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85
MIMO broadcast channels with finite rate feedback
 IEEE Trans. on Inform. Theory
, 2006
"... Multiple transmit antennas in a downlink channel can provide tremendous capacity (i.e. multiplexing) gains, even when receivers have only single antennas. However, receiver and transmitter channel state information is generally required. In this paper, a system where each receiver has perfect channe ..."
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Cited by 93 (9 self)
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Multiple transmit antennas in a downlink channel can provide tremendous capacity (i.e. multiplexing) gains, even when receivers have only single antennas. However, receiver and transmitter channel state information is generally required. In this paper, a system where each receiver has perfect channel knowledge, but the transmitter only receives quantized information regarding the channel instantiation is analyzed. The well known zero forcing transmission technique is considered, and simple expressions for the throughput degradation due to finite rate feedback are derived. A key finding is that the feedback rate per mobile must be increased linearly with the SNR (in dB) in order to achieve the full multiplexing gain, which is in sharp contrast to pointtopoint MIMO systems in which it is not necessary to increase the feedback rate as a function of the SNR. I.
MIMO Broadcast Channels With FiniteRate Feedback
, 2006
"... Multiple transmit antennas in a downlink channel can provide tremendous capacity (i.e., multiplexing) gains, even when receivers have only single antennas. However, receiver and transmitter channel state information is generally required. In this correspondence, a system where each receiver has per ..."
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Cited by 45 (1 self)
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Multiple transmit antennas in a downlink channel can provide tremendous capacity (i.e., multiplexing) gains, even when receivers have only single antennas. However, receiver and transmitter channel state information is generally required. In this correspondence, a system where each receiver has perfect channel knowledge, but the transmitter only receives quantized information regarding the channel instantiation is analyzed. The wellknown zeroforcing transmission technique is considered, and simple expressions for the throughput degradation due to finiterate feedback are derived. A key finding is that the feedback rate per mobile must be increased linearly with the signaltonoise ratio (SNR) (in decibels) in order to achieve the full multiplexing gain. This is in sharp contrast to pointtopoint multipleinput multipleoutput (MIMO) systems, in which it is not necessary to increase the feedback rate as a function of the SNR.
An overview of limited feedback in wireless communication systems
 IEEE J. SEL. AREAS COMMUN
, 2008
"... It is now well known that employing channel adaptive signaling in wireless communication systems can yield large improvements in almost any performance metric. Unfortunately, many kinds of channel adaptive techniques have been deemed impractical in the past because of the problem of obtaining channe ..."
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Cited by 43 (8 self)
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It is now well known that employing channel adaptive signaling in wireless communication systems can yield large improvements in almost any performance metric. Unfortunately, many kinds of channel adaptive techniques have been deemed impractical in the past because of the problem of obtaining channel knowledge at the transmitter. The transmitter in many systems (such as those using frequency division duplexing) can not leverage techniques such as training to obtain channel state information. Over the last few years, research has repeatedly shown that allowing the receiver to send a small number of information bits about the channel conditions to the transmitter can allow near optimal channel adaptation. These practical systems, which are commonly referred to as limited or finiterate feedback systems, supply benefits nearly identical to unrealizable perfect transmitter channel knowledge systems when they are judiciously designed. In this tutorial, we provide a broad look at the field of limited feedback wireless communications. We review work in systems using various combinations of single antenna, multiple antenna, narrowband, broadband, singleuser, and multiuser technology. We also provide a synopsis of the role of limited feedback in the standardization of next generation wireless systems.
On the capacity of fading MIMO broadcast channels with imperfect transmitter sideinformation
 in Annual Allerton Conference on Communication, Control, and Computing
, 2005
"... A fading broadcast channel is considered where the transmitter employs two antennas and each of the two receivers employs a single receive antenna. It is demonstrated that even if the realization of the fading is precisely known to the receivers, the high signaltonoise (SNR) throughput is greatly ..."
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Cited by 29 (2 self)
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A fading broadcast channel is considered where the transmitter employs two antennas and each of the two receivers employs a single receive antenna. It is demonstrated that even if the realization of the fading is precisely known to the receivers, the high signaltonoise (SNR) throughput is greatly reduced if, rather than knowing the fading realization precisely, the trasmitter only knows the fading realization approximately. The results are general and are not limited to memoryless Gaussian fading. 1
From Single user to Multiuser Communications: Shifting the MIMO paradigm
 IEEE Sig. Proc. Magazine
, 2007
"... In multiuser MIMO networks, the spatial degrees of freedom offered by multiple antennas can be advantageously exploited to enhance the system capacity, by scheduling multiple users to simultaneously share the spatial channel. This entails a fundamental paradigm shift from single user communications, ..."
