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## Joint Tx-Rx beamforming design for multicarrier MIMO channels: a unified framework for convex optimization (2003)

Venue: | IEEE TRANS. SIGNAL PROCESSING |

Citations: | 288 - 19 self |

### Citations

12168 | Elements of Information Theory - Cover, Thomas |

7509 |
Matrix Analysis
- Horn, Johnson
- 1985
(Show Context)
Citation Context ...,i (9) where Rk,i � HkBkBH k HH k + Rnk − Hkbk,ibH k,iHH k is the interference-plus-noise covariance matrix seen by the (kth, ith) substream, the inequality comes from the Cauchy-Schwarz’s inequality =-=[31]-=- (with vectors (R −1/2 k,i Hkbk,i) and(R 1/2 k,i ak,i)), and the upper bound is achieved by ak,i ∝ R −1 k,i Hkbk,i ∝ R −1 yk Hkbk,i, i.e., the Wiener filter again. Noting that the MSE can be expressed... |

2858 | Capacity of multi-antenna Gaussian channels
- Telatar
- 1999
(Show Context)
Citation Context ... the receiver have recently attracted a significant interest because they provide an important increase in capacity over single-input single-output (SISO) channels under some uncorrelation conditions =-=[4, 5]-=-. In terms of spectral efficiency, a MIMO system should be designed to approach the capacity of the channel [6, 2, 7]. In light of this observation, a frequency-selective MIMO channel can be dealt wit... |

2353 | On limits of wireless communications in a fading environment when using multiple antennas
- Foschini, Gans
- 1998
(Show Context)
Citation Context ... the receiver have recently attracted a significant interest because they provide an important increase in capacity over single-input single-output (SISO) channels under some uncorrelation conditions =-=[4, 5]-=-. In terms of spectral efficiency, a MIMO system should be designed to approach the capacity of the channel [6, 2, 7]. In light of this observation, a frequency-selective MIMO channel can be dealt wit... |

1542 |
Fundamentals of Statistical Signal Processing: Estimation Theory
- Kay
- 1993
(Show Context)
Citation Context ...particularizing c for all the vectors of the canonical base, it follows that A opt k = ( HkBkB H k HH k + Rnk ) −1 HkBk. (7) Expression (7) is the linear minimum MSE (LMMSE) receiver or Wiener filter =-=[30]-=-. Using the optimal receive matrix A opt k , we obtain the following concentrated error matrix: Ek (Bk) � Ek(Bk, A opt k ) = I − B H k HH ( k HkBkB H k HHk ) −1 RHkBk = ( I + B H k + Rnk ) −1 HkBk (8)... |

1426 | Multiuser Detection
- Verdú
- 1998
(Show Context)
Citation Context ...nd Q is the Q-function defined as ∫ ∞ x e−λ2 /2dλ [32]. It is sometimes convenient to use the Chernoff upper bound of the tail of Q (x) = 1 √ 2π the Gaussian distribution function Q (x) ≤ 1 2 e−x2 /2 =-=[33]-=- to approximate the symbol error probability as Pe ≈ 1 2 αe−β/2 SINR (which becomes a good approximation for high values of the SINR). The BER can be approximately obtained from the symbol error proba... |

1404 |
Layered space-time architecture for wireless communication in a fading environment when using multi-element antennas
- Foschini
- 1996
(Show Context)
Citation Context ... the unified notation of a channel matrix such as a frequency-selective channel employing transmit and receive filterbanks [3], a bundle of twisted pairs in DSL [1], or a wireless multiantenna system =-=[27, 2]-=-. Although the results in this paper are valid for any MIMO channel, we focus on a wireless multi-antenna system to gain insight into beamforming issues traditionally associated to arrays of antennas.... |

1207 | Optimization by Vector Space Methods
- Luenberger
- 1969
(Show Context)
Citation Context ...spect to x is written as ∇xf (x). We define (x) + � max (0,x). 2 Preliminaries In Section 5, a variety of objective functions are considered under the powerful framework of convex optimization theory =-=[19, 20, 21]-=-. For this purpose, we first give an overview in subsection 2.1 of the potential and advantages of this framework. Roughly speaking, one can say that once a problem has been expressed in convex form, ... |

