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## Scaling up MIMO: Opportunities and challenges with very large arrays (2011)

Citations: | 213 - 26 self |

### Citations

1468 | Fundamentals of Wireless Communication
- Tse, Viswanath
- 2005
(Show Context)
Citation Context ...n more impressive, because such systems offer the possibility to transmit simultaneously to several users and the flexibility to select what users to schedule for reception at any given point in time =-=[2]-=-. The price to pay for MIMO is increased complexity of the hardware (number of RF chains) and the complexity and energy consumption of the signal processing at both ends. For point-to-point links, com... |

1404 |
Layered space-time architecture for wireless communication in a fading environment when using multi-element antennas
- Foschini
- 1996
(Show Context)
Citation Context ... Inr + ρ GG H ) , (3) nt October 21, 2011 DRAFT7 where I(x;s) denotes the mutual information operator, Inr denotes the nr × nr identity matrix and the superscript “H” denotes the Hermitian transpose =-=[9]-=-. The actual capacity of the channel results if the inputs are optimized according to the water-filling principle. In the case that GG H equals a scaled identity matrix, C is in fact the capacity. To ... |

850 |
Antenna theory: analysis and design
- Balanis
- 1982
(Show Context)
Citation Context ...the impedance matrix Zr 2 , one for small adjacent antenna spacing (0.05λ) and one for moderate spacing (0.5λ). The following numerical values are obtained from the induced electromotive force method =-=[24]-=- for a ULA consisting of three parallel dipole antennas: ⎡ ⎤ 72.9+j42.4 71.4+j24.3 67.1+j7.6 Zr(0.05λ) = ⎢ 71.4+j24.3 72.9+j42.4 71.4+j24.3 ⎥ ⎣ ⎦ 67.1+j7.6 71.4+j24.3 72.9+j42.4 , and ⎡ Zr(0.5λ) = ⎢ ⎣... |

367 |
Random matrix theory and wireless communications
- Tulino, Verdú
(Show Context)
Citation Context ...s several consequences. Things that were random before, now start to look deterministic. For example, the distribution of the singular values of the channel matrix approaches a deterministic function =-=[6]-=-. Another fact is that very tall or very wide matrices tend to be very well conditioned. Also when dimensions are large, some matrix operations such as inversions can be done fast, by using series exp... |

347 |
Improved methods for calculating vectors of short length in a lattice, including a complexity analysis
- Fincke, Pohst
- 1985
(Show Context)
Citation Context ...moving away to new areas of the search space. This strategy gave rise to the algorithm’s name. 3) Tree-based algorithms: The most prominent algorithm within this class is the Sphere Decoder (SD) [3], =-=[41]-=-. The SD is in fact an ML decoder, but which only considers points inside a sphere with certain radius. If the sphere is too small for finding any signaling points, it has to be increased. Many tree-b... |

332 | The capacity region of the Gaussian multiple-input multiple-output broadcast channel
- Weingarten, Steinberg, et al.
- 2006
(Show Context)
Citation Context ...portional to the ratio of power to noise-variance. The total transmit power is independent of the number of antennas, E { ‖sf‖ 2} = 1 . (23) The known capacity result for this channel, see e.g. [11], =-=[12]-=-, assumes that the terminals as well as the base station know the channel. Let Dγ be a diagonal matrix whose diagonal elements constitute a K × 1 vector γ. To obtain the sum-capacity October 21, 2011 ... |

323 | A vectorperturbation technique for near-capacity multiantenna multiuser communication – part II: Perturbation
- Hochwald, Peel, et al.
- 2005
(Show Context)
Citation Context ...as M → ∞. We now move on to practical precoding methods. The conceptually simplest approach is to invert the channel by means of the pseudo-inverse. This is referred to as Zero-Forcing (ZF) precoding =-=[29]-=-. A variant of zero forcing is Block Diagonalization [30], which is not covered in this paper. Intuitively, when M grows, G tends to have nearly orthogonal columns as the terminals are not correlated ... |

310 | Spectral efficiency of CDMA with random spreading
- Verdú, Shamai
- 1999
(Show Context)
Citation Context ...s about soft detection from hard detection. Literature investigating schemes similar to the ones above, but operating in the coded large system limit, are in agreement with Figures 12, 13, and 14. In =-=[44]-=-, analytic CDMA spectral efficiency expressions for both MF, ZF, and linear MMSE, are given. The results are the following. In the limit of large ratios α, all three methods perform likewise, and as w... |

