The probability of intercept for single bursts of an FH transmitter will be examined first. The considerations are also valid for the detection of any single burst, ie of any signal with the length Th that occurs only once within an extended observation period Tt .
3.1 Probabiltiy of intercept during single trial As can be seen from FIG 5, the transmitter may use any of the MFH channels, and the receiver be in any of the MSc channels, so MFH x MSc combinations are possible. It is possible for both to meet in one of the Mg common channels. If the number Mg of a possible coincidence between the transmitter and receiver is related to the number of possible combinations, the probability of intercept for a single burst in a single trial is [3]:
P 1 = MG / MFH x MSc (2)
The following applies to multichannel receivers. If K parallel filters with associated detectors are implemented in the receiver at channel spacing at each frequency position, the probability of hitting the burst in one of the Kchannels increases by the factor K compared with (2):
P 1 = Mg K / MFH x MSc (3)
This applies when the number of parallel receiver channels is less than the number of common hopper and receiver channels (K < Mg ). In the case of K ³ Mg , K should be replaced by Mg in equation (3).
In the following cases, the use of a multichannel receiver is generally assumed. The relationships for a single-channel receiver are then obtained with K = 1.
The following special cases should be mentioned: 1. The frequency range of the hopper is greater than that of the receiver and covers the latter completely (MFH > MSc ) (FIG 5b). With Mg = MSc the following is obtained from (3) for a multichannel receiver:
P 1 = K / MFH (4)
FIG 6 Search sequence of receiver and hop duration Th (burst)
and for a single-channel receiver:
P 1 = 1 / MFH (5)
The probability of intercept for a single burst in a single trial is independent of the total number of receiver channels MSc when the ranges overlap as shown in FIG 5b.
2. The frequency range of the receiver is greater than that of the hopper and covers the latter completely (MSc > MFH ) (FIG 5c). With Mg = MSc the following is obtained from equation (3):
P 1 =K / MSc (6)
The possibility of performing irrelevant measurements outside the transmitter frequency range entails reduced probability of intercept for a single burst in a single trial as against (4) at a constant value of MFH .
