On MIMO beamforming systems using quantized feedback

Kim, Young Gil; Beaulieu, N.C.

doi:10.1109/tcomm.2010.03.0801402

Cited by 18 publications

(6 citation statements)

References 18 publications

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“…A throughput-based switching scheme is proposed in [12], this scheme is also based on low-rate feedback channel. Other schemes like transmit antenna selection [13], precoding for spatial multiplexing systems [14,15], beamforming [16][17][18], combining space-time codes with beamforming [19,20], opportunistic beamforming [21] and code diversity [22] all…”

Section: Related Workmentioning

confidence: 99%

Rate‐varying space‐time coding scheme for multiple‐input multiple‐output fading channel with zero‐forcing receiver

Wang

Zhang

2016

IET Communications

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Section: Related Workmentioning

confidence: 99%

Rate‐varying space‐time coding scheme for multiple‐input multiple‐output fading channel with zero‐forcing receiver

Wang

Zhang

2016

IET Communications

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“…We observe that the surfaces intersect at a single point φ(V; {1, 2, 3}) and the three-dimensional space is partitioned into regions (cells) each of which corresponds to a distinct candidate M PSK sequence s ∈ S(V). 6 Two basic properties of such intersections are presented in the following proposition. The proof is given in the Appendix.…”

Section: Decision Boundariesmentioning

confidence: 99%

Fixed-Rank Rayleigh Quotient Maximization by an MPSK Sequence

Kyrillidis

Karystinos

2014

IEEE Trans. Commun.

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Abstract-Certain optimization problems in communication systems, such as limited-feedback constant-envelope beamforming or noncoherent M -ary phase-shift keying (M PSK) sequence detection, result in the maximization of a fixed-rank positive semidefinite quadratic form over the M PSK alphabet. This form is a special case of the Rayleigh quotient of a matrix and, in general, its maximization by an M PSK sequence is N P-hard. 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 polynomial-size set of regions, each of which corresponds to a distinct M PSK sequence. The sequence that maximizes the Rayleigh quotient is shown to belong to this polynomial-size 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, AND CONTRIBUTION A. Problem statementWe consider the optimization problemwhere is the Euclidean 2 -norm. Problem P in (1) can be recast as the special case of the maximization of the Rayleigh quotient of VV H over the M PSK alphabet, i.e.,and solved by an exponential-complexity exhaustive search among M N −1 length-N sequences.1 However, such a solver would be impractical even for moderate values of the problem size N .Of particular interest is the case where V in P is fullcolumn-rank (i.e., it is a "tall" matrix) and its rank D is independent of its row dimension N , which appears in certain optimization problems in communication systems, such as limited-feedback multiple-input multiple-output (MIMO) beamforming which has polynomial cardinality |S(V)| and can be built with polynomial complexity. After S(V) is constructed, the optimal sequence s opt can be identified by a polynomial-complexity exhaustive search among the elements of S(V).In this work, we present a new algorithm to solve P for any even 2 M and arbitrary D and prove that it has lower complexity than the current state of the art [7], [9], [12], is fully parallelizable and rank-scalable, and requires minimum memory resources. B. Prior workCase (i): M = 2. A lot of effort has been made to solve P when M = 2, i.e., s is a binary 3 sequence, and V is a realvalued matrix. We note that, for the special case D = 1, V becomes a N ×1 vector and the solution of P is simply s opt = sgn(V). 4 Equivalently, we can say that S(V) = {s...

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“…We consider the new FFS for N = 4, T = 1 constructed using the procedure in Section III-B using γ = e i 1+ √ 5 2 and the 4 × 4 full-diversity algebraic rotation (5). The new FFS is compared with five other schemes for the bitrate of 8 bpcu: (i) the N = 4, T = 1 scheme of Love & Heath, Jr. [2] that chooses according the feedback function f = f d a precoding matrix from a set of 4 × 2 matrices to transmit a twostream spatial multiplexing input over N t = 4 antennas, (ii) Grassmannian Beamforming [6] (T = 1) with N = 64-ary feedback, (iii) Grassmannian Beamforming [6] with N = 4, (iv) the N = 4, T = 2 scheme of Love & Heath, Jr. [8] that chooses, based on the feedback index, a precoding matrix from a given set of 4×2 matrices to transmit an Alamouti code over and the 6 × 6 full-diversity algebraic rotation labeled 'mixed 2x3' in [23].…”

Section: Schemes For 4 × 4 Mimo With N ≥ N Tmentioning

confidence: 99%

“…MIMO with N ≥ N tWe consider the new FFS for N = 4, T = 1 constructed using the procedure in Section III-B using γ = e i 1+ 4 full-diversity algebraic rotation(5). The new FFS is compared with five other schemes for the bitrate of 8 bpcu: (i) the N = 4, T = 1 scheme of Love & Heath, Jr [2].…”

mentioning

confidence: 99%

Full-Rate Full-Diversity Finite Feedback Space-Time Schemes with Minimum Feedback and Transmission Duration

Natarajan

Rajan

2013

IEEE Trans. Wireless Commun.

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In this paper a universal necessary condition for any FFS to achieve full-diversity is given, using which the notion of FeedbackTransmission duration optimal (FT-Optimal) FFSs -schemes that use minimum amount of feedback N given the transmission duration T , and minimum transmission duration given the amount of feedback to achieve full-diversity -is introduced. When there is no feedback, i.e., when N = 1, an FT-optimal scheme consists of a single STBC with T = Nt, and the universal necessary condition reduces to the well known necessary and sufficient condition for an STBC to achieve full-diversity viz., every non-zero codeword difference matrix of the STBC must be of rank Nt. Also, a sufficient condition for full-diversity is given for the class of FFSs in which the feedback chooses the component STBC with the largest minimum Euclidean distance. Using this sufficient condition full-rate (rate Nt) full-diversity FT-Optimal schemes are constructed for all triples (Nt, T, N ) with N T = Nt. These are the first full-rate full-diversity FFSs reported in the literature for T < Nt. Finally, simulation results are presented that show that the new FFSs have the best error performance among all the schemes available in the literature.

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On MIMO beamforming systems using quantized feedback

Cited by 18 publications

References 18 publications

Rate‐varying space‐time coding scheme for multiple‐input multiple‐output fading channel with zero‐forcing receiver

Rate‐varying space‐time coding scheme for multiple‐input multiple‐output fading channel with zero‐forcing receiver

Fixed-Rank Rayleigh Quotient Maximization by an MPSK Sequence

Full-Rate Full-Diversity Finite Feedback Space-Time Schemes with Minimum Feedback and Transmission Duration

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