## Unitary Space-Time Modulation for Multiple-Antenna Communications in Rayleigh Flat Fading (1998)

### Cached

### Download Links

- [mars.bell-labs.com]
- [www.mast.queensu.ca]
- DBLP

### Other Repositories/Bibliography

Venue: | IEEE Trans. Inform. Theory |

Citations: | 240 - 17 self |

### BibTeX

@ARTICLE{Hochwald98unitaryspace-time,

author = {Bertrand Hochwald and Thomas Marzetta},

title = {Unitary Space-Time Modulation for Multiple-Antenna Communications in Rayleigh Flat Fading},

journal = {IEEE Trans. Inform. Theory},

year = {1998},

volume = {46},

pages = {543--564}

}

### Years of Citing Articles

### OpenURL

### Abstract

Motivated by information-theoretic considerations, we propose a signalling scheme, unitary space-time modulation, for multiple-antenna communication links. This modulation is ideally suited for Rayleigh fast-fading environments, since it does not require the receiver to know or learn the propagation coefficients. Unitary space-time modulation uses constellations of T \cross M space-time signals {\Phi_l, l= 1,...L},where T represents the coherence interval during which the fading is approximately constant, and M > M . We design some multiple-antenna signal constellations and simulate their effectiveness as measured by bit error probability with maximum likelihood decoding. We demonstrate that two antennas have a 6-dB diversity gain over one antenna at 15-db SNR.

### Citations

8564 |
Elements of Information Theory
- Cover, Thomas
- 2003
(Show Context)
Citation Context ...(1): (A.16) We have that p a + p b = ap a + bp b = 1. Therefore, by Jensen's theorem, p a ln a + p b ln bsln(ap a + bp b ) = 0; (A.17) with equality if and only if a = b = 1. Furthermore, as shown in =-=[4]-=-, for any density p() supported ons0 and satisfying R 1 0 dsp() = 1, \Gamma Z 1 0 d p() ln p()s1; with equality if and only if p() = e \Gamma . Hence \Gamma Z 1 0 d i p a a e \Gamma=a + p b b e \Gamma... |

1832 | Capacity of multi-antenna gaussian channels,” Eur
- Telatar
- 1999
(Show Context)
Citation Context ...se modulation, interleaving, or the transmission of pilot or training signals [1]. But, paradoxically, Rayleigh flat fading can be beneficial for a multiple-antenna communication link. It is shown in =-=[6, 19]-=- that, in a Rayleigh flat-fading environment, a link has a theoretical capacity that increases linearly with the smaller of the number of transmitter and receiver antennas, provided that the complex-v... |

1482 | Information theory and reliable communications - Gallager - 1968 |

1241 | calderbank, “Space-Time Codes for High Data Rate Wireless Communication: Performance Criterion and Code Construction
- Tarokh, Seshadri, et al.
- 1998
(Show Context)
Citation Context ... channel coding, our proposed signal constellations can theoretically attain a high fraction of the channel capacity. Some multiple-antenna coding issues for receivers that know the channel appear in =-=[18]-=-. Section 2 presents the signal model and operating assumptions, and Section 3 reviews the informationtheoretic foundations for unitary space-time modulation. In Section 4, we extend the information-t... |

1106 |
Microwave Mobile Communications
- Jakes
- 1984
(Show Context)
Citation Context ... within a symbol interval, one way to model the sampled received signal is to assign an autocorrelation function to the fading coefficients. One common autocorrelation function is Jakes', proposed in =-=[9]-=-. It is usually possible to select some value for T such that the fading is approximately constant over T symbols; in doing so, however, adjacent blocks of T symbols may be correlated as in Figure 10.... |

944 |
Layered space-time architecture for wireless communication a fading environment when using multi-element antennas
- Foschini
- 1996
(Show Context)
Citation Context ...se modulation, interleaving, or the transmission of pilot or training signals [1]. But, paradoxically, Rayleigh flat fading can be beneficial for a multiple-antenna communication link. It is shown in =-=[6, 19]-=- that, in a Rayleigh flat-fading environment, a link has a theoretical capacity that increases linearly with the smaller of the number of transmitter and receiver antennas, provided that the complex-v... |

372 | Capacity of a mobile multiple-antenna communication link in rayleigh flat fading
- Marzetta, Hochwald
- 1999
(Show Context)
Citation Context ... to 500 km/hr [20]) and hence it may be impractical to learn even the single coefficient between one transmitter and one receiver antenna. Motivated by these considerations, we used Shannon theory in =-=[8]-=- to analyze multiple-antenna links without imposing any training schemes and with no assumed knowledge of the random fading coefficients. The complex fading coefficients between all pairs of transmitt... |

