## Systematic design of unitary space-time constellations (2000)

### Cached

### Download Links

- [www.ece.utexas.edu]
- [mars.bell-labs.com]
- DBLP

### Other Repositories/Bibliography

Venue: | IEEE TRANS. INFORM. THEORY |

Citations: | 154 - 9 self |

### BibTeX

@ARTICLE{Hochwald00systematicdesign,

author = {Bertrand M. Hochwald and Thomas L. Marzetta and Thomas J. Richardson and Wim Sweldens and Rüdiger Urbanke},

title = {Systematic design of unitary space-time constellations},

journal = {IEEE TRANS. INFORM. THEORY},

year = {2000},

volume = {46},

number = {6},

pages = {1962--1973}

}

### Years of Citing Articles

### OpenURL

### Abstract

We propose a systematic method for creating constellations of unitary space–time signals for multiple-antenna communication links. Unitary space–time signals, which are orthonormal in time across the antennas, have been shown to be well-tailored to a Rayleigh fading channel where neither the transmitter nor the receiver knows the fading coefficients. The signals can achieve low probability of error by exploiting multiple-antenna diversity. Because the fading coefficients are not known, the criterion for creating and evaluating the constellation is nonstandard and differs markedly from the familiar maximum-Euclidean-distance norm. Our construction begins with the first signal in the constellation—an oblong complex-valued matrix whose columns are orthonormal—and systematically produces the remaining signals by successively rotating this signal in a high-dimensional complex space. This construction easily produces large constellations of high-dimensional signals. We demonstrate its efficacy through examples involving one, two, and three transmitter antennas.

### Citations

1965 | Matrix Computations - Golub, Loan - 1996 |

1838 | Capacity of multi-antenna Gaussian channels
- Telatar
- 1999
(Show Context)
Citation Context ...roduction Recent theoretical treatments have shown that communication systems that employ multiple antennas can have very high channel capacities, especially in Rayleigh flat-fading environments [5], =-=[16]-=-, [9]. In [5], a constructive approach to achieving some of this capacity is proposed under the assumption that the receiver knows the complex-valued Rayleigh fading coefficients. Under the same assum... |

1249 | Space–time codes for high data rate wireless communications: Performance criterion and code construction
- Tarokh, Seshadri, et al.
- 1998
(Show Context)
Citation Context ...In [5], a constructive approach to achieving some of this capacity is proposed under the assumption that the receiver knows the complex-valued Rayleigh fading coefficients. Under the same assumption, =-=[14]-=- presents a trellisbased approach for designing space-time codes, and [15] gives a space-time signaling method based on orthogonal designs. However, the known-channel assumption may not be realistic i... |

1006 | Space–time block codes from orthogonal designs
- Tarokh, Jafarkhani, et al.
- 1999
(Show Context)
Citation Context ...osed under the assumption that the receiver knows the complex-valued Rayleigh fading coefficients. Under the same assumption, [14] presents a trellisbased approach for designing space-time codes, and =-=[15]-=- gives a space-time signaling method based on orthogonal designs. However, the known-channel assumption may not be realistic in a rapidly changing fading environment or with a large number of transmit... |

951 |
Layered space–time architecture for wireless communications in a fading environment when using multi-element antennas
- Foschini
- 1996
(Show Context)
Citation Context ...1 Introduction Recent theoretical treatments have shown that communication systems that employ multiple antennas can have very high channel capacities, especially in Rayleigh flat-fading environments =-=[5]-=-, [16], [9]. In [5], a constructive approach to achieving some of this capacity is proposed under the assumption that the receiver knows the complex-valued Rayleigh fading coefficients. Under the same... |

373 | Capacity of a mobile multipleantenna communication link in Rayleigh flat fading
- Marzetta, Hochwald
- 1999
(Show Context)
Citation Context ...ion Recent theoretical treatments have shown that communication systems that employ multiple antennas can have very high channel capacities, especially in Rayleigh flat-fading environments [5], [16], =-=[9]-=-. In [5], a constructive approach to achieving some of this capacity is proposed under the assumption that the receiver knows the complex-valued Rayleigh fading coefficients. Under the same assumption... |

299 |
Information theoretic considerations for cellular mobile radio
- Ozaroq, Shamai, et al.
- 1994
(Show Context)
Citation Context ...9] for more details. We assume that the fading coefficients change to new independent realizations every T # 1 symbol periods. This piecewise constant fading process (also called a block fading model =-=[12, 2]-=-) mimics, in a tractable manner, the approximate coherence interval of a continuously fading process. Furthermore, it is 2 h MN h 2N h 1N 11 2 t s 1 t h h 1/2 M) (r/ 1/2 M) (r/ (r/ 22 h 12 h M1 1/2 M)... |

