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Criteria of Convergence

Criteria of Convergence. Gill Jul. 27, 2010. Criteria of convergence. 2X2, 3 links. 3X3, 3 links. C1: |SINR(k) - SINR(k+1)| <= 10^(-6) (‘absolute’ measure ) C2: |10*log SINR(k) - 10*log SINR(k+1)| <=  β ( ‘relative’ measure) β = 0.1, 0.05, and 0.01. Criteria of convergence (cont.).

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Criteria of Convergence

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  1. Criteria of Convergence Gill Jul. 27, 2010

  2. Criteria of convergence 2X2, 3 links 3X3, 3 links • C1: |SINR(k) - SINR(k+1)| <= 10^(-6) (‘absolute’ measure) • C2: |10*log SINR(k) - 10*log SINR(k+1)| <=  β (‘relative’ measure) • β=0.1, 0.05, and 0.01

  3. Criteria of convergence (cont.) 4X4, 3 links Compared with MMSE using C1, performance of MMSE is worse when β=0.1. performance of MMSE is closer when β=0.01.

  4. Convergence table • Conv. criterion: C2 with β=0.01. • If non-convergent, value at 500th iteration will be kept. • ML-DIA: it always does good actually, but its value of SINR fluctuates due to extra degrees of freedom when L < M= N.

  5. Convergence table (cont.) • Conv. criterion: C2 with β=0.1. • MMSE : small median #, high conv. percentage due to small change of SINR in each iteration. •  MMSE is the best choice under this conv. criterion.

  6. Relative complexity per iteration • ML-DIA: 2 times of eigendecomposition, avoiding matrix inversion • MS-DIA: 4 times of eigendecompostion, avoiding matrix inversion. • The complexity of MS-DIA is two times that of ML-DIA per iteration. • DIA-MMSE: 1 time of eigendecomposition and 1 time of matrix inversion • MMSE: 2 times of matrix inversion

  7. Sum-rate & convergence 4×4 3 links Convergence

  8. Sum-rate & convergence (cont.) 3×3 3 links Convergence

  9. Sum-rate & convergence (cont.) 2×2 3 links Convergence

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