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## 1Achievable Rates of FDD Massive MIMO Systems with Spatial Channel Correlation

Citations: | 1 - 1 self |

### Citations

12397 |
Elements of Information Theory
- Cover, Thomas
- 1991
(Show Context)
Citation Context ...f Rn. Putting aside the channel training error ên for ease of exposition5, this yields M mutually independent Gaussian variables with non-identical variances. The reverse waterfilling approach (RWF) =-=[30]-=- can be implemented to achieve the rate-distortion function (in terms of MSE distortion) in 5Normally the channel training error is small, therefore we ignore it when designing feedback codebooks. thi... |

1359 | P.: Least Squares Quantization in PCM
- LLOYD
- 1982
(Show Context)
Citation Context ...d form. Notwithstanding the difficulty in deriving the optimal codebook in closed form, the Lloyd algorithm can be implemented to find the optimal codebook, however with high computational complexity =-=[34]-=-. Observing that the CCMs of the users are usually rankdeficient, in the sense that a number of singular values of the CCMs are extremely small (see numerical results in Section V for eigenvalue distr... |

589 |
On the achievable throughput of a multiantenna gaussian broadcast channel
- Caire, Shamai
- 2003
(Show Context)
Citation Context ...the transmitter (CSIT). Without CSIT, e.g., when the user channels are identically distributed and are i.i.d. (independent identically distributed) in time and frequency, the total DoF reduces to one =-=[3]-=-.1 In practice, a pilot-assisted CSIT acquisition approach is widely adopted, where the BS first broadcasts downlink channel training sequences, and then listens to the channel feedback from the users... |

550 | Fading correlation and its effect on the capacity of multielement antenna systems
- Shiu, Foschini, et al.
- 2000
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Citation Context ...ative probability function (CDF) of the singular values of the user CCMs is shown. We adopt two models to calculate the CCM of a uniform linear antenna array. The first one is the one-ring model (OR) =-=[38]-=-, based on which [R]i,j = 1 2∆ ∫ ∆+θ −∆+θ e−j2piD(i−j) sin(α)dα, (63) where ∆ denotes the angular spread, θ denotes the mean user azimuth angle seen from the BS and D is the antenna spacing. Alternati... |

508 | How much training is needed in multiple-antenna wireless links
- Hassibi, Hochwald
- 2003
(Show Context)
Citation Context ...ed training sequences with per-user CCMs, is shown in Fig. 5. For comparison purposes, the simulation also considers the unitary training sequences, which are shown to be optimal with i.i.d. channels =-=[39]-=-. We assume, for the unitary training 11 10 20 30 40 50 10−2 10−1 100 101 Normalized number of feedback bits N or m al iz edsM SE VQ, Isotropical codebook VQ, Skewed codebook SQ−RWF, with SL SQ−RWF, w... |

394 |
Convex optimization. Cambridge university press,
- Boyd, Vandenberghe
- 2004
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Citation Context ... = λXopt, (15) where λ ≥ 0 is a constant chosen to satisfy the power constraint. Proof: The proof is straightforward by deriving the Karush-Kuhn-Tucker (KKT) conditions of the Lagrangian dual problem =-=[27]-=- of (14). Remark 1: Unfortunately, in general, the problem in (14) is not a convex problem. Consider the special case where N = 1 and R1 is rank-deficient, then any Xτ satisfying Xτ = [x0,x0, , ...,x0... |

322 | A vector-perturbation technique for near-capacity multiantenna multiuser communication — Part I: Channel inversion and regularization,”
- Peel, Hochwald, et al.
- 2005
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Citation Context ...coding matrix is expressed as Wrzf = ζKrzf ˆ̄H † , (42) where ˆ̄H = [ ˆ̄h1, ˆ̄h2, ..., ˆ̄hN ]† , ζ is a normalization scalar to fulfill the power constraint in (2), and α is the regularization factor =-=[36]-=-. Based on (2), we obtain ζ2 = N tr [ ˆ̄HK2rzf ˆ̄H †] , (43) where equal power allocation is assumed, i.e., [ E[ss†] ] i,i = P N . The signal-to-interference-and-noise-ratio (SINR) of user n is γn,rzf... |

