## From Single user to Multiuser Communications: Shifting the MIMO paradigm (2007)

Venue: | IEEE Sig. Proc. Magazine |

Citations: | 24 - 8 self |

### BibTeX

@INPROCEEDINGS{Gesbert07fromsingle,

author = {David Gesbert and Marios Kountouris and Robert W. Heath and Chan-byoung Chae and Thomas Sälzer},

title = {From Single user to Multiuser Communications: Shifting the MIMO paradigm},

booktitle = {IEEE Sig. Proc. Magazine},

year = {2007}

}

### OpenURL

### Abstract

In multiuser MIMO networks, the spatial degrees of freedom offered by multiple antennas can be advantageously exploited to enhance the system capacity, by scheduling multiple users to simultaneously share the spatial channel. This entails a fundamental paradigm shift from single user communications, since multiuser systems can experience substantial benefit from channel state information at the transmit-ter and, at the same time, require more complex scheduling strategies and transceiver methodologies. This paper reviews multiuser MIMO communication from an algorithmic perspective, discussing performance gains, tradeoffs, and practical considerations. Several approaches including non-linear and linear channel-aware precoding are reviewed, along with more practical limited feedback schemes that require only partial channel state information. The interaction between precoding and scheduling is discussed. Several promising strategies for limited multiuser feedback design are looked at, some of which are inspired from the single user MIMO precoding scenario while others are fully specific to the multiuser setting. 1 DRAFT

### Citations

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Citation Context ...ng points in the region was revealed by the seminal work [4]. Assuming a unit variance for the noise, it is now known that the capacity region for a given matrix channel realization can be written as =-=[9]-=-: CBC = � P1,..PU s.t.Èk Pk=P ⎧ ⎨ ⎩ (R1, ..RU) ∈ ℜ +U � det I + Hi( , Ri ≤ log2 � j≥i Qj)HH i � det I + Hi( � j>i Qj)HH i 7 �⎫ ⎬ � ⎭ (4) where the above expression should in turn be optimized over eac... |

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Citation Context ...es on reducing the number of parameters and the required resolution. The feedback problem has been solved in single user MIMO communication systems using a concept known as limited feedback precoding =-=[39]-=-. The key idea of this line of research has been to quantize the precoder for a MIMO channel and not simply the channel coefficients. The challenge of extending this work to the multiuser channel is t... |

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Citation Context ... feedback in MU-MIMO channels assume a single receive antenna at the mobile - extensions to multiple receive antennas is an ongoing research topic. Some of the main results on this subject are due to =-=[40]-=-, [41], where the random codebook and Grassmannian quantization ideas are used to quantize the direction of each user’s channel hk. The main observation in [40] is that the feedback requirements scale... |

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Citation Context ...thms can be implemented. There are other methods to simplify the search based methods [26]. Several algorithms have also been proposed based on variations of Tomlinson-Harashima precoding (THP) [25], =-=[27]-=-. THP was originally proposed for use with an Z point one-dimension pulse amplitude modulation (PAM) signal as a temporal equalization. For this constellation, THP is the same as the inverse channel f... |

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Citation Context ...back as this concerns only a very small number of users compared with the number of cell users. Feedback reduction during the scheduling stage can be obtained via use of threshold-based pre-selection =-=[36]-=- combined with any of the approaches described below. Thresholding can be practically implemented using opportunistic feedback [37], 18 DRAFTswhere users who exceed the threshold compete on a random a... |

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Citation Context ... some scheduling algorithms for different multiuser MIMO solutions. It is known that linear beamforming can achieve the sum capacity when the number of active users in the system is large [12], [28], =-=[30]-=-. In [28], the users are equipped with only one receive antenna and ZFBF is performed at the transmitter. Analogous to BD, this full search 15 DRAFTsbased user selection algorithm can be extended to t... |

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Citation Context ...ack in MU-MIMO channels assume a single receive antenna at the mobile - extensions to multiple receive antennas is an ongoing research topic. Some of the main results on this subject are due to [40], =-=[41]-=-, where the random codebook and Grassmannian quantization ideas are used to quantize the direction of each user’s channel hk. The main observation in [40] is that the feedback requirements scale linea... |