262 |
Noncooperative cellular wireless with unlimited numbers of base station antennas
- Marzetta
- 2010
(Show Context)
Citation Context ...laws are known for ideal situations. More recently, however, this view is changing, and a number of practically important system aspects in the large-(nt,nr) regime have been discovered. For example, =-=[5]-=- showed that asymptotically as nt → ∞ and under realistic assumptions on the propagation channel with a bandwidth of 20 MHz, a timedivision multiplexing cellular system may accommodate more than 40 si... |

261 |
A stochastic MIMO radio channel model with experimental validation
- Kermoal, Schumacher, et al.
- 2002
(Show Context)
Citation Context ... impact of mutual coupling on MIMO performance. In MU-MIMO systems 3 , the terminals are autonomous so that we can assume that the transmit array is uncoupled and uncorrelated. If the Kronecker model =-=[25]-=- is assumed for the propagation channel G = Ψ 1/2 1/2 r GIIDΨt , where Ψt and Ψr are the transmit and receive correlation matrices, respectively, and GIID is the matrix with IID Rayleigh entries [23].... |

149 | On the complexity of the sphere decoding in digital communications
- Jalden, Ottersten
- 2005
(Show Context)
Citation Context ...point links, complexity at the receiver is usually a greater concern than complexity at the transmitter. For example, the complexity of optimal signal detection alone grows exponentially with nt [3], =-=[4]-=-. In multiuser systems, complexity at the transmitter is also a concern since advanced coding schemes must often be † Dept. of Electrical and Information Technology, Lund University, Lund, Sweden ‡ De... |

136 |
A transmit preprocessing technique for multiuser MIMO systems using a decomposition approach
- Choi, Murch
- 2004
(Show Context)
Citation Context ...The conceptually simplest approach is to invert the channel by means of the pseudo-inverse. This is referred to as Zero-Forcing (ZF) precoding [29]. A variant of zero forcing is Block Diagonalization =-=[30]-=-, which is not covered in this paper. Intuitively, when M grows, G tends to have nearly orthogonal columns as the terminals are not correlated due to their physical separation. This assures that the p... |

62 | Iterative multiuser joint decoding: Optimal power allocation and low-complexity implementation
- Caire, Müller, et al.
- 2004
(Show Context)
Citation Context ...a-priori information is easily incorporated in the MMSE filter derivation by conditioning. This requires the computation of the filters for each user, each symbol interval, and each decoder iteration =-=[45]-=-. Another MMSE filter is derived by unconditional incorporation of the a-priori probabilities, which results in MMSE filters varying for each user and iteration, similarly to for BI-GDFE above. Densit... |

58 |
achievable rates, and sum-rate capacity of MIMO broadcast channels
- Vishwanath, Jindal, et al.
- 2003
(Show Context)
Citation Context ...is proportional to the ratio of power to noise-variance. The total transmit power is independent of the number of antennas, E { ‖sf‖ 2} = 1 . (23) The known capacity result for this channel, see e.g. =-=[11]-=-, [12], assumes that the terminals as well as the base station know the channel. Let Dγ be a diagonal matrix whose diagonal elements constitute a K × 1 vector γ. To obtain the sum-capacity October 21,... |

56 | Space-time multiple access: linear growth in the sum rate
- Hochwald, Vishwanath
- 2002
(Show Context)
Citation Context ... Tr(G T G ∗ ) −1. (30) When both the number of terminals K and the number of base station antennas M grow large, but with fixed ratio α = M/K, Tr(G T G ∗ ) −1 converges to a fixed deterministic value =-=[31]-=- Tr(G T G ∗ ) −1 → 1 M , as K, M → ∞, α−1 K = α. (31) Substituting (31) into (30) gives the expression in Table I. The conclusion is that ZF precoding achieves an SNR that tends to the optimal SNR for... |

56 | Performance of reduced-rank linear interference suppression - Honig, Xiao - 2001 |

