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19
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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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.
Zero Forcing Precoding and Generalized Inverses
"... We consider the problem of linear zero forcing precoding design, and discuss its relation to the theory of generalized inverses in linear algebra. Special attention is given to a specific generalized inverse known as the pseudoinverse. We begin with the standard design under the assumption of a tot ..."
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We consider the problem of linear zero forcing precoding design, and discuss its relation to the theory of generalized inverses in linear algebra. Special attention is given to a specific generalized inverse known as the pseudoinverse. We begin with the standard design under the assumption of a total power constraint and prove that precoders based on the pseudoinverse are optimal in this setting. Then, we proceed to examine individual perantenna power constraints. In this case, the pseudoinverse is not necessarily the optimal generalized inverse. In fact, finding the optimal inverse is nontrivial and depends on the specific performance measure. We address two common criteria, fairness and throughput, and show that the optimal matrices may be found using standard convex optimization methods. We demonstrate the improved performance offered by our approach using computer simulations.
Transmit equal gain precoder in Rayleigh fading channels
 IEEE Trans. Signal Process
, 2009
"... Abstract—Precoding with limited feedback information can achieve satisfactory performance while the amount of feedback information is kept small. In this paper, we analyze the theoretical performance of equal gain precoder and find that its performance is at most 1.049 dB worse than the optimal prec ..."
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Abstract—Precoding with limited feedback information can achieve satisfactory performance while the amount of feedback information is kept small. In this paper, we analyze the theoretical performance of equal gain precoder and find that its performance is at most 1.049 dB worse than the optimal precoder no matter how the number of transmit antennas increases. Moreover, we analyze the performance degradation of the equal gain precoder due to scalar quantization theoretically. The result shows that 2–3 bits per transmit antenna (excluding the first antenna) can achieve 0.5–0.25dB performance gap compared with the same scheme without quantization. Furthermore, we found that the equal gain precoder in general can achieve comparable performance with the Grassmannian precoder in the same moderate feedback bits. Simulation results are provided to corroborate the theoretical results. Index Terms—Beamforming, equal gain precoding, limited feedback, MIMO, precoding, scalar quantization. I.
Fixedrank Rayleigh quotient maximization by an MPSK sequence,” submitted to
 IEEE Trans. Commun
, 2013
"... Abstract—Certain optimization problems in communication systems, such as limitedfeedback constantenvelope beamforming or noncoherent Mary phaseshift keying (MPSK) sequence detection, result in the maximization of a fixedrank positive semidefinite quadratic form over the MPSK alphabet. This for ..."
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Abstract—Certain optimization problems in communication systems, such as limitedfeedback constantenvelope beamforming or noncoherent Mary phaseshift keying (MPSK) sequence detection, result in the maximization of a fixedrank positive semidefinite quadratic form over the MPSK alphabet. This form is a special case of the Rayleigh quotient of a matrix and, in general, its maximization by an MPSK sequence is NPhard. However, if the rank of the matrix is not a function of its size, then the optimal solution can be computed with polynomial complexity in the matrix size. In this work, we develop a new technique to efficiently solve this problem by utilizing auxiliary continuousvalued angles and partitioning the resulting continuous space of solutions into a polynomialsize set of regions, each of which corresponds to a distinct MPSK sequence. The sequence that maximizes the Rayleigh quotient is shown to belong to this polynomialsize set of sequences, thus efficiently reducing the size of the feasible set from exponential to polynomial. Based on this analysis, we also develop an algorithm that constructs this set in polynomial time and show that it is fully parallelizable, memory efficient, and rank scalable. The proposed algorithm compares favorably with other solvers for this problem that have appeared recently in the literature. Index Terms—Algorithms, maximum likelihood detection, MIMO systems, noncoherent communication, optimization methods, phase shift keying, Rayleigh quotient, sequences. I. PROBLEM STATEMENT, PRIOR WORK,
http://urn.kb.se/resolve?urn=urn:nbn:se:liu:diva91313 AmplifierAware MultipleInput MultipleOutput Power Allocation
"... N.B.: When citing this work, cite the original article. ©2013 IEEE. Personal use of this material is permitted. However, permission to reprint/republish this material for advertising or promotional purposes or for creating new collective works for resale or redistribution to servers or lists, or to ..."
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N.B.: When citing this work, cite the original article. ©2013 IEEE. Personal use of this material is permitted. However, permission to reprint/republish this material for advertising or promotional purposes or for creating new collective works for resale or redistribution to servers or lists, or to reuse any copyrighted component of this work in other works must be obtained from the IEEE.
On the Beamforming Optimality Range in TIMO Channels with Common and Individual Input Power Constraints
"... Abstract—In this letter, the effect of the input power constraint on the beamforming optimality range in Gaussian twoinput multipleoutput (TIMO) channels is investigated. The obtained expressions, using standard Lagrangian formulation, determine explicitly the range of the input signaltonoise ra ..."
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Abstract—In this letter, the effect of the input power constraint on the beamforming optimality range in Gaussian twoinput multipleoutput (TIMO) channels is investigated. The obtained expressions, using standard Lagrangian formulation, determine explicitly the range of the input signaltonoise ratio (SNR) for which beamforming (rank1 signaling) is optimal for TIMO channels for both the common power constraint and the individual power constraint cases. Moreover, the obtained results are extended to random TIMO channels, with channel state information at the receiver only, using the Jensen’s upper bound on the mutual information. Index Terms—MIMO channels, mutual information, input covariance matrix, beamforming, common power constraint, individual power constraints. I.