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Cited by 23 (8 self)
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In multiuser MIMO networks, the spatial degrees of freedom offered by multiple antennas can be advantageously exploited to enhance the system capacity, by scheduling multiple users to simultaneously share the spatial channel. This entails a fundamental paradigm shift from single user communications, since multiuser systems can experience substantial benefit from channel state information at the transmitter and, at the same time, require more complex scheduling strategies and transceiver methodologies. This paper reviews multiuser MIMO communication from an algorithmic perspective, discussing performance gains, tradeoffs, and practical considerations. Several approaches including nonlinear and linear channelaware precoding are reviewed, along with more practical limited feedback schemes that require only partial channel state information. The interaction between precoding and scheduling is discussed. Several promising strategies for limited multiuser feedback design are looked at, some of which are inspired from the single user MIMO precoding scenario while others are fully specific to the multiuser setting. 1 DRAFT
Signature Optimization for CDMA with Limited Feedback
 IEEE TRANS. INFORM. THEORY
, 2005
"... We study the performance of joint signaturereceiver optimization for Direct Sequence (DS)Code Division Multiple Access (CDMA) with limited feedback. The receiver for a particular user selects the signature from a signature codebook, and relays the corresponding B index bits to the transmitter over ..."
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Cited by 18 (8 self)
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We study the performance of joint signaturereceiver optimization for Direct Sequence (DS)Code Division Multiple Access (CDMA) with limited feedback. The receiver for a particular user selects the signature from a signature codebook, and relays the corresponding B index bits to the transmitter over a noiseless channel. We study the performance of a Random Vector Quantization (RVQ) scheme in which the codebook entries are independent and isotropically distributed. Assuming the interfering signatures are independent, and have independent, identically distributed elements, we evaluate the received SignaltoInterference plus Noise Ratio (SINR) in the large system limit as the number of users, processing gain, and feedback bits B all tend to infinity with fixed ratios. This SINR is evaluated for both the matched filter and linear Minimum Mean Squared Error (MMSE) receivers. Furthermore, we show that this large system SINR is the maximum that can be achieved over any sequence of codebooks. Numerical results show that with the MMSE receiver one feedback bit per signature coefficient achieves close to singleuser performance. We also consider a less complex and suboptimal reducedrank signature optimization scheme in which the user's signature is constrained to lie in a lower dimensional subspace. The optimal subspace coefficients are scalarquantized and relayed to the transmitter. The large system performance of the quantized reducedrank scheme can be approximated, and numerical results show that it performs in the vicinity of the RVQ bound. Finally, we extend our analysis to the scenario in which a subset of users optimize their signatures in the presence of random interference.
Space division multiple access with a sum feedback rate constraint
 IEEE Trans. Signal Processing
, 2007
"... Abstract—On a multiantenna broadcast channel, simultaneous transmission to multiple users by joint beamforming and scheduling is capable of achieving high throughput, which grows double logarithmically with the number of users. The sum rate for channel state information (CSI) feedback, however, incr ..."
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Cited by 16 (2 self)
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Abstract—On a multiantenna broadcast channel, simultaneous transmission to multiple users by joint beamforming and scheduling is capable of achieving high throughput, which grows double logarithmically with the number of users. The sum rate for channel state information (CSI) feedback, however, increases linearly with the number of users, reducing the effective uplink capacity. To address this problem, a novel space division multiple access (SDMA) design is proposed, where the sum feedback rate is upper bounded by a constant. This design consists of algorithms for CSI quantization, thresholdbased CSI feedback, and joint beamforming and scheduling. The key feature of the proposed approach is the use of feedback thresholds to select feedback users with large channel gains and small CSI quantization errors such that the sum feedback rate constraint is satisfied. Despite this constraint, the proposed SDMA design is shown to achieve a sum capacity growth rate close to the optimal one. Moreover, the feedback overflow probability for this design is found to decrease exponentially with the difference between the allowable and the average sum feedback rates. Numerical results show that the proposed SDMA design is capable of attaining higher sum capacities than existing ones, even though the sum feedback rate is bounded. Index Terms—Broadcast channels, feedback communication, multiuser channels, space division multiplexing. I.
