 it requires that the jammer inter- cept the FH signal, detect the frequency of the M-ary band, and synthesize an appropriate narrowband signal, all within each hop dwell time. 2.1 BROADBAND NOISE JAMMING Consider a non-coherent FH/MFSK communication link with received power S transmitting data at a bit rate R: the received energy per bit is Eb=S/Rb. (2.3) Suppose this signal is jammed by Gaussian noise with received power J and an approximately rectangular spectrum which coincides with the FH band- width WSS. This is equivalent to an AWGN channel, with an effective noise power spectral density N = J/W ss (2.4) The SS system can therefore be characterized by the SNR Eb/NJ (S/J)(Wss/Rb). (2.5) Identifying PG = WSSIR SIJ as the signal-to-jamming power ratio prior to despreading, and Eb/N, as the despread SNR in the information bandwidth, we see that this particular example agrees with Dixon's definition of PG as the ratio of the despread-to-spread SNR's. Non-Coherent Frequency-Hopped Systems We will initially restrict our attention to uncoded SFH systems with an alphabet of M = 2K orthogonal signals, each containing K bits of informa- tion. The chip, M-ary symbol, bit, and hop rates satisfy (2.6) The received symbol energy is then (2.7) Without loss of generality, assume that symbol 1 is sent on a given data transmission. Referring to the block diagram of Figure 2.1, the output e1 of the first energy detector, normalized for convenience by 1/N , is a non-cen- tral chi-square random variable with 2 degrees of freedom, whose probability density function is given by (2.8) where Io() is the zeroeth-order modified Bessel function of the first kind. Since the symbols are separated in frequency by the symbol rate Rs, the other M - 1 energy detectors contain no signal components. Their outputs are identically distributed central chi-square random variables with 2 degrees of freedom: (2.9) Because the M signals are orthogonal, the e;'s are all statistically indepen- dent. The system performance in this example is the same a