Upper Bounds on MIMO Channel Capacity with Channel Frobenius Norm Constraints
|
|
- Wilfred McCarthy
- 6 years ago
- Views:
Transcription
1 Upper Bounds on IO Channel Capacity with Channel Frobenius Norm Constraints Zukang Shen, Jeffrey G. Andrews, Brian L. Evans Wireless Networking Communications Group Department of Electrical Computer Engineering The University of Texas at Austin, Austin, Texas {shen, jrews, Abstract The motivation of this paper is to find the class of channels that provides the largest capacity with both the transmit power constraint channel Frobenius norm constraints. We study both the point-to-point case the broadcast case. For point-to-point IO channels, the optimal channels must have T equal singular values, where T is dependent on the available transmit power the channel Frobenius norm. This result agrees with the previous work by Chiurtu et al. For multiuser broadcast channels, we obtain an upper bound on the sum capacity. We also show that the bound is asymptotically tight for high SNR when all user channels have the same Frobenius norm constraint N t N r, where N t N r are the numbers of transmit receive antennas is the number of users. I. INTRODUCTION ultiple-input-multiple-output IO) systems have drawn a lot of attention in the last decade. The spatial dimension, in addition to the time frequency dimensions, can be exploited with multiple antennas at the transmitter receiver. The fundamental information theoretic results on IO channel capacity, e.g. [1] [6] just to name a few, are important because they not only show the performance limits, but also shed light on how to achieve the capacity, which helps to design IO systems. The Gaussian IO channel capacity problem can be generally formulated into an optimization problem. Given a fixed channel or a rom channel with certain probability distributions, the objective is to optimize the input covariance matrix under a power constraint so that the channel capacity is achieved. For example, for a fixed channel H, the point-topoint IO channel capacity can be formulated as log Q I + 1 σ 2 HQH 1) subject to trq) P where Q is the input covariance matrix the only constraint in 1) is the power constraint, i.e. trq) P. While the IO channel capacity is a function of the available transmit power, it is also dependent on the channel characteristics, such as the channel power. In [7], Sayeed et al. studied the optimal This work was supported by a gift from Texas Instruments an equipment donation from Intel. IO channel capacity scaling law under different channel power scaling laws with respect to the number of antennas. While [7] focused on the optimal capacity scaling law, in this paper, we study the imum channel capacity with both transmit power channel power represented by the channel Frobenius norm) constraints. The term imum capacity in this paper refers to the imum capacity over all possible channels satisfying the norm constraint, while capacity is defined to be the imum mutual information over the transmit signal covariance matrix for a fixed channel. The motivation for optimizing the channel jointly with the input covariance matrix under the transmit power channel power constraints are: 1) for the class of power-constrained channels, an upper bound on the IO channel capacity can be found; 2) the characteristics of the channels providing the imum capacity can be obtained, which may be used to direct the adaptive antenna array configuration if possible. We study both single user point-to-point IO systems multiuser broadcast channels. For the point-to-point case, Chiurtu et al. in [8] showed that the class of channels that provides imum capacity must have equal singular values, the optimal transmit signal covariance matrix also assigns equal power to those non-zero eigenmodes. While Chiurtu et al. obtained the solution with Lagrange multipliers in [8], we study the problem using iterative water-filling. For the multiuser broadcast channel case, we obtain an upper bound on the largest sum capacity for the channels bounded by Frobenius norm. We also show that the bound is asymptotically tight for high SNR when N t N r all user channels have the same Frobenius norm constraint. II. SYSTE ODEL AND PROBLE FORULATION A. Single User: Point-to-point Case The symbolwise discrete-time input-output relationship of a narrowb point-to-point IO system can be written as y = Hx + v 2) where H is the N r N t channel matrix; x y are the transmitted received symbol vector, respectively; v is the additive white Gaussian noise vector, with E[vv ] = σ 2 I, ) denotes matrix complex conjugate transpose. Without loss of generality, we assume σ 2 = 1.
2 In this paper, we consider the IO channel capacity with both total transmit power constraint channel Frobenius norm constraint. The motivation is to find the bounds on the IO channel capacity with a channel Frobenius constraint, i.e. H 2 F W, to identify the channels imize capacity. For a point-to-point IO system, we have the following problem formulation. log I + HQH 3) H Q subject to : trq) P H 2 F W. B. ultiple Users: Broadcast Case For a broadcast multiuser IO system, the received signal for user k can be expressed as y k = H k x i + v k 4) where x i is the user i s transmitted signal; H k of size N r N t denotes the channel for user k; y k is the received signal for user k; v k is the additive white Gaussian noise at receiver k; is the total number of users. Furthermore, in this paper, we assume all users are equipped with an equal number of receiver antennas N r the transmitter has N t N r transmit antennas. It has been shown that Dirty Paper Coding DPC) [] achieves the sum capacity in a Gaussian broadcast IO channel [13]. And the duality results in [13] show that for a fixed set of channels {H k }, the sum capacity of a Gaussian broadcast IO channel can found by solving the following problem: log {Q k } I + 5) subject to TrQ k ) P. Similar to the point-to-point case, with a set of channel Frobenius norm constraints, we have the following problem formulation for a Gaussian broadcast channel: log {H k } {Q k } I + 6) subject to TrQ k ) P H k 2 F W k for k = 1, 2,,. Remarks: The emphasis of this paper is to find what kind of channels provide the imum IO channel capacity with a channel norm constraint. It is