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85
A VectorPerturbation technique for NearCapacity . . .
 IEEE TRANS. COMMUN
, 2005
"... Recent theoretical results describing the sum capacity when using multiple antennas to communicate with multiple users in a known rich scattering environment have not yet been followed with practical transmission schemes that achieve this capacity. We introduce a simple encoding algorithm that achi ..."
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Cited by 261 (9 self)
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Recent theoretical results describing the sum capacity when using multiple antennas to communicate with multiple users in a known rich scattering environment have not yet been followed with practical transmission schemes that achieve this capacity. We introduce a simple encoding algorithm that achieves nearcapacity at sum rates of tens of bits/channel use. The algorithm is a variation on channel inversion that regularizes the inverse and uses a “sphere encoder ” to perturb the data to reduce the power of the transmitted signal. This paper is comprised of two parts. In this first part, we show that while the sum capacity grows linearly with the minimum of the number of antennas and users, the sum rate of channel inversion does not. This poor performance is due to the large spread in the singular values of the channel matrix. We introduce regularization to improve the condition of the inverse and maximize the signaltointerferenceplusnoise ratio at the receivers. Regularization enables linear growth and works especially well at low signaltonoise ratios (SNRs), but as we show in the second part, an additional step is needed to achieve nearcapacity performance at all SNRs.
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 41 (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.
Multiuser MIMO Downlink Made Practical: Achievable Rates with Simple Channel State Estimation and Feedback Schemes
"... 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 explicit channel feedback is performed to provide transmitter channel state information (CSIT). Both “analog” and quantized (digital) ..."
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Cited by 21 (6 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 explicit channel feedback is performed to provide transmitter channel state information (CSIT). Both “analog” and quantized (digital) channel feedback are analyzed, and digital feedback is shown to be potentially superior when the feedback channel uses per channel coefficient is larger than 1. Also, we show that by proper design of the digital feedback link, errors in the feedback have a relatively minor effect even if simple uncoded modulation is used on the feedback channel. We extend our analysis to the case of fading MIMO Multiaccess Channel (MIMOMAC) in the feedback link, as well as to the case of a timevarying channel and feedback delay. We show that by exploiting the MIMOMAC nature of the uplink channel, a fully scalable system with both downlink multiplexing gain and feedback redundancy proportional to the number of base station antennas can be achieved. Furthermore, the feedback strategy is optimized by a nontrivial combination of timedivision and spacedivision multipleaccess. 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.
Lattice Reduction  A survey with applications in wireless communications
, 2011
"... Lattice reduction is a powerful concept for solving diverse problems involving point lattices. Signal processing applications where lattice reduction has been successfully used include global positioning system (GPS), frequency estimation, color space estimation in JPEG pictures, and particularly da ..."
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Cited by 18 (0 self)
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Lattice reduction is a powerful concept for solving diverse problems involving point lattices. Signal processing applications where lattice reduction has been successfully used include global positioning system (GPS), frequency estimation, color space estimation in JPEG pictures, and particularly data detection and precoding in wireless communication systems. In this article, we first provide some background on point lattices and then give a tutorialstyle introduction to the theoretical and practical aspects of lattice reduction. We describe the most important lattice reduction algorithms and comment on their performance and computational complexity. Finally, we discuss the application of lattice reduction in wireless communications and statistical signal processing. Throughout the article, we point out open problems and interesting questions for future research.
Precoding for the multiantenna downlink: Multiuser SNR gap and optimal user ordering
 IEEE Trans. Commun
, 2007
"... Abstract—This paper develops a practical design method for implementing Tomlinson–Harashima precoding (THP) in a downlink channel with multiple antennas at the transmitter and a single antenna at each receiver. A twostep design process is proposed for minimizing the total transmit power while satis ..."
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Cited by 17 (1 self)
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Abstract—This paper develops a practical design method for implementing Tomlinson–Harashima precoding (THP) in a downlink channel with multiple antennas at the transmitter and a single antenna at each receiver. A twostep design process is proposed for minimizing the total transmit power while satisfying every user’s minimum data rate and maximum biterror rate (BER) requirements. First, the BER and rate requirements are converted to “virtual rate ” requirements, which account for the gaptocapacity introduced by practical quadrature amplitude modulation (QAM) and THP. The second step is to determine the transmit covariance matrices (which specify the entire THP system) that will provide these virtual rates at the minimum total transmit power. As one of the main features in the proposed scheme, an algorithm for finding the optimal user encoding (or presubtraction) order in polynomial time is proposed. In addition, we also propose an algorithm that finds a nearoptimal order, but which is much less complex. The proposed method outperforms existing zeroforcingbased THP systems in term of power efficiency. Index Terms—Broadcast channel (BC), multipleaccess channel (MAC), multiple antennas, signaltonoise ratio (SNR) gap approximation, spatial multiplex, Tomlinson–Harashima precoding (THP), uplink–downlink duality. I.
Nonlinear multiuser transmission using multiple antennas for TDDCDMA
 in Proc. IEEE WPMC
, 2003
"... Abstract — Multiuser Transmission (MUT), the counterpart of Multiuser Detection(MUD) in the transmitter, can substantially enhance the performance of the CDMA downlink in frequencyselective channels. Besides linear Multiuser Transmission, known as Joint Transmission and Transmit Wiener filters, rece ..."
