## A FRAMEWORK FOR DESIGNING MIMO SYSTEMS WITH DECISION FEEDBACK EQUALIZATION OR TOMLINSON-HARASHIMA PRECODING

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Citations: | 16 - 1 self |

### BibTeX

@MISC{Shenouda_aframework,

author = {M. Botros Shenouda and T. N. Davidson},

title = {A FRAMEWORK FOR DESIGNING MIMO SYSTEMS WITH DECISION FEEDBACK EQUALIZATION OR TOMLINSON-HARASHIMA PRECODING},

year = {}

}

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### Abstract

We consider joint transceiver design for general Multiple-Input Multiple-Output communication systems that implement interference (pre-)subtraction, such as those based on Decision Feedback Equalization (DFE) or Tomlinson-Harashima precoding (THP). We develop a unified framework for joint transceiver design by considering design criteria that are expressed as functions of the Mean Square Error (MSE) of the individual data streams. By deriving two inequalities that involve the logarithms of the individual MSEs, we obtain optimal designs for two classes of communication objectives, namely those that are Schur-convex and Schur-concave functions of these logarithms. For Schur-convex objectives, the optimal design results in data streams with equal MSEs. This design simultaneously minimizes the total MSE and maximizes the mutual information for the DFE-based model. For Schur-concave objectives, the optimal DFE design results in linear equalization and the optimal THP design results in linear precoding. The proposed framework embraces a wide range of design objectives and can be regarded as a counterpart of the existing framework of linear transceiver design.

### Citations

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Matrix Analysis
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(Show Context)
Citation Context ...lar matrix with positive diagonal elements, we can rewrite the objective as tr(CMC H )=�CL� 2 F , where �·�F denotes the Frobenius norm and the product CL is positive definite lower triangular matrix =-=[8]-=-. Let λ1(CL) ≥ ...,≥ λK(CL) and σ1(CL) ≥ ... ≥ σK(CL) denote the ordered eigen values and singular values, respectively, of the matrix CL. Then the unit diagonal lower triangular C that minimizes tr(C... |

154 | Joint TX-RX beamforming design for multicarrier MIMO channels: a unified framework for convex optimization
- Palomar, Cioffi, et al.
- 2003
(Show Context)
Citation Context ...d to mitigate the interference between the received streams at reasonable computational cost. One approach to the design of such a scheme is to focus on linear precoding and linear equalization; e.g. =-=[1, 2]-=-. An alternative approach that offers some advantages is to allow interference (pre-)subtraction at either the transmitter or the receiver. This approach includes schemes with linear precoding and Dec... |

141 | Redundant filterbank precoders and equalizers part I: Unification and optimal designs
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(Show Context)
Citation Context ...e the performance of the proposed Schur-convex designs for THP and DFE (which minimize the total MSE among other objectives), with the corresponding linear transceiver design that minimizes total MSE =-=[1, 2]-=-, and the optimal linear transceiver that maximizes the mutual information (minimizes log det(E)) [1]. The performance advantages of interference cancellation are quite clear from Fig. 4. 6. CONCLUSIO... |

97 |
Precoding and Signal Shaping for Digital Transmission
- Fischer
- 2002
(Show Context)
Citation Context ...sing an MMSE criterion receiver were considered in [3, 4], and designs subject to a zero-forcing constraint were considered in [5, 6]. Some THP counterparts of these designs were presented in [3] and =-=[7]-=-, respectively. In this paper, we develop a broadly applicable framework for joint transmitter and receiver design for MIMO systems with a DFE or a THP. We consider the broad range of design criteria ... |

57 |
Inequalities between two kinds of eigenvalues of a linear transformation
- Weyl
- 1949
(Show Context)
Citation Context ...obtained using the following lower bound: �CL� 2 F = P K i=1 σ2 i (CL) ≥ = KX λ 2 i (CL) (6) i=1 KX i=1 (CL) 2 ii = KX i=1 L 2 ii, (7) where the bound in (6) is obtained by applying Weyl’s inequality =-=[9]-=-, and (7) follows from the fact that CL is lower triangular and C is unit diagonal. The inequality in (6) is satisfied with equality when the matrix is normal [9]. Since our matrix CL is a triangular ... |

29 | Joint transceiver design for MIMO communications using geometric mean decomposition
- Jiang, Li, et al.
- 2005
(Show Context)
Citation Context ... class of interference (pre-)subtraction, designs for DFE based schemes using an MMSE criterion receiver were considered in [3, 4], and designs subject to a zero-forcing constraint were considered in =-=[5, 6]-=-. Some THP counterparts of these designs were presented in [3] and [7], respectively. In this paper, we develop a broadly applicable framework for joint transmitter and receiver design for MIMO system... |

27 | Equal diagonal QR decomposition and its application to precoder design for successiveWSEAS
- Zhang, Kavcic, et al.
(Show Context)
Citation Context ... class of interference (pre-)subtraction, designs for DFE based schemes using an MMSE criterion receiver were considered in [3, 4], and designs subject to a zero-forcing constraint were considered in =-=[5, 6]-=-. Some THP counterparts of these designs were presented in [3] and [7], respectively. In this paper, we develop a broadly applicable framework for joint transmitter and receiver design for MIMO system... |

13 | Design of Block Transceivers with Decision Feedback Detection
- Xu, Davidson, et al.
- 2006
(Show Context)
Citation Context ...oncave functions of the mean square error (MSE) of each data stream. For the class of interference (pre-)subtraction, designs for DFE based schemes using an MMSE criterion receiver were considered in =-=[3, 4]-=-, and designs subject to a zero-forcing constraint were considered in [5, 6]. Some THP counterparts of these designs were presented in [3] and [7], respectively. In this paper, we develop a broadly ap... |

11 |
A determinant maximization problem occurring in the theory of data communication
- Witsenhausen
- 1975
(Show Context)
Citation Context ...M with equal diagonal elements. Minimizing det(M) is equivalent to maximizing the Gaussian mutual information, and the family of optimal precoders is obtained using a standard water-filling algorithm =-=[11]-=-. In particular, if RH = σ 2 H H R −1 n H = UΛHU H , the family of optimal precodersstakes the form: P = U1 ˆ ΦV = U1[Φ 0]V, (13) where U1 ∈ C Nt× ˆ K contains the eigen vectors of RH correspondingtot... |

8 | Linear and nonlinear preequalization/equalization for MIMO systems with long-term channel state information at the transmitter
- Simeone, Bar-Ness, et al.
- 2004
(Show Context)
Citation Context ...oncave functions of the mean square error (MSE) of each data stream. For the class of interference (pre-)subtraction, designs for DFE based schemes using an MMSE criterion receiver were considered in =-=[3, 4]-=-, and designs subject to a zero-forcing constraint were considered in [5, 6]. Some THP counterparts of these designs were presented in [3] and [7], respectively. In this paper, we develop a broadly ap... |