## Universal Space-Time Coding (2003)

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Venue: | IEEE Trans. Inform. Theory |

Citations: | 122 - 6 self |

### BibTeX

@ARTICLE{Gamal03universalspace-time,

author = {Hesham El Gamal and Mohamed Oussama Damen},

title = {Universal Space-Time Coding},

journal = {IEEE Trans. Inform. Theory},

year = {2003},

volume = {49},

pages = {1097--1119}

}

### Years of Citing Articles

### OpenURL

### Abstract

A universal framework is developed for constructing full-rate and full-diversity coherent space--time codes for systems with arbitrary numbers of transmit and receive antennas. The proposed framework combines space--time layering concepts with algebraic component codes optimized for single-input--single-output (SISO) channels. Each component code is assigned to a "thread" in the space--time matrix, allowing it thus full access to the channel spatial diversity in the absence of the other threads. Diophantine approximation theory is then used in order to make the different threads "transparent" to each other. Within this framework, a special class of signals which uses algebraic number-theoretic constellations as component codes is thoroughly investigated. The lattice structure of the proposed number-theoretic codes along with their minimal delay allow for polynomial complexity maximum-likelihood (ML) decoding using algorithms from lattice theory. Combining the design framework with the Cayley transform allows to construct full diversity differential and noncoherent space--time codes. The proposed framework subsumes many of the existing codes in the literature, extends naturally to time-selective and frequency -selective channels, and allows for more flexibility in the tradeoff between power efficiency, bandwidth efficiency, and receiver complexity. Simulation results that demonstrate the significant gains offered by the proposed codes are presented in certain representative scenarios.

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Citation Context ...time codes in quasi-static fading channels [4], [5]. Subsequent works resulted in new trellis and graphical space–time codes that exhibit better coding advantages [6]–[16], new block space–time =-=codes [17]–[-=-22], and extensions to more realistic frequency-selective and time-selective channels [23]–[30]. Despite this recent progress, Manuscript received January 2, 2002; revised November 19, 2002. The mat... |

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Citation Context ...nput–multiple-output (MIMO) systems, number theory. I. INTRODUCTION TAROKH et al. coined the term “space–time codes” to describe the two-dimensional signals used in multiple transmit antennas =-=systems [4]. -=-In the coherent scenario, where the channel state information (CSI) is available a priori only at the receiver, Guey et al. and Tarokh et al. derived the design criteria for full diversity space–tim... |

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Citation Context ... the layered space–time architectures in [32] achieve high transmission rates with low complexity receivers at the expense of reduced diversity advantages. Finally, the orthogonal space–time codes=-= in [18] and-=- the diagonal algebraic space–time (DAST) codes in [19]–[21] achieve full diversity and allow for a low-complexity receiver, but entail a significant loss in the transmission rates, in general. On... |

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Citation Context ...erent space–time signals (e.g., [48]). Two approaches for space–time signal design in this scenario have been investigated. In the first approach, noncoherent space–time codes have been proposed=-= [49]–[51]-=-. These codes assume that the channel is fixed over only one matrix symbol duration and can exploit the spatial diversity without the need of any training symbols. The second approach extends differen... |

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Citation Context ...thers (each thread will lie in a different algebraic subspace). It is also worth noting that a suitable class of SISO codes satisfying Theorem 4 contains the codes optimized for block-fading channels =-=[25]. Th-=-is is because by exploiting all the degrees of freedom in the MIMO channel, a “thread” transforms the quasi-static MIMO fading channel into a single-input multiple-output block-fading channel. Not... |

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Citation Context ...transmission rates with low complexity receivers at the expense of reduced diversity advantages. Finally, the orthogonal space–time codes in [18] and the diagonal algebraic space–time (DAST) codes=-= in [19]–[-=-21] achieve full diversity and allow for a low-complexity receiver, but entail a significant loss in the transmission rates, in general. Only few sporadic examples of space–time codes are known in t... |

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Citation Context ...scussed in the next section. A DAST code is obtained by rotating an -dimensional (i.e., ) information symbol vector by an rotation , which maximizes the associated minimum product distance defined as =-=[36]-=- where belong to the multidimensional constellation considered (QAM or PAM). The rotation matrix (complex or real) is constructed on an algebraic number field with an algebraic number of degree . In t... |