299 |
Information theoretic considerations for cellular mobile radio
- Ozarow
- 1994
(Show Context)
Citation Context ...g process mimics, in a tractable manner, the behavior of a continuously fading process. Furthermore, it is a very accurate representation of many TDMA, frequency hopping, or block-interleaved systems =-=[13]-=-. We consider continuous fading processes later. Each channel use (consisting of a block of T transmitted symbols) is independent of every other. Thus, data can be transmitted reliably at any rate les... |

264 |
Modulation Theory: Part I
- Detection
- 1968
(Show Context)
Citation Context ...st, in the above proof we assume that the fading is cyclically stationary. This is not restrictive since any wide-sense stationary fading process asymptotically becomes cyclically stationary as T ! 1 =-=[21]-=-. Second, the role of the block length T is secondary to that of the coherence times. We impose the constraint that blocks of T symbols be independent because it allows 20 us to use the standard notio... |

244 |
System Identification
- Soderstrom, Stoica
- 1989
(Show Context)
Citation Context ...Probability— Unknown: Suppose that two unitary space–time modulation signals and are transmitted with equal probability, and decoded with an ML receiver. Then the probability of error is and are used =-=[17]-=-. The ML receiver seeks to maximize the energy contained in the inner products that comprise . Suppose now that , and and are transmitted with equal probability. The probability of decoding error is t... |

182 | Computation of channel capacity and rate-distortion functions
- Blahut
- 1972
(Show Context)
Citation Context ...city is achieved as ae ! 1 by setting v 1 = p T with probability 1. Proof: See Appendix A. 7 Figure 1 displays, for M = N = 1 and T = 2, the exact capacity (obtained with the Blahut-Arimoto algorithm =-=[2]-=-, [8]), the perfect-knowledge upper bound (10), the lower bound (11), and the expansion (12) as a function of ae. Figure 2 is similar, except that T = 5, and we see that the lower bounds, asymptotic e... |

136 |
Bounds on the Maximum Cross Correlation of Signals
- Welch, “Lower
- 1974
(Show Context)
Citation Context ...e their pairwise Euclidean distances (see [3] and the many references therein). However, the literature on choosing vectors that minimize their pairwise correlations appears to be smaller [10], [12], =-=[22]-=-. Moreover, the constellation design problem in T -dimensional complex space does not reduce to a design problem in 2T - dimensional real space, because d 1 = j\Phi y 2 \Phi 1 j does not equal the mag... |

117 |
Communication Systems and Techniques
- Schwartz, Bennett, et al.
- 1966
(Show Context)
Citation Context ...t We obtain a closed-form expression for the probability of error by inverting the characteristic function of . The use of the characteristic function for this type of calculation is well known [14], =-=[16]-=-. Equation (B.3) may be written as (B.5) (B.7) The exponential decay of the inner integral in (B.7) as for justifies the above interchange of integration. With a change of variables, we obtain (B.8) w... |

113 |
Two signaling schemes for improving the error performance of frequency-division-duplex (FDD) transmission systems using transmitter antenna diversity
- Seshadri, Winters
- 1994
(Show Context)
Citation Context ...tter antennas increases. In an effort to increase channel capacity or lower error probability, it is accepted practice to increase the number of transmitter antennas (thereby gaining "diversity&q=-=uot; [9], [15]-=-). But increasing the number of transmitter antennas increases the required training interval and reduces the available time in which data may be transmitted before the fading coefficients change. At ... |

90 |
Shitz), “Fading channels: Information-theoretic and communications aspects
- Biglieri, Proakis, et al.
- 1998
(Show Context)
Citation Context ... the designers of wireless communications systems. Its effects are often mitigated by some combination of differential phase modulation, interleaving, or the transmission of pilot or training signals =-=[1]-=-. But, paradoxically, Rayleigh flat fading can be beneficial for a multiple-antenna communication link. It is shown in [6] and [19] that, in a Rayleigh flat-fading environment, a link has a theoretica... |

21 |
Modulation Theory—Part I
- Trees, Detection
- 1968
(Show Context)
Citation Context ...s. First, in the above proof we assume that the fading is cyclically stationary. This is not restrictive since any wide-sense stationary fading process asymptotically becomes cyclically stationary as =-=[21]-=-. Second, the role of the block length is secondary to that of the coherence time . We impose the constraint that blocks of symbols be independent because it allows us to use the standard notions of m... |

