## Performance of Orthogonal Beamforming for SDMA with Limited Feedback (2007)

Venue: | IEEE TRANS. VEHICULAR TECHNOLOGY |

Citations: | 10 - 2 self |

### BibTeX

@ARTICLE{Huang07performanceof,

author = {Kaibin Huang and Jeffrey G. Andrews and Robert W. Heath. Jr.},

title = { Performance of Orthogonal Beamforming for SDMA with Limited Feedback},

journal = {IEEE TRANS. VEHICULAR TECHNOLOGY},

year = {2007}

}

### OpenURL

### Abstract

On the multi-antenna broadcast channel, the spatial degrees of freedom support simultaneous transmission to multiple users. Optimal multi-user transmission, known as dirty paper coding, requires non-causal channel state information (CSI) and extreme complexity and is hence not directly realizable. A more practical design, named per user unitary and rate control (PU2RC), has been proposed for emerging cellular standards. PU2RC supports multi-user simultaneous transmission, enables limited feedback, and is capable of exploiting multi-user diversity. Its key feature is an orthogonal beamforming (or precoding) constraint, where each user selects a beamformer (or precoder) from a codebook of multiple orthonormal bases. In this paper, the asymptotic throughput scaling laws for PU2RC with a large user pool are derived for different regimes. In the interference-limited regime, the throughput of PU2RC is shown to scale logarithmically with the number of users. In the normal and noise-limited regimes, the throughput is found to scale double logarithmically with the number of users and also linearly with the number of antennas at the base station. In addition, numerical results show that PU2RC achieves higher throughput and is more robust against CSI quantization errors than the popular alternative of zero-forcing beamforming if the number of users is sufficiently large.

### Citations

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Citation Context ...nal fairness is a topic under investigation. Furthermore, the optimal deign for PU2RC for the non-asymptotic regime of the user pool remains as an open issue. APPENDIX I PROOF OF LEMMA 1 Lemma 4.8 in =-=[37]-=- can be generalized from R3 to CNt as follows. [37, Lemma 4.8] concerns N congruent disks on the surface of a sphere in R3 , and its derivation relies on two results: the first one is the stereographi... |

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Citation Context ...su = hu/‖hu‖ is the shape. The uth user quantizes and sends back to the base station two quantities: the channel shape and the SINR. The channel shape su is quantized using a codebook-based quantizer =-=[32]-=- with a codebook comprised of multiple sets of orthonormal vectors in C Nt . Let F denote the codebook, V (m) the mth orthonormal set in the codebook, and M the number of such sets. Thus, F = ⋃ M m=1 ... |

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Citation Context ...from the codebook besides choosing a particular user for each codebook vector. Such a challenge motivates our use of a new analytical tool, namely uniform convergence in the weak law of large numbers =-=[30]-=-, for analyzing the throughput of PU2RC instead of extreme value theory as applied in [22]. Theory of uniform convergence in the weak law of large numbers is also applied in our previous work [31] for... |

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Citation Context ...ecently included in the IEEE 802.16e standard [2], and has been proposed for the emerging 3GPP long term evolution (LTE) standard [3]–[6]. While the optimal SDMA strategy is known, dirty paper coding =-=[7]-=- is non-causal and hence not directly realizable. Moreover, closeto-optimal techniques such as Tomlinson-Harashima precoding and vector perturbation are sensitive to CSI The authors are with Wireless ... |

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Citation Context ... F = ⋃ M m=1 V(m) and the codebook size is N = |F| = MNt. For our design, the M orthonormal bases of F are generated randomly and independently using a method such as that in [33]. Following [34] and =-=[35]-=-, the quantized channel shape, represented by ˆsu, is the member of F that forms the smallest angle with the channel shape su. Mathematically, where the distortion function d(v,su) is given as ∣ d(v,s... |

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Citation Context ...e-input-multiple-output (MIMO) or space division multiple access (SDMA), is capable of achieving much higher throughput than other multiple-access schemes such as time division multiple access (TDMA) =-=[1]-=-. Due to this advantage, SDMA has been recently included in the IEEE 802.16e standard [2], and has been proposed for the emerging 3GPP long term evolution (LTE) standard [3]–[6]. While the optimal SDM... |

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Citation Context ...proposed in [14]. The main drawback of the optimal approach is its complexity, which increases exponentially with the number of users. This motivates the designs of more efficient SDMA algorithms. In =-=[22]-=-, a practical SDMA algorithm, called opportunistic SDMA (OSDMA), is proposed, which supports low-rate beamforming feedback and satisfies the orthogonal beamforming constraint. As shown in [22], for a ... |

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Citation Context ...n: Assumption 1: The downlink channel hu ∀ u = 1,2, · · · ,U is an i.i.d. vector with CN(0,1) coefficients. Given this assumption commonly made in the literature of SDMA and multiuser diversity [18], =-=[19]-=-, [21], [22], [27], the channel direction vector hu/‖hu‖ of each user follows a uniform distribution. Assumption 1 greatly simplifies the throughput analysis of PU2RC in Section IV but has no effect o... |

