Performance with Random Signatures

Peacock, M.J.M.; Collings, Iain B.; Honig, Michael L.

doi:10.1002/9780470473818.ch4

Cited by 5 publications

(2 citation statements)

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“…1 First consider a preliminary random experiment with unit norm vectors v 1 and g 1 that are isotropically distributed on the unit sphere, and the matrix H 11 , which has unit-variance complex Gaussian i. i. d. elements. In a large system, the singular values of H 11 are deterministic [8]. Furthermore, the matrix containing the left and right singular bases are unitary, so that when they are multiplied with any unit norm vector, the resulting unit norm vector is also isotropically distributed on the unit sphere.…”

Section: Max-of-l Alignment (Mla)mentioning

confidence: 99%

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Large System Performance of Interference Alignment in Single-Beam MIMO Networks

Schmidt

Utschick

Honig

2010

2010 IEEE Global Telecommunications Conference GLOBECOM 2010

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Abstract-We consider a network of K interfering transmitterreceiver pairs, where each node has N antennas and at most one beam is transmitted per user. We investigate the asymptotic performance of different beamforming strategies, as characterized by the slope and y-axis intercept (or offset) of the high signal-tonoise-ratio (SNR) sum rate asymptote. It is known that a slope (or multiplexing gain) of 2N − 1 is achievable with interference alignment. On the other hand, a strategy achieving a slope of only N might allow for a significantly higher offset. Assuming that the number of fully aligned beamformer sets that achieve a slope of 2N − 1 is finite for a given channel realization, we approximate the average offset when the best out of a large number L of these sets is selected. We also derive a simple large system approximation for the sum rate of a successive beam allocation scheme when K = N . We show that both approximations accurately predict simulated results for moderate system dimensions and characterize the large-system asymptotes for different relationships between L and N .

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Section: Max-of-l Alignment (Mla)mentioning

confidence: 99%

“…Proof Sketch: In a large system, the singular values of H 11 are deterministic and are governed by the Marčenko-Pastur distribution; the maximum singular value approaches 2 √ N (see, e. g., [8]). Therefore, the rate for the first user approaches log(4N ).…”

Section: Achievable Rate Offset With K = Nmentioning

confidence: 99%