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Multiuser MIMO Achievable Rates with Downlink Training and Channel State Feedback
"... We consider a MIMO fading broadcast channel and compute achievable ergodic rates when channel state information is acquired at the receivers via downlink training and it is provided to the transmitter by channel state feedback. Unquantized (analog) and quantized (digital) channel state feedback sche ..."
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Cited by 114 (8 self)
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We consider a MIMO fading broadcast channel and compute achievable ergodic rates when channel state information is acquired at the receivers via downlink training and it is provided to the transmitter by channel state feedback. Unquantized (analog) and quantized (digital) channel state feedback schemes are analyzed and compared under various assumptions. Digital feedback is shown to be potentially superior when the feedback channel uses per channel state coefficient is larger than 1. Also, we show that by proper design of the digital feedback link, errors in the feedback have a minor effect even if simple uncoded modulation is used on the feedback channel. We discuss first the case of an unfaded AWGN feedback channel with orthogonal access and then the case of fading MIMO multiaccess (MIMOMAC). We show that by exploiting the MIMOMAC nature of the uplink channel, a much better scaling of the feedback channel resource with the number of base station antennas can be achieved. Finally, for the case of delayed feedback, we show that in the realistic case where the fading process has (normalized) maximum Doppler frequency shift 0 ≤ F < 1/2, a fraction 1 − 2F of the optimal multiplexing gain is achievable. The general conclusion of this work is that very significant downlink throughput is achievable with simple and efficient channel state feedback, provided that the feedback link is properly designed.
Degrees of freedom region of the MIMO X Channel
, 2007
"... hop, is especially interesting, as the intermediate hop takes place over an interference channel with single antenna nodes. While the two user interference channel with single antenna nodes has only one degree of freedom by itself, it is able to deliver degrees of freedom when used as an intermediat ..."
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Cited by 92 (28 self)
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hop, is especially interesting, as the intermediate hop takes place over an interference channel with single antenna nodes. While the two user interference channel with single antenna nodes has only one degree of freedom by itself, it is able to deliver degrees of freedom when used as an intermediate stage between a antenna source and a antenna destination [5]. The key is an amplify and forward scheme where the relay nodes, instead of trying to decode the messages, simply scale and forward their received signals. [1]–[3] consider end to end channel orthogonalization with distributed sources, relays and destination nodes and determine the capacity scaling behavior with the number of relay nodes. It is shown that distributed orthogonalization can be obtained even with synchronization errors if a minimum amount of coherence at the relays can be sustained. Degrees of freedom for linear interference networks with local sideinformation are explored in [22] and cognitive message sharing is found to improve the degrees of freedom for certain structured channel matrices. The MIMO MAC and BC channels show that there is no loss in degrees of freedom even if antennas are distributed among users at one end (either transmitters or receivers) making joint signal processing infeasible, as long as joint signal processing is possible at the other end of the communication link. The multiple hop example of [5], described above, shows that there is no loss of degrees of freedom even with distributed antennas at both ends of a communication hop (an interference channel) as long as the distributed antenna stages are only intermediate
Degrees of freedom region of the MIMO . . .
, 2008
"... We provide achievability as well as converse results for the degrees of freedom region of a multipleinput multipleoutput (MIMO) X channel, i.e., a system with two transmitters, two receivers, each equipped with multiple antennas, where independent messages need to be conveyed over fixed channels fr ..."
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Cited by 91 (19 self)
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We provide achievability as well as converse results for the degrees of freedom region of a multipleinput multipleoutput (MIMO) X channel, i.e., a system with two transmitters, two receivers, each equipped with multiple antennas, where independent messages need to be conveyed over fixed channels from each transmitter to each receiver. The inner and outer bounds on the degrees of freedom region are tight whenever integer degrees of freedom are optimal for each message. With M =1antennas at each node, we find that the total (sum rate) degrees of freedom are bounded above and below as 1? 4 X.IfM>1 and channel
On the compound mimo broadcast channel
, 2007
"... Abstract — We consider the Gaussian multiantenna compound broadcast channel where one transmitter transmits several messages, each intended for a different user whose channel realization is arbitrarily chosen from a finite set. Our investigation focuses on the behavior of this channel at high SNRs ..."
