SPECIAL REPORT: ELECTRONIC COUNTERMEASURES
generation. Instead, the survival threshold could be dynamically chosen in step 3 according to the distribution of scores in the not-yet-culled population; this way, the survival threshold could be set – at least temporarily – to cause a certain minimum percentage of the population to survive. The effect of this adaptation is to sidestep “population extinction” by temporarily relaxing the fitness criteria, which also sidesteps the computational overhead of a complete genetic algorithm reboot if all the candidate solutions happen to disappear. Remember, design of a genetic algorithm is like a cake recipe, so it’s part art and part science.
Solution Disambiguation Here’s the next layer of onion skin: if the ECM transmits at a single frequency, the solution(s) only have to match the measured power at a single frequency. This can, and does, lead to solution ambiguity – that’s where multiple combinations of the four parameters produce the same observed power. An example of solution ambiguity is shown in figure 5; it’s an overlay of predicted power vs. range for 100 candidate solutions (reminder: one candidate solution is a single value for ECM antenna height, a single value for sensor antenna height, a single value for ECM-sensor range, and a single value for ECM antenna relative gain). The solutions each produce the same observed power at the measurement range, but different, diverging answers elsewhere; the degree of divergence is a measure of the diversity of the solutions – how different they are from each other. For readers paying very close attention: the range axes of all data sets in figure 5 have been aligned so the predicted sensor range – not the predicted power – occurs at 62.2 m; the common power crossover point, visually striking in the graphs, is a genuine property of the population of solutions. The alignment has been done for visual clarity. So how can we tell which solution set is right? The question is more slippery even than it sounds – ambiguity is more tolerable in some variables than others, since the overall objective is not to determine the parameters, but ultimately to estimate the variability of ECM toggle ranges. An analysis of the effect of parameter ambiguity on toggle range variability is relatively straightforward, but beyond the scope of this paper. Instead, let’s have a brief discussion about how to get rid of solutions that don’t make sense. I’ll call this solution disambiguation. One way to disambiguate the solutions is to perform the same analysis at a second frequency. And a third, and fourth, etc. The more frequencies
you use, the more the group of candidate solution sets become constrained, because the acceptable solutions must match the measured power at each frequency. There are a lot of different ways of understanding how pilot signals can be used to characterize the local propagation environment, but they all boil down to this: because the signals at different frequencies all travel through the same physical path between the ECM antenna and sensor (PRE device), and because “different frequency” means “different wavelength”, each frequency will appear at the PRE device a different power level. The pattern of power levels is like a fingerprint of the local propagation environment. Of course you never get something for nothing; there is a relationship between the number of pilot signals, their frequency distribution, and the precision with which the four values comprising a single solution (two heights, range and antenna gain) can be determined. However, the objective is to use pilot signals and genetic algorithms to get just enough information about the environment to give “sufficient” precision when calculating the answer we need: the distribution of ECM toggle ranges. An example of disambiguation by frequency diversity is shown in figure 6, where three frequencies are used. Note that in this example, disambiguation isn’t perfect – the power vs. range curves are clustered more closely than before, but they still diverge as one moves away from the power crossover point. This divergence is caused by “smearing” of the estimated parameters values. There are several other methods of disambiguation, besides frequency diversity. One way is to use two or more antennas that are separated in elevation by a known distance; this approach is more hardware-complex, but it also solves some other problems and provides some other valuable information. Another method is uses range diversity, and another is based on temporal diversity (although that one is trickier). Some disambiguation can be done phenomenologically, for example by considering the time history of all solutions in the context of known properties of short range propagation. In some cases, disambiguation may not be immediately possible, but may become possible as the engagement progresses and with the introduction of new information, possibly from a secondary or tertiary source. In these cases, it may be advisable to carry forward multiple hypotheses about the solution until all but one (or a practically indistinguishable few) can be ruled inadmissible. As an example, consider the case where everything is known except the height of the receive antenna. A single power measurement will, in general, cause the genetic algorithms
Some frequency choices provide more information than others about the local propagation environment.
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