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Tham khảo tài liệu 'wimax, new developments 2011 part 16', kỹ thuật - công nghệ, cơ khí - chế tạo máy phục vụ nhu cầu học tập, nghiên cứu và làm việc hiệu quả | 398 WIMAX New Developments duration we can get D - L noise plus interference power estimates defined as r 2 J u L u D -1 with 1 M -ỴD-1 J u .A tt I y k N D m -y k N D N m I2 2M D - u k 0 m u 20 21 where M denotes the number of OFDM symbols in the observation window. Note that non data-aided synchronisation can be done thanks to the detection algorithm of subsection 4.3 or to more general algorithms such as those discussed in van de Beek et al. 1997 Park et al. 2001 Xiaoli et al. 2001 . It can be easily shown that the estimator with the smallest variance is found for u L . The difficulty is then to estimate L. Cui et al. suggested an estimator in Cui Tellambura 2006 but it has the major disadvantage of being based on a threshold level chosen arbitrarily. To overcome this limitation we hereafter propose a method inspired by maximum likelihood estimation. From Eq. 21 J u can be expressed as J u 11 --- I J u 1 ệ u I D - u 22 where ệ u is a random variable given by ệ u 1 2M D - u M-1 t k 0 I y k N D u -y k N D N u 2. 23 For L u D -1 and M large enough ệ u is Gaussian and verifies ệ u N Ì. D - u M D - u 2 24 L is then estimated using the likelihood function f Xu IL u with Xu the multivariate observation variables defined as Xu u u 1 --- D -1 . The different ệ u being independent is given by argmax 0 u D-1 D-1 nf ơ m i L u m u 1 D -Ù 25 where f m I L u is computed thanks to Eq. 24 by making the approximation that Ơ2 J u . Note that because the observations X are of variable lengths Eq. 25 is defined as an average likelihood which is the geometric mean of the individual likelihood elements. Signal Metrics for Vertical Handoff Towards Cognitive WiMAX 399 5.2. Signal power estimation Thanks to equations 7 and 9 it is straightforward to show that the signal power can be estimated as S 1 2 Nc 1 x Rịqa N sln qao eixqa D-1 N y a sin xqa D 26 where a 1 N D and Nc represents the number of considered cycle frequencies to estimate the signal power. We assume that the interference .