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Cited by 9 (5 self)
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Abstract — Multiuser Transmission (MUT), the counterpart of Multiuser Detection(MUD) in the transmitter, can substantially enhance the performance of the CDMA downlink in frequencyselective channels. Besides linear Multiuser Transmission, known as Joint Transmission and Transmit Wiener filters, recently nonlinear MUT was proposed. The contribution of this paper is the extension of nonlinear Minimum BER Transmission to multiple transmit and receive antennas. Furthermore linear and nonlinear multiple antennae MUT schemes are compared for the application of PreRAKE, RAKE and Eigenprecoder. The simulation environment is similar to 3GPP TDD CDMA or the Chinese TDSCDMA.
Vector precoding for wireless MIMO systems and its replica analysis
 IEEE J. Sel. Areas Commun
"... We apply the replica method to analyze vector precoding, a method to reduce transmit power in antenna array communications. The analysis applies to a very general class of channel matrices. The statistics of the channel matrix enter the transmitted energy per symbol via its Rtransform. We find that ..."
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Cited by 9 (2 self)
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We apply the replica method to analyze vector precoding, a method to reduce transmit power in antenna array communications. The analysis applies to a very general class of channel matrices. The statistics of the channel matrix enter the transmitted energy per symbol via its Rtransform. We find that vector precoding performs much better for complex than for real alphabets. As a byproduct, we find a nonlinear precoding method with polynomial complexity that outperforms NPhard TomlinsonHarashima precoding for binary modulation on complex channels if the number of transmit antennas is slightly larger than twice the number of receive antennas. Index Terms Multipleantenna wireless, multipleinput multipleoutput (MIMO), spatial equalization, TomlinsonHarashima precoding, replica method, random matrices, Rtransform. I.
TomlinsonHarashima Precoding for Broadcast Channels with Uncertainty
"... Abstract — We consider the design of TomlinsonHarashima (TH) precoders for broadcast channels in the presence of channel uncertainty. For systems in which uplinkdownlink reciprocity is used to obtain a channel estimate at the transmitter, we present a robust design based on a statistical model for ..."
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Cited by 9 (1 self)
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Abstract — We consider the design of TomlinsonHarashima (TH) precoders for broadcast channels in the presence of channel uncertainty. For systems in which uplinkdownlink reciprocity is used to obtain a channel estimate at the transmitter, we present a robust design based on a statistical model for the channel uncertainty. We provide a convex formulation of the design problem subject to two types of power constraints: a set of constraints on the power transmitted from each antenna and a total power constraint. For the case of the total power constraint, we present a closedform solution for the robust TH precoder that incurs essentially the same computational cost as the corresponding designs that assume perfect channel knowledge. For systems in which the receivers feed back quantized channel state information to the transmitter, we present a robust design based on a bounded model for the channel uncertainty. We provide a convex formulation for the TH precoder that maximizes the performance under the worstcase channel uncertainty subject to both types of power constraints. We also present a conservative robust design for this type of channel uncertainty that has reduced computational complexity for the case of power constraints on individual antennas and leads to a closedform solution for the total power constraint case. Simulation studies verify our analytical results and show that the robust TH precoders can significantly reduce the rather high sensitivity of broadcast transmissions to errors in channel state information. Index Terms — TomlinsonHarashima precoding, broadcast channel, channel uncertainty, robust precoding.
Nonlinear chiplevel multiuser transmission for TDDCDMA in frequencyselective MIMO channels
 in Proc. International ITG Conference on Source and Channel Coding (SCC
, 2004
"... Multiuser Transmission (MUT), the counterpart of Multiuser Detection (MUD) in the transmitter, can substantially enhance the performance of the CDMA downlink in frequencyselective channels. Besides linear Multiuser Transmission, known as Joint Transmission and Transmit Wiener filters, recently nonl ..."
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Cited by 7 (4 self)
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Multiuser Transmission (MUT), the counterpart of Multiuser Detection (MUD) in the transmitter, can substantially enhance the performance of the CDMA downlink in frequencyselective channels. Besides linear Multiuser Transmission, known as Joint Transmission and Transmit Wiener filters, recently nonlinear MUT was proposed. The contribution of this paper is the extension of nonlinear Minimum BER Transmission from the symbollevel to the more general chiplevel. A phaseonly nonlinear MUT scheme is proposed, which requires considerably less computational complexity. The linear and nonlinear multiple antennae MUT schemes are compared for different receiver configurations and for the application of multiple antennas both in the transmitter and in the receiver. The simulation environment is similar to 3GPP TDD CDMA or the Chinese TDSCDMA. 1
A LowComplexity Precoder for Large Multiuser MISO Systems
"... Abstract — In this paper, we consider the problem of precoding in large multiuser MISO systems, where by ‘large ’ we mean i) large number of transmit antennas (Nt) at the base station of the order of tens to hundreds of transmit antennas, and ii) large number of downlink users (Nu) of the order of t ..."
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Cited by 7 (3 self)
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Abstract — In this paper, we consider the problem of precoding in large multiuser MISO systems, where by ‘large ’ we mean i) large number of transmit antennas (Nt) at the base station of the order of tens to hundreds of transmit antennas, and ii) large number of downlink users (Nu) of the order of tens to hundreds of users where each user has one receive antenna. Such large MISO systems will be of immense interest because of the high capacities (sumrates) of the order of hundreds of bits/channel use possible in such systems. We propose a vector perturbation based lowcomplexity precoder, termed as norm descent search (NDS) precoder, which has a complexity of just O(NuNt) per information symbol. This low complexity attribute of the precoder is achieved by searching for the perturbation vector over a reduced search space. Interestingly, in terms of BER performance, the proposed precoder achieves increasingly better BER for increasing Nt,Nu, such that for large Nt,Nu it achieves nearexponential diversity with some SNR loss, thus making it suited for large MISO systems both in terms of complexity as well as performance. The results of uncoded/turbocoded simulations without and with channel estimation errors are presented.