assumed that the transmitter knows the channel perfectly in order to optimize its signal covariance matrix. III. POINT-TO-POINT CASE Let N = {N t, N r } = min{n t, N r }, let the singular value decomposition SVD) of H H be H H = UDU, where D is a diagonal matrix whose non-zero elements are denoted as {λ i } ; U is a unitary matrix. Notice that λ i = H 2 F 7) log I + HQH = log 1 + S i λ i ) 8) where S i is the power allocated to the ith non-zero eigenmode, the original problem in 3) can be reformulated as Λ S log 1 + S i λ i ) 9) subject to : S i P λ i W where S = {S 1 S 2 S } Λ = {λ 1 λ 2 λ }. Notice that the objective function in 9) is symmetric with S Λ. For a given Λ, the optimal S i = Γ s 1 λ i is obtained by water-filling, where Γ s is the water level which satisfies S i = P. For a given S, the optimal λ i = Γ λ 1 S i λ i = W. Hence iterative water-filling can be used between S Λ, i.e. 1) starting from an initial value S, imize the objective function in 9) over Λ. And let Λ = arg Λ log 1 + S i λ i). 2) For the Λ, imize the objective function in 9) over S. Let S = arg S log 1 + S iλ i ). 3) Repeat step 1 2 until an equilibrium is reached. Based on the above iterative water-filling procedure, we have the following two Lemmas: Lemma 1: At each equilibrium point, the following equations hold Si = Γ s 1 λ i λ i = Γ λ 1 S i for i = 1, 2,, T ) for i = 1, 2,, T 11) T Si = P 12) T λ i = W 13) for some 1 T. Proof: Equations ) 11) are easy to justify because at each equilibrium point, {Si }T are the water-filling results for {λ i }T. Otherwise, the iterative water-filling procedure
3 can be continued until an equilibrium point is reached. Equations 12) 13) are true because the transmitter is supposed to use as much power as possible the channel shall also provide imal energy. Hence, the power channel norm constraints are binding. Lemma 2: The global ima must be one of these equilibrium points. Proof: This result is straightforward because the objective function, i.e. log 1 + S iλ i ) is not decreasing as the iterative water-filling procedure progresses. Suppose the global ima does not satisfy the conditions in Lemma 1, then performing the iterative water-filling algorithm can further improve the objective function. Theorem 1: For a fixed channel H with channel norm constraint H 2 F W transmit power constraint TrQ) P, the imum possible channel capacity is log I + HQH = T log Q, H T : T =1,2,, 1 + P W ). 14) Proof: First, we will find the equilibrium points from Lemma 1. ultiply ) with Λ i multiply 11) with S i Hence to obtain S i λ i = Γ s λ i 1 15) λ i S i = Γ λ S i 1 16) S i = Γ s Γ λ λ i 17) for i = 1, 2,, T. Substituting 17) into 11) results in λ i = Γ λ Γ λ Γ s 1 λ i 18) for i = 1, 2,, T. Notice that from 18), λ i only depends on Γ λ Γ s, which is the same for all i = 1, 2,, T. Although λ i may be one of the two possible solutions to 18), the Lemma in [8] proves that in order to imize 9), we must have λ i = λ j 19) S i = S j 2) for 1 i, j T. Combined with 12) 13), we obtain S i = P T λ i = W T for i = 1, 2,, T. Also it is easy to see that 21) 22) Γ s Γ λ = P W. 23) Notice that there are for 1 T ) cidate equilibrium points for the global ima. From Lemma 2, the global imum of the original problem in 3) can be obtained by finding the imum among those equilibrium points, i.e. log I + HQH = T log 1 + P W ) Q, H T : T =1,2,, 24) which is straightforward to evaluate. Let T = arg T log ) 1 + P W T : T =1,2,, T. The interpretation of the above results is that among all possible channel 2 H which is limited by the Frobenius norm constraint, i.e. H 2 F W, the class of H imizing the channel capacity has T equal singular values of W/T. Notice that the product of P W completely decides T, leading to the following observation. Lemma 3: For sufficiently small P W, T = 1, for sufficiently large P W, T =. This is reasonable because when P W is sufficiently small, those channels providing the largest capacity shall focus both the channel energy transmit power to one eigenmode. This is somehow related to the optimality of beamforming in low SNR regime. When P W is sufficiently large, then T =, meaning all possible spatial dimensions shall be utilized. IV. BROADCAST CASE For a multi-user broadcast channel, the optimization problem in 6) is difficult to solve. Even for a set of fixed user channels, the boradcast sum capacity in 5) is a difficult optimization problem. Several algorithms have been proposed, e.g. the iterative water-filling algorithm by Jindal, et al. in [16]. In this section, we show an upper bound for the problem in 6) in following theorem. Theorem 2: For multiuser broadcast channels with individual channel norm constraints H k 2 F W k for k = 1, 2,,, a total transmit power constraint TrQ k) P, the imum sum capacity is upper bounded by P {H k }: H k 2 F W i {Q k }: TrQ k ) P T log T : T =1,2,, c log I P ) W k 25) where c = min{n t, N r }. Proof: Notice that if we denote H c = [H 1 H 2 H ], then log P I + {Q k }: TrQ k ) P log I + Hc QH c. 26) Q: TrQ) P This is true because the right h side RHS) of 26) is the capacity of a point-to-point channel H c, which represents the scenario in which users may cooperate in the broadcast channel.
4 Since 26) holds true for any channel {H k }, notice that H c 2 F = H k 2 F, we have P {H k }: H k 2 F W i {Q k }: TrQ k ) P H c : H c 2 F P W k log I + log I + H c QH c 27) Q: TrQ) P Let c = min{n t, N r }. From Theorem 1, the solution to the RHS of 27) can be easily obtained as H c : H c 2 F P W k = T : T =1,2,, c T log log I + H c QH c Q: TrQ) P 1 + P ) W k 28) Hence combining 27) 28) completes the proof. Theorem 2 only gives an upper bound on the imum sum capacity with channel norm constraints. In the following, we show a special case where the upper bound in Theorem 2 is actually tight. Before stating the Lemma, we first define some notation. Let T be the ima of the RHS of 28), i.e. T = arg T log 1 + P ) W k T : T =1,2,, c. Let the SVD of H k = U k D k V k, where U k is a unitary matrix of size N r N r ; V k is a unitary matrix of size N t N r ; D k is a diagonal matrix of size N r N r the diagonal elements denoted as {λ k,i } Nr. Lemma 4: When T = N N t for some integer 1 N N r W 1 = W 2 = = W = W, the bound in 25) is tight. Proof: With the conditions given in Lemma 4, the