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Citation Context ...terest in compressing the CSI and using it in both the scheduling and the beam design algorithms. Interestingly, although it was shown that the multiplexing gain disappears in the absence of any CSIT =-=[33]-=-, recent findings suggest that the BS can live with limited channel information at the transmitter and still achieve a significant fraction of the capacity promised by the full CSIT case, although the... |

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Citation Context ...network where all users have the same signal-to-noise ratio (SNR), the scaling law of the sum rate capacity of MIMO Gaussian BC, denoted as R DPC , for Mk = M, fixed N and P , and large U is given by =-=[12]-=- lim U→∞ E(R DPC ) N log log(UM) = 1. (5) DRAFTsThe result in (5) indicates that, with full CSIT, the system can enjoy a multiplexing gain of N, obtained by the BS sending data to N carefully selected... |

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Citation Context .... This problem can be regarded as K-dimensional integer-lattice least squares problem and thus search based algorithms can be implemented. There are other methods to simplify the search based methods =-=[26]-=-. Several algorithms have also been proposed based on variations of Tomlinson-Harashima precoding (THP) [25], [27]. THP was originally proposed for use with an Z point one-dimension pulse amplitude mo... |

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Citation Context ...plexity of the optimal scheduling is high, thus there has been several suboptimal algorithms that were proposed to reduce the computational complexity for user group selection, among which [28], [30]–=-=[32]-=-. In the capacity-based greedy user selection algorithm, the transmitter chooses the single user with the highest channel capacity. Then, it finds the next user that provides the maximum sum rate from... |

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Citation Context ...lem then becomes selecting {Wk,Vk} K k=1 jointly such that VH k Hk K� l=1,l�=k 13 Wl = 0, ∀k. This cannot be solved in closed form, thus several iterative solutions have been proposed, including e.g. =-=[17]-=-, [19]. In such approaches, the transmitter generally computes a new effective channel for each user k using the initial receive combining vector. Using this new effective channel, the transmitter rec... |

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Citation Context ...p between DPC and ZFBF but this gap is decreased when the receivers have multiple antennas. For additional tradeoff analysis between linear and non-linear precoding stategies, the reader may also see =-=[29]-=-. IV. USER SCHEDULING IN MU-MIMO NETWORKS In this section, we consider the problem of choosing a subset of users for transmission in the MIMO BC. A brute-force complete search over all possible combin... |

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Citation Context ...e to channel quantizing. An improvement can be obtained by quantizing the channel vector and a certain received SINR upper bound that is a function of the error between the true and quantized channel =-=[42]-=-. This increases the performance of the system and helps in user selection. Thresholds based on sum rate constraints on the feedback channel can also be used to reduce required feedback, yet maintain ... |

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Citation Context ...the performance of the system and helps in user selection. Thresholds based on sum rate constraints on the feedback channel can also be used to reduce required feedback, yet maintain capacity scaling =-=[43]-=-. 19 DRAFTsB. Dimension reduction and projection techniques In addition to quantization-based approaches where the channel metric is discretized, dimension reduction techniques can be used that involv... |

13 |
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Citation Context ...ting the feedback load across the scheduling stage and the beam design stage is an interesting open problem, although design rules exploiting known rate scaling laws and bounds give promising results =-=[38]-=-. A. Quantization-based techniques Quantization is the first idea that comes to mind when dealing with source compression, in this case the random channel matrix or the corresponding precoders being t... |

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Citation Context ...nder the BD constraint, Wk can be further optimized based on waterfilling. If excess antennas are available, eigenmode selection or antenna subset selection can be used to further improve performance =-=[23]-=-. A disadvantage of BD is that it requires Mk = Sk. This can be solved by including the receive processing in the problem formulation. For example, with a linear receive combining matrix Vk for user k... |