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Citation Context ...–time coding have focused on systems with relatively small numbers of transmit antennas and low data rates [52], [53]. More recently, a novel approach based on the Cayley transform have been propose=-=d [54]-=-. The so-called Cayley differential (CD) codes allow for high transmission rates with reasonable receiver complexity. The proposed CD codes, however, fail to achieve full spatial diversity [54]. In th... |

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Citation Context ...codes in quasi-static fading channels [4], [5]. Subsequent works resulted in new trellis and graphical space–time codes that exhibit better coding advantages [6]–[16], new block space–time codes=-= [17]–[22], -=-and extensions to more realistic frequency-selective and time-selective channels [23]–[30]. Despite this recent progress, Manuscript received January 2, 2002; revised November 19, 2002. The material... |

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Citation Context ...finition 1: The information loss of a TAST code is given by the difference between the ergodic capacity of the equivalent uncoded system in (12) and the ergodic capacity of the original channel [31], =-=[45]-=-. From (12), the ergodic capacity of symmetric TAST precoded system with transmit and receive antennas is given by [31] (27) where is the TAST precoder, is the covariance matrix of the information sym... |

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Citation Context ...HEORY, VOL. 49, NO. 5, MAY 2003 Fig. 9. The performances of the differential TAST code „ and the differential code by Hassibi and Hochwald. real rotation [38] and , 13 and the corresponding code fro=-=m [57]-=- when using a 4-QAM constellation, at the same rate and number of transmit and receive antennas. 14 Here again, one notes the gain offered by the TAST code. In addition, and as in the preceding figure... |

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Citation Context ... the threads (e.g., one refers to the first thread). frequency-division multiplexing (OFDM) front end(s) such that the channel seen by the TAST code can be well approximated by the block-fading model =-=[26]. -=-The previous TAST construction can then be used as a full diversity space–frequency code. V. DIFFERENTIAL AND NONCOHERENT TAST CODES: (N-CSI) Here, we suppose that neither the transmitter nor the re... |

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Citation Context ...6 Suboptimal detectors based on the turbo principle suitable for large array sizes will be considered in a separate paper.s1102 IEEE TRANSACTIONS ON INFORMATION THEORY, VOL. 49, NO. 5, MAY 2003 [41], =-=[43]. Th-=-e generalized sphere decoder can be implemented via the quadratic-residue (QR) decomposition of the equivalent channel matrix and has an additional exponential complexity in “ ” [41]. This observa... |

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Citation Context ...ve a local optima of the coding gain for a 4-QAM constellation. 14 A typographical error in the SNR scaling in the corresponding figure in [57] was corrected after consultation with the first author. =-=[55] 1-=-5 at a rate of 2 bits per channel use. Both schemes have comparable performances (according to the authors’ knowledge, the code in [55] currently represents the state of the art). In addition, the T... |

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Citation Context ...riteria for full diversity space–time codes in quasi-static fading channels [4], [5]. Subsequent works resulted in new trellis and graphical space–time codes that exhibit better coding advantages =-=[6]–[16], new -=-block space–time codes [17]–[22], and extensions to more realistic frequency-selective and time-selective channels [23]–[30]. Despite this recent progress, Manuscript received January 2, 2002; r... |

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Citation Context ...of space–time codes are known in the literature to achieve full rate and full diversity with a polynomial complexity receiver; for , with -quadrature amplitude modulation (QAM) constellation in [34]=-=, [33], an-=-d for with all QAM and pulse amplitude modulation (PAM) constellations in [22]. In this paper, we develop a universal framework for constructing multiple-input–multiple-output (MIMO) space–time co... |

12 |
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Citation Context ...ion symbols of the threads. The received signal in (12) represents an uncoded system with a new channel matrix with equations and unknowns. This motivates ML decoding using the sphere decoder 6 [34], =-=[41]-=-. The sphere decoder computes the ML metric over all constellation points enclosed in a sphere of a given radius . Finding the closest constellation point to the received signal is done by enumerating... |

12 |
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(Show Context)
Citation Context ...ystems in the noncoherent scenario if the channel coherence time is not very small (e.g., [3]). Follow-up works have investigated the signal design criterion for noncoherent space–time signals (e.g.=-=, [48]). Two-=- approaches for space–time signal design in this scenario have been investigated. In the first approach, noncoherent space–time codes have been proposed [49]–[51]. These codes assume that the ch... |

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