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42
Capacity Limits of MIMO Channels
 IEEE J. SELECT. AREAS COMMUN
, 2003
"... We provide an overview of the extensive recent results on the Shannon capacity of singleuser and multiuser multipleinput multipleoutput (MIMO) channels. Although enormous capacity gains have been predicted for such channels, these predictions are based on somewhat unrealistic assumptions about t ..."
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Cited by 217 (10 self)
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We provide an overview of the extensive recent results on the Shannon capacity of singleuser and multiuser multipleinput multipleoutput (MIMO) channels. Although enormous capacity gains have been predicted for such channels, these predictions are based on somewhat unrealistic assumptions about the underlying timevarying channel model and how well it can be tracked at the receiver, as well as at the transmitter. More realistic assumptions can dramatically impact the potential capacity gains of MIMO techniques. For timevarying MIMO channels there are multiple Shannon theoretic capacity definitions and, for each definition, different correlation models and channel information assumptions that we consider. We first provide a comprehensive summary of ergodic and capacity versus outage results for singleuser MIMO channels. These results indicate that the capacity gain obtained from multiple antennas heavily depends
On the optimality of multiantenna broadcast scheduling using zeroforcing beamforming
 IEEE J. SELECT. AREAS COMMUN
, 2006
"... Although the capacity of multipleinput/multipleoutput (MIMO) broadcast channels (BCs) can be achieved by dirty paper coding (DPC), it is difficult to implement in practical systems. This paper investigates if, for a large number of users, simpler schemes can achieve the same performance. Specifica ..."
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Cited by 116 (5 self)
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Although the capacity of multipleinput/multipleoutput (MIMO) broadcast channels (BCs) can be achieved by dirty paper coding (DPC), it is difficult to implement in practical systems. This paper investigates if, for a large number of users, simpler schemes can achieve the same performance. Specifically, we show that a zeroforcing beamforming (ZFBF) strategy, while generally suboptimal, can achieve the same asymptotic sum capacity as that of DPC, as the number of users goes to infinity. In proving this asymptotic result, we provide an algorithm for determining which users should be active under ZFBF. These users are semiorthogonal to one another and can be grouped for simultaneous transmission to enhance the throughput of scheduling algorithms. Based on the user grouping, we propose and compare two fair scheduling schemes in roundrobin ZFBF and proportionalfair ZFBF. We provide numerical results to confirm the optimality of ZFBF and to compare the performance of ZFBF and proposed fair scheduling schemes with that of various MIMO BC strategies.
Sum power iterative waterfilling for multiantenna Gaussian broadcast channels
 IEEE Trans. Inform. Theory
, 2005
"... In this paper we consider the problem of maximizing sum rate of a multipleantenna Gaussian broadcast channel. It was recently found that dirty paper coding is capacity achieving for this channel. In order to achieve capacity, the optimal transmission policy (i.e. the optimal transmit covariance str ..."
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Cited by 82 (16 self)
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In this paper we consider the problem of maximizing sum rate of a multipleantenna Gaussian broadcast channel. It was recently found that dirty paper coding is capacity achieving for this channel. In order to achieve capacity, the optimal transmission policy (i.e. the optimal transmit covariance structure) given the channel conditions and power constraint must be found. However, obtaining the optimal transmission policy when employing dirty paper coding is a computationally complex nonconvex problem. We use duality to transform this problem into a wellstructured convex multipleaccess channel problem. We exploit the structure of this problem and derive simple and fast iterative algorithms that provide the optimum transmission policies for the multipleaccess channel, which can easily be mapped to the optimal broadcast channel policies.
On the duality of Gaussian multipleaccess and broadcast channels
 IEEE Trans. Inf. Theory
, 2004
"... Abstract—We define a duality between Gaussian multipleaccess channels (MACs) and Gaussian broadcast channels (BCs). The dual channels we consider have the same channel gains and the same noise power at all receivers. We show that the capacity region of the BC (both constant and fading) can be writt ..."