11 |
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Citation Context ...tic view of MIMO as a pure PHY technology. A better understanding of the impact of MIMO antennas on multiuser communications is, by large, due to progress in the field of multiuser information theory =-=[2]-=-. Fundamental recent results in this area have hinted at how deeply connected PHY layer modulation/coding and link layer resource allocation and scheduling can be, at least when having overall optimum... |

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(Show Context)
Citation Context ...less than the number of active cell users. Studies show in fact 9 DRAFTsthat the optimal number of users with non zero allocated power for any given realization of the channel is upper bounded by N 2 =-=[14]-=-. In the remainder of the paper we shall refer to this subset of users as the "selected" users. When restricting to linear precoding techniques such as ZF, the number of served users is directly limit... |

10 |
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Citation Context ...n the channel matrix One of the simplest approaches for finding the precoder is to premultiply the transmitted signal by a suitably normalized ZF or MMSE inverse of the multiuser matrix channel [21], =-=[22]-=-. In this case, it can be assumed for simplification that Mk = Sk = 1. Thus Hk = hk is a row vector and Wk (the precoding vector for the k-th user) is chosen as the k-th column of the right �T . In th... |

9 |
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(Show Context)
Citation Context ...AC capacity region, which stipulate that the BC region can be calculated through the union of regions of the dual MAC with all uplink power allocation vectors meeting the sum power constraint P [10], =-=[11]-=-. The fundamental role played by the multiple antennas at either the BS or the users in expanding the channel capacity is best apprehended by examining how the sum rate (the point yielded by the maxim... |

8 |
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(Show Context)
Citation Context ...scheduling and the final beam design (or "user serving") stages, thus taking profit from the fact the numbers users to be served at each scheduling slot is much less than the number of cell users. In =-=[35]-=- it is proposed to reduce feedback during the scheduling phase, which can be performed using rough channel estimates, while the stage of serving the scheduled group of K users is accomplished with nea... |

8 |
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(Show Context)
Citation Context ...ck. Similarly, a maximum-likelihood (ML) estimation framework maximizing the log-likelihood function of the probability density function (pdf) of hk under the scalar constraint (15) can be formulated =-=[49]-=-. Let L = 1 and hk ∼ CN(0,Rk) and CQI feedback γk = |hkqk| 2 . The solution to the ML problem is given by max hk hkRkh H k s.t. |hkqk| 2 = γk �hk = arg max hk hkRkh H k hk(qkq H k )hH k which correspo... |

7 | Coordinated Beamforming for Multiuser MIMO Systems with Limited Feedforward
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(Show Context)
Citation Context ...hemes, also relying on full CSIT, yet allowing a compromise between complexity and performance. We summarize several practical transmission techniques using either linear or non-linear precoding [16]–=-=[19]-=-. A. Linear precoding Linear precoding is a generalization of traditional SDMA, where users are assigned different precoding matrices at the transmitter. The precoders are designed jointly based on CS... |

5 |
Interface for Fixed and Mobile Broadband Wireless Access Systems; Amendment 2
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(Show Context)
Citation Context ...The need for CSIT feedback places a significant burden on uplink capacity in most systems, exacerbated in systems with wideband (e.g. OFDM) communication or high mobility (such as 3GPP-LTE [6], WiMax =-=[7]-=-, etc.). Finally, another challenge related to MUMIMO cross-layer design lies in the complexity of the scheduling procedure associated with the selection of a group of users that will be served simult... |

4 |
Memory-based opportunistic multi-user beamforming
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(Show Context)
Citation Context ...ics of the channel, either in the temporal or in the spatial domain. The time domain approach consists in exploiting the natural temporal correlation of the channel to help refine the beams over time =-=[46]-=-, [47]. In the spatial domain, statistics give information about spatial separability, which is instrumental to a proper beamforming design. Such aspect is described below. D. Use of spatial statistic... |

4 |
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(Show Context)
Citation Context ... the channel, either in the temporal or in the spatial domain. The time domain approach consists in exploiting the natural temporal correlation of the channel to help refine the beams over time [46], =-=[47]-=-. In the spatial domain, statistics give information about spatial separability, which is instrumental to a proper beamforming design. Such aspect is described below. D. Use of spatial statistical fee... |