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Citation Context ... scheduling. A. Related Work and Motivation In this paper, we consider a practical scenario where partial CSI is acquired by the base station through quantized CSI feedback, known as limited feedback =-=[24]-=-. Quantized CSI feedback for point-to-point communications has been extensively studied recently (see e.g. [24], [25] and the references therein). The effects of CSI quantization on a SDMA system have... |

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Citation Context ...-to-point communications has been extensively studied recently (see e.g. [24], [25] and the references therein). The effects of CSI quantization on a SDMA system have been investigated in [20], [26], =-=[27]-=-. The key result of [20] is that the number of CSI feedback bits can be reduced by exploiting multiuser diversity. In [26], combined quantized CSI feedback and zero-forcing dirty paper coding are show... |

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Citation Context ...r OSDMA are marginal. An alternative beamforming SDMA algorithm is proposed in [20], referred to as ZF-SDMA, where feedback CSI is quantized using the random vector quantization (RVQ) algorithm [27], =-=[29]-=- and greedysearch scheduling is performed prior to zero-forcing beamforming. A design similar to ZF-SDMA [6] has been proposed to the emerging 3GPP-LTE standard [3], which is the latest cellular commu... |

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Citation Context ...ck for point-to-point communications has been extensively studied recently (see e.g. [24], [25] and the references therein). The effects of CSI quantization on a SDMA system have been investigated in =-=[20]-=-, [26], [27]. The key result of [20] is that the number of CSI feedback bits can be reduced by exploiting multiuser diversity. In [26], combined quantized CSI feedback and zero-forcing dirty paper cod... |

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Citation Context ...umption: Assumption 1: The downlink channel hu ∀ u = 1,2, · · · ,U is an i.i.d. vector with CN(0,1) coefficients. Given this assumption commonly made in the literature of SDMA and multiuser diversity =-=[18]-=-, [19], [21], [22], [27], the channel direction vector hu/‖hu‖ of each user follows a uniform distribution. Assumption 1 greatly simplifies the throughput analysis of PU2RC in Section IV but has no ef... |

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Citation Context ... point-to-point communications has been extensively studied recently (see e.g. [24], [25] and the references therein). The effects of CSI quantization on a SDMA system have been investigated in [20], =-=[26]-=-, [27]. The key result of [20] is that the number of CSI feedback bits can be reduced by exploiting multiuser diversity. In [26], combined quantized CSI feedback and zero-forcing dirty paper coding ar... |

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Citation Context ...er of feedback bits from all users. Nevertheless, the sum feedback from all users can be reduced by allowing only a small subset of users for feedback, which is an topic addressed in a separate paper =-=[36]-=-.ACCEPTED FOR PUBLICATION IN IEEE TRANSACTIONS ON VEHICULAR TECHNOLOGY, REVISED ON MAY 3, 2008 8 where the index set I (m) n that I (m) n = ∅, the vector v (m) n and the function SINRu are expressed ... |

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7 |
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Citation Context ...ired by the base station through quantized CSI feedback, known as limited feedback [24]. Quantized CSI feedback for point-to-point communications has been extensively studied recently (see e.g. [24], =-=[25]-=- and the references therein). The effects of CSI quantization on a SDMA system have been investigated in [20], [26], [27]. The key result of [20] is that the number of CSI feedback bits can be reduced... |

6 |
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Citation Context ...hieving much higher throughput than other multiple-access schemes such as time division multiple access (TDMA) [1]. Due to this advantage, SDMA has been recently included in the IEEE 802.16e standard =-=[2]-=-, and has been proposed for the emerging 3GPP long term evolution (LTE) standard [3]–[6]. While the optimal SDMA strategy is known, dirty paper coding [7] is non-causal and hence not directly realizab... |

4 | Performance analysis of random vector quantization limited feedback beamforming - Yeung, Love - 2005 |

2 |
Downlink MIMO summary
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Citation Context ...igher throughput. The above results motivate the need for choosing an optimal codebook size for a given number of users. B. Comparison with ZF-SDMA and Dirty Paper Coding Presently, PU2RC and ZF-SDMA =-=[4]-=-, [6], [20] are two main solutions for multiuser MIMO downlink for 3GPP-LTE. In this section, their performance is compared using numerical results. Moreover, the throughput of PU2RC is evaluated agai... |

2 |
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Citation Context ...ers [30], for analyzing the throughput of PU2RC instead of extreme value theory as applied in [22]. Theory of uniform convergence in the weak law of large numbers is also applied in our previous work =-=[31]-=- for analyzing the throughput of uplink SDMA with limited feedback. Despite using the same tool, the analysis in this paper differs from [31] due to differences between the uplink and downlink. Specif... |