bound in 25) becomes log ) N 1 + P W ) 2 N = log 1 + P W ) NT N 2 29) In the following, we construct a set of user channels {H k } such that the bound in 29) is achieved. Let V 1 V 2 V k, which means all user channels are orthogonal to { each other. Let V = [V 1 V 2 } V ]. W W Let D k = diag W for k = N N N 1, 2,,. { } P P Let E = diag P. Let Q N N N k = U k EU k for k = 1, 2,,. Then I + = = I + V k D k U k U keu k U kd k V k I + V k D 2 kev k a) = I + VDV = I + D 3) where D is a diagonal matrix of size N r N r, It has N non-zero diagonal element the jth element d j is d j = P W N N 31) for all j = 1, 2,, N. And equality a) holds because V 1 V 2 V k D 2 ke is diagonal for all k = 1, 2,,. With 31), we have log I + N H k Q kh k = log1 + d j ) j=1 = N log 1 + P W ) N 2 32) with equals 29). Hence Lemma 3 is proved. Lemma 5: When N r N t W 1 = W 2 = = W = W, the bound in 25) is asymptotically tight for high SNR. Proof: For high SNR, we have T = min{n t, N r } = N r. This is true because for large enough SNR, the transmitter needs to utilize as many eigenmodes as possible. Hence Lemma 5 is a special case of Lemma 4 where N = N r. Remarks: The results in Lemma 4 Lemma 5 are not surprising because when the user channels are mutually orthogonal, the sum capacity of the broadcast channel is the same as the cooperative channel with the same total transmit power constraint. V. NUERICAL RESULTS In this section, we provide a few numerical results on the imum IO channel capacity with both transmit power channel norm constraints. For a point-to-point IO channel, since the optimal number of non-zero eigenmodes T is determined by the product of P W, we define SNR = P W in this paper. Fig. 1 shows the largest possible IO channel capacity vs. SNR for different, which is the minimum of the number of transmit receive antennas. For low SNR, the capacity is the same regardless of the value of. This is true since under low SNR, the optimal transmit strategy is to allocate all power to the largest eigenmode. And those channels providing the most capacity shall focus all its energy to one eigenmode. As SNR increases, more eigenmodes shall be utilized. And Fig. 2 shows the optimal number of eigenmodes vs. SNR. Fig. 3 shows the largest capacity vs. for different SNR. It
5 Capacity bits/s/hz) = 2, 3,..., Capacity bits/s/hz) SNR=, 2, 3, 4, 5 db SNR db) Fig. 1. Point-to-point IO channels. aximum capacity vs. SNR, which is defined as SNR P W. = min{n t, N r } Fig. 3. Point-to-point IO channels. aximal capacity vs., which is defined as = min{n t, N r}. And SNR P W. T * SNR db) Fig. 2. Point-to-point IO channels. Optimal number of eigenmodes T ) vs. SNR, which is defined as SNR P W. = min{n t, N r } =. is simply a different view of Fig. 1. From Fig. 3, we confirmed that for low SNR, the largest capacity is the same for all. VI. CONCLUSION In this paper, the IO channel capacity with channel Frobenius norm constraints is studied. For a point-to-point IO channel, the optimal channel that provides the largest capacity must have T equal eigenmodes, where T is dependent on the total transmit power constraint P the channel norm constraint W. For a multiuser broadcast channel, we obtain an upper bound on the largest sum capacity when the user channels have Frobenius norm constraints. It is also shown that the bound is asymptotically tight for high SNR when N t N r all user channels have the same Frobenius norm constraint. REFERENCES [1] I. E. Telatar, Capacity of ulti-antenna Gaussian channels, European Transactions on Telecommunications, vol., no. 6, pp , Nov./Dec [2] A. Goldsmith, S. A. Jafar, N. Jindal, S. Vishwanath, Capacity Limits of IO Channels, IEEE Journal on Selected Area in Communications, vol. 21, no. 5, p , Jun. 23. [3] S.. Jayaweera H. V. Poor, Capacity of ultiple-antenna Systems with Both Receiver Transmitter Channel State Information, IEEE Transactions on Information Theory, vol. 49, no., pp , Oct. 23. [4] E. Biglieri, G. Caire, G. Taricco, Limiting Performance of Block- Fading Channels with ultiple Antennas, IEEE Transactions on Information Theory, vol. 47, no. 4, pp , ay 21. [5] A. S. Y. Poon, D. N. C. Tse, R. W. Brodersen, An Adaptive ultiantenna Transceiver for Slowly Flat Fading Channels, IEEE Transactions on Communications, vol. 51, no. 11, pp , Nov. 23. [6] Z. Shen, R. W. Heath. Jr., J. G. Andrews, B. L. Evans, Comparison of Space-Time Water-filling Spatial Water-filling for IO Fading Channels, in Proc. IEEE Global Communications Conference., vol. 1, pp , Dec. 24. [7] A. Sayeed, V. Raghavan, J. otecha, Capacity of Space-Time Wireless Channels: A Physical Perspective, in IEEE Information Theory Workshop, Oct. 24. [8] N. Chiurtu B. Rimoldi, Varying the Antenna Locations to Optimize the Capacity of ulti-antenna Gaussian Channels, in Proc. IEEE International Conference on Acoustics, Speech, Signal Processing, vol. 5, pp , Jun. 2. [9] N. Chiurtu, B. Rimoldi, E. Telatar, On the Capacity of ulti- Antenna Gaussian Channels, in Proc. IEEE International Symposium on Information Theory, pp. 53, Jun. 21. []. Costa, Writing on Dirty Paper, IEEE Transactions on Information Theory, vol. 29, no. 3, pp , ay [11] G. Caire S. Shamai, On the Achievable Throughput of a ultiantenna Gaussian Broadcast Channel, IEEE Transactions on Information Theory, vol. 49, no. 7, pp , Jul. 23 [12] P. Viswanath D. N. C. Tse, Sum Capacity of the Vector Gaussian Broadcast Channel Uplink-Downlink Duality, IEEE Transactions on Information Theory, vol. 49, no. 8, pp Aug. 23. [13] S. Vishwanath, N. Jindal, A. Goldsmith, Duality, Achievable Rates, Sum-Rate Capacity of Gaussian IO Broadcast Channels, IEEE Trans. on Information Theory, vol. 49, no., pp , Oct. 23. [14] W. Yu J.. Cioffi, Sum Capacity of Gaussian Vector Broadcast Channels, IEEE Transactions on Information Theory, vol. 5, no. 9, pp , Sep. 24. [15] W. Yu, W. Rhee, S. Boyd, J.. Cioffi, Iterative Water-Filling for Gaussian Vector ultiple-access Channels, IEEE Transactions on Information Theory, vol. 5, no. 1, pp , Jan. 24. [16] N. Jindal, W. Rhee, S. Vishwanath, S. A. Jafar, A. Goldsmith, Sum Power Iterative Water-filling for ulti-antenna Gaussian Broadcast Channels, to appear in IEEE Trans. on Information Theory, 25. [17] T.. Cover J. A. Thomas, Elements of Information Theory, John Wiley & Sons, Inc., 1991.
