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## Outage Diversity of MIMO Block-Fading Channels with Causal Channel State Information (2010)

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1141 | Diversity and multiplexing: A fundamental tradeoff in multiple-antenna channels,”
- Zheng, Tse
- 2003
(Show Context)
Citation Context ...ems where CSIT delay is also a practical system constraint. APPENDIX The power constraint in (2) is written as∫ H(B) B∑ b=1 tr ( P b ( H (b−u) )) f H(B) ( H (B) ) dH(B) ≤ P. Following the analysis in =-=[18]-=-, define the normalised fading gains ωb,t,r = − log |hb,t,r | 2 log P , where hb,t,r = |hb,t,r|eiθb,t,r are the entries of Hb. The fading gains ωb,t,r are collected into a matrix Ωb ∈ RNr×Nt , b = 1, ... |

1068 |
Large Deviations Techniques and Applications,
- Dembo, Zeitouni
- 1998
(Show Context)
Citation Context ...fore satisfies Pout(P,R)≤̇Pr { Ω (B) ∈ O() } , (23) where, by letting S()b denotes the complement of S()b , O() = { Ω (B) ∈ RBNtNr : B∑ b=1 ∣∣∣S()b ∣∣∣ ≥ duni(R)Nr } . (24) From Varadhan’s lemma =-=[19]-=-, the outage diversity satisfies d(R) ≥ inf Ω(B)∈O()∩R BNtNr + ⎧⎨ ⎩ ∑ b,t,r ωb,t,r ⎫⎬ ⎭ . (25) Since the argument of the infimum in (25) is increasing with ωb,t,r, it follows from (24) that the infim... |

582 | Capacity of fading channel with channel side information,
- Goldsmith, Varayia
- 1986
(Show Context)
Citation Context ...ng channels, the channel can be considered ergodic. In this case, longinterleaved fixed-rate codes not exceeding the channel capacity can be employed to ensure an arbitrarily low probability of error =-=[2, 3]-=-. On the other hand, for slowly fading channels with delay constraints, the codeword may only experience a small finite number of independent fading realisations and hence the channel is non-ergodic. ... |

407 |
Information theoretic considerations for cellular mobile radio,”
- Ozarow, Shamai, et al.
- 1994
(Show Context)
Citation Context ...slowly fading channels with delay constraints, the codeword may only experience a small finite number of independent fading realisations and hence the channel is non-ergodic. The block-fading channel =-=[2, 4]-=- is a simple model that captures the essence of non-ergodic channels. Here, each codeword comprises a finite number of blocks, where each block experiences an independent fading realisation, which rem... |

268 |
A general formula for channel capacity,”
- Verdu, Han
- 1994
(Show Context)
Citation Context ...s subject to the long-term power constraint, E [ 1 B B∑ b=1 tr ( P b ( H (b−u) ))] ≤ P. (2) III. PRELIMINARIES The channel described by (1) under the quasi-static assumption is not information stable =-=[15]-=- and therefore, the capacity in the strict Shannon sense is zero. We therefore study the information outage probability, Pout(P,R) = Pr { 1 B B∑ b=1 IX ( HbP 1 2 b ( H (b−u) )) < R } , (3) which lower... |

65 |
Coded diversity on block-fading channel
- Malkamaki, Leib
- 1999
(Show Context)
Citation Context ...rnational Travel Grant 2009/R2; and the Swedish Research Council under VR grant 621-2009-4666. probability is the lowest achievable word error probability of codes with sufficiently long block length =-=[5]-=-. As such, a rate-reliability tradeoff exists, whereby for a fixed number of blocks, a high rate is penalised by a large error probability. Most works that study the block-fading channel focus on adap... |

40 |
A unified construction of space-time codes with optimal rate-diversity tradeoff
- Lu, Kumar
- 2005
(Show Context)
Citation Context ...ower allocation, the outage diversity is duni(R) = BNtNr, achieved with Gaussian input constellation. With a discrete constellation X of size 2M , the outage diversity is given by the Singleton bound =-=[6, 16]-=- duni(R) = dS(R) = Nr ( 1 + ⌊ B ( Nt − R M )⌋) , (8) with x being the largest integer not greater than x. Note that duni(R) is also the outage diversity of systems with short-term power constraint ∑... |

