sphere decoding implementation.

10 citations

Proceedings ArticleDOI
01 Sep 2009
TL;DR: It is shown that, in LOS environments, the capacity of the channel is invariant under arbitrary rotations of the transmit and/or receive antennas about their centres, and the performance is stable as the propagation environment varies from rich scattering to pure LOS.
Abstract: Multiple-Input Multiple-Output (MIMO) function- ality has been shown to dramatically increase the capacity of wireless communication systems when the environment provides rich multipath scattering In a predominantly Line-of-Sight (LOS) environment, the loss of diversity reduces the potential gain considerably This can be remedied in part by the use of dual-polarized antennas, which increases the rank of the wireless channel and introduces diversity, while minimizing the antenna's form factor However the performance of a dual- polarized antenna is still degraded by antenna rotations that are typical of mobile terminal operation This paper presents a solution which uses a triad antenna at the transmitter and a triad at the receiver, to provide a 8-10 dB gain over the baseline dual-polarized system A triad is composed of three orthogonal dipoles oriented in perpendicular directions A triad antenna can generate an arbitrary oscillating dipole moment at the transmitter and consequently an arbitrary polarized electric field at the receiver, subject only to the constraints imposed by the physics of the Electromagnetic (EM) fi eld We show that, in LOS environments, the capacity of the channel is invariant under arbitrary rotations of the transmit and/or receive antennas about their centres Simulation results show that the performance is stable as the propagation environment varies from rich scattering to pure LOS A full rate 3 × 3 Space-Time Block Code (STBC) is proposed for the triad system that is designed for low complexity decoding

7 citations


Cites background from "Low complexity essentially maximum ..."

  • ...However, this sub-code still provides rate 2 and can be decoded with essentially maximum likelihood performance using an algorithm introduced in [8] with complexity N(3), where N is the size of an underlying signal constellation....

    [...]

References
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Journal ArticleDOI
Siavash Alamouti1
TL;DR: This paper presents a simple two-branch transmit diversity scheme that provides the same diversity order as maximal-ratio receiver combining (MRRC) with one transmit antenna, and two receive antennas.
Abstract: This paper presents a simple two-branch transmit diversity scheme. Using two transmit antennas and one receive antenna the scheme provides the same diversity order as maximal-ratio receiver combining (MRRC) with one transmit antenna, and two receive antennas. It is also shown that the scheme may easily be generalized to two transmit antennas and M receive antennas to provide a diversity order of 2M. The new scheme does not require any bandwidth expansion or any feedback from the receiver to the transmitter and its computation complexity is similar to MRRC.

13,706 citations

Journal ArticleDOI
TL;DR: A generalization of orthogonal designs is shown to provide space-time block codes for both real and complex constellations for any number of transmit antennas and it is shown that many of the codes presented here are optimal in this sense.
Abstract: We introduce space-time block coding, a new paradigm for communication over Rayleigh fading channels using multiple transmit antennas. Data is encoded using a space-time block code and the encoded data is split into n streams which are simultaneously transmitted using n transmit antennas. The received signal at each receive antenna is a linear superposition of the n transmitted signals perturbed by noise. Maximum-likelihood decoding is achieved in a simple way through decoupling of the signals transmitted from different antennas rather than joint detection. This uses the orthogonal structure of the space-time block code and gives a maximum-likelihood decoding algorithm which is based only on linear processing at the receiver. Space-time block codes are designed to achieve the maximum diversity order for a given number of transmit and receive antennas subject to the constraint of having a simple decoding algorithm. The classical mathematical framework of orthogonal designs is applied to construct space-time block codes. It is shown that space-time block codes constructed in this way only exist for few sporadic values of n. Subsequently, a generalization of orthogonal designs is shown to provide space-time block codes for both real and complex constellations for any number of transmit antennas. These codes achieve the maximum possible transmission rate for any number of transmit antennas using any arbitrary real constellation such as PAM. For an arbitrary complex constellation such as PSK and QAM, space-time block codes are designed that achieve 1/2 of the maximum possible transmission rate for any number of transmit antennas. For the specific cases of two, three, and four transmit antennas, space-time block codes are designed that achieve, respectively, all, 3/4, and 3/4 of maximum possible transmission rate using arbitrary complex constellations. The best tradeoff between the decoding delay and the number of transmit antennas is also computed and it is shown that many of the codes presented here are optimal in this sense as well.

7,348 citations


"Low complexity essentially maximum ..." refers methods in this paper

  • ...Orthogonal STBCs (OSTBC) [2] were designed to use more than two transmit antennas....

    [...]

Journal ArticleDOI
TL;DR: In this article, the Golden code for a 2/spl times/2 multiple-input multiple-output (MIMO) system is presented, where the Golden number 1+/spl radic/5/2 is used.
Abstract: In this paper, the Golden code for a 2/spl times/2 multiple-input multiple-output (MIMO) system is presented. This is a full-rate 2/spl times/2 linear dispersion algebraic space-time code with unprecedented performance based on the Golden number 1+/spl radic/5/2.

825 citations

Journal ArticleDOI
TL;DR: The notion of perfect space-time block codes (STBCs) are introduced and algebraic constructions of perfect STBCs for 2, 3, 4, and 6 antennas are presented.
Abstract: In this paper, we introduce the notion of perfect space-time block codes (STBCs). These codes have full-rate, full-diversity, nonvanishing constant minimum determinant for increasing spectral efficiency, uniform average transmitted energy per antenna and good shaping. We present algebraic constructions of perfect STBCs for 2, 3, 4, and 6 antennas

483 citations


"Low complexity essentially maximum ..." refers background in this paper

  • ...The perfect STBC can be decoded with sphere decoder [3], but these suffer from the draw back that when the channel matrix is close to singular, the preprocessing stage of the sphere decoding algorithm yields a plane of possibilities rather than a single initial estimate....

    [...]

  • ...[3] introduced perfect space-time block codes which satisfy all of the following criteria: fullrate, full-diversity, non-vanishing determinant, good shaping and uniform average transmitted energy per antenna....

    [...]

01 Jan 2004

219 citations


"Low complexity essentially maximum ..." refers background in this paper

  • ...The perfect STBC can be decoded with sphere decoder [3], but these suffer from the draw back that when the channel matrix is close to singular, the preprocessing stage of the sphere decoding algorithm yields a plane of possibilities rather than a single initial estimate....

    [...]

  • ...Oggier et al.[3] introduced perfect space-time block codes which satisfy all of the following criteria: fullrate, full-diversity, non-vanishing determinant, good shaping and uniform average transmitted energy per antenna....

    [...]