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which can be evaluated in closed form using (5A.75). Before proceeding, it is worth pointing out that exact expressions as well as upper bounds on PEP for space-time trellis codes have also been obtained by other researchers using a variety of techniques. Speci cally, in Ref. 10 the PEP is upper-bounded with the traditional Chernoff bound in the same manner as done in Ref. 34 for time coding, for instance, TCM alone. More recently, Aktas and Fitz [35] considered the distance spectrum of space-time trellis codes and along with that an upper bound on the PEP in combination with the union bound to compute average BEP. In Ref. 36, a method for exactly evaluating PEP using an eigenanalysis based on Turin s results [33] for the characteristic function associated with a quadratic form of a complex Gaussian vector is developed. This method also led to an upper bound on PEP that is asymptotically tight at high SNR and tighter than the Chernoff bound. Finally, in Ref. 37, the characteristic function technique previously used in the performance of TCM [38] is extended to the space-time problem to allow for exact evaluation of PEP by residue methods. The advantage of the MGF-based method presented in this paper is that (1) in certain cases it can allow for evaluation of the PEP (and therefore approximation to the average BEP) in a simple closed form, and (2) it can allow for direct evaluation of the transfer function upper bound on average BEP for the fast fading case. The latter will be demonstrated in a later section of the chapter. 14.6.3 An Example

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To put (9.129) in the form of an integral with nite limits, we now make the change of variables v = tan . Furthermore, recognizing that Pb (E) is real, it is necessary to take only the real part of the right-hand side of (9.129) since the imaginary part must equate to zero. Finally, after making this change of variables, performing some routine complex algebraic manipulations, and taking advantage of the fact that the resulting integrand is an even function of , we obtain the desired generic result, namely Pb (E) = 2(log2 M) 1 2log2 M 1

1 0 0 0 0 1 0 0 0 0 0 1 0 0 1 0

(14.16)

Test the impact of key variables in each scenario. Develop action plans based on either (a) the solutions that play most robustly across scenarios, or (b) The most

Watch for noise When adjusting colors in the hs l pa nel, keep an eye out for the introduction of noise as a result. This especially applies when lowering Luminance, such as when darkening skies. Hiding and showing panel adjustments Figure 4-56 Most of the panels in the Develop module include a small button (like a switch; see Figure 4 56) to temporarily hide and show the effects of that panel s adjustments. Like a light switch, up is on and down is off . Rather than Before and After or Undo/Redo, you can use this to show all the effects of a single panel. This is especially useful with the hs l pa nel. Turning on and off a panel s adjustments is tracked in history, is undoable, and can be saved as part of a preset.

1. As root user from a Terminal window, open the /etc/auto.master file and look for the following line:

WebSite has good opportunities for logging of actlvlties to discover irregularities and suspicious situations. Figure 11.14 shows the interface where logging is adminlstered.

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