1137 |
Inequalities: Theory of Majorization and Its Applications
- Marshall, Olkin
- 1979
(Show Context)
Citation Context ...s by considering two families of objective functions that embrace most reasonable criteria to design a communication system: Schur-concave and Schurconvex functions which arise in majorization theory =-=[17]-=-. For Schur-concave objective functions, the channel-diagonalizing structure is always optimal, whereas for Schur-convex functions, an optimal solution diagonalizes the channel only after a very speci... |

407 | Spatio-temporal coding for wireless communication
- Raleigh, Cioffi
- 1998
(Show Context)
Citation Context ... arise in many different scenarios such as when a bundle of twisted pairs in digital subscriber lines (DSL) is treated as a whole [1], when multiple antennas are used at both sides of a wireless link =-=[2]-=-, or simply when a frequency-selective channel is properly modeled by using, for example, transmit and receive filterbanks [3]. In particular, MIMO channels arising from the use of multiple antennas a... |

304 |
S.: Interior-point polynomial methods in convex programming
- Nesterov, Nemirovsky
- 1994
(Show Context)
Citation Context ...rovsky in 1988. They showed that interior-point methods (initially proposed only for linear programming by Karmarkar in 1984) can, in principle, be generalized to all convex optimization problems. In =-=[26]-=- a very general framework was developed for solving convex optimization problems using interior-point methods. In addition, the difference between the objective value at each iteration and the optimum... |

273 |
Giannakis, “Wireless multicarrier communications: Where Fourier meets Shannon
- Wang, B
- 2000
(Show Context)
Citation Context ...ation, a frequency-selective MIMO channel can be dealt with by taking a multicarrier approach which is a well-known capacity-lossless structure and allows to treat each carrier as a flat MIMO channel =-=[2, 8]-=-. A capacity-achieving design dictates that the channel matrix at each carrier must be diagonalized and then a water-filling power allocation must be used on the spatial subchannels (or channel eigenm... |

193 | Generalized linear precoder and decoder design for MIMO channels using the weighted MMSE criterion
- Sampath, Stoica, et al.
- 2001
(Show Context)
Citation Context ...ll channel substreams (the trace of the MSE matrix) was used as the objective to minimize under an average power constraint. This criterion was generalized by using a weighted sum (weighted trace) in =-=[14]-=-. In [3], a maximum signal to interference-plus-noise ratio (SINR) criterion with a zero-forcing (ZF) constraint was also considered. For these criteria, the original complicated design problem is gre... |

187 | Optimal Designs for Space-time Linear Precoders and Decoders
- Scaglione, Barbarossa, et al.
- 2002
(Show Context)
Citation Context ...se the channel turns out to be diagonalized by the transmit-receive processing. In [15], the determinant of the MSE matrix was minimized and the diagonal structure was found to be optimal as well. In =-=[16]-=-, the results were extended to the case of a peak power constraint (maximum eigenvalue constraint) with similar results. We remark that the channel-diagonalizing property is of paramount importance in... |

183 | Redundant filterbank precoders and equalizers, Part II: Blind channel estimation, synchronization, and direct estimation
- Scaglione, Giannakis, et al.
(Show Context)
Citation Context ...a scalarization of the problem (meaning that all matrix equations are substituted with scalar ones). Examples are the minimization of the (weighted) sum of the MSE’s of all channel spatial substreams =-=[13, 3, 14]-=-, the minimization of the determinant of the MSE matrix [15], and the maximization of the mutual information [6, 2, 7]. Recall that for other interesting design criteria (such as the minimization of t... |

162 | 11: Wireless LAN medium access control (MAC) and physical layer (PHY) specifications - “Part - 2012 |

138 | Optimal sequences and sum capacity of synchronous cdma systems - Viswanath, Anantharam - 1984 |