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Cited by 50 (3 self)
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Abstract — We consider the Gaussian multiantenna compound broadcast channel where one transmitter transmits several messages, each intended for a different user whose channel realization is arbitrarily chosen from a finite set. Our investigation focuses on the behavior of this channel at high SNRs and we obtain the multiplexing gain of the sum capacity for a number of cases, and point out some implications of the total achievable multiplexing gain region.1 I.
MIMO wireless linear precoding
 IEEE Signal Processing Magazine
, 2006
"... The benefits of using multiple antennas at both the transmitter and the receiver in a wireless system are well established. Multipleinput multipleoutput (MIMO) systems enable a growth in transmission rate linear in the minimum of the number of antennas at either end [1][2]. MIMO techniques also en ..."
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Cited by 43 (0 self)
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The benefits of using multiple antennas at both the transmitter and the receiver in a wireless system are well established. Multipleinput multipleoutput (MIMO) systems enable a growth in transmission rate linear in the minimum of the number of antennas at either end [1][2]. MIMO techniques also enhance link reliability and
Retrospective interference alignment
 in Information Theory, 2011. ISIT 2011. IEEE International Symposium on, 2011
"... We explore similarities and differences in recent works on blind interference alignment under different models such as staggered block fading model and the delayed CSIT model. In particular we explore the possibility of achieving interference alignment with delayed CSIT when the transmitters are di ..."
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Cited by 39 (14 self)
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We explore similarities and differences in recent works on blind interference alignment under different models such as staggered block fading model and the delayed CSIT model. In particular we explore the possibility of achieving interference alignment with delayed CSIT when the transmitters are distributed. Our main contribution is an interference alignment scheme, called retrospective interference alignment in this work, that is specialized to settings with distributed transmitters. With this scheme we show that the 2 user X channel with only delayed channel state information at the transmitters can achieve 8/7 DoF, while the interference channel with 3 users is able to achieve 9/8 DoF. We also consider another setting where delayed channel output feedback is available to transmitters. In this setting the X channel and the 3 user interference channel are shown to achieve 4/3 and 6/5 DoF, respectively. 1
On the Degrees of Freedom of Finite State Compound Wireless Networks  Settling a Conjecture by Weingarten et. al.
, 2009
"... We explore the degrees of freedom (DoF) of three classes of finite state compound wireless networks in this paper. First, we study the multipleinput singleoutput (MISO) finite state compound broadcast channel (BC) with arbitrary number of users and antennas at the transmitter. In prior work, Weing ..."
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Cited by 32 (19 self)
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We explore the degrees of freedom (DoF) of three classes of finite state compound wireless networks in this paper. First, we study the multipleinput singleoutput (MISO) finite state compound broadcast channel (BC) with arbitrary number of users and antennas at the transmitter. In prior work, Weingarten et. al. have found inner and outer bounds on the DoF with 2 users. The bounds have a different character. While the inner bound collapses to unity as the number of states increases, the outer bound does not diminish with the increasing number of states beyond a threshold value. It has been conjectured that the outer bound is loose and the inner bound represents the actual DoF. In the complex setting (all signals, noise, and channel coefficients are complex variables) we solve a few cases to find that the outer bound – and not the inner bound – of Weingarten et. al. is tight. For the real setting (all signals, noise and channel coefficients are real variables) we completely characterize the DoF, once again proving that the outer bound of Weingarten et. al. is tight. We also extend the results to arbitrary number of users. Second, we characterize the DoF of finite state scalar (single antenna nodes) compound X networks with arbitrary number of users in the real setting. Third, we characterize the DoF of finite state scalar compound interference networks with arbitrary number of users in both the real and complex setting. The key finding is that scalar interference networks and (real) X networks do not lose any DoF due to channel uncertainty at the transmitter in the finite state compound setting. The finite state compound MISO BC does lose DoF relative to the perfect CSIT scenario. However, what is lost is only the DoF benefit of joint processing at transmit antennas, without which the MISO BC reduces to an X network.