264 |
Modulation Theory: Part I
- Detection
- 1968
(Show Context)
Citation Context ...s that are distributed as , while the GLRT interpretation is less restrictive because it does not assume anything about the statistics of the propagation matrix. Built into the philosophy of the GLRT =-=[17]-=- is the notion that when the correct decision is made the associated ML estimate is good. With this in mind, our case for using unitary space–time signals is further strengthened by the fact that thes... |

255 |
A class of nonharmonic Fourier series
- Duffin, C
- 1952
(Show Context)
Citation Context ...rm an overcomplete or linear dependent system. Overcomplete representations are becoming increasingly popular in signal representation and are often studied using the mathematical technique of frames =-=[4]-=-. Even though there is no immediate reason why frames would form good constellations, we draw inspiration from existing methods for building frames. We say that a collection of L vectors # # in a T di... |

240 | Unitary space-time modulation for multiple-antenna communications in rayleigh at fading - Hochwald, Marzetta - 2000 |

91 |
Shitz), “Fading channels: Information-theoretic and communications aspects
- Biglieri, Proakis, et al.
- 1998
(Show Context)
Citation Context ...9] for more details. We assume that the fading coefficients change to new independent realizations every symbol periods. This piecewise-constant fading process (also called a block-fading model [12], =-=[2]-=-) mimics, in a tractable manner, the approximate coherence interval of a continuously fading process. Furthermore, it is an accurate representation of many time-division multipleaccess (TDMA), frequen... |

86 | Packing lines, planes, etc.: packings in Grassmannian spaces, Experiment
- Conway, Hardin, et al.
- 1996
(Show Context)
Citation Context ...n space. Some examples of packings 1 The performance of a given constellation always improves with increasing N . For the remainder of the paper we set N = 1. 7 in real Grasmannian space are given in =-=[3]-=-. The design criterion of minimizing # is markedly different from the familiar maximum-Euclideandistance criterion, and it arises entirely because the fading coefficients are unknown to the receiver. ... |

75 | BLAST training: Estimating channel characteristics for high capacity space–time wireless
- Marzetta
- 1999
(Show Context)
Citation Context ...ade the associated ML estimate H # is good. With this in mind, our case for using unitary space-time signals is further strengthened by the fact that these signals constitute optimal training signals =-=[13, 8]-=- for learning H . Specifically, if a known signal is transmitted from which the receiver obtains an ML estimate for H , the energy-constrained signal that minimizes the total error variance is a unita... |

62 |
Packing lines, planes, etc
- Conway, Hardin, et al.
- 1996
(Show Context)
Citation Context ...subspaces and for ( ) is precisely . This shows that our design problem is related to so-called packings in complex Grasmannian space. Some examples of packings in real Grasmannian space are given in =-=[3]-=-. The design criterion of minimizing is markedly different from the familiar maximum-Euclidean-distance criterion, and it arises entirely because the fading coefficients are unknown to the receiver. B... |

26 |
Pre-frame operators, Besselian frames, and near-Riesz bases in Hilbert spaces
- Holub
- 1994
(Show Context)
Citation Context ... use a well-known result that any tight frame with L vectors in T dimensions can be seen as the projection into a T dimensional space of an orthogonal basis in L dimensions and vice versa, see, e.g., =-=[7]-=-. Balan and Daubechies construct tight frames by projecting an L dimensional Discrete Fourier Transform (DFT) basis onto a T dimensional space [1]. The projection simply retains the first T components... |

8 |
Shitz), "Fading Channels: Information-Theoretic and Communications Aspects
- Biglieri, Proakis, et al.
- 1998
(Show Context)
Citation Context ...9] for more details. We assume that the fading coefficients change to new independent realizations every T # 1 symbol periods. This piecewise constant fading process (also called a block fading model =-=[12, 2]-=-) mimics, in a tractable manner, the approximate coherence interval of a continuously fading process. Furthermore, it is 2 h MN h 2N h 1N 11 2 t s 1 t h h 1/2 M) (r/ 1/2 M) (r/ (r/ 22 h 12 h M1 1/2 M)... |

2 |
Application of orthogonal codes to the calibration of active phased array antennas for communication satellites
- Silverstein
- 1997
(Show Context)
Citation Context ...ade the associated ML estimate H # is good. With this in mind, our case for using unitary space-time signals is further strengthened by the fact that these signals constitute optimal training signals =-=[13, 8]-=- for learning H . Specifically, if a known signal is transmitted from which the receiver obtains an ML estimate for H , the energy-constrained signal that minimizes the total error variance is a unita... |

1 |
personal communication
- Balan, Daubechies
- 1998
(Show Context)
Citation Context ...onal basis in L dimensions and vice versa, see, e.g., [7]. Balan and Daubechies construct tight frames by projecting an L dimensional Discrete Fourier Transform (DFT) basis onto a T dimensional space =-=[1]-=-. The projection simply retains the first T components of the L dimensional vectors. Inspired by this construction, we propose the one antenna constellation # # = 1 # T # # # # # # # # # # # # # 1 e i... |