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Unlike ta and tb , tQ is not strictly monotonic. This means that very different arrays of scores, or pairs of arrays based on different ns, may produce the same value for tQ . Therefore, tQ does not discriminate between certain subsets of relations for which ta and tb do (see Agresti, 1984, chapter 9). In terms of values of the coef cients, this means that |tQ | |tb | |ta |. Yet another type of tau correlation can be computed, one that corrects for ties only on the response variable, Y. This correlation is Somers d, which is symbolized as dyx . The yx in the subscript indexes the fact that the correlation adjusts for ties on Y but not X. The sample tdyx is computed as dihx dihy tdyx =

where (8.78) follows from the fact that the mean of X is the best estimator for X and the last inequality follows from the fact that the Gaussian distribution has the maximum entropy for a given variance. We have equality only in (8.78) only if X is the best estimator (i.e., X is the mean of X and equality in (8.80) only if X is Gaussian). Corollary Given side information Y and estimator X(Y ), it follows that E(X X(Y ))2 1 2h(X|Y ) e . 2 e

Figure 7-12

(9.105)

Finally, the target function to be minimized is the number of distinct frequency blocks, i.e., | f (B)| = |{ f (v, B) : (v, B) B}|. We can now formulate the ensemble planning problem in the usual decision format as follows: Problem 1 (Ensemble Planning Problem) Given G = (V, E), R : V 2S, M and K , decide whether there is an admissible ensemble assignment B and corresponding admissible block assignment f s.t. | f (B)| K.

Finally, since all starting positions are equally likely to be used, the average BER P can be written as

device data communication equipment (DCE). This equipment has two interfaces, one on each side, as shown in Figure 10.9. The rst, which is discussed in this section, is on the user side, which is called data terminating equipment (DTE), and the applicable interface is the DTE DCE interface. The second interface is on the line side, which is covered in Section 10.9. It should be noted that the DTE-DCE interface is well de ned. The most well-known DTE DCE standard was developed by the (U.S.) Electronics Industries Association (EIA) and is called EIA-232E (Ref. 5). It is essentially equivalent to international standards covered by CCITT Recs. V.24 and V.28, and ISO IS2110. EIA-232E and most of the other standards discussed here are applicable to the DTE DCE interface employing serial binary data interchange. It de nes signal characteristics, mechanical interface characteristics, and functional descriptions of the interchange circuits. EIA-232E is applicable for data transmission rates up to 20,000 bps and for synchronous/ asynchronous serial binary data systems. Section 2.1.3 is quoted from EIA-232E (Ref. 5). It is crucial to the understanding of signal state convention and level:

between core and radio access network are standardized to allow the core network and radio access networks from different vendors to work smoothly together and ensure that both sides can evolve without the need for end-to-end upgrade of the network in case of such a new feature is added that impacts only the other side of the network. Standardized interfaces also de ne explicitly which interfaces should carry some information related to a particular feature, thus revealing information on which network elements need to be updated when the feature is implented. The core network has been developed since the rst release of the WCDMA standards in 1999. The release 99-based core network currently being operated with WCDMA is basically the same as that been used with GSM previously. The main elements shown in Figure 2.1 for the release 99 architecture are . The HLR (home location register) database stores the master copy of the user s service pro le, including information on allowed services. It is created when a new user subscribes to the system, and remains stored as long as the subscription is active. For routing incoming transactions to the UE, the HLR also contains the UE location on the level of serving MSC or SGSN. . The MSC/VLR (mobile services switching center/visitor location register) is the switch (MSC) and database (VLR) that serves the UE in its current location for circuit-switched (CS) services. The MSC function is used to switch the CS transactions, and the VLR function holds a copy of the visiting user s service pro le, as well as more precise information on the UE s location within the serving system.