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Hence this approach reduces the (L + 1)-fold integral with in nite limits of (9.113) to a single nite-range integral (9.115) whose integrand contains only elementary functions (i.e., no special functions) and that can therefore be easily evaluated numerically. 9.4.1.3 Bounds on Average Bit Error Probability While the results found above are exact, they still require the numerical evaluation of an integral. Our goal in this section is to derive a closed-form upper bound on the BER performance. We start with the conditional BER expression given in (9.108). Recall that the arguments of the second generalized Marcum Q-function in (9.108) are in reverse order to those in the rst one. Thus, if a < b (the case of practical interest in communication problems), then, using the tight upper bound (4.57a) for the rst term and the tight lower bound of (4.64a) for the second would produce a tight upper bound on the conditional BER. The next step would be to average the resulting conditional BER expression over the PDFs of the fading RVs. If we assume that the SNRs per bit per path l ; l = 1, 2, . . . , L are independent, unfortunately, the presence of the term in (4.64a) with the summation would prevent the desired partitioning of the integrand, thereby precluding averaging on a channelby-channel basis. To circumvent this dif culty, we simplify (with the understanding that it becomes negligibly looser as shown in Figs. 4.2 4.4) the lower bound of (4.64a) by ignoring this term (which is always positive), which is tantamount to using the lower bound on Q1 ( , ) as given by (4.31b) for Qm ( , ). When this is done, the following upper bound on the conditional BER results Pb (E | t ) 1 22L 1

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Once all the dimensions have been populated, the fact table can be loaded. Dimension primary keys generally take one of two forms: the key is either a natural key based on dimension data (e.g., ProductCode) or it is a surrogate key without any relationship to the data (e.g., the identity column). Surrogate keys are more general and adapt well to data from multiple sources, but each surrogate key requires a join while loading. For example, suppose our simple fact table is related to dimTime, dimCustomer, and dimProduct. If dimCustomer and dimProduct use surrogate keys, the load might look like the following:

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To get the best results with the least amount of effort, you should follow a standard set of steps for all your work in Develop. In this chapter we ll cover all the individual adjustments you can make, and you ll learn how to dramatically speed up your workflow using Develop presets. First, let s outline the order of the Develop workflow you ll use to process most of your photos: 1. Global rendering

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Figure 4.3-3 Spectrum of CO with pressure of 54 hPa, temperature of 25 "C and optical pathlength of 10 cm at a spectral resolution of 0.05 c m - ' ; the fundamental region is enlarged in the inset showing also the rotation-vibration features of the ''Cl'O isotope (see also text).

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