55 | Lattice-reduction-aided broadcast precoding
- Windpassinger, Fischer, et al.
- 2004
(Show Context)
Citation Context ... � 1.79 N.A. TABLE I SNR AND SINR EXPRESSIONS FOR A COLLECTION OF STANDARD PRECODING TECHNIQUES. Non-linear precoding techniques, such as DPC, Vector Perturbation (VP) [32], and lattice-aided methods =-=[33]-=- are important techniques when M is not much larger than K. This is true since in the M ≈ K regime, the performance gap of ZF to the IF benchmark is significant, see Table I, and there is room for imp... |

54 |
Matrix Algorithms: Basic decompositions
- Stewart
- 1998
(Show Context)
Citation Context ...wing, we review an intuitive method for approximate matrix inversion. It is known that if a K×K matrix Z has the property lim n→∞ (IK −Z) n = 0K, then its inverse can be expressed as a Neumann series =-=[49]-=- Z −1 ∞∑ = (IK −Z) n . (39) n=0 Ostensibly, it appears that matrix inversion using (39) is even more complex than direct inversion since both matrix inversion and multiplication are O(K 3 ) operations... |

51 |
Mutual coupling in MIMO wireless systems: a rigorous network theory analysis
- Wallace, Jensen
- 2004
(Show Context)
Citation Context ...18] and references therein). One interesting result is that coupling among co-polarized antennas can be perfectly mitigated by the use of optimal multiport impedance matching radio frequency circuits =-=[19]-=-. This technique has been experimentally demonstrated only for up to four antennas, though in principle it can be applied to very large MIMO arrays [20]. Nevertheless, the effective cancellation of co... |

50 | Time reversal of electromagnetic waves
- Lerosey, Rosny, et al.
(Show Context)
Citation Context ...ratio transmission (beamforming with h H /||h||) on the downlink is optimal. This resulting processing is reminiscent of time-reversal, a technique used for focusing electromagnetic or acoustic waves =-=[7]-=-, [8]. The second effect of scaling up the dimensions is that thermal noise can be averaged out so that the system is predominantly limited by interference from other transmitters. This is intuitively... |

48 |
3G Evolution HSPA and LTE for Mobile Broadband
- Dahlman, Parkvall, et al.
- 2008
(Show Context)
Citation Context ...k G. Larsson ‡ , Thomas L. Marzetta § , Ove Edfors † , and Fredrik Tufvesson † I. INTRODUCTION MIMO technology is becoming mature, and incorporated into emerging wireless broadband standards like LTE =-=[1]-=-. For example, the LTE standard allows for up to 8 antenna ports at the base station. Basically, the more antennas the transmitter/receiver is equipped with, and the more degrees of freedom that the p... |

45 |
Fixing the Complexity of the Sphere Decoder for MIMO Detection
- Barbero, Thompson
- 2008
(Show Context)
Citation Context ...signal. The average complexity of the sphere decoder is however exponential in K [4], and SD is thus not suitable in the large MIMO regime where K is large. The Fixed Complexity Sphere Decoder (FCSD) =-=[43]-=- is a low-complexity, suboptimal, version of the SD. All combinations of the first, say r, scalar symbols in q are enumerated, i.e., with a full search, and for each such combination, the remaining K−... |

41 | A lowcomplexity detector for large MIMO systems and multicarrier CDMA systems
- Vardhan, Mohammed, et al.
- 2008
(Show Context)
Citation Context ...ghborhood with NNeigh vectors. The neighboring vector with smallest MSE is chosen, and the process restarts, and continues like this for NIter iterations. The Likelihood Ascent Search (LAS) algorithm =-=[38]-=- only permits transitions to states with lower MSE, and converges monotonically to a local minima in this way. An upper bound of bit error rate and a lower bound on asymptotic multiuser efficiency for... |

36 |
Communication through a diffusive medium: Coherence and capacity
- Moustakas, Baranger, et al.
- 2000
(Show Context)
Citation Context ...h antenna element, and in 3D there are up to 6. A further problem that is specific to 3D arrays is that only the antennas located on the surface of the 3D array contribute to the information capacity =-=[22]-=-, which in effect restricts the usefulness of dense 3D array implementations. This is a consequence of the integral representation of Maxwell’s equations, by which the electromagnetic field inside the... |