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Cited by 70 (13 self)
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Abstract—We define a duality between Gaussian multipleaccess channels (MACs) and Gaussian broadcast channels (BCs). The dual channels we consider have the same channel gains and the same noise power at all receivers. We show that the capacity region of the BC (both constant and fading) can be written in terms of the capacity region of the dual MAC, and vice versa. We can use this result to find the capacity region of the MAC if the capacity region of only the BC is known, and vice versa. For fading channels we show duality under ergodic capacity, but duality also holds for different capacity definitions for fading channels such as outage capacity and minimumrate capacity. Using duality, many results known for only one of the two channels can be extended to the dual channel as well. Index Terms—Broadcast channel (BC), channel capacity, duality, fading channels, multipleinput multipleoutput (MIMO) systems, multipleaccess channel (MAC). I.
On the Asymptotic Optimality of the Gradient Scheduling Algorithm for MultiUser Throughput Allocation
 Operations Research
"... informs ..."
On downlink beamforming with greedy user selection: performance analysis and a simple new algorithm
 IEEE Trans. Signal Processing
, 2005
"... Abstract—This paper considers the problem of simultaneous multiuser downlink beamforming. The idea is to employ a transmit antenna array to create multiple “beams ” directed toward the individual users, and the aim is to increase throughput, measured by sum capacity. In particular, we are interested ..."
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Cited by 42 (1 self)
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Abstract—This paper considers the problem of simultaneous multiuser downlink beamforming. The idea is to employ a transmit antenna array to create multiple “beams ” directed toward the individual users, and the aim is to increase throughput, measured by sum capacity. In particular, we are interested in the practically important case of more users than transmit antennas, which requires user selection. Optimal solutions to this problem can be prohibitively complex for online implementation at the base station and entail socalled Dirty Paper (DP) precoding for known interference. Suboptimal solutions capitalize on multiuser (selection) diversity to achieve a significant fraction of sum capacity at lower complexity cost. We analyze the throughput performance in Rayleigh fading of a suboptimal greedy DPbased scheme proposed by Tu and Blum. We also propose another userselection method of the same computational complexity based on simple zeroforcing beamforming. Our results indicate that the proposed method attains a significant fraction of sum capacity and throughput of Tu and Blum’s scheme and, thus, offers an attractive alternative to DPbased schemes. Index Terms—Beamforming, downlink, multiuser diversity. I.
Dirtypaper coding versus TDMA for MIMO broadcast channels
 IEEE Trans. Inf. Theory
, 2005
"... Abstract—We compare the capacity of dirtypaper coding (DPC)to that of timedivision multiple access (TDMA)for a multipleantenna (multipleinput multipleoutput (MIMO)) Gaussian broadcast channel (BC). We find that the sumrate capacity (achievable using DPC)of the multipleantenna BC is at most ��� ..."
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Cited by 42 (3 self)
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Abstract—We compare the capacity of dirtypaper coding (DPC)to that of timedivision multiple access (TDMA)for a multipleantenna (multipleinput multipleoutput (MIMO)) Gaussian broadcast channel (BC). We find that the sumrate capacity (achievable using DPC)of the multipleantenna BC is at most ��� @ A times the largest singleuser capacity (i.e., the TDMA sumrate)in the system, where is the number of transmit antennas and is the number of receivers. This result is independent of the number of receive antennas and the channel gain matrix, and is valid at all signaltonoise ratios (SNRs). We investigate the tightness of this bound in a timevarying channel (assuming perfect channel knowledge at receivers and transmitters)where the channel experiences uncorrelated Rayleigh fading and in some situations we find that the dirty paper gain is upperbounded by the ratio of transmittoreceive antennas. We also show that ��� @ A upperbounds the sumrate gain of successive decoding over TDMA for the uplink channel, where is the number of receive antennas at the base station and is the number of transmitters. Index Terms—Broadcast channel (BC), channel capacity, dirtypaper coding (DPC), multipleinput multipleoutput (MIMO) systems, timedivision multiple access (TDMA). I.