Interpolation based unitary precoding for spatial multiplexing MIMOOFDM with limited feedback
 in Proc. IEEE Glob. Telecom. Conf
, 2004
"... Abstract—Spatial multiplexing with linear precoding is a simple technique for achieving high spectral efficiency in multipleinput multipleoutput orthogonal frequency division multiplexing (MIMOOFDM) systems. Linear precoding requires channel state information for each OFDM subcarrier, which can b ..."
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Cited by 14 (3 self)
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Abstract—Spatial multiplexing with linear precoding is a simple technique for achieving high spectral efficiency in multipleinput multipleoutput orthogonal frequency division multiplexing (MIMOOFDM) systems. Linear precoding requires channel state information for each OFDM subcarrier, which can be achieved using feedback. To reduce the amount of feedback, this paper proposes a limited feedback architecture that combines precoder quantization with a special matrix interpolator. In the proposed system, the receiver sends information about a fraction of the precoding matrices to the transmitter and the transmitter reconstructs the precoding matrices for all the subcarriers. A new interpolator is proposed inspired by spherical interpolation that respects the orthogonal columns of the precoding matrices and the performance invariance to right multiplication by a unitary matrix. The interpolator is parameterized by a set of unitary matrices; a construction of a suitable set is briefly described. Simulations illustrate the performance of limited feedback precoding with coding, estimation or prediction error, and time variation for bit error rate (BER), mutual information, and mean squared error (MSE). Index Terms—Interpolation, multipleinput multipleoutput (MIMO), spatial multiplexing.
Opportunistic space division multiple access with beam selection
 IEEE TRANS. ON COMMUNICATIONS
, 2006
"... In this paper, a novel transmission technique for the multipleinput multipleoutput (MIMO) broadcast channel is proposed that allows simultaneous transmission to multiple users with limited feedback from each user. During a training phase, the base station modulates a training sequence on multiple ..."
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Cited by 14 (10 self)
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In this paper, a novel transmission technique for the multipleinput multipleoutput (MIMO) broadcast channel is proposed that allows simultaneous transmission to multiple users with limited feedback from each user. During a training phase, the base station modulates a training sequence on multiple sets of randomly chosen orthogonal beamforming vectors. Each user sends the index of the best beamforming vector and the corresponding signaltointerfenceplusnoise ratio for that set of orthogonal vectors back to the base station. The base station opportunistically determines the users and corresponding orthogonal vectors that maximize the sum capacity. Based on the capacity expressions, the optimal amount of training to maximize the sum capacity is derived as a function of the system parameters. The main advantage of the proposed system is that it provides throughput gains for the MIMO broadcast channel with a small feedback overhead, and provides these gains even with a small number of active users. Numerical simulations show that a 20 % gain in sum capacity is achieved (for a small number of users) over conventional opportunistic space division multiple access, and a 100 % gain (for a large number of users) over conventional opportunistic beamforming when the number of transmit antennas is four.
MIMO relaying with linear processing for multiuser transmission in fixed relay networks
 IEEE TRANS. SIGNAL PROCESSING
, 2006
"... In this paper, a novel relaying strategy that uses multiple input multiple output (MIMO) fixed relays with linear processing to support multiuser transmission in cellular networks is proposed. The fixed relay processes the received signal with linear operations and forwards the processed signal to m ..."
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Cited by 14 (1 self)
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In this paper, a novel relaying strategy that uses multiple input multiple output (MIMO) fixed relays with linear processing to support multiuser transmission in cellular networks is proposed. The fixed relay processes the received signal with linear operations and forwards the processed signal to multiple users creating a multiuser MIMO relay. This paper proposes upper and lower bounds on the achievable sum rate for this architecture assuming zero forcing dirty paper coding at the base station, neglecting the direct links from the base station to the users, and with certain structure in the relay. These bounds are used to motivate an implementable multiuser precoding strategy that combines TomlinsonHarashima precoding at the base station and linear signal processing at the relay, adaptive stream selection, and QAM modulation. Reduced complexity algorithms based on the sum rate lower bounds are used to select a subset of users. Simulations compare the upper bounds, lower bounds, and the throughput with TomlinsonHarashima precoding without coding. These results show that the sum rates achieved by the proposed system architecture and algorithms are close to the sum rate upper bound and the sum rate achieved by the decodeandforward relaying though decoding at the relay is not required.