equently to his results below. 2.2.1 Partial-Band Noise Jamming Suppose a Gaussian noise jammer chooses to restrict its total power J (ref- erenced to the FH receiver input) to a fraction p (0, p < 1) of the full SS bandwidth Wss. SS* As shown in Figure 2.6, the jamming noise power is spread Non-Coherent Frequency-Hopped Systems FH CARRIER JAMMED BAND W = p Wss Figure 2.6. Partial-band noise jamming of FH system: jammer concentrates power in fraction p E (0,1] of SS bandwidth, and hops noise band to prevent FH band avoid- ance countermeasure. uniformly over W1 = pWsss resulting in an increased power density (2.21) and a correspondingly degraded SNR level (2.22) in the jammed band, where N1 is still defined by (1.4). Recall that an FH system can in principle avoid certain frequency bands that it determines are particularly noisy. Consequently, we assume as in Figure 2.6 that the jammer hops the jammed band over Wss, slowly relative to the FH dwell time 1/Rh, but often enough to deny the FH system the opