## Uniform channel decomposition for MIMO communications (2005)

Venue: | IEEE Transactions on Signal Processing |

Citations: | 18 - 5 self |

### BibTeX

@INPROCEEDINGS{Jiang05uniformchannel,

author = {Yi Jiang and Student Member and Jian Li and William W. Hager},

title = {Uniform channel decomposition for MIMO communications},

booktitle = {IEEE Transactions on Signal Processing},

year = {2005},

pages = {4283--4294}

}

### Years of Citing Articles

### OpenURL

### Abstract

Abstract—Assuming the availability of the channel state information at the transmitter (CSIT) and receiver (CSIR), we consider the joint optimal transceiver design for multi-input multi-output (MIMO) communication systems. Using the geometric mean decomposition (GMD), we propose a transceiver design that can decompose, in a strictly capacity lossless manner, a MIMO channel into multiple subchannels with identical capacities. This uniform channel decomposition (UCD) scheme has two implementation forms. One is the combination of a linear precoder and a minimum mean-squared-error VBLAST (MMSE-VBLAST) detector, which is referred to as UCD-VBLAST, and the other includes a dirty paper (DP) precoder and a linear equalizer followed by a DP decoder, which we refer to as UCD-DP. The UCD scheme can provide much convenience for the modulation/demodulation and coding/decoding procedures due to obviating the need for bit allocation. We also show that UCD can achieve the maximal diversity gain. The simulation results show that the UCD scheme exhibits excellent performance, even without the use of any error correcting codes. Index Terms—Channel capacity, DBLAST, dirty paper precoder, diversity gain, geometric mean decomposition, joint transceiver

### Citations

1965 |
Matrix Computations
- Golub, Loan
- 1996
(Show Context)
Citation Context ...ite: http://www.sal.ufl.edu/ yjiang/papers/gmd.m. Given the SVD, this algorithm for the GMD requires flops. For comparison, reduction of to bidiagonal form by the Golub–Kahan bidiagonalization scheme =-=[21]-=-, which is often the first step in the computation of the SVD, requires flops. Rewrite (21) APPENDIX B PROOF OF LEMMA III.3 (63) Let denote the submatrix containing the first columns of and the th col... |

1838 | Capacity of multi-antenna Gaussian channels
- Telatar
- 1999
(Show Context)
Citation Context ...or “informed transmitter”. Denote the SVD of H as H = UΛV ∗ , where Λ is a K × K diagonal matrix whose diagonal elements {λH,k} K k=1 are the nonzero singular values of H. The solution to F in (4) is =-=[9]-=- F = VΦ 1/2 . (5) Here Φ is diagonal whose kth (1 ≤ k ≤ K) diagonal element φk determines the power loaded to the kth subchannel and is found via “water filling” to be φk(µ) = � µ − α λ2 � + H,k , (6)... |

1145 | An Introduction to Multivariate Statistical Analysis - Anderson - 1984 |

951 |
Layered space–time architecture for wireless communications in a fading environment when using multi-element antennas
- Foschini
- 1996
(Show Context)
Citation Context ...e subject of intense research over the past several years because MIMO channels can support much greater data rate and higher reliability than their single-input single-output (SISO) counterpart [1], =-=[2]-=-. The majority of the researches focus on the scenarios where only the channel state information at receiver (CSIR) is available. Nevertheless, if the communication environment is slowly time varying,... |

673 |
Writing on dirty paper
- Costa
- 1983
(Show Context)
Citation Context ...what the VBLAST detector does at the em cancellation step. Now, reconsider the channel of (12), where the interference is unknown to the receiver but known to the transmitter. The dirty paper theorem =-=[12]-=- predicts the existence of an amazing precoder that can cancel out the interference completely without consuming additional input power. That is, we can still obtain an equivalent AWGN channel . As th... |

670 | Fundamentals of wireless communication - Tse, Viswanath - 2005 |

651 | Diversity and multiplexing: A fundamental tradeoff in multiple antenna channels
- Zheng, Tse
- 2003
(Show Context)
Citation Context ...for high SNR. It is a direct consequence of the fact that GMD is asymptotically for high SNR capacity lossless [5]. Another important performance metric is diversity gain, which is defined as follows =-=[18]-=-. Definition IV.2: Let denote the average error probability of a scheme at SNR . The diversity gain of the scheme is (58) The diversity gain measures how fast the error probability decays with SNR. We... |

325 |
On the achievable throughput of a multiantenna Gaussian broadcast channel
- Caire, Shamai
- 2003
(Show Context)
Citation Context ...s decomposed into parallel scalar subchannels . . . . . . (9) (11) B. DP Precoder As a dual form of the known interference cancellation at the receiver, the DP precoder can be used at the transmitter =-=[10]-=-, [11] to suppress known interferences at transmitter. Consider a scalar Gaussian channel (12) where , are independent Gaussian noise with known to the receiver. Clearly, the channel of (12) is exactl... |

178 | Sum capacity of the vector Gaussian broadcast channel and uplink-downlink duality
- Viswanath, Tse
- 2003
(Show Context)
Citation Context ...precoding, which we refer to as UCD-DP. For UCD-DP, a direct construction of the linear precoder , as done in Section IV-A, is not obvious. Instead, we exploit the uplink-downlink duality revealed in =-=[17]-=- to obtain UCD-DP. We convert the UCD-DP problem into the UCD-VBLAST problem in the reverse channel, where the roles of the transmitter and receiver are exchanged: (49) The UCD-VBLAST scheme can be ap... |

170 | Simplified processing for high spectral efficiency wireless communication employing multi-element arrays
- Foschini, Golden, et al.
- 1999
(Show Context)
Citation Context ...r design based on the geometric mean decomposition (GMD) algorithm is proposed in [5]. By combining the GMD matrix decomposition algorithm [6] with either the zero-forcing VBLAST (ZF-VBLAST) detector =-=[7]-=- or the zero-forcing dirty paper precoder (ZFDP), the GMD scheme 1 decomposes a MIMO channel into multiple identical parallel subchannels. The GMD scheme is proven to be asymptotically optimal for hig... |

128 | Joint tx-rx beamforming design for multicarrier mimo channels: A unified framework for convex optimization
- Palomar, Cioffi, et al.
(Show Context)
Citation Context ...611-6130, USA. ‡ William W. Hager is with the Department of Electrical and Computer Engineering, University of Florida, Gainesville, FL 32611-8105, USA.srecently attracted considerable attention (see =-=[3]-=- and the references therein). Almost all the researchers have concentrated on the linear transceiver designs. To maximize the channel throughput, the channel must be diagonalized via the singular valu... |

79 |
Optimum decision feedback multiuser equalization with successive decoding achieves the total capacity of the Gaussian multiple-access channel
- Varanasi, Guess
- 1997
(Show Context)
Citation Context ...erfere-and-noise ratio (SINR) of the th layer (i.e., the signal corresponding to ) using is (23) Inserting (19) into (23), we can simplify (23) via some straightforward calculations to be (see, e.g., =-=[16]-=-) (24) where . The SINRs given in (24) are related to , as shown in the following lemma. Lemma III.3: The diagonal of given in (21) and given in (24) satisfy (25) Proof: See Appendix B. An immediate c... |

62 |
New automatic equaliser employing modulo arithmetic
- Tomlinson
- 1971
(Show Context)
Citation Context ...etely without consuming additional input power. That is, we can still obtain an equivalent AWGN channel . As the practical implementation of the dirty paper precoder, the Tomlinson–Harashima precoder =-=[13]-=- can be used to achieve known-interference cancellation at the transmitter with only a small amount of power amplification. C. GMD The GMD algorithm is based on the following lemma. [We abuse the nota... |

36 |
Spatial-temporal coding for wireless communication
- Raleigh, Cioffi
(Show Context)
Citation Context ...to-noise ratios (SNR), which can add much complexity to the subsequent modulation/demodulation and coding/decoding procedures. For example, to achieve the channel capacity, bit allocation (see, e.g., =-=[4]-=-) is required to match each subchannel capacity, which not only makes modulation rather complicated but also causes capacity loss due to the finite constellation granularity. On the other hand, if the... |

28 | Joint transceiver design for MIMO communications using geometric mean decomposition
- Jiang, Li, et al.
- 2005
(Show Context)
Citation Context ...ndard HIPERLAN/2 and the IEEE 802.11 standards for wireless local area networks (WLANs), then more power should be allocated to the poorer subchannels, which can lead to considerable performance loss =-=[5]-=-. There is apparently a tradeoff between the channel throughput and the bit-error-rate (BER) performance if one attempts to avoid bit allocation. We show the contrary as detailed below. An efficient n... |

27 |
A fast square-root implementation for BLAST
- Hassibi
(Show Context)
Citation Context ...ctor. D. Closed-Form Representation of MMSE-VBLAST For MMSE-VBLAST, the nulling vector for the th layer is (19) The MMSE-VBLAST algorithm can be represented in a concise matrix form that was given in =-=[14]-=- (also see the more detailed version [15]). Consider the augmented matrix (20)s4286 IEEE TRANSACTIONS ON SIGNAL PROCESSING, VOL. 53, NO. 11, NOVEMBER 2005 Applying the QR decomposition to yields (21) ... |

24 |
Capacity of the multiple antenna Gaussian channel
- Telatar
- 1999
(Show Context)
Citation Context ...en the subject of intense research over the past several years because MIMO channels can support much greater data rate and higher reliability than their single-input single-output (SISO) counterpart =-=[1]-=-, [2]. The majority of the researches focus on the scenarios where only the channel state information at receiver (CSIR) is available. Nevertheless, if the communication environment is slowly time var... |

17 |
A multi-user precoding scheme achieving crosstalk cancellation with application to DSL systems
- Ginis, Cioffi
- 2000
(Show Context)
Citation Context ...mposed into parallel scalar subchannels . . . . . . (9) (11) B. DP Precoder As a dual form of the known interference cancellation at the receiver, the DP precoder can be used at the transmitter [10], =-=[11]-=- to suppress known interferences at transmitter. Consider a scalar Gaussian channel (12) where , are independent Gaussian noise with known to the receiver. Clearly, the channel of (12) is exactly the ... |

16 | Generalized triangular decomposition
- Jiang, Hager, et al.
- 2008
(Show Context)
Citation Context ...chose the permutation matrices and Givens rotations to achieve a wide variety of channel decompositions with some prescribed SINRs, as suggested by the generalized triangular decomposition (GTD) [8], =-=[20]-=-. Finally, we link UCD with DBLAST [2], which has been shown to be able to achieve the optimal tradeoff between the channel diversity and multiplexing [18]. We observe that each diagonal layer of DBLA... |

6 |
The geometric mean decomposition
- Jiang, Hager, et al.
- 2005
(Show Context)
Citation Context ...contrary as detailed below. An efficient nonlinear transceiver design based on the geometric mean decomposition (GMD) algorithm is proposed in [5]. By combining the GMD matrix decomposition algorithm =-=[6]-=- with either the zero-forcing VBLAST (ZF-VBLAST) detector [7] or the zero-forcing dirty paper precoder (ZFDP), the GMD scheme 1 decomposes a MIMO channel into multiple identical parallel subchannels. ... |

5 |
The Geometric Mean Decomposition,” Linear Algebra and its Applications
- Jiang, Hager, et al.
- 2005
(Show Context)
Citation Context ...contrary as detailed below. An efficient nonlinear transceiver design based on the geometric mean decomposition (GMD) algorithm is proposed in [5]. By combining the GMD matrix decomposition algorithm =-=[6]-=- with either the zero-forcing VBLAST (ZF-VBLAST) detector [7] or the zero-forcing dirty paper precoder (ZFDP), the GMD scheme 1 decomposes a MIMO channel into multiple identical parallel subchannels. ... |

4 |
Foschini Jr., “Layered space-time architecture for wireless communication in a fading environment when using multi-element antennas
- J
- 1996
(Show Context)
Citation Context ...e subject of intense research over the past several years because MIMO channels can support much greater data rate and higher reliability than their single-input single-output (SISO) counterpart [1], =-=[2]-=-. The majority of the researches focus on the scenarios where only the channel state information at receiver (CSIR) is available. Nevertheless, if the communication environment is slowly time varying,... |