## High-Rate Codes that are Linear in Space and Time (2000)

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Venue: | IEEE Trans. Inform. Theory |

Citations: | 308 - 9 self |

### BibTeX

@ARTICLE{Hassibi00high-ratecodes,

author = {Babak Hassibi and Bertrand Hochwald},

title = {High-Rate Codes that are Linear in Space and Time},

journal = {IEEE Trans. Inform. Theory},

year = {2000},

volume = {48},

pages = {1804--1824}

}

### Years of Citing Articles

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### Abstract

Multiple-antenna systems that operate at high rates require simple yet effective space-time transmission schemes to handle the large traffic volume in real time. At rates of tens of bits/sec/Hz, V-BLAST, where every antenna transmits its own independent substream of data, has been shown to have good performance and simple encoding and decoding. Yet V-BLAST suffers from its inability to work with fewer receive antennas than transmit antennas---this deficiency is especially important for modern cellular systems where a basestation typically has more antennas than the mobile handsets. Furthermore, because V-BLAST transmits independent data streams on its antennas there is no built-in spatial coding to guard against deep fades from any given transmit antenna. On the other hand, there are many previously-proposed space-time codes that have good fading resistance and simple decoding, but these codes generally have poor performance at high data rates or with many antennas. We propose a high-rate coding scheme that can handle any...

### Citations

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Citation Context ...h at high rates will be an important part of future telecommunications systems. One way to get high rates on a scattering-rich wireless channel is to use multiple transmit and/or receive antennas. In =-=[1, 2]-=-, theoretical and experimental evidence demonstrates that channel capacity grows linearly as the number of transmit and receive antennas grow simultaneously. Early uses of multiple transmit antennas i... |

1242 | Spacetime codes for high data rate wireless communication: performance criterion and code construction
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Citation Context ...uence of nulling and cancelling steps. Since then there has been considerable work on a variety of space-time transmission schemes and performance measures [9] such as the space-time trellis codes of =-=[10]-=- and the space-time block codes of [11, 12] for the known channel and [13, 14, 15] for the unknown channel. At very high rates and with a large number of antennas, many of these space-time codes suffe... |

1005 | Spacetime block codes from orthogonal designs
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Citation Context ...Since then there has been considerable work on a variety of space-time transmission schemes and performance measures [9] such as the space-time trellis codes of [10] and the space-time block codes of =-=[11, 12]-=- for the known channel and [13, 14, 15] for the unknown channel. At very high rates and with a large number of antennas, many of these space-time codes suffer from complexity or performance difficulti... |

945 |
Layered space-time architecture for wireless communication in a fading environment when using multi-element antennas
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Citation Context ...h at high rates will be an important part of future telecommunications systems. One way to get high rates on a scattering-rich wireless channel is to use multiple transmit and/or receive antennas. In =-=[1, 2]-=-, theoretical and experimental evidence demonstrates that channel capacity grows linearly as the number of transmit and receive antennas grow simultaneously. Early uses of multiple transmit antennas i... |

297 | How much training is needed in multiple-antenna wireless links
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Citation Context ...ption is reasonable if training or pilot signals are sent to learn the channel, which is then constant for some coherence interval. The coherence interval of the channel should be large compared to M =-=[18]-=-. When the channel is known at the receiver, the resulting channel capacity (often referred to as the perfectknowledgescapacity) is [2, 1] C(ae; M;N) = max Rs0;tr Rs=M E log det i I N + ae M HR s H j ... |

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

235 |
A simple transmitter diversity scheme for wireless communications
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Citation Context ...Since then there has been considerable work on a variety of space-time transmission schemes and performance measures [9] such as the space-time trellis codes of [10] and the space-time block codes of =-=[11, 12]-=- for the known channel and [13, 14, 15] for the unknown channel. At very high rates and with a large number of antennas, many of these space-time codes suffer from complexity or performance difficulti... |

234 |
Signal design for transmitter diversity wireless communication systems over Rayleigh fading channels
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Citation Context ... receiver decodes the substreams using a sequence of nulling and cancelling steps. Since then there has been considerable work on a variety of space-time transmission schemes and performance measures =-=[9]-=- such as the space-time trellis codes of [10] and the space-time block codes of [11, 12] for the known channel and [13, 14, 15] for the unknown channel. At very high rates and with a large number of a... |