288 | Mutual information and minimum mean-square error in Gaussian channels
- Guo, Shamai, et al.
- 2005
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Citation Context ...+XτX † τ )−2 Xτ . (17) The matrix ( R−1n +XτX † τ ) is often ill-conditioned, when Rn is rank-deficient, whereas in the CMI problem, the matrices involved are all well-conditioned. Moreover, based on =-=[28]-=-, the MMSE and the mutual information have very strong relationships, and the numerical results show that the obtained training sequences have very good MSE performance. The iterative algorithm, which... |

276 |
Noncooperative cellular wireless with unlimited numbers of base station antennas,”
- Marzetta
- 2010
(Show Context)
Citation Context ...DoF), plays a pivotal role in boosting the capacity of next generation wireless communication systems. In cellular systems, it is desirable to deploy a large number of antennas at base stations (BSs) =-=[1]-=-, resulting in what is referred to as the massive MIMO system. Such designs have several advantages, including significant improvements of spectral efficiency and radiated energy efficiency [2], immun... |

128 |
Maximum ratio transmission,"
- Lo
- 1999
(Show Context)
Citation Context ...d form. Notwithstanding the difficulty in deriving the optimal codebook in closed form, the Lloyd algorithm can be implemented to find the optimal codebook, however with high computational complexity =-=[24]-=-. Observing that the CCMs of the users are usually rank-deficient, in the sense that a number of eigenvalues of the CCMs are extremely small (see numerical results in Section V for eigenvalue distribu... |

114 | Multiuser MIMO achievable rates with downlink training and channel state feedback.
- Caire, Jindal, et al.
- 2010
(Show Context)
Citation Context ...= RnXτ (X † τRnXτ + Iτ ) −1yτ,n. (11) Applying the MMSE decomposition, the user channel hn and the covariance matrix of the channel estimation error due to imperfect channel training are expressed as =-=[25]-=- hn = ĥn + ên, Cên = Cov(hn)− Cov(ĥn) = Rn −RnXτ (X†τRnXτ + Iτ )−1X†τRn = (R−1n +XτX † τ ) −1, (12) respectively. The last equation in (12) follows from the matrix inversion lemma3. The total mean... |

110 | A stochastic MIMO channel model with joint correlation of both link ends,”
- Weichselberger, Herdin, et al.
- 2006
(Show Context)
Citation Context ...e, the BS can obtain the downlink CCMs by direct transformation from the uplink CCMs without using any training symbols [20]. In addition, we assume the receive and transmit antennas are uncorrelated =-=[21]-=-, and we only consider the transmit correlation since we assume single-antenna users [22]. We adopt the block fading channel model, where the channel is constant for T channel uses measured on the tim... |

109 | Energy and spectral efficiency of very large multiuser MIMO systems
- Ngo, Larsson, et al.
- 2013
(Show Context)
Citation Context ... (BSs) [1], resulting in what is referred to as the massive MIMO system. Such designs have several advantages, including significant improvements of spectral efficiency and radiated energy efficiency =-=[2]-=-, immunity to small-scale channel fading due to the channel hardening effect, simplification of the media-access-control (MAC) layer design, etc. Striving to reap the dramatic throughput gain of massi... |

108 |
On the performance of random vector quantization limited feedback beamforming in a MISO system,” Wireless Communications,
- Au-Yeung, Love
- 2007
(Show Context)
Citation Context ...ptotic regime where the number of feedback bits B goes to infinity, the quantization MSE scales down with B as MSE ∼ 2 −BM−1 , regardless whether the channel distribution is i.i.d. or correlated [31] =-=[32]-=-. However, when the number of feedback bits B is limited, which is the case for FDD massive MIMO systems due to scarce channel estimation resources, the exact analysis for the quantization MSE perform... |

83 | Channel capacity and beamforming for multiple transmit and receive antennas with covariance feedback,” in
- Jafar, Vishwanath, et al.
- 2001
(Show Context)
Citation Context ...out using any training symbols [20]. In addition, we assume the receive and transmit antennas are uncorrelated [21], and we only consider the transmit correlation since we assume single-antenna users =-=[22]-=-. We adopt the block fading channel model, where the channel is constant for T channel uses measured on the timefrequency plane, i.e., in complex dimensions, and evolves independently to another block... |

75 | Transceiver optimization for multiuser MIMO systems
- Serbetli, Yener
- 2004
(Show Context)
Citation Context ...l method to get convergent schemes that yield local optimum of the objective function, which aims at solving a non-convex problem. KKT-based iterations have been proposed in different contexts, e.g., =-=[29]-=-. Remark 5: Notice that X(0)τ 6= 0, otherwise the algorithm would be stuck at zero. In our simulations, letting X(0)τ have orthogonal rows works well. Also notice that in the algorithm, we normalize t... |