19 |
Bounds for packings on a sphere and in space
- Kabatiansky, Levenshtein
(Show Context)
Citation Context ...that maximize their pairwise Euclidean distances (see [3] and the many references therein). However, the literature on choosing vectors that minimize their pairwise correlations appears to be smaller =-=[10]-=-, [12], [22]. Moreover, the constellation design problem in T -dimensional complex space does not reduce to a design problem in 2T - dimensional real space, because d 1 = j\Phi y 2 \Phi 1 j does not e... |

8 |
Shitz), "Fading Channels: Information-Theoretic and Communications Aspects
- Biglieri, Proakis, et al.
- 1998
(Show Context)
Citation Context ... the designers of wireless communications systems. Its effects are often mitigated by some combination of differential phase modulation, interleaving, or the transmission of pilot or training signals =-=[1]-=-. But, paradoxically, Rayleigh flat fading can be beneficial for a multiple-antenna communication link. It is shown in [6, 19] that, in a Rayleigh flat-fading environment, a link has a theoretical cap... |

4 |
Some theoretical observations on spread-spectrum communications
- Mazo
- 1979
(Show Context)
Citation Context ...aximize their pairwise Euclidean distances (see [3] and the many references therein). However, the literature on choosing vectors that minimize their pairwise correlations appears to be smaller [10], =-=[12]-=-, [22]. Moreover, the constellation design problem in T -dimensional complex space does not reduce to a design problem in 2T - dimensional real space, because d 1 = j\Phi y 2 \Phi 1 j does not equal t... |

4 |
Multiple access proposal for UMTS radio
- FRAMES
- 1996
(Show Context)
Citation Context ...r only a few antennas can be learned before a fresh fade occurs. Next-generation cellular systems in Europe will be expected to operate under very fast fading (trains moving at speeds up to 500 km/hr =-=[20]-=-) and hence it may be impractical to learn even the single coefficient between one transmitter and one receiver antenna. Motivated by these considerations, we used Shannon theory in [8] to analyze mul... |

4 |
Bounds for packings on a sphere and in space,” Probl
- Kabatyanskii, Levenshtein
- 1978
(Show Context)
Citation Context ...that maximize their pairwise Euclidean distances (see [3] and the many references therein). However, the literature on choosing vectors that minimize their pairwise correlations appears to be smaller =-=[10]-=-, [12], [22]. Moreover, the constellation design problem in -dimensional complex space does not reduce to a design problem in -dimensional real space, because does not equal the magnitude of the inner... |

3 |
muliple access proposal for UMTS radio interface-SMG2
- “Frames
- 1996
(Show Context)
Citation Context ...or only a few antennas can be learned before a fresh fade occurs. Next-generation cellular systems in Europe will be expected to operate under very fast fading (trains moving at speeds up to 500 km/h =-=[20]-=-) and hence it may be impractical to learn even the single coefficient between one transmitter and one receiver antenna. Motivated by these considerations, we used Shannon theory in [8] to analyze mul... |

1 |
Rank-preserving extensions of band matrices
- Ellis, Lay
- 1990
(Show Context)
Citation Context ... ). The Hadamard product in (24) therefore causes the conditional probability density (4) to depend on only the 2 min(; T ) \Gamma 1 central diagonal bands of SS y . A covariance-extension theorem in =-=[5]-=- states that one can always find a T \Theta T Hermitian nonnegative-definite matrix Q whose rank is less than or equal to min(; T ), and whose 2 min(; T ) \Gamma 1 central diagonal bands are proportio... |

1 |
Shitz), "nd-Convolutional codes---Parts I and II
- Kofman, Zehavi, et al.
- 1997
(Show Context)
Citation Context ...each signal (except the very first) can be transmitted in 15 T \Gamma 1 time samples rather than T , but the receiver can still exploit the T -symbol coherence interval to demodulate each signal; see =-=[11]-=- for single-antenna codes with this feature. It follows that the size of the signal constellation can be reduced from L = 2 RT to L = 2 R(T \Gamma1) . For example, with R = 1 half the number of signal... |

1 |
Shitz), “nd-convolutional codes—Parts
- Kofman, Zehavi, et al.
- 1997
(Show Context)
Citation Context ... rows of . Hence, each signal (except the very first) can be transmitted in time samples rather than , but the receiver can still exploit the -symbol coherence interval to demodulate each signal; see =-=[11]-=- for single-antenna codes with this feature. It follows that the size of the signal constellation can be reduced from to . For example, with half the number of signals are needed. Let binary message b... |