1.3 PERFORMANCE AND STRATEGIES ASSESSMENT
1.3.1 Communicator Modulation and Intercept Detectors
Section 1.2 contained a very detailed examination of intercept detector types from both practical (or attainable) performance (as measured by the S/N0 required) and implementation (assessed by functional and circuit complex- ity) perspectives. Using a fixed set of system parameters, the relative merits of four well-known detectors (optimum multichannel, full-band filter bank combiner (FB-FBC), partial-band filter bank combiner, wideband energy or
fˆ
max
radiometer) were compared, and it was observed that only the minimum channel partial-band filter bank combiner (PB-FBC) and the wideband energy detector have utility. Further, the minimum channel PB-FBC would be employed only when its S/N0performance advantage over the wideband radiometer justifies its complexity as reflected by the cost of mechanizing the number of channels needed.
To further strengthen these earlier conclusions, the performance of these same detectors will now be calculated for several different hop rates and in addition PN spreading of the hop pulses. The results are tabulated in Table 1.5. To repeat an earlier observation, in comparing the S/N0requirements of various intercept detectors, relative to, say, that of the wideband energy detector as a reference, it is not necessary to specify the SS bandwidth Wss, the message duration TM, or the hop rate Rh⫽1/Th. Rather, the product of WssandTM, the total number of hops NTinWss, and, if a partial-band con- figuration, the fractional number of channels fused in the implementation are all that are needed to perform the calculations. If PN spreading is used in hybrid with the assumed FH modulation, then one must, in addition, spec- ify the ratio of PN code chip rate Rcto the hop rate. In Table 1.5 the PN code chip rate is held constant as the hop rate is varied over two decades (the effects of varying the chip rate will be discussed toward the end of this sec- tion). Thus, the ratio Rc/Rhalso varies over two decades.
The central column in Table 1.5 repeats the numbers tabulated in Table 1.3 for FH modulation, with the modification that the time and frequency asynchronous losses derived in Sections 1.2.2.1 and 1.2.2.2, respectively, have been added. All other entries also include losses for lack of time and fre- quency synchronization. A double crosshatched line has been placed to sep- arate the practical versus impractical detector realizations as measured by the number of channels required. As can be seen, only two entries represent a potential gain over the wideband energy detector; these are further reviewed in the following paragraphs.
For Rhsuch that NT⫽106, a 125-channel PB-FBC is capable of achieving a lower S/N0threshold than a wideband energy radiometer of a mere 0.5 dB.
Considering the complexity of a 125-channel PB-FBC relative to that of the one-channel wideband detector, the gain is clearly not worth the cost. Thus, the interceptor will opt to use the wideband radiometer.
There is another pure-FH entry in Table 1.5 that warrants some view, namely, the minimum channel PB-FBC requiring 12,500 channels with Rh chosen to give NT⫽107. The 10.2 dB performance advantage over the wide- band energy detector is very significant, and some form of implementation is therefore tempting. Postulating that mechanization of 12,500 channels is out of the question, even for a 10.2 dB S/N0advantage, it may be logically asked: Is there some implementable realization that can attain some of the gain?
Since it is mandatory that 12,500 channels be equivalently manifest, the only choice is to construct a PB-FBC with fewer real channels, say, by a fac-
Table 1.5 A comparison detector performance as a function of hop rate and FH versus FH/PN (WssTM⫽8⫻109). Rc/Rh1⫽1000Rc/Rh2⫽100Rc/Rh3⫽10 Detector TypeRh1(NT⫽107)Rh2(NT⫽106)Rh3(NT⫽105) No.of⌬S/N0No.of⌬S/N0No.of⌬S/N0 Channels(dB)Channels(dB)Channels(dB) OptimumFH107⫺17.5106⫺9.1105⫺1.9 MultichannelFH/PH104⫺7.3104⫺3.7104⫹0.2 FB-FBCFH107⫺11.6106⫺5.9105⫹3.3 FH/PN104⫺5.0104⫹0.1104⫹5.3 Minimum ChannelFH12,500⫺10.2125⫺0.52⫹9.0 PB-FBC (f⫽1.25⫻10⫺3)FH/PN13⫺2.12⫹3.71⫹10.4 Wideband EnergyFH101010 FH/PN (Includes Average Time and Frequency Asynchronous Losses)
tor of 1/K, and further reduce the integration time in each channel by the same factor so that the 12,500/Kchannels may be “hopped” to different (unique) sub-band locations Ktimes per hop pulse inteval. Table 1.6 sum- marizes the results of such a strategy. As can be seen, a reduction of the num- ber of channels by a factor of 10 (to 1250 channels) decreases the gain from 10.2 dB to 2.4 dB, while another factor of 10 decrease (to 125 channels) causes worse performance than the wideband energy detector by 6.1 dB.
Thus, the attempt is in vain. there is just no way the minimum channel requirement can be ignored. This being the case, the communicator need never fear that the PB-FBC will ever be used by the interceptor as long as the required number of minimum channels is forced (by design) at low hop rates to be above some threshold (say, greater than 100) for which the cost per dB of advantage is u ntenable.
Turning now to the FH/PN performance entry in Table 1.5 for the mini- mum channel PB-FBC at Rhcorresponding to NT⫽107, the 2.1 dB advan- tage over the wideband radiometer requires only 13 channels. This therefore represents a situation where the interceptor might indeed justify the PB- FBC. A good strategy for the communicator should be to avoid designing an FH/PN system with the subject parameters. If such a low hop rate is deemed necessary, the communicator should avoid PN spreading, at least at such a high chip rate. Table 1.7 shows the level of PB-FBC performance which may be expected if a lower chip rate is employed with the above hop rate. Again it can be seen that the tradeoff is a better intercept S/N0require- ment, but at the expense of a significantly increased number of minimum channels. Thus, although the interceptor might opt to build a 13-channel detector when the PN chip rate is 1000 times the hop rate, he will likely refrain from a 125-channel unit when the chip rate is 100 times the hop rate, in favor of some more economical approach.
Having now reviewed a rather wide range of FH and FH/PN parameters, it appears reasonable to conclude that:
1. For any of the pure FH cases, the interceptor will be forced to the wide- band energy detector.
2. PN spreading to the FH pulses is not essential to the prevention of chan- nelized detector usage, nor does it directly add to the state of LPI.
Table 1.6
Hopped-channel PB-FBC performance.
Detector 1/K No. of Channels ⌬S/N0(dB)
PB-FBC 1 12,500 ⫺10.2
PB-FBC 0.1 1,250 ⫺2.4
PB-FBC 0.01 125 ⫹6.1
Wideband Energy 1 1 0
Restating, then, the basic strategy that should be employed by the commu- nicator:
1. He should choose FH or FH/PN parameters so that any channelized detector requires larger S/N0than that for the wideband radiometer, or 2. He should choose FH or FH/PN parameters so that, if any channelized detector requires lower S/N0than that for the wideband radiometer, it is uneconomical to build because of the large minimum number of chan- nels needed.
No channelized detector can be expected to be used against pure FH pro- vided that the hop cell bandwidth is set equal to the hop rate and all possi- ble hop frequencies are employed (i.e., can be synthesized).