Dirty Paper Coding vs. TDMA for MIMO Broadcast Channels
TO APPEAR IEEE INTERNATIONAL CONFERENCE ON COUNICATIONS, JUNE 004 1 Dirty Paper Coding vs. TDA for IO Broadcast Channels Nihar Jindal & Andrea Goldsmith Dept. of Electrical Engineering, Stanford University
More informationUSING multiple antennas has been shown to increase the
IEEE TRANSACTIONS ON COMMUNICATIONS, VOL. 55, NO. 1, JANUARY 2007 11 A Comparison of Time-Sharing, DPC, and Beamforming for MIMO Broadcast Channels With Many Users Masoud Sharif, Member, IEEE, and Babak
More informationOn the Capacity of MIMO Rician Broadcast Channels
On the Capacity of IO Rician Broadcast Channels Alireza Bayesteh Email: alireza@shannon2.uwaterloo.ca Kamyar oshksar Email: kmoshksa@shannon2.uwaterloo.ca Amir K. Khani Email: khani@shannon2.uwaterloo.ca
More informationDuality, Achievable Rates, and Sum-Rate Capacity of Gaussian MIMO Broadcast Channels
2658 IEEE TRANSACTIONS ON INFORMATION THEORY, VOL 49, NO 10, OCTOBER 2003 Duality, Achievable Rates, and Sum-Rate Capacity of Gaussian MIMO Broadcast Channels Sriram Vishwanath, Student Member, IEEE, Nihar
More informationOn the Capacity of the Multiple Antenna Broadcast Channel
DIMACS Series in Discrete Mathematics and Theoretical Computer Science On the Capacity of the Multiple Antenna Broadcast Channel David Tse and Pramod Viswanath Abstract. The capacity region of the multiple
More informationSum-Power Iterative Watefilling Algorithm
Sum-Power Iterative Watefilling Algorithm Daniel P. Palomar Hong Kong University of Science and Technolgy (HKUST) ELEC547 - Convex Optimization Fall 2009-10, HKUST, Hong Kong November 11, 2009 Outline
More informationOptimal Power Allocation for Parallel Gaussian Broadcast Channels with Independent and Common Information
SUBMIED O IEEE INERNAIONAL SYMPOSIUM ON INFORMAION HEORY, DE. 23 1 Optimal Power Allocation for Parallel Gaussian Broadcast hannels with Independent and ommon Information Nihar Jindal and Andrea Goldsmith
More informationOn the Duality of Gaussian Multiple-Access and Broadcast Channels
On the Duality of Gaussian ultiple-access and Broadcast Channels Xiaowei Jin I. INTODUCTION Although T. Cover has been pointed out in [] that one would have expected a duality between the broadcast channel(bc)
More informationOn the Optimality of Multiuser Zero-Forcing Precoding in MIMO Broadcast Channels
On the Optimality of Multiuser Zero-Forcing Precoding in MIMO Broadcast Channels Saeed Kaviani and Witold A. Krzymień University of Alberta / TRLabs, Edmonton, Alberta, Canada T6G 2V4 E-mail: {saeed,wa}@ece.ualberta.ca
More informationA Proof of the Converse for the Capacity of Gaussian MIMO Broadcast Channels
A Proof of the Converse for the Capacity of Gaussian MIMO Broadcast Channels Mehdi Mohseni Department of Electrical Engineering Stanford University Stanford, CA 94305, USA Email: mmohseni@stanford.edu
More informationOptimum Power Allocation in Fading MIMO Multiple Access Channels with Partial CSI at the Transmitters
Optimum Power Allocation in Fading MIMO Multiple Access Channels with Partial CSI at the Transmitters Alkan Soysal Sennur Ulukus Department of Electrical and Computer Engineering University of Maryland,
More informationMorning Session Capacity-based Power Control. Department of Electrical and Computer Engineering University of Maryland
Morning Session Capacity-based Power Control Şennur Ulukuş Department of Electrical and Computer Engineering University of Maryland So Far, We Learned... Power control with SIR-based QoS guarantees Suitable
More informationSum-Rate Analysis of MIMO Broadcast Channel with Random Unitary Beamforming
This full text paper was peer reviewed at the direction of IEEE Communications Society subject matter experts for publication in the WCNC 8 proceedings. Sum-Rate Analysis of IO Broadcast Channel with Random
More informationI. Introduction. Index Terms Multiuser MIMO, feedback, precoding, beamforming, codebook, quantization, OFDM, OFDMA.
Zero-Forcing Beamforming Codebook Design for MU- MIMO OFDM Systems Erdem Bala, Member, IEEE, yle Jung-Lin Pan, Member, IEEE, Robert Olesen, Member, IEEE, Donald Grieco, Senior Member, IEEE InterDigital
More informationMultiple Antennas in Wireless Communications
Multiple Antennas in Wireless Communications Luca Sanguinetti Department of Information Engineering Pisa University luca.sanguinetti@iet.unipi.it April, 2009 Luca Sanguinetti (IET) MIMO April, 2009 1 /
More informationOn the Required Accuracy of Transmitter Channel State Information in Multiple Antenna Broadcast Channels
On the Required Accuracy of Transmitter Channel State Information in Multiple Antenna Broadcast Channels Giuseppe Caire University of Southern California Los Angeles, CA, USA Email: caire@usc.edu Nihar
More informationInput Optimization for Multi-Antenna Broadcast Channels with Per-Antenna Power Constraints
Input Optimization for Multi-Antenna Broadcast Channels with Per-Antenna Power Constraints Tian Lan and Wei Yu Electrical and Computer Engineering Department University of Toronto, Toronto, Ontario M5S
More informationMultiuser Capacity in Block Fading Channel
Multiuser Capacity in Block Fading Channel April 2003 1 Introduction and Model We use a block-fading model, with coherence interval T where M independent users simultaneously transmit to a single receiver
More informationImproved Sum-Rate Optimization in the Multiuser MIMO Downlink