Multimode transmission for the MIMO broadcast channel with imperfect channel state information
 IEEE Transactions on Communications
"... This paper proposes a multimode transmission strategy to improve the spectral efficiency achieved by the multipleinput multipleoutput (MIMO) broadcast channel with delayed and quantized channel state information. It adaptively adjusts the number of active users, denoted as the transmission mode, ..."
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Cited by 25 (10 self)
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This paper proposes a multimode transmission strategy to improve the spectral efficiency achieved by the multipleinput multipleoutput (MIMO) broadcast channel with delayed and quantized channel state information. It adaptively adjusts the number of active users, denoted as the transmission mode, to balance transmit array gain, spatial division multiplexing gain, and residual interuser interference. Accurate closedform approximations are derived for the achievable rates for different modes, which are used to select the active mode that maximizes the ergodic throughput. User scheduling algorithms based on multimode transmission are then proposed for the network with a large number of users, to reduce the overall amount of feedback. It is shown that the proposed algorithms provide throughput gains at moderate yet practically relevant signaltonoise ratio. Index Terms MIMO systems, space division multiplexing, broadcast channels, scheduling, feedback, delay effects, adaptive systems. I.
Exploiting channel correlations – simple interference alignment schemes with no CSIT
, 2009
"... We explore 5 network communication problems where the possibility of interference alignment, and consequently the total number of degrees of freedom (DoF) with channel uncertainty at the transmitters are unknown. These problems share the common property that in each case the best known outer bounds ..."
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Cited by 22 (6 self)
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We explore 5 network communication problems where the possibility of interference alignment, and consequently the total number of degrees of freedom (DoF) with channel uncertainty at the transmitters are unknown. These problems share the common property that in each case the best known outer bounds are essentially robust to channel uncertainty and represent the outcome with interference alignment, but the best inner bounds – in some cases conjectured to be optimal – predict a total collapse of DoF, thus indicating the infeasibility of interference alignment under channel uncertainty at transmitters. Our main contribution is to show that even with no knowledge of channel coefficient values at the transmitters, the knowledge of the channels ’ correlation structure can be exploited to achieve interference alignment. In each case, we show that under a staggered block fading model, the transmitters are able to align interference without the knowledge of channel coefficient values. The alignment schemes are based on linear beamforming – which can be seen as a repetition code over a small number of symbols – and involve delays of only a few coherence intervals.
On the Degrees of Freedom of the Compound MIMO Broadcast Channels with Finite States
, 2009
"... Multipleantenna broadcast channels with M transmit antennas and K singleantenna receivers is considered, where the channel of receiver r takes one of the Jr finite values. It is assumed that the channel states of each receiver are randomly selected from R M×1 (or from C M×1). It is shown that no m ..."
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Cited by 22 (2 self)
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Multipleantenna broadcast channels with M transmit antennas and K singleantenna receivers is considered, where the channel of receiver r takes one of the Jr finite values. It is assumed that the channel states of each receiver are randomly selected from R M×1 (or from C M×1). It is shown that no matter what Jr is, the degrees of freedom (DoF) of MK M+K−1 is achievable. The achievable scheme relies on the idea of interference alignment at receivers, without exploiting the possibility of cooperation among transmit antennas. It is proven that if Jr ≥ M, r = 1,...,K, this scheme achieves the optimal DoF. This results implies that when the uncertainty of the base station about the channel realization is considerable, the system loses the gain of cooperation. However, it still benefits from the gain of interference alignment. In fact, in this case, the compound broadcast channel is treated as a compound X channel. Moreover, it is shown that when the base station knows the channel states of some of the receivers, a combination of transmit cooperation and interference alignment would achieve the optimal DoF. Like timeinvariant Kuser interference channels, the naive vectorspace approaches of interference management seem insufficient to achieve the optimal DoF of this channel. In this paper, we use the NumberTheory approach of alignment, recently developed by Motahari et al. [1]. We extend the approach of [1] to complex channels as well, therefore all the results that we present are valid for both real and complex channels.