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Proposition 6 shows that when all paths in the outdoor model have different arrival time, full diversity can be captured by using an outer code across s u b carriers. In other words, the angle diversity is readily transferred into the frequency diversity in the OFDM systems. Combined with a proper beamformer, the transmission scheme can achieve both diversity and SNR gain as well. However, such a scheme can not fully exploit the available diversity in the channel when several paths have the same delay. This loss of diversity can be shown by observing (4.21). Notice that when two paths, say hl and h2, have the same delay 7 1 and 7 2 , these two coherent paths will always be combined in the same way on all subcarriers. Therefore, the available diversity in the effective channel seen by the channel coding is reduced. To capture this otherwise lost diversity, a space-time code is needed. The size of the STC needed is dependent on the number of paths having the same delay, as shown in the following proposition.

However, this shifting could limit the maximum measurable height range because the object may be shifted out of the focus range or the fringe frequency may become too dense to be resolved (see Eq (1531)) The resolution of the measured height, in addition to the wavelength scanning range, also depends on the roughness of the tested object and the distance from the point of best focus (Yamaguchi et al, 1998) In a Fizeau setup multiple re ections between the reference and the object must be accounted for in the signal analysis (Yamaguchi et al, 2000), and although the.

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In this paragraph, the linear stability and oscillation conditions so far described are modi ed to take into account the nonlinearity, that is, the dependence of the oscillator parameters on the amplitude of the signal. The stability and oscillation conditions given so far are valid only in linear regime. However, the behaviour of actual oscillating circuits always involves the nonlinear characteristics of the active device. A rigorous study requires the use of full-nonlinear analysis methods that will be described in Section 5.4. However, many conclusions of the previous paragraph are extended to the nonlinear regime by means of simple considerations requiring a general knowledge of the dependence of circuit parameters on the amplitude of the signal. First of all, let us extend the stability and oscillation considerations described in the previous paragraph to a circuit with parameters varying with the amplitude of the signal. Let us rst consider the re ection coef cients (e.g. those shown in Figure 5.5) dependent on the amplitude of the signal within the oscillator. Intuition and experience suggest that a growing instability will not grow forever but will saturate at a certain amplitude, because of the limitations of the active device. Therefore, let us

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Ray, HN Najm, RB Milne, KD Devine, and S Kempka Triple ame structure and dynamics at the stabilization point of an unsteady lifted jet diffusion ame Proc Combust Inst, 25(1):219 226, 2000 8 A Calder, H Tufo, J Turan, M Zingale, G Henry, B Curtis, L Dursi, B Fryxell, P MacNeice, K Olson, P Ricker, R Rosner, and F Timmes High performance reactive uid ow simulations using adaptive mesh re nement on thousands of processors in Proceedings of the 2000 ACM/IEEE Conference on Supercomputing (CDROM), 2000 9 LV Kale Charm http://charmcsuiucedu/research/charm/ 10 RD Hornung and SR Kohn Managing application complexity in the SAMRAI object-oriented framework Concurrency Comput Pract Exper, 14(5):347 368, 2002 11 G Karypis and V Kumar Parmetis http://www-userscsumnedu/ karypis/metis/parmetis/ indexhtml, 2003 12 P MacNeice Paramesh http://esdcdgsfcnasagov/ESS/macneice/paramesh/parameshhtml 13 M.

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