Improved Sum-Rate Optimization in the Multiuser MIMO Downlin Adam J. Tenenbaum and Raviraj S. Adve Dept. of Electrical and Computer Engineering, University of Toronto 10 King s College Road, Toronto, Ontario,
More informationUnder sum power constraint, the capacity of MIMO channels
IEEE TRANSACTIONS ON COMMUNICATIONS, VOL 6, NO 9, SEPTEMBER 22 242 Iterative Mode-Dropping for the Sum Capacity of MIMO-MAC with Per-Antenna Power Constraint Yang Zhu and Mai Vu Abstract We propose an
More information12.4 Known Channel (Water-Filling Solution)
ECEn 665: Antennas and Propagation for Wireless Communications 54 2.4 Known Channel (Water-Filling Solution) The channel scenarios we have looed at above represent special cases for which the capacity
More informationWeighted Sum Rate Optimization for Cognitive Radio MIMO Broadcast Channels
IEEE TRANSACTIONS ON WIRELESS COMMUNICATIONS (SUBMITTED) Weighted Sum Rate Optimization for Cognitive Radio MIMO Broadcast Channels Lan Zhang, Yan Xin, and Ying-Chang Liang Abstract In this paper, we consider
More informationThe Optimality of Beamforming: A Unified View
The Optimality of Beamforming: A Unified View Sudhir Srinivasa and Syed Ali Jafar Electrical Engineering and Computer Science University of California Irvine, Irvine, CA 92697-2625 Email: sudhirs@uciedu,
More informationSum Capacity of the Vector Gaussian Broadcast Channel and Uplink-Downlink Duality
Sum Capacity of the Vector Gaussian Broadcast Channel and Uplink-Downlink Duality Pramod Viswanath and David Tse March 22, 2003 Abstract We characterize the sum capacity of the vector Gaussian broadcast
More informationVector Channel Capacity with Quantized Feedback
Vector Channel Capacity with Quantized Feedback Sudhir Srinivasa and Syed Ali Jafar Electrical Engineering and Computer Science University of California Irvine, Irvine, CA 9697-65 Email: syed@ece.uci.edu,
More informationAn Uplink-Downlink Duality for Cloud Radio Access Network
An Uplin-Downlin Duality for Cloud Radio Access Networ Liang Liu, Prati Patil, and Wei Yu Department of Electrical and Computer Engineering University of Toronto, Toronto, ON, 5S 3G4, Canada Emails: lianguotliu@utorontoca,
More informationLecture 5: Antenna Diversity and MIMO Capacity Theoretical Foundations of Wireless Communications 1. Overview. CommTh/EES/KTH
: Antenna Diversity and Theoretical Foundations of Wireless Communications Wednesday, May 4, 206 9:00-2:00, Conference Room SIP Textbook: D. Tse and P. Viswanath, Fundamentals of Wireless Communication
More informationCHANNEL FEEDBACK QUANTIZATION METHODS FOR MISO AND MIMO SYSTEMS
CHANNEL FEEDBACK QUANTIZATION METHODS FOR MISO AND MIMO SYSTEMS June Chul Roh and Bhaskar D Rao Department of Electrical and Computer Engineering University of California, San Diego La Jolla, CA 9293 47,
More informationPilot Optimization and Channel Estimation for Multiuser Massive MIMO Systems
1 Pilot Optimization and Channel Estimation for Multiuser Massive MIMO Systems Tadilo Endeshaw Bogale and Long Bao Le Institute National de la Recherche Scientifique (INRS) Université de Québec, Montréal,
More informationWIRELESS networking constitutes an important component
IEEE TRANSACTIONS ON INFORMATION THEORY, VOL. 51, NO. 1, JANUARY 2005 29 On the Capacity of MIMO Relay Channels Bo Wang, Student Member, IEEE, Junshan Zhang, Member, IEEE, and Anders Høst-Madsen, Senior
More informationMulti-User Gain Maximum Eigenmode Beamforming, and IDMA. Peng Wang and Li Ping City University of Hong Kong
Multi-User Gain Maximum Eigenmode Beamforming, and IDMA Peng Wang and Li Ping City University of Hong Kong 1 Contents Introduction Multi-user gain (MUG) Maximum eigenmode beamforming (MEB) MEB performance
More informationIEEE TRANSACTIONS ON INFORMATION THEORY, VOL. 52, NO. 2, FEBRUARY Uplink Downlink Duality Via Minimax Duality. Wei Yu, Member, IEEE (1) (2)
IEEE TRANSACTIONS ON INFORMATION THEORY, VOL. 52, NO. 2, FEBRUARY 2006 361 Uplink Downlink Duality Via Minimax Duality Wei Yu, Member, IEEE Abstract The sum capacity of a Gaussian vector broadcast channel
More informationThe Capacity Region of the Gaussian Cognitive Radio Channels at High SNR
The Capacity Region of the Gaussian Cognitive Radio Channels at High SNR 1 Stefano Rini, Daniela Tuninetti and Natasha Devroye srini2, danielat, devroye @ece.uic.edu University of Illinois at Chicago Abstract
More informationOn the Optimality of Beamformer Design for Zero-forcing DPC with QR Decomposition
IEEE ICC 2012 - Communications Theory On the Optimality of Beamformer Design for Zero-forcing DPC with QR Decomposition Le-Nam Tran, Maru Juntti, Mats Bengtsson, and Björn Ottersten Centre for Wireless
More informationSingle-User MIMO systems: Introduction, capacity results, and MIMO beamforming
Single-User MIMO systems: Introduction, capacity results, and MIMO beamforming Master Universitario en Ingeniería de Telecomunicación I. Santamaría Universidad de Cantabria Contents Introduction Multiplexing,
More informationSum Rate of Multiterminal Gaussian Source Coding
DIMACS Series in Discrete Mathematics and Theoretical Computer Science Sum Rate of Multiterminal Gaussian Source Coding Pramod Viswanath Abstract We characterize the sum rate of a class of multiterminal
More informationMULTIPLE-INPUT multiple-output (MIMO) systems
IEEE TRANSACTIONS ON INFORMATION THEORY, VOL. 56, NO. 10, OCTOBER 2010 4793 Maximum Mutual Information Design for MIMO Systems With Imperfect Channel Knowledge Minhua Ding, Member, IEEE, and Steven D.