31 |
On performance of sphere decoding and Markov chain Monte Carlo detection methods
- Zhu, Farhang-Boroujeny, et al.
- 2005
(Show Context)
Citation Context ... LLR as in [46], the PM algorithm keeps a sum of terms [47]. There are many other approaches which may be suitable for soft-output large scale MIMO detection, e.g., Markov chain MonteCarlo techniques =-=[48]-=-. October 21, 2011 DRAFT39 10 −1 BER 10 −2 MMSE MMSE-SIC BI-GDFE TS FCSD IF 10 −3 10 0 2 4 6 8 10 12 14 16 18 20 −4 α Fig. 12. Comparisons of BER for K = 15 and varying values of α. 10 −2 MMSE MMSE-S... |

25 |
Multipath-enabled super-resolution for rf and microwave communication using phase-conjugate arrays
- Henty, Stancil
(Show Context)
Citation Context ... of Time Reversal (TR) where the transmitted signal is a time-reversed replica of the channel impulse response. TR with single as well as multiple antennas has been demonstrated lately in, e.g., [7], =-=[13]-=-. In the context of this paper the most interesting case is MISO, and here we speak of Time-Reversal Beam Forming (TRBF). While most communications applications of TRBF address a relatively small numb... |

21 |
Effect of Element Mutual Coupling on the Capacity of Fixed Length Linear Arrays
- Janaswamy
(Show Context)
Citation Context ...he antenna separation decreases. This problem has been examined in recent papers, although the focus is often on spatial correlation and the effect of coupling is often neglected, as in [14]–[16]. In =-=[17]-=-, the effect of coupling on the capacity of fixed length ULAs is studied. In general, it is found that mutual coupling has a substantial impact on capacity as the number of antennas is increased for a... |

19 |
MIMO detection methods: how they work
- Larsson
- 2009
(Show Context)
Citation Context ...t-to-point links, complexity at the receiver is usually a greater concern than complexity at the transmitter. For example, the complexity of optimal signal detection alone grows exponentially with nt =-=[3]-=-, [4]. In multiuser systems, complexity at the transmitter is also a concern since advanced coding schemes must often be † Dept. of Electrical and Information Technology, Lund University, Lund, Sweden... |

19 | On the condition number distribution of complex Wishart matrices
- Matthaiou, McKay, et al.
- 2010
(Show Context)
Citation Context ...ransmit antennas grow large while keeping the number of receive antennas constant. We furthermore assume that the row-vectors of the propagation matrix are asymptotically orthogonal. As a consequence =-=[10]-=- ( H) GG ≈ Inr , (11) and the achievable rate (3) becomes nt nt≫nr Cnt≫nr ≈ log 2det(Inr +ρ·Inr) = nr ·log2(1+ρ) , (12) which matches the upper bound (9). Then, let the number of receive antennas grow... |

19 |
Extending a fixed-complexity sphere decoder to obtain likelihood information for turboMIMO systems
- Barbero, Thompson
- 2008
(Show Context)
Citation Context ...hieve this result, for creating an approximate max-log LLR. If a bit value for a bit position is missing, or if higher accuracy is needed, one can add vectors in the vicinity of the obtained set, see =-=[46]-=-. A soft-output version of the LAS algorithm has been shown to operate around 7 dB away from capacity in a coded V-BLAST setting with M = K = 600 [38]. Instead of using the max-log approximations for ... |

18 | Molisch, “Impact of matching network on bandwidth of compact antenna arrays
- Lau, Andersen, et al.
- 2006
(Show Context)
Citation Context ...an be applied to very large MIMO arrays [20]. Nevertheless, the effective cancellation of coupling also brings about diminishing bandwidth in one or more output ports as the antenna spacing decreases =-=[21]-=-. This can be understood intuitively in that, in the limit of small antenna spacing, the array effectively reduces to only one antenna. Thus, one can only expect the array to offer the same characteri... |

15 | Antenna saturation effects on MIMO capacity
- Pollock, Abhayapala, et al.
- 2003
(Show Context)
Citation Context ...implies that the antenna separation decreases. This problem has been examined in recent papers, although the focus is often on spatial correlation and the effect of coupling is often neglected, as in =-=[14]-=-–[16]. In [17], the effect of coupling on the capacity of fixed length ULAs is studied. In general, it is found that mutual coupling has a substantial impact on capacity as the number of antennas is i... |

12 | On the asymptotic capacity of MIMO systems with antenna arrays of fixed length - Wei, Goeckel, et al. - 2005 |

12 |
Multiple antenna terminals,” in MIMO: From Theory to Implementation
- Lau
- 2011
(Show Context)
Citation Context ...r the effect of mutual coupling. Indeed, coupling compensation is a topic of current interest, much driven by the desire of implementing MIMO arrays in a compact volume, such as mobile terminals (see =-=[18]-=- and references therein). One interesting result is that coupling among co-polarized antennas can be perfectly mitigated by the use of optimal multiport impedance matching radio frequency circuits [19... |

11 |
Optimal single-port matching impedance for capacity maximization in compact MIMO arrays
- Fei, Fan, et al.
- 2008
(Show Context)
Citation Context ...n offered by dense 2D or 3D arrays to perform signaling in the vertical dimension. The complete Single-User MIMO (SU-MIMO) signal model with antennas and matching circuit in Figure 3 (reproduced from =-=[23]-=-) is used to demonstrate the performance degradation resulting from correlation and mutual coupling in very large arrays with fixed apertures. In the figure, Zt and Zr are the impedance matrices of th... |

10 |
Time reversal focusing applied to lithotripsy. Ultrason. Imag
- Thomas, Wu, et al.
- 1996
(Show Context)
Citation Context ... transmission (beamforming with h H /||h||) on the downlink is optimal. This resulting processing is reminiscent of time-reversal, a technique used for focusing electromagnetic or acoustic waves [7], =-=[8]-=-. The second effect of scaling up the dimensions is that thermal noise can be averaged out so that the system is predominantly limited by interference from other transmitters. This is intuitively clea... |

9 | Modeling the ultra-wideband outdoor channel - measurements and parameter extraction method
- Santos, Kåredal, et al.
- 2010
(Show Context)
Citation Context ... but the large spatial resolution will make it possible to split up clusters in many cases. There are measurements showing that a cluster can be seen differently from different parts of a large array =-=[28]-=-, which is beneficial since the correlation between individual contributions from a cluster then is decreased. To exemplify the channel properties in a real situation we consider a measured channel ma... |

8 | Performance of vector perturbation multiuser MIMO systems with limited feedback
- Ryan, Collings, et al.
- 2009
(Show Context)
Citation Context ... behave as if α ≈ 4. Hence, linear precoding is virtually optimal and one can dispense with DPC. For completeness we give an approximate large limit SNR expression for VP, derived from the results of =-=[34]-=-, in Table I. The expression is strictly speaking an October 21, 2011 DRAFT28 Sum rate capacity, bits/channel use 200 150 100 K = 15 IF, DPC, ZF M=100 M=40 M=15 MF 50 M = 100 M = 40 M = 15 0 −5 0 5 1... |

7 |
An eigen-analysis of compact antenna arrays and its application to port decoupling
- Volmer, Weber, et al.
- 2008
(Show Context)
Citation Context ...ort impedance matching radio frequency circuits [19]. This technique has been experimentally demonstrated only for up to four antennas, though in principle it can be applied to very large MIMO arrays =-=[20]-=-. Nevertheless, the effective cancellation of coupling also brings about diminishing bandwidth in one or more output ports as the antenna spacing decreases [21]. This can be understood intuitively in ... |

7 |
Tabu search detection for MIMO systems
- Zhao, Long, et al.
- 2007
(Show Context)
Citation Context ...local minima in this way. An upper bound of bit error rate and a lower bound on asymptotic multiuser efficiency for the LAS detector were presented in [39]. October 21, 2011 DRAFT36 Tabu Search (TS) =-=[40]-=- is superior to the LAS algorithm in that it permits transitions to states with larger MSE values, and it can in this way avoid local minima. TS also keeps a list of recently traversed signaling vecto... |

6 | A family of likelihood ascent search multiuser detectors: an upper bound of bit error rate and a lower bound of asymptotic multiuser efficiency
- Sun
- 2009
(Show Context)
Citation Context ...with lower MSE, and converges monotonically to a local minima in this way. An upper bound of bit error rate and a lower bound on asymptotic multiuser efficiency for the LAS detector were presented in =-=[39]-=-. October 21, 2011 DRAFT36 Tabu Search (TS) [40] is superior to the LAS algorithm in that it permits transitions to states with larger MSE values, and it can in this way avoid local minima. TS also k... |

5 | On improved multiuser detection with iterated soft decision interference cancellation
- Lampe, Huber
- 1999
(Show Context)
Citation Context ...remove some of the complexity stemming from matrix inversions. As an example of a soft information-based method, we describe the conditional MMSE with soft interference cancellation (MMSE-SIC) scheme =-=[35]-=-. The algorithm is initialized with a linear MMSE estimate ˜q of q. Then for each user k, an interferencecanceled signal xi,k, where subscript i is the iteration number, is constructed by removing int... |

5 |
Partial marginalization soft MIMO detection with higher order constellations
- Persson, Larsson
- 2011
(Show Context)
Citation Context ...te around 7 dB away from capacity in a coded V-BLAST setting with M = K = 600 [38]. Instead of using the max-log approximations for approximating LLR as in [46], the PM algorithm keeps a sum of terms =-=[47]-=-. There are many other approaches which may be suitable for soft-output large scale MIMO detection, e.g., Markov chain MonteCarlo techniques [48]. October 21, 2011 DRAFT39 10 −1 BER 10 −2 MMSE MMSE-S... |

4 |
Wireless communication systems with-spatial diversity: a volumetric model
- Hanlen, Fu
- 2006
(Show Context)
Citation Context ...es that the antenna separation decreases. This problem has been examined in recent papers, although the focus is often on spatial correlation and the effect of coupling is often neglected, as in [14]–=-=[16]-=-. In [17], the effect of coupling on the capacity of fixed length ULAs is studied. In general, it is found that mutual coupling has a substantial impact on capacity as the number of antennas is increa... |

4 | Block-iterative generalized decision feedback equalizers for large MIMO systems: algorithm design and asymptotic performance analysis
- Liang, Sun, et al.
- 2006
(Show Context)
Citation Context ... reduce the number of matrix inversions to 1 per iteration. The idea is to formulate the inversion for user k as a rank one update of a general inverse matrix at each iteration. The BI-GDFE algorithm =-=[36]-=- is equation-wise similar to MMSE-SIC [37]. Compared to MMSE-SIC, it has two differences. The linear MMSE filters of MMSE-SIC depend on the received vector x, while the BI-GDFE filters, which are func... |

2 |
Correia (ed), Mobile Broadband Multimedia Networks, Techniques, Models and Tools for 4G
- M
- 2006
(Show Context)
Citation Context ...ups with similar delays, angle-of-arrivals and angle-of-departures and they form so-called clusters. Usually the number of active clusters and distinct scatterers are reported to be limited, see e.g. =-=[26]-=-, also when the number of physical objects is large. The contributions from individual multipath components belonging to the same cluster are often correlated which reduces the number of effective sca... |

2 |
Significance of common scatterers in multi-link scenarios
- Poutanen, Haneda, et al.
- 2010
(Show Context)
Citation Context ... number of effective scatterers. Similarly it has been shown that a cluster seen by different users, so called joint clusters, introduces correlation between users also when they are widely separated =-=[27]-=-. It is still an open question whether the use of large arrays makes it possible to resolve clusters completely, but the large spatial resolution will make it possible to split up clusters in many cas... |

1 |
On the relationship between MMSE-SIC and BI-GDFE receivers for large multiple-input multiple-output channels
- Liang, Cheu, et al.
- 2008
(Show Context)
Citation Context ... 1 per iteration. The idea is to formulate the inversion for user k as a rank one update of a general inverse matrix at each iteration. The BI-GDFE algorithm [36] is equation-wise similar to MMSE-SIC =-=[37]-=-. Compared to MMSE-SIC, it has two differences. The linear MMSE filters of MMSE-SIC depend on the received vector x, while the BI-GDFE filters, which are functions of a parameter that varies with iter... |

1 |
New soft stack decoder for MIMO channel
- Salah, Othman, et al.
- 2008
(Show Context)
Citation Context ...e increased. Many tree-based low-complexity algorithms try to reduce the search by only expanding the fraction of the tree-nodes that appear the most “promising”. One such method is the stack decoder =-=[42]-=-, where the nodes of the tree are expanded in the order of least Euclidean distance to the received signal. The average complexity of the sphere decoder is however exponential in K [4], and SD is thus... |

1 | Desing and analysis of low-compelxity interference mitigation on vector channels - Müller, Verdu - 2001 |