Optimality of zeroforcing beamforming with multiuser diversity
 in Proc. IEEE International Conference on Communications
, 2005
"... Abstract — In MIMO downlink channels, the capacity is achieved by dirty paper coding (DPC). However, DPC is difficult to implement in practical systems. This work investigates if, for a large number of users, simpler schemes can achieve the same performance. Specifically, we show that a zeroforcing ..."
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Cited by 33 (2 self)
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Abstract — In MIMO downlink channels, the capacity is achieved by dirty paper coding (DPC). However, DPC is difficult to implement in practical systems. This work investigates if, for a large number of users, simpler schemes can achieve the same performance. Specifically, we show that a zeroforcing beamforming (ZFBF) strategy, while generally suboptimal, can achieve the same asymptotic sumrate capacity as that of DPC, as the number of users goes to infinity. In proving this asymptotic result, we propose an algorithm for determining which users should be active in ZFBF transmission. These users are semiorthogonal to one another, and when fairness among users is required, can be grouped for simultaneous transmissions to enhance the throughput of fair schedulers. We provide numerical results to confirm the optimality of ZFBF and to compare its performance with that of various MIMO downlink strategies. I.
Sum Rate Characterization of Joint Multiple CellSite Processing
, 2005
"... The sumrate capacity of a cellular system model is analyzed, considering the uplink and downlink channels, while addressing both nonfading and flatfading channels. The focus is on a simple Wynerlike multicell model, where the system cells are arranged on a circle, assuming the cellsites are lo ..."
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Cited by 25 (9 self)
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The sumrate capacity of a cellular system model is analyzed, considering the uplink and downlink channels, while addressing both nonfading and flatfading channels. The focus is on a simple Wynerlike multicell model, where the system cells are arranged on a circle, assuming the cellsites are located at the boundaries of the cells. For the uplink channel, analytical expressions of the sumrate capacities are derived for intracell TDMA scheduling, and a “WideBand ” (WB) scheme (where all users are active simultaneously utilizing all bandwidth for coding). Assuming individual percell power constraints, and using the Lagrangian uplinkdownlink duality principle, an analytical expression for the sumrate capacity of the downlink channel is derived for nonfading channels, and shown to coincide with the corresponding uplink result. Introducing flatfading, lower and upper bounds on the average percell sumrate capacity are derived. The bounds exhibit an O(loge K) multiuser diversity factor for a number of users percell K ≫ 1, in addition to the array diversity gain. Joint multicell processing is shown to eliminate outofcell interference, which is traditionally considered to be a limiting factor in highrate reliable communications. This paper was presented in part at the 9
On the user selection in MIMO broadcast channels
 IN PROC. OF INTERNATIONAL SYMPOSIUM ON INFORMATION THEORY
, 2005
"... In this paper, a downlink communication system, in which a Base Station (BS) equipped with M antennas communicates with N users each equipped with K receive antennas, is considered. An efficient suboptimum algorithm is proposed for selecting a set of users in order to maximize the sumrate throughpu ..."
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Cited by 20 (3 self)
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In this paper, a downlink communication system, in which a Base Station (BS) equipped with M antennas communicates with N users each equipped with K receive antennas, is considered. An efficient suboptimum algorithm is proposed for selecting a set of users in order to maximize the sumrate throughput of the system. For the asymptotic case when N tends to infinity, the necessary and sufficient conditions in order to achieve the maximum sumrate throughput, such that the difference between the achievable sumrate and the maximum value approaches zero, is derived. The complexity of our algorithm is investigated in terms of the required amount of feedback from the users to the base station, as well as the number of searches required for selecting the users. It is shown that the proposed method is capable of achieving a large portion of the sumrate capacity, with a very low complexity.