More informationACHIEVING QOS AND EFFICIENCY IN THE MIMO DOWNLINK WITH LIMITED POWER. Thomas Michel and Gerhard Wunder
ACHIEVING QOS AND EFFICIENCY IN THE MIMO DOWNLINK WITH LIMITED POWER Thomas Michel and Gerhard Wunder Fraunhofer German-Sino Lab Mobile Communications, Heinrich-Hertz-Institut Einstein-Ufer 37, D-587 Berlin
More informationTransmit Directions and Optimality of Beamforming in MIMO-MAC with Partial CSI at the Transmitters 1
2005 Conference on Information Sciences and Systems, The Johns Hopkins University, March 6 8, 2005 Transmit Directions and Optimality of Beamforming in MIMO-MAC with Partial CSI at the Transmitters Alkan
More informationCompetition and Cooperation in Multiuser Communication Environments
Competition and Cooperation in Multiuser Communication Environments Wei Yu Electrical Engineering Department Stanford University April, 2002 Wei Yu, Stanford University Introduction A multiuser communication
More information(Article begins on next page)
Chalmers Publication Library Copyright Notice 2010 IEEE. Personal use of this material is permitted. However, permission to reprint/republish this material for advertising or promotional purposes or for
More informationLecture 7 MIMO Communica2ons
Wireless Communications Lecture 7 MIMO Communica2ons Prof. Chun-Hung Liu Dept. of Electrical and Computer Engineering National Chiao Tung University Fall 2014 1 Outline MIMO Communications (Chapter 10
More informationTight Lower Bounds on the Ergodic Capacity of Rayleigh Fading MIMO Channels
Tight Lower Bounds on the Ergodic Capacity of Rayleigh Fading MIMO Channels Özgür Oyman ), Rohit U. Nabar ), Helmut Bölcskei 2), and Arogyaswami J. Paulraj ) ) Information Systems Laboratory, Stanford
More informationOptimal Transmit Strategies in MIMO Ricean Channels with MMSE Receiver
Optimal Transmit Strategies in MIMO Ricean Channels with MMSE Receiver E. A. Jorswieck 1, A. Sezgin 1, H. Boche 1 and E. Costa 2 1 Fraunhofer Institute for Telecommunications, Heinrich-Hertz-Institut 2
More informationParallel Additive Gaussian Channels
Parallel Additive Gaussian Channels Let us assume that we have N parallel one-dimensional channels disturbed by noise sources with variances σ 2,,σ 2 N. N 0,σ 2 x x N N 0,σ 2 N y y N Energy Constraint:
More informationOptimum Transmission through the Gaussian Multiple Access Channel
Optimum Transmission through the Gaussian Multiple Access Channel Daniel Calabuig Institute of Telecommunications and Multimedia Applications Universidad Politécnica de Valencia Valencia, Spain Email:
More informationMode Selection for Multi-Antenna Broadcast Channels
Mode Selection for Multi-Antenna Broadcast Channels Gill November 22, 2011 Gill (University of Delaware) November 22, 2011 1 / 25 Part I Mode Selection for MISO BC with Perfect/Imperfect CSI [1]-[3] Gill
More informationConjugate Gradient Projection Approach for Multi-Antenna Gaussian Broadcast Channels
Conjugate Gradient Projection Approach for Multi-Antenna Gaussian Broadcast Channels Jia Liu Y. Thomas Hou Hanif D. Sherali The Bradley Department of Electrical and Computer Engineering The Grado Department
More informationDegrees-of-Freedom Robust Transmission for the K-user Distributed Broadcast Channel
/33 Degrees-of-Freedom Robust Transmission for the K-user Distributed Broadcast Channel Presented by Paul de Kerret Joint work with Antonio Bazco, Nicolas Gresset, and David Gesbert ESIT 2017 in Madrid,
More informationOn the Throughput of Proportional Fair Scheduling with Opportunistic Beamforming for Continuous Fading States
On the hroughput of Proportional Fair Scheduling with Opportunistic Beamforming for Continuous Fading States Andreas Senst, Peter Schulz-Rittich, Gerd Ascheid, and Heinrich Meyr Institute for Integrated
More informationOn Compound Channels With Side Information at the Transmitter
IEEE TRANSACTIONS ON INFORMATION THEORY, VOL 52, NO 4, APRIL 2006 1745 On Compound Channels With Side Information at the Transmitter Patrick Mitran, Student Member, IEEE, Natasha Devroye, Student Member,
More informationVECTOR QUANTIZATION TECHNIQUES FOR MULTIPLE-ANTENNA CHANNEL INFORMATION FEEDBACK
VECTOR QUANTIZATION TECHNIQUES FOR MULTIPLE-ANTENNA CHANNEL INFORMATION FEEDBACK June Chul Roh and Bhaskar D. Rao Department of Electrical and Computer Engineering University of California, San Diego La
More informationWE study the capacity of peak-power limited, single-antenna,
1158 IEEE TRANSACTIONS ON INFORMATION THEORY, VOL. 56, NO. 3, MARCH 2010 Gaussian Fading Is the Worst Fading Tobias Koch, Member, IEEE, and Amos Lapidoth, Fellow, IEEE Abstract The capacity of peak-power
More informationHow Much Training and Feedback are Needed in MIMO Broadcast Channels?
How uch raining and Feedback are Needed in IO Broadcast Channels? ari Kobayashi, SUPELEC Gif-sur-Yvette, France Giuseppe Caire, University of Southern California Los Angeles CA, 989 USA Nihar Jindal University
More informationErgodic and Outage Capacity of Narrowband MIMO Gaussian Channels
Ergodic and Outage Capacity of Narrowband MIMO Gaussian Channels Yang Wen Liang Department of Electrical and Computer Engineering The University of British Columbia April 19th, 005 Outline of Presentation
More informationOptimal Data and Training Symbol Ratio for Communication over Uncertain Channels
Optimal Data and Training Symbol Ratio for Communication over Uncertain Channels Ather Gattami Ericsson Research Stockholm, Sweden Email: athergattami@ericssoncom arxiv:50502997v [csit] 2 May 205 Abstract
More informationAn Analysis of Uplink Asynchronous Non-Orthogonal Multiple Access Systems
1 An Analysis of Uplink Asynchronous Non-Orthogonal Multiple Access Systems Xun Zou, Student Member, IEEE, Biao He, Member, IEEE, and Hamid Jafarkhani, Fellow, IEEE arxiv:18694v1 [csit] 3 Jun 18 Abstract
More informationOptimal Power Control in Decentralized Gaussian Multiple Access Channels
1 Optimal Power Control in Decentralized Gaussian Multiple Access Channels Kamal Singh Department of Electrical Engineering Indian Institute of Technology Bombay. arxiv:1711.08272v1 [eess.sp] 21 Nov 2017
More informationMinimum Mean Squared Error Interference Alignment
Minimum Mean Squared Error Interference Alignment David A. Schmidt, Changxin Shi, Randall A. Berry, Michael L. Honig and Wolfgang Utschick Associate Institute for Signal Processing Technische Universität