233 | Detection algorithm and initial laboratory results using the V-BLAST space-time communication architecture
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Citation Context ...lexity low, linear processing is often preferred [3]. To achieve the high data rates promised in [2], however, new approaches for space-time transmission are needed. One such approach is presented in =-=[7, 8]-=- where a practical scheme, called V-BLAST (Vertical Bell Labs Layered Space-Time), encodes and decodes rates of tens of bits/sec/Hz with eight transmit and twelve receive antennas. The V-BLAST archite... |

217 |
Differential space-time modulation
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Citation Context ...ble work on a variety of space-time transmission schemes and performance measures [9] such as the space-time trellis codes of [10] and the space-time block codes of [11, 12] for the known channel and =-=[13, 14, 15, 16, 17]-=- for the unknown channel. At very high rates and with a large number of antennas, many of these space-time codes suffer from complexity or performance difficulties. The number of states in the trellis... |

173 | Lattice code decoder for space-time codes
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Citation Context ...o encode 5. Can be decoded in a variety of ways including simple linear-algebraic techniques such as: (a) Successive nulling and cancelling (V-BLAST [7], square-root V-BLAST [16]) (b) Sphere decoding =-=[17]-=- 6. Are designed with the numbers of both the transmit and receive antennas in mind 7. Satisfy an information-theoretic optimality criterion - the codes are designed to maximize the mutual information... |

166 | Simplified processing for high spectral efficiency wirelesscommunication employing multi-element arrays - Foschini, Golden, et al. - 1999 |

161 | A differential detection scheme for transmit diversity
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Citation Context ... no longer "full-rate" (see [12]) and therefore generally perform poorly in the maximum mutual information they can achieve, even when N = 1. We give an example of these non-square orthogona=-=l designs [12, 20, 21]-=-. For M = 3, we have, for example, the rate 3 4 orthogonal design S = r 4 3 2 6 6 6 6 6 6 6 6 6 6 4 s 1 s 2 s 3 \Gammas 2 s 1 0 \Gammas 3 0 s 1 0 \Gammas 3 s 2 3 7 7 7 7 7 7 7 7 7 7 5 : (14) The facto... |

113 |
Two signaling schemes for improving the error performance of frequency-division-duplex (FDD) transmission systems using transmitter antenna diversity
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Citation Context ...ironment achieve reliability through "diversity, " where redundant information is sent or received on two or more antennas in the hope that at least one path from the transmitter reaches the=-= receiver [3, 4, 5, 6]-=-. To keep the transmitter and receiver complexity low, linear processing is often preferred [3]. To achieve the high data rates promised in [2], however, new approaches for space-time transmission are... |

103 | Representation theory for high-rate multiple-antenna code design
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- 2001
(Show Context)
Citation Context ...ble work on a variety of space-time transmission schemes and performance measures [9] such as the space-time trellis codes of [10] and the space-time block codes of [11, 12] for the known channel and =-=[13, 14, 15]-=- for the unknown channel. At very high rates and with a large number of antennas, many of these space-time codes suffer from complexity or performance difficulties. The number of states in the trellis... |

88 |
A new bandwidth-efficient transmit antenna modulation diversity scheme for linear digital modulation
- Wittneben
- 1993
(Show Context)
Citation Context ...ironment achieve reliability through "diversity, " where redundant information is sent or received on two or more antennas in the hope that at least one path from the transmitter reaches the=-= receiver [3, 4, 5, 6]-=-. To keep the transmitter and receiver complexity low, linear processing is often preferred [3]. To achieve the high data rates promised in [2], however, new approaches for space-time transmission are... |

68 | An efficient square-root algorithm for blast
- Hassibi
- 2000
(Show Context)
Citation Context ...ennas 4. Are very simple to encode 5. Can be decoded in a variety of ways including simple linear-algebraic techniques such as: (a) Successive nulling and cancelling (V-BLAST [7], square-root V-BLAST =-=[16]-=-) (b) Sphere decoding [17] 6. Are designed with the numbers of both the transmit and receive antennas in mind 7. Satisfy an information-theoretic optimality criterion - the codes are designed to maxim... |

67 |
Base-station modulation diversity for digital SIMULCAST
- Wittneben
- 1991
(Show Context)
Citation Context ...ironment achieve reliability through "diversity, " where redundant information is sent or received on two or more antennas in the hope that at least one path from the transmitter reaches the=-= receiver [3, 4, 5, 6]-=-. To keep the transmitter and receiver complexity low, linear processing is often preferred [3]. To achieve the high data rates promised in [2], however, new approaches for space-time transmission are... |