75 | Giannakis, “Design and analysis of transmit beamforming based on limited-rate feedback
- Xia, B
(Show Context)
Citation Context ...er of feedback bits B is limited, which is the case for FDD massive MIMO systems due to scarce channel estimation resources, the exact analysis for the quantization MSE performance is unavailable. In =-=[33]-=-, a “skewed codebook” (i.e., a codebook based on skewing an isotropical codebook) that matches the eigenspace of the CCM is shown to be close to optimal by simulation results. The authors of [31] try ... |

67 |
Transmit signal design of optimal estimation of correlated MIMO channels
- Kotecha, Sayeed
- 2004
(Show Context)
Citation Context ...onetheless, let R̄n = Rn+ ∗IM such that ∗ is small but R̄n is invertible. Then (12) holds true if we substitute R̄n for Rn. Then we can let ∗ → 0 due to the continuity of the function involved. In =-=[26]-=-, the optimal training sequences where users have identical CCMs are given, in the sense of minimizing the MSE or the mutual information between the channel coefficients and received signals condition... |

52 | Large system analysis of linear precoding in correlated MISO broadcast channels under limited feedback,”
- Wagner, Couillet, et al.
- 2012
(Show Context)
Citation Context ...nt rank, rn. The optimal rn can be determined by a simple onedimensional search over 1:M , performed by the n-th user. C. Data Transmission For fair comparisons, also in line with the work in [7] and =-=[35]-=-, we consider the RZF linear precoder schemes. The precoder treats the channel estimates as the real channel coefficients. Corresponding achievable rates on account of the imperfect channel estimation... |

50 |
On universal quantization
- Ziv
- 1985
(Show Context)
Citation Context ...tial entropies of a Gaussian and a uniform distribution with the same (unit) variance. A full thorough treatment of entropy-coded scalar quantization in an information theoretic sense can be found in =-=[40]-=-. 12 4 5 6 7 8 9 10 0 0.05 0.1 0.15 0.2 0.25 Dominant Rank,sN or m al iz edsM SE #FB: 42, SK #FB: 61, SK #FB: 79, SK #FB: 42, iid #FB: 61, iid #FB: 79, iid rn Fig. 8. The quantization MSE, normalized ... |

39 |
Joint spatial division and multiplexing – the large-scale array regime,”
- Adhikary, Nam, et al.
- 2013
(Show Context)
Citation Context ...he CCMs can be leveraged, in many ways, to facilitate FDD massive MIMO transmission. While the optimal transmission scheme with the aid of CCMs is still unclear, significant rate gain can be expected =-=[7]-=-. A large body of work has been done studying TDD massive MIMO systems. The seminal work in [1] first proposes to deploy BS antennas with a number much larger than the number of users, eliminating the... |

32 | A direct derivation of a single-antenna reciprocity relationfor the time domain,”
- Smith
- 2004
(Show Context)
Citation Context ...) system or the uncalibrated time-division-duplex (TDD) system.2 For the calibrated TDD system, the channel reciprocity is exploited to allow the BS to obtain the CSIT through uplink channel training =-=[5]-=-. Assuming the channel coefficients are i.i.d. for different users and BS antennas, the CSIT acquisition overhead, which leads to a dimensionality loss of the time-frequency resource, scales with the ... |

32 | Training and feedback optimization for multiuser MIMO downlink
- Kobayashi, Jindal, et al.
(Show Context)
Citation Context ...orrelated channels, we use an exhaustive search to find the optimal training and feedback length. The analysis of the optimal training and feedback length for i.i.d. channels can be found in [35] and =-=[37]-=-. IV. PERFORMANCE ANALYSIS In this section, we provide expressions for the downlink achievable sum rate under the per-user CCMs, leveraging the deterministic equivalent techniques provided in [35], wi... |

29 | Massive MIMO Systems With Non-Ideal Hardware: Energy Efficiency, Estimation, and Capacity Limits,” - Bjornson, Hoydis, et al. - 2014 |