More informationRate-Optimum Beamforming Transmission in MIMO Rician Fading Channels
Rate-Optimum Beamforming Transmission in MIMO Rician Fading Channels Dimitrios E. Kontaxis National and Kapodistrian University of Athens Department of Informatics and telecommunications Abstract In this
More informationTwo-Stage Channel Feedback for Beamforming and Scheduling in Network MIMO Systems
Two-Stage Channel Feedback for Beamforming and Scheduling in Network MIMO Systems Behrouz Khoshnevis and Wei Yu Department of Electrical and Computer Engineering University of Toronto, Toronto, Ontario,
More informationJoint FEC Encoder and Linear Precoder Design for MIMO Systems with Antenna Correlation
Joint FEC Encoder and Linear Precoder Design for MIMO Systems with Antenna Correlation Chongbin Xu, Peng Wang, Zhonghao Zhang, and Li Ping City University of Hong Kong 1 Outline Background Mutual Information
More informationFundamentals of Multi-User MIMO Communications
Chapter 7 Fundamentals of Multi-User MIMO Communications Luca Sanguinetti and H. Vincent Poor 7.1 Introduction In recent years, the remarkable promise of multiple-antenna techniques has motivated an intense
More informationGame Theoretic Solutions for Precoding Strategies over the Interference Channel
Game Theoretic Solutions for Precoding Strategies over the Interference Channel Jie Gao, Sergiy A. Vorobyov, and Hai Jiang Department of Electrical & Computer Engineering, University of Alberta, Canada
More informationOn the Rate Duality of MIMO Interference Channel and its Application to Sum Rate Maximization
On the Rate Duality of MIMO Interference Channel and its Application to Sum Rate Maximization An Liu 1, Youjian Liu 2, Haige Xiang 1 and Wu Luo 1 1 State Key Laboratory of Advanced Optical Communication
More informationMULTIPLE-input multiple-output (MIMO) wireless systems,
IEEE TRANSACTIONS ON INFORMATION THEORY, VOL. 55, NO. 8, AUGUST 2009 3735 Statistical Eigenmode Transmission Over Jointly Correlated MIMO Channels Xiqi Gao, Senior Member, IEEE, Bin Jiang, Student Member,
More informationOn Gaussian MIMO Broadcast Channels with Common and Private Messages
On Gaussian MIMO Broadcast Channels with Common and Private Messages Ersen Ekrem Sennur Ulukus Department of Electrical and Computer Engineering University of Maryland, College Park, MD 20742 ersen@umd.edu
More informationDistributed MIMO Network Optimization Based on Duality and Local Message Passing
Forty-Seventh Annual Allerton Conference Allerton House, UIUC, Illinois, USA September 30 - October 2, 2009 Distributed MIMO Network Optimization Based on Duality and Local Message Passing An Liu 1, Ashutosh
More informationResearch Article Optimal Multiuser MIMO Linear Precoding with LMMSE Receiver
Hindawi Publishing Corporation EURASIP Journal on Wireless Communications and Networing Volume 009, Article ID 9768, 0 pages doi:055/009/9768 Research Article Optimal Multiuser MIMO Linear Precoding with
More informationMultiple Antenna Broadcast Channels with Shape Feedback and Limited Feedback
Multiple Antenna Broadcast Channels with Shape Feedback and Limited Feedback Peilu Ding, David J. Love, and Michael D. Zoltowski School of Electrical and Computer Engineering Purdue University West Lafayette,
More informationTHE CAPACITY region for the multiple-input multipleoutput
IEEE JOURNAL ON SELECTED AREAS IN COMMUNICATIONS, VOL. 26, NO. 8, OCTOBER 2008 1505 Coordinated Beamforming with Limited Feedback in the MIMO Broadcast Channel Chan-Byoung Chae, Student Member, IEEE, David
More informationCapacity optimization for Rician correlated MIMO wireless channels
Capacity optimization for Rician correlated MIMO wireless channels Mai Vu, and Arogyaswami Paulraj Information Systems Laboratory, Department of Electrical Engineering Stanford University, Stanford, CA
More informationTransmit Covariance Matrices for Broadcast Channels under Per-Modem Total Power Constraints and Non-Zero Signal to Noise Ratio Gap
1 Transmit Covariance Matrices for Broadcast Channels under Per-Modem Total Power Constraints and Non-Zero Signal to Noise Ratio Gap Vincent Le Nir, Marc Moonen, Jochen Maes, Mamoun Guenach Abstract Finding
More informationTransmitter optimization for distributed Gaussian MIMO channels
Transmitter optimization for distributed Gaussian MIMO channels Hon-Fah Chong Electrical & Computer Eng Dept National University of Singapore Email: chonghonfah@ieeeorg Mehul Motani Electrical & Computer
More informationIN this paper, we show that the scalar Gaussian multiple-access
768 IEEE TRANSACTIONS ON INFORMATION THEORY, VOL. 50, NO. 5, MAY 2004 On the Duality of Gaussian Multiple-Access and Broadcast Channels Nihar Jindal, Student Member, IEEE, Sriram Vishwanath, and Andrea
More informationOutage-Efficient Downlink Transmission Without Transmit Channel State Information
1 Outage-Efficient Downlink Transmission Without Transmit Channel State Information Wenyi Zhang, Member, IEEE, Shivaprasad Kotagiri, Student Member, IEEE, and J. Nicholas Laneman, Senior Member, IEEE arxiv:0711.1573v1
More information1402 IEEE JOURNAL ON SELECTED AREAS IN COMMUNICATIONS, VOL. 25, NO. 7, SEPTEMBER 2007
40 IEEE JOURNAL ON SELECTED AREAS IN COMMUNICATIONS, VOL. 5, NO. 7, SEPTEMBER 007 Optimum Power Allocation for Single-User MIMO and Multi-User MIMO-MAC with Partial CSI Alkan Soysal, Student Member, IEEE,
More informationONE of the key motivations for the use of multiple antennas
IEEE TRANSACTIONS ON INFORMATION THEORY, VOL 57, NO 7, JULY 2011 4123 On the Ergodic Capacity of Correlated Rician Fading MIMO Channels With Interference Giorgio Taricco, Fellow, IEEE, and Erwin Riegler,
More informationScheduling of Multi-Antenna Broadcast Systems with Heterogeneous Users
Scheduling of Multi-Antenna Broadcast Systems with Heterogeneous Users Krishna Jagannathan, Sem Borst, Phil Whiting and Eytan Modiano Abstract We consider a two transmit antenna broadcast system with heterogeneous
More information2318 IEEE TRANSACTIONS ON SIGNAL PROCESSING, VOL. 54, NO. 6, JUNE Mai Vu, Student Member, IEEE, and Arogyaswami Paulraj, Fellow, IEEE