115 |
Optimal power control in interference-limited fading wireless channels with outageprobabilityspecifications,”IEEETransactionsonWirelessCommunications,vol.1,Jan.2002. [41
- Kandukuri, Boyd
(Show Context)
Citation Context ...gnal (c.f. Section 6). Convex programming has been used in related areas such as FIR filter design [23], antenna array pattern synthesis [24], power control for interference-limited wireless networks =-=[25]-=-, and transmit downlink beamforming in a multiuser scenario with a multi-antenna base station [22]. Solving Convex Optimization Problems In some cases, convex optimization problems can be analytically... |

110 |
On joint transmitter and receiver optimization for multipleinput-multiple-output (MIMO) transmission systems
- Yang, Roy
- 1994
(Show Context)
Citation Context ...design of linear processing at both ends of the link (commonly referred to as linear precoder at the transmitter and equalizer at the receiver) according to a variety of criteria as we now review. In =-=[11, 12, 13, 3]-=-, the sum of the mean square error (MSE) of all channel substreams (the trace of the MSE matrix) was used as the objective to minimize under an average power constraint. This criterion was generalized... |

106 |
Part 11: Wireless LAN medium access control (MAC) and physical layer (PHY) specifications: High-speed physical layer
- IEEE
- 1999
(Show Context)
Citation Context ...s with a sufficiently high gain), i.e., an equal-rate transmission. Examples of this pragmatic and simple solution are found in the European standard HIPERLAN/2 [9] and in the US standard IEEE 802.11 =-=[10]-=- for Wireless Local Area Networks (WLAN). Assuming that the specific signal constellations and coding schemes for all the substreams have been selected either after some bit distribution method or sim... |

92 |
radio access networks (BRAN); HIPERLAN Type 2 technical specification, Part I: physical layer
- ETSI
- 1999
(Show Context)
Citation Context ...h to transmit only over those eigenmodes with a sufficiently high gain), i.e., an equal-rate transmission. Examples of this pragmatic and simple solution are found in the European standard HIPERLAN/2 =-=[9]-=- and in the US standard IEEE 802.11 [10] for Wireless Local Area Networks (WLAN). Assuming that the specific signal constellations and coding schemes for all the substreams have been selected either a... |

72 | Introduction to Convex Optimization with Engineering Applications - Boyd, Vandenberghe - 1995 |

69 |
Optimal and suboptimal transmit beamforming
- Bengtsson, Ottersten
- 2002
(Show Context)
Citation Context ...an be straightforwardly added as long as they are convex. For example, in the problem addressed in this paper, it is very simple to add constraints to control the dynamic range of the power amplifier =-=[22]-=- and the PAR of the transmitted signal (c.f. Section 6). Convex programming has been used in related areas such as FIR filter design [23], antenna array pattern synthesis [24], power control for inter... |

62 | Giannakis, “Filterbank transceivers optimizing information rate in block transmissions over dispersive channels - Scaglione, Barbarossa, et al. - 1999 |

61 |
Optimal linear coding for vector channels
- Lee, Petersen
- 1976
(Show Context)
Citation Context ...design of linear processing at both ends of the link (commonly referred to as linear precoder at the transmitter and equalizer at the receiver) according to a variety of criteria as we now review. In =-=[11, 12, 13, 3]-=-, the sum of the mean square error (MSE) of all channel substreams (the trace of the MSE matrix) was used as the objective to minimize under an average power constraint. This criterion was generalized... |

53 |
Joint transmitter–receiver optimization for multiinput multi-output systems with decision feedback
- Yang, Roy
- 1994
(Show Context)
Citation Context ...nstraint was also considered. For these criteria, the original complicated design problem is greatly simplified because the channel turns out to be diagonalized by the transmit-receive processing. In =-=[15]-=-, the determinant of the MSE matrix was minimized and the diagonal structure was found to be optimal as well. In [16], the results were extended to the case of a peak power constraint (maximum eigenva... |

48 |
Digital transmission over cross-coupled linear channels
- Salz
- 1985
(Show Context)
Citation Context ...design of linear processing at both ends of the link (commonly referred to as linear precoder at the transmitter and equalizer at the receiver) according to a variety of criteria as we now review. In =-=[11, 12, 13, 3]-=-, the sum of the mean square error (MSE) of all channel substreams (the trace of the MSE matrix) was used as the objective to minimize under an average power constraint. This criterion was generalized... |