4 |
Gesbert D. Transmit diversity vs. opportunistic beamforming in packet data downlink transmission
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(Show Context)
Citation Context ...elay constraints. In addition a poorly designed feedback channel can suffer from delays and cause the reported channel quality metrics to the transmitter to be outdated, bringing further degradations =-=[51]-=-. Another fundamental aspect is the impact of realistic traffic models and system loads, especially on schemes relying on high user loads (e.g. random beamforming). In recent wireless systems based on... |

3 |
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(Show Context)
Citation Context ...tain MAC capacity region, which stipulate that the BC region can be calculated through the union of regions of the dual MAC with all uplink power allocation vectors meeting the sum power constraint P =-=[10]-=-, [11]. The fundamental role played by the multiple antennas at either the BS or the users in expanding the channel capacity is best apprehended by examining how the sum rate (the point yielded by the... |

3 |
the capacity of MIMO broadcast channel with partial side information
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(Show Context)
Citation Context ...arch work on schemes employing partial CSIT. Partial CSIT refers to any possible form of incomplete information on the channel, obtained by any of several means detailed later. Fortunately, work like =-=[13]-=- demonstrates that the optimal capacity scaling of capacity for the MIMO Gaussian BC, i.e. N log(SNR log U) assuming U single antenna users, can be achieved for U → ∞ even though the transmitter has o... |

2 |
der Veen (Eds.), Space-Time Wireless Systems: From Array Processing to MIMO Communications, Cambridge Univ
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(Show Context)
Citation Context ... last ten years have witnessed the transition of multiple-input multiple-output (MIMO) communication from a theoretical concept to a practical technique for enhancing performance of wireless networks =-=[1]-=-. Point-to-point (single user) MIMO communication promises large gains for both channel capacity and reliability, essentially via the use of space-time codes (diversity gain oriented) combined with st... |

2 |
Term Evolution, Evolved Universal Terrestrial Radio Access
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Citation Context ...echniques. The need for CSIT feedback places a significant burden on uplink capacity in most systems, exacerbated in systems with wideband (e.g. OFDM) communication or high mobility (such as 3GPP-LTE =-=[6]-=-, WiMax [7], etc.). Finally, another challenge related to MUMIMO cross-layer design lies in the complexity of the scheduling procedure associated with the selection of a group of users that will be se... |

2 |
On the balance of multiuser diversity and spatial multiplexing gain
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- 2007
(Show Context)
Citation Context ...roach, the unitary constraint is relaxed by introducing a power control across the beams. The SINR feedback is used to adjust the power allocated to each beam [35] or simply to turn off certain beams =-=[45]-=-, thus reducing inter-user interference when the random beams are not well aligned with users’ channels. In Fig. 4, we compare the robustness of the single-beam ORBF [44] and multi-beam ORBF [13], bot... |

2 |
Acquiring partial CSI for spatially selective transmission by instantaneous channel norm feedback
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(Show Context)
Citation Context ...relation at the transmitter can be calculated as the conditional expectations 23 (15) �hk = E(hk|γk) � Rk = E(h H k hk|γk) (16) which can be used to provide an MMSE estimate of the instantaneous SINR =-=[48]-=-. Note that with Qk = I, equation (15) falls back to a channel norm feedback. Similarly, a maximum-likelihood (ML) estimation framework maximizing the log-likelihood function of the probability densit... |

1 |
Eds.), “Exploiting limited feedback in tomorrow’s wireless communications networks
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(Show Context)
Citation Context ...is still much open. MU-MIMO transmission design with limited CSIT has in fact evolved in a topic of research in its own right and many possible strategies can be pointed out. The reader is pointed to =-=[34]-=- for a complete state-of-the-art in this area. A few selected approaches are briefly exposed here. One first key idea is based on splitting the feedback between the scheduling and the final beam desig... |