2318 IEEE TRANSACTIONS ON SIGNAL PROCESSING, VOL. 54, NO. 6, JUNE 2006 Optimal Linear Precoders for MIMO Wireless Correlated Channels With Nonzero Mean in Space Time Coded Systems Mai Vu, Student Member,
More informationA New SLNR-based Linear Precoding for. Downlink Multi-User Multi-Stream MIMO Systems
A New SLNR-based Linear Precoding for 1 Downlin Multi-User Multi-Stream MIMO Systems arxiv:1008.0730v1 [cs.it] 4 Aug 2010 Peng Cheng, Meixia Tao and Wenjun Zhang Abstract Signal-to-leaage-and-noise ratio
More information1424 IEEE JOURNAL ON SELECTED AREAS IN COMMUNICATIONS, VOL. 25, NO. 7, SEPTEMBER 2007
1424 IEEE JOURNAL ON SELECTED AREAS IN COMMUNICATIONS, VOL. 25, NO. 7, SEPTEMBER 2007 Scheduling of Multi-Antenna Broadcast Systems with Heterogeneous Users Krishna Jagannathan, Sem Borst, Phil Whiting
More informationThe Capacity of the Semi-Deterministic Cognitive Interference Channel and its Application to Constant Gap Results for the Gaussian Channel
The Capacity of the Semi-Deterministic Cognitive Interference Channel and its Application to Constant Gap Results for the Gaussian Channel Stefano Rini, Daniela Tuninetti, and Natasha Devroye Department
More informationComparisons of Performance of Various Transmission Schemes of MIMO System Operating under Rician Channel Conditions
Comparisons of Performance of Various ransmission Schemes of MIMO System Operating under ician Channel Conditions Peerapong Uthansakul and Marek E. Bialkowski School of Information echnology and Electrical
More informationBlind MIMO communication based on Subspace Estimation
Blind MIMO communication based on Subspace Estimation T. Dahl, S. Silva, N. Christophersen, D. Gesbert T. Dahl, S. Silva, and N. Christophersen are at the Department of Informatics, University of Oslo,
More informationOVER the past ten years, research (see the references in
766 IEEE TRANSACTIONS ON SIGNAL PROCESSING, VOL. 54, NO. 2, FEBRUARY 2006 Duplex Distortion Models for Limited Feedback MIMO Communication David J. Love, Member, IEEE Abstract The use of limited feedback
More informationJoint Multi-Cell Processing for Downlink Channels with Limited-Capacity Backhaul
Joint Multi-Cell Processing for Downlink Channels with Limited-Capacity Backhaul Shlomo Shamai (Shitz) Department of Electrical Engineering Technion Haifa, 3000, Israel sshlomo@ee.technion.ac.il Osvaldo
More informationOptimum Transmission Scheme for a MISO Wireless System with Partial Channel Knowledge and Infinite K factor
Optimum Transmission Scheme for a MISO Wireless System with Partial Channel Knowledge and Infinite K factor Mai Vu, Arogyaswami Paulraj Information Systems Laboratory, Department of Electrical Engineering
More informationDownlink MU-MIMO with THP Combined with Pre- and Post-processing and Selection of the Processing Vectors for Maximization of Per Stream SNR
IEEE Transactions on Vehicular Technology, DOI: 9/TVT65739 Downlink MU-MIMO with THP Combined with Pre- and Post-processing and Selection of the Processing Vectors for Maximization of Per Stream SNR Nanda
More informationMultiple Antennas for MIMO Communications - Basic Theory
Multiple Antennas for MIMO Communications - Basic Theory 1 Introduction The multiple-input multiple-output (MIMO) technology (Fig. 1) is a breakthrough in wireless communication system design. It uses
More informationDegrees of Freedom for the MIMO Interference Channel REFERENCES
IEEE TRANSACTIONS ON INFORMATION THEORY, VOL. 53, NO. 7, JULY 2007 2637 the interrelations between the infinite linear array and the isolated cluster setups, it can be shown that C IC M C M + 2 M CIC (M+2)
More informationEnergy Efficiency Optimization in MIMO Broadcast Channels with Fairness Constraints
Energy Efficiency Optimization in MIMO Broadcast Channels with Fairness Constraints Christoph Hellings and Wolfgang Utschick 14th IEEE International Workshop on Signal Processing Advances for Wireless
More informationOptimization of Multiuser MIMO Networks with Interference
Optimization of Multiuser MIMO Networks with Interference Jia Liu, Y. Thomas Hou, Yi Shi, and Hanif D. Sherali Department of Electrical and Computer Engineering Department of Industrial and Systems Engineering
More informationQuantifying the Performance Gain of Direction Feedback in a MISO System
Quantifying the Performance Gain of Direction Feedback in a ISO System Shengli Zhou, Jinhong Wu, Zhengdao Wang 3, and ilos Doroslovacki Dept. of Electrical and Computer Engineering, University of Connecticut
More informationAchievable rates of MIMO downlink beamforming with non-perfect CSI: a comparison between quantized and analog feedback
Achievable rates of MIMO downlink beamforming with non-perfect CSI: a comparison between quantized and ana feedback Giuseppe Caire University of Sourthern California Los Angeles CA, 989 USA Nihar Jindal
More informationLattice Reduction Aided Precoding for Multiuser MIMO using Seysen s Algorithm
Lattice Reduction Aided Precoding for Multiuser MIMO using Seysen s Algorithm HongSun An Student Member IEEE he Graduate School of I & Incheon Korea ahs3179@gmail.com Manar Mohaisen Student Member IEEE
More informationCapacity Bounds of Downlink Network MIMO Systems with Inter-Cluster Interference
Capacity Bounds of Downlink Network MIMO Systems with Inter-Cluster Interference Zhiyuan Jiang, Sheng Zhou, Zhisheng Niu Tsinghua National Laboratory for Information Science and Technology Department of
More informationRandom Beamforming in Spatially Correlated Multiuser MISO Channels
andom Beamforming in Spatially Correlated Multiuser MISO Channels Jae-Yun Ko and Yong-Hwan ee School of lectrical ngineering and INMC Seoul National University Kwana P. O. Box 34 Seoul 5-600 Korea Abstract
More informationWhen does vectored Multiple Access Channels (MAC) optimal power allocation converge to an FDMA solution?
When does vectored Multiple Access Channels MAC optimal power allocation converge to an FDMA solution? Vincent Le Nir, Marc Moonen, Jan Verlinden, Mamoun Guenach Abstract Vectored Multiple Access Channels
More informationAn Alternative Proof for the Capacity Region of the Degraded Gaussian MIMO Broadcast Channel
IEEE TRANSACTIONS ON INFORMATION THEORY, VOL. 58, NO. 4, APRIL 2012 2427 An Alternative Proof for the Capacity Region of the Degraded Gaussian MIMO Broadcast Channel Ersen Ekrem, Student Member, IEEE,
More information