48 | S.: Antenna array pattern synthesis via convex optimization
- Lebret, Boyd
- 1997
(Show Context)
Citation Context ...e of the power amplifier [22] and the PAR of the transmitted signal (c.f. Section 6). Convex programming has been used in related areas such as FIR filter design [23], antenna array pattern synthesis =-=[24]-=-, power control for interference-limited wireless networks [25], and transmit downlink beamforming in a multiuser scenario with a multi-antenna base station [22]. Solving Convex Optimization Problems ... |

44 | BAdaptive antennas at the mobile and base station in an OFDM/TDMA system
- Wong, Cheng, et al.
(Show Context)
Citation Context ...xl ∀k, l) [31], it follows that the optimal solution is a uniform power allocation: (41) zk,i = PT / ˇ LT . (42) Note that the uniform power distribution is commonly used due to its simplicity, e.g., =-=[38]-=-. 5.2.3 Maximization of the HARM-SINR The maximization of the harmonic mean of the SINR’s (HARM-SINR) was considered in [35] for the case of single beamforming. Using the unified framework of Theorem ... |

35 |
A Method to Reduce the Probability of Clipping in DMT-Based Transceivers
- Mestdagh, Spruyt
- 1996
(Show Context)
Citation Context ...ge). In practice, the transmitted signal has to be clipped when it exceeds a certain threshold which has detrimental effects on the BER. A variety of techniques have been devised to deal with the PAR =-=[41, 42]-=-. In this section we show how the PAR can be taken into account into the design of the beamvectors using a convex optimization framework. Note that the already existing techniques to cope with the PAR... |

29 |
Generalized decision-feedback equalization for packet transmission with ISI and Gaussian noise
- Cioffi, Forney
- 1997
(Show Context)
Citation Context ...nt. Alternatively, we can obtain A opt k so that Ek(Bk, A opt k ) ≤ Ek (Bk, Ak) which in particular implies that the diagonal elements are minimized (in fact, both criteria are equivalent as shown in =-=[29]-=-). In other words, we want to solve: min A ∗ k c H Ek (Bk, Ak) c ∀c. Setting the gradient of c H Ekc =Tr ( Ekcc H) to zero, ∇A ∗ k Tr ( Ekcc H) = Ryk Akcc H −HkBkcc H = 0 ∀c, and particularizing c for... |

28 | L.: FIR filter design via semidefinite programming and spectral factorization
- Wu, Boyd, et al.
- 1996
(Show Context)
Citation Context ...onstraints to control the dynamic range of the power amplifier [22] and the PAR of the transmitted signal (c.f. Section 6). Convex programming has been used in related areas such as FIR filter design =-=[23]-=-, antenna array pattern synthesis [24], power control for interference-limited wireless networks [25], and transmit downlink beamforming in a multiuser scenario with a multi-antenna base station [22].... |

28 |
A unified framework for communications through MIMO channels,” Ph.D. dissertation, Universitat politecnica de Catalunya
- Palomar
- 2003
(Show Context)
Citation Context ...marks Some observations are in order: • Most of the presented methods under the framework of convex optimization theory have nice closedform solutions which can be easily implemented in practice (see =-=[36]-=- for simple practical algorithms derived from the KKT optimality conditions to implement the water-filling solutions). • Method ARITH-BER is clearly the best in terms of average BER and is therefore c... |

20 | Multi channel signal processing for data communications in the presence of crosstalk
- Honig, Steiglitz, et al.
- 1990
(Show Context)
Citation Context ...00268. 01 Introduction Multiple-input multiple-output (MIMO) channels arise in many different scenarios such as when a bundle of twisted pairs in digital subscriber lines (DSL) is treated as a whole =-=[1]-=-, when multiple antennas are used at both sides of a wireless link [2], or simply when a frequency-selective channel is properly modeled by using, for example, transmit and receive filterbanks [3]. In... |

