Error probability modulation

The error probability as a function of Ei/No for a given modulation scheme tells only half of the story, and is often referred to as a measure of its power efficiency. Also important is its bandwidth effiiciency, defined to be the ratio of the bandwidth required to accept a given data rate divided by the data rate. 

The power efhciency of a modulation method is indicated by the value of E, /Nq required to yield a desired bit error probability, such as 10 . This being the case, it is necessary to convert horn symbol error probability to bit error probability and from Ej /No to E ,/No for M-ary modulation schemes. The latter is straightforward since the difference between symbol energy and bit energy is symbol duration vs. bit duration, which are related by... 

Conversion between symbol error probability and bit error probability is somewhat more complicated. First, considering two-dimensional modulation schemes such as MPSK and MQASK, it is assumed that... 

The various modulation schemes considered in this section are compared on the basis of bit error probability versus Ei,/Nq in Fig. 12.65 to Fig. 12.69. 

In test programs, where the numerical solution is compared with the analytical solution, the latter often involves the error function erf or the complementary error function erfc. The latter could be obtained simply by subtracting erf from unity but a better approximation is obtained by the direct algorithm. The two routines, ERF and ERFC, were given to the author by a colleague, who probably obtained them from an IBM collection. They have been adapted to Fortran 90/95 by the author, and coupled to the above module. The comments in capitals are the original comments. 

Although TCSPC is used successfully for BIFL experiments, little has been published about applications for FID A. The reason is probably that the dead time of TCSPC is considered a drawback. However, a simple consideration shows that the detectable burst rate is not substantially reduced by the dead time of the TCSPC device. The commonly used detectors lose 50% of the photons at an input rate of about 1610 s" [408], fast TCSPC modules at 10-10 s" (see Fig. 5.94, page 162). This means the dead time of the TCSPC module is only slightly longer than the dead time of the detector. The use of TCSPC for PCH experiments therefore does not result in a considerable increase of dead-time-related errors. Moreover, BIFL applications have shown that the burst count rates are well within the counting capability of TCSPC (see below). 

Under the assumptions leading to (7.174), and considering the various modulation schemes discussed previously, the probability of error in the presence of the lognormal turbulent atmosphere is given by... 

Probably the most common error occurs when specifying streams. You must specify total flow and the composition of each component. The default for composition is molar flows. If the sum of the component molar flows is not equal to the total flow. Aspen Plus still lets you run, but results are often fouled up. Best practice Always use mole or mass fractions. Another common error is to input the wrong numbers or with the wrong units (e.g., using a feed tenperature of 30K when you mean 30°C. Separation modules won t work with a feed this cold.)... 

ProbabUity of (bit) (symbol) error The average number of symbol errors over a long string (ideally infinite) of transmitted signals for any digital modulation scheme. If expressed in terms of the number of bits per symbol, the probability of bit error results. 

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