38 |
Delay-constrained capacity with causal feedback
- Negi, Cioffi
- 2002
(Show Context)
Citation Context ...of H(b−u), P b(H (b−u)) is the solution to the minimisation problem{ minimise Pout(P,R) subject to: E [ 1 B ∑B b=1 tr ( P b ( H (b−u) ))] ≤ P. (6) For u = 0, (6) can be solved via dynamic programming =-=[8, 10]-=-. The extension to u > 0 is also possible, although the problem becomes exceedingly difficult as u increases. As we shall see, it is possible to examine the asymptotic behaviour of Pout(P,R) without e... |

11 |
Fading channels: Informatictheoretic and communications aspects
- Biglieri, Proakis, et al.
- 1998
(Show Context)
Citation Context ...ng channels, the channel can be considered ergodic. In this case, longinterleaved fixed-rate codes not exceeding the channel capacity can be employed to ensure an arbitrarily low probability of error =-=[2, 3]-=-. On the other hand, for slowly fading channels with delay constraints, the codeword may only experience a small finite number of independent fading realisations and hence the channel is non-ergodic. ... |

11 |
Fundamentals of differential Equations and Boundary value problems , Eight edition
- Nagle, Saff, et al.
- 2011
(Show Context)
Citation Context ...TECHNOLOGY. Downloaded on August 05,2010 at 08:09:42 UTC from IEEE Xplore.sRestrictions apply.soutage diversity requires the solution to a linear homogeneous recurrence relation (difference equation) =-=[12]-=-, which admits no closed form in general, but can be easily computed numerically. For the special case of a single block delay, the outage diversity can be solved in closed form and coincides with rec... |

6 | i Fàbregas, “Outage probability of the gaussian MIMO free-space optical channel with PPM - Letzepis, Guillén - 2009 |

5 |
Adaptive transmission for block-fading channels
- Nguyen
- 2009
(Show Context)
Citation Context ...bility. Most works that study the block-fading channel focus on adaptive transmission techniques in which the power and/or rate is adapted to the channel conditions subject to system constraints (see =-=[6]-=- for a recent review). Adaptation, however, requires a certain degree of knowledge of the channel fades, also referred to as channel state information (CSI), at the transmitter and receiver. A large b... |

5 |
Guillén i Fàbregas, “Coded modulation with mismatched CSIT over MIMO blockfading channels,” accepted for
- Kim, Nguyen, et al.
- 2010
(Show Context)
Citation Context ...w prohibitively complex with increasing delay in acquiring CSIT. Dynamic programming therefore provides little insight in the outage performance of systems with causal CSIT. Using recent results from =-=[6, 11]-=-, we derive the outage diversity without explicitly solving the optimal power allocation problem. We show that the ISIT 2010, Austin, Texas, U.S.A., June 13 - 18, 2010 2168978-1-4244-7892-7/10/$26.00 ... |

2 |
Communication with causal CSIT and controlled information outage
- Chen, Wong
- 2009
(Show Context)
Citation Context ...of H(b−u), P b(H (b−u)) is the solution to the minimisation problem{ minimise Pout(P,R) subject to: E [ 1 B ∑B b=1 tr ( P b ( H (b−u) ))] ≤ P. (6) For u = 0, (6) can be solved via dynamic programming =-=[8, 10]-=-. The extension to u > 0 is also possible, although the problem becomes exceedingly difficult as u increases. As we shall see, it is possible to examine the asymptotic behaviour of Pout(P,R) without e... |

1 | Stochastic power allocation using causal channel state information for delay-limited communications - Wong - 2006 |

1 |
Guillén i Fàbregas, and N. Letzepis, “MIMO INR-ARQ systems with multi-bit feedback
- Nguyen, Rasmussen, et al.
- 2009
(Show Context)
Citation Context ... For the special case of a single block delay, the outage diversity can be solved in closed form and coincides with recent results on incremental redundancy, automatic repeatrequest (INR-ARQ) systems =-=[13, 14]-=-. For a two-block delay, the difference equation can be solved analytically, yielding a closed-form expression for the outage diversity. Furthermore, the outage diversity of the single-input single-ou... |

1 |
tradeoff for ARQ systems over the MIMO block-fading channels
- “Diversity-rate-delay
- 2009
(Show Context)
Citation Context ... For the special case of a single block delay, the outage diversity can be solved in closed form and coincides with recent results on incremental redundancy, automatic repeatrequest (INR-ARQ) systems =-=[13, 14]-=-. For a two-block delay, the difference equation can be solved analytically, yielding a closed-form expression for the outage diversity. Furthermore, the outage diversity of the single-input single-ou... |

1 | Differential and Difference Equations - Brane - 1966 |