17 |
Multiple-input multipleoutput (MIMO) wireless systems,” The Communications Handbook, 2nd edion, 90.1–90.14
- Bölcskei, Paulraj, et al.
- 2002
(Show Context)
Citation Context ..., the matrix channel has Kk ≤ min (nT ,nR) channel eigenmodes or spatial subchannels (i.e., nonvanishing singular values of the channel matrix) [2]. We can use them as a means of spatial multiplexing =-=[28]-=- to transmit simultaneously Lk symbols by having Lk established substreams. Notice that established substreams and spatial subchannels ( or channel eigenmodes) are different concepts which may or may ... |

14 | Efficient signaling schemes for wideband space-time wireless channels using channel state information
- Onggosanusi, Sayeed, et al.
- 2003
(Show Context)
Citation Context ...in fact, for codes based on hard decisions, both quantities are strictly related). In such cases, it suffices to focus on the uncoded BER when designing the uncoded part of a communication system. In =-=[39]-=-, the minimization of the average BER (and also of the Chernoff upper bound) is treated in detail when a diagonal structure is imposed. This design criterion has been independently considered in [40] ... |

13 |
Convex Analysis, 2nd ed
- Rockafellar
- 1970
(Show Context)
Citation Context ...INRk,i ≤ SINRk,i+1 in the convex problem formulation since an optimal solution always satisfies them. k,i 18The problem expressed in convex form (the weighted geometric mean is a concave function 11 =-=[20, 21]-=-) is 10 max {zk,i} s.t. ∏ k,i (λk,i zk,i) ˜wk,i ∑ k,i zk,i ≤ PT , zk,i ≥ 0 1 ≤ k ≤ N, 1 ≤ i ≤ ˇ Lk, ( ∑ where ˜wk,i = wk,i/ l,j wl,j ) anditisassumedthatλk,i > 0 ∀k, i (otherwise the problem has trivi... |

9 |
models for HIPERLAN/2 in different indoor scenarios
- ETSI
- 1998
(Show Context)
Citation Context ... design either from a worst-case or from a Bayesian perspective (c.f. [36]). 24The frequency selectivity of the channel is modeled using the power delay profile type C for HIPERLAN/2 as specified in =-=[43]-=- (see Figure 5(a)), which corresponds to a typical large open space indoor environment for NLOS15 conditions with 150ns average r.m.s. delay spread and 1050ns maximum delay (the sampling period is 50n... |

4 | Convex optimization theory applied to joint beamforming design
- Palomar, Cioffi, et al.
(Show Context)
Citation Context ...se of having minimum average BER. A convex optimization approach for the simple case of utilizing a single spatial eigenmode (in other words, using a single beamforming per carrier) was also taken in =-=[18]-=-. Additional constraints on the Peak-to-Average Ratio (PAR) or on the signal dynamic range are easily included in the design within the convex optimization framework. We propose two multi-level water-... |

4 | Joint beamforming strategies in OFDM-MIMO systems
- Iserte, Perez-Neira, et al.
- 2002
(Show Context)
Citation Context ...t each transmission, i.e., a single spatial eigenmode L = 1 is utilized, Theorem 1 simplifies and the diagonal structure simply means that the spatial subchannel (eigenmode) with highest gain is used =-=[35, 18]-=-. For Schur-concave objective functions, the global communication process including pre- and postprocessing AHHB is fully diagonalized (see Figure 4(b)) as well as the MSE matrix E. Among the 12L est... |

4 |
MIMO channel characterisation,” Deliverable D2 V1.1 of IST-1999-11729 METRA project
- Schumacher, Kermoal, et al.
- 2001
(Show Context)
Citation Context ...tions with 150ns average r.m.s. delay spread and 1050ns maximum delay (the sampling period is 50ns) [9]. The spatial correlation of the MIMO channel is modeled according to the Nokia model defined in =-=[44]-=- (which corresponds to a reception hall) specified by the correlation matrices of the envelope of the channel fading at the transmit and receive side given in Figure 5(b) where the base station is the... |

2 | On the optimal structure of transmit-receive linear processing for MIMO systems - Palomar, Lagunas, et al. - 2002 |