57 |
The Diversity Gain of Transmit Diversity in Wireless Systems With Rayleigh Fading
- winters
- 1998
(Show Context)
Citation Context |

53 |
On the expected complexity of sphere decoding
- Hassibi, Vikalo
(Show Context)
Citation Context ...o encode 5. Can be decoded in a variety of ways including simple linear-algebraic techniques such as: (a) Successive nulling and cancelling (V-BLAST [7], square-root V-BLAST [18]) (b) Sphere decoding =-=[19, 20]-=- 6. Are designed with the numbers of both the transmit and receive antennas in mind 7. Satisfy an information-theoretic optimality criterion - the codes are designed to maximize the mutual information... |

38 |
Space-time diversity using orthogonal and amicable orthogonal designs
- Ganesan, Stoica
- 2001
(Show Context)
Citation Context ... no longer "full-rate" (see [12]) and therefore generally perform poorly in the maximum mutual information they can achieve, even when N = 1. We give an example of these non-square orthogona=-=l designs [12, 20, 21]-=-. For M = 3, we have, for example, the rate 3 4 orthogonal design S = r 4 3 2 6 6 6 6 6 6 6 6 6 6 4 s 1 s 2 s 3 \Gammas 2 s 1 0 \Gammas 3 0 s 1 0 \Gammas 3 s 2 3 7 7 7 7 7 7 7 7 7 7 5 : (14) The facto... |

29 |
Differential unitary space time modulation
- Hochwald, Sweldens
- 2000
(Show Context)
Citation Context ...ble work on a variety of space-time transmission schemes and performance measures [9] such as the space-time trellis codes of [10] and the space-time block codes of [11, 12] for the known channel and =-=[13, 14, 15]-=- for the unknown channel. At very high rates and with a large number of antennas, many of these space-time codes suffer from complexity or performance difficulties. The number of states in the trellis... |

9 |
A construction of a space-time code based on the theory of numbers
- Damen, Tewfik, et al.
- 2002
(Show Context)
Citation Context ...l efficiencies. The LD code (31) may be modified as in Remark 4 in Section 3.2, without changing its mutual information, by premultiplying the transmitted signal vector by an orthogonal matrix t . In =-=[24]-=- it is shown that full diversity is achieved for this two-antenna code transmitting QPSK if we choose to be the block diagonal matrix = diag 02 @4 1 0 5 ; 0 1 3 2 4 R I , I R 3 5 ; 2 4 R I , I R 3 5 ;... |

8 |
Differential space-time modulation," Submitted to
- Hughes
- 1999
(Show Context)
Citation Context ...ble work on a variety of space-time transmission schemes and performance measures [9] such as the space-time trellis codes of [10] and the space-time block codes of [11, 12] for the known channel and =-=[13, 14, 15]-=- for the unknown channel. At very high rates and with a large number of antennas, many of these space-time codes suffer from complexity or performance difficulties. The number of states in the trellis... |

4 |
Space-time autocoding," submitted to
- Hassibi, Hochwald, et al.
- 1999
(Show Context)
Citation Context ...; 1) entries), the optimizing covariance is R s;opt = I M , and (3) becomes C(ae; M;N) = E log det i I N + ae M HH j : (4) This expectation can sometimes be computed in closed form (see, for example, =-=[19]-=-). 1 Equation (3) actually slightly generalizes [2, 1], which assume that H has independent CN (0; 1) entries. 6 When the channel is constant for at least T channel uses we may write xs= r ae M Hss+ v... |

3 |
Space-time autocoding,” submitted to
- Hassibi, Hochwald, et al.
- 1999
(Show Context)
Citation Context ...endentCN(0; 1) entries), the optimizing covariance is Rs;opt = IM, and (3) becomes C( ; M; N ) = E log det IN + M HH : (4) This expectation can sometimes be computed in closed form (see, for example, =-=[22]-=-). When the channel is constant for at least T channel uses we may write x = so that defining X = x 1 x 2 ::: xT (where the superscript t denotes “transpose”), we obtain r Hs + v ; =1;:::;T; M t , S =... |

1 | A wireless communication technique of extraordinary spectral efficiency - Foschini, Golden, et al. - 1999 |