1Subspace Estimation and Decomposition for Large MillimeterWave MIMO systems
"... Abstract—Channel estimation and precoding in hybrid analogdigital millimeterwave (mmWave) MIMO systems is a fundamental problem that has yet to be addressed, before any of the promised gains can be harnessed. For that matter, we propose a method (based on the wellknown Arnoldi iteration) exploit ..."
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Abstract—Channel estimation and precoding in hybrid analogdigital millimeterwave (mmWave) MIMO systems is a fundamental problem that has yet to be addressed, before any of the promised gains can be harnessed. For that matter, we propose a method (based on the wellknown Arnoldi iteration) exploiting channel reciprocity in TDD systems and the sparsity of the channel’s eigenmodes, to estimate the right (resp. left) singular subspaces of the channel, at the BS (resp. MS). We first describe the algorithm in the context of conventional MIMO systems, and derive bounds on the estimation error in the presence of distortions at both BS and MS. We later identify obstacles that hinder the application of such an algorithm to the hybrid analogdigital architecture, and address them individually. In view of fulfilling the constraints imposed by the hybrid analogdigital architecture, we further propose an iterative algorithm for subspace decomposition, whereby the above estimated subspaces, are approximated by a cascade of analog and digital precoder / combiner. Finally, we evaluate the performance of our scheme against the perfect CSI, fully digital case (i.e., an equivalent conventional MIMO system), and conclude that similar performance can be achieved, especially at mediumtohigh SNR (where the performance gap is less than 5%), however, with a drastically lower number of RF chains ( ∼ 4 to 8 times less). Keywords—Millimeter wave MIMO systems, sparse channel estimation, hybrid architecture, hybrid precoding, subspace decomposition, Arnoldi iteration, subspace estimation, echobased channel estimation. I.
Robust Joint SourceRelayDestination Design Under PerAntenna Power Constraints
"... Abstract—This paper deals with joint sourcerelaydestination beamforming (BF) design for an amplifyandforward (AF) relay network. Considering the channel state information (CSI) from the relay to the destination is imperfect, we first aim to maximize the worst case received SNR under perantenna ..."
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Abstract—This paper deals with joint sourcerelaydestination beamforming (BF) design for an amplifyandforward (AF) relay network. Considering the channel state information (CSI) from the relay to the destination is imperfect, we first aim to maximize the worst case received SNR under perantenna power constraints. The associated optimization problem is then solved in two steps. In the first step, by revealing the rankone property of the optimal relay BF matrix, we establish the semiclosed form solution of the joint optimal BF design that only depends on a vector variable. Based on this result, in the second step, we propose a lowcomplexity iterative algorithm to obtain the remaining unknown variable. We also study the problem for minimizing the maximum perantenna power at the relay while ensuring a received signaltonoise ratio (SNR) target, and show that it reduces to the SNR maximization problem. Thus the same methods can be applied to solve it. The differences between our result and the existing related work are also discussed in details. In particular, we show that in the perfect CSI case, our algorithm has the same performance but with much lower cost of computational complexity than the existing method. Finally, in the simulation part, we investigate the impact of imperfect CSI on the system performance to verify our analysis. Index Terms—Amplifyandforward, beamforming, multiantenna relay system, perantenna power.
On the Role of the Input Power Constraint in the Beamforming Optimality Range in TIMO Channels
"... Abstract — In this paper, the effect of the input power constraint on the beamforming optimality range in Gaussian twoinput multipleoutput (TIMO) channels is explored. The obtained results, using standard Lagrangian formulation, determine explicitly the range of the input SNR for which rank1 sign ..."
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Abstract — In this paper, the effect of the input power constraint on the beamforming optimality range in Gaussian twoinput multipleoutput (TIMO) channels is explored. The obtained results, using standard Lagrangian formulation, determine explicitly the range of the input SNR for which rank1 signaling (beamforming) is optimal in TIMO channels for both the common power constraint and the individual power constraint cases. Moreover, the obtained results are extended to random TIMO channels, with channel state information at the receiver only, using the Jensen’s upper bound on the mutual information.
Equal Gain MIMO Beamforming in the RF Domain for OFDMWLAN Systems
"... Abstract. Equal gain beamforming (EGB) schemes are typically applied in the baseband domain and hence require complex RF transceivers. In order to simplify the circuitry and energy consumption of the MIMO transceiver, in this paper we consider an EGB scheme that operates in the RF domain by means o ..."
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Abstract. Equal gain beamforming (EGB) schemes are typically applied in the baseband domain and hence require complex RF transceivers. In order to simplify the circuitry and energy consumption of the MIMO transceiver, in this paper we consider an EGB scheme that operates in the RF domain by means of analog phase shifters. Under OFDM transmissions, the design of the optimal phases is a complicated nonconvex problem with no closedform solution. Building upon a previously proposed solution for flatfading MIMO channels, this paper describes an alternating minimization algorithm to find an approximate (suboptimal) solution for the OFDM case. MonteCarlo simulations are performed in order to demonstrate the effectiveness of this new analog beamforming scheme under coded and uncoded WLAN 802.11a transmissions.