19 |
Blind pilot decontamination,”
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- 2014
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Citation Context ...ement, the massive MIMO system increases the radiated energy efficiency by a factor of M , where M is the number of BS antennas, or √ M in the presence of imperfect channel estimation. Recent work in =-=[11]-=- further shows the pilot-contamination problem is not inherent. Several other issues are also studied extensively, such as downlink precoding, detection, hardware impairment, etc. [12]–[14] For FDD ma... |

17 | Joint spatial division and multiplexing: Opportunistic beamforming, user grouping and simplified downlink scheduling,”
- Nam, Adhikary, et al.
- 2014
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Citation Context ...23.5◦, 41.5◦, 57.5◦}, (65) and the angular spread for the quantization matrices are identical with the user-angular-spread, which is specified in Fig. 3. To keep the IGI under control, similarly with =-=[8]-=-, we further divide the user-groups into 2 patterns, where only the users in the same pattern are scheduled simultaneously7. The ER in each virtual sector, i.e. r? in [7], is chosen while neglecting e... |

15 | Downlink training techniques for FDD massive MIMO systems: Open-loop and closed-loop training with memory,”
- Choi, Love, et al.
- 2014
(Show Context)
Citation Context ...nel matrix due to limited number of scatterers around the BS, using a compressive sensing approach. Moreover, the time correlation of the channels is leveraged to reduce the CSIT overhead, e.g., [16]–=-=[18]-=- and references therein, where a trellis-code based quantization codebooks are leveraged to decrease the CSIT estimation overhead in [16] [17] and a memory-based channel training sequence design is pr... |

11 |
Joint spatial division and multiplexing for mm-wave channels,”
- Adhikary
- 2014
(Show Context)
Citation Context ...JSDM scheme [7], [8], which was the first to exploit the spatial correlation to benefit the FDD massive MIMO system. Note that the uplink CSIT feedback is not treated in the previous JSDM papers [7], =-=[9]-=-. To make fair comparison, we assume that the JSDM scheme uses an isotropical VQ feedback codebook, since it is unknown whether the JSDM scheme can also benefit from a better-designed codebook for cor... |

11 |
Noncoherent trellis coded quantization: A practical limited feedback technique for massive MIMO systems,”
- Choi, Chance, et al.
- 2013
(Show Context)
Citation Context ...nels is leveraged to reduce the CSIT overhead, e.g., [16]–[18] and references therein, where a trellis-code based quantization codebooks are leveraged to decrease the CSIT estimation overhead in [16] =-=[17]-=- and a memory-based channel training sequence design is presented in [18]. The other direction is exploiting the spatial correlation of channel coefficients, pioneered by the work in [7] and extended ... |

11 | Wireless communications”. 2nd edition. - Molisch - 2011 |

10 |
Correlated fading in broadcast MIMO channels: Curse or blessing
- Clerckx, Kim, et al.
- 2008
(Show Context)
Citation Context ... the same task as the CSIT. To this end, it is found that the second order channel statistics, specifically the channel correlation matrices (CCMs) of the channel coefficients, are of tremendous help =-=[6]-=-–[10]. Compared with the instantaneous CSIT realizations, the CCMs, which are determined by user-locations and large-scale fading, vary at a much slower time scale, e.g., seconds to tens of seconds in... |

10 | PAR-aware large-scale multi-user MIMO-OFDM downlink
- Studer, Larsson
- 2013
(Show Context)
Citation Context ... Recent work in [11] further shows the pilot-contamination problem is not inherent. Several other issues are also studied extensively, such as downlink precoding, detection, hardware impairment, etc. =-=[12]-=-–[14] For FDD massive MIMO systems, the research can be categorized into three directions: Compressive-sensing-based, temporal-correlation-based and spatial-correlation-based. In [15] and references t... |

8 | Aligned image sets under channel uncertainty: Settling a conjecture by lapidoth, shamai and wigger on the collapse of degrees of freedom under finite precision csit,” arXiv preprint arXiv:1403.1541
- Davoodi, Jafar
(Show Context)
Citation Context ...instantaneous CSIT. In the mean time, recent 1In such condition it has been shown that even when the CSIT is known within a mean-square error that does not decrease with SNR, the DoF collapses to one =-=[4]-=-. 2Since in practice TDD reciprocity is quite difficult to obtain, which requires reciprocity calibration of the transmit and receive radio frequency chains. In fact, the only current system that uses... |

6 | and L.Zhong, “ArgosV2: A Flexible Many-Antenna Research Platform,” in
- Shepard
- 2013
(Show Context)
Citation Context ...nt work in [11] further shows the pilot-contamination problem is not inherent. Several other issues are also studied extensively, such as downlink precoding, detection, hardware impairment, etc. [12]–=-=[14]-=- For FDD massive MIMO systems, the research can be categorized into three directions: Compressive-sensing-based, temporal-correlation-based and spatial-correlation-based. In [15] and references therei... |

5 |
OFDMA Mobile Broadband Communications: A Systems Approach.
- Li, Wu, et al.
- 2013
(Show Context)
Citation Context ...the time-frequency plane. In Long-Term Evolution (LTE) systems, a resource block is a tile of 14 OFDM symbols in time multiplied by 12 subcarriers in frequency, for a total of T = 168 complex symbols =-=[23]-=-, over which the channel is constant (within the time and frequency selectivity for which the system is designed). III. FDD MASSIVE MIMO ACHIEVABLE RATES In this section, we will specify the rate-achi... |

5 | Molisch, Wireless Communications, 2nd edition - F - 2011 |

4 |
Distributed compressive CSIT estimation and feedback for FDD multi-user massive
- Rao, Lau
- 2014
(Show Context)
Citation Context ...impairment, etc. [12]–[14] For FDD massive MIMO systems, the research can be categorized into three directions: Compressive-sensing-based, temporal-correlation-based and spatial-correlation-based. In =-=[15]-=- and references therein, the authors exploit the sparsity in massive MIMO channel matrix due to limited number of scatterers around the BS, using a compressive sensing approach. Moreover, the time cor... |

3 |
Transformation based downlink beamforming techniques for frequency division duplex systems
- Hugl, Laurila, et al.
- 2000
(Show Context)
Citation Context ... of all users, i.e., Rn,∀n, and the users know their respective CCMs. In practice, the BS can obtain the downlink CCMs by direct transformation from the uplink CCMs without using any training symbols =-=[20]-=-. In addition, we assume the receive and transmit antennas are uncorrelated [21], and we only consider the transmit correlation since we assume single-antenna users [22]. We adopt the block fading cha... |

2 | Fundamental limits in correlated fading MIMO broadcast channels: Benefits of transmit correlation diversity,” 2014. [Online]. Available: http://arxiv.org/abs/1401.7114
- Nam
(Show Context)
Citation Context ... same task as the CSIT. To this end, it is found that the second order channel statistics, specifically the channel correlation matrices (CCMs) of the channel coefficients, are of tremendous help [6]–=-=[10]-=-. Compared with the instantaneous CSIT realizations, the CCMs, which are determined by user-locations and large-scale fading, vary at a much slower time scale, e.g., seconds to tens of seconds in cell... |

2 | Trellis-extended codebooks and successive phase adjustment: A path from LTE-Advanced to FDD massive MIMO systems
- Choi, Love, et al.
(Show Context)
Citation Context ... channel matrix due to limited number of scatterers around the BS, using a compressive sensing approach. Moreover, the time correlation of the channels is leveraged to reduce the CSIT overhead, e.g., =-=[16]-=-–[18] and references therein, where a trellis-code based quantization codebooks are leveraged to decrease the CSIT estimation overhead in [16] [17] and a memory-based channel training sequence design ... |

2 |
Ensemble properties of RVQbased limited-feedback beamforming codebooks
- Raghavan, Veeravalli
- 2013
(Show Context)
Citation Context ... asymptotic regime where the number of feedback bits B goes to infinity, the quantization MSE scales down with B as MSE ∼ 2 −BM−1 , regardless whether the channel distribution is i.i.d. or correlated =-=[31]-=- [32]. However, when the number of feedback bits B is limited, which is the case for FDD massive MIMO systems due to scarce channel estimation resources, the exact analysis for the quantization MSE pe... |

1 |
pilot decontamination,” arXiv preprint arXiv:1309.6806
- Müller, Cottatellucci, et al.
- 2013
(Show Context)
Citation Context ...ement, the massive MIMO system increases the radiated energy efficiency by a factor of M , where M is the number of BS antennas, or √ M in the presence of imperfect channel estimation. Recent work in =-=[10]-=- further shows the pilot-contamination problem is not inherent. Several other issues are also studied extensively, such as downlink precoding, detection, hardware impairment, etc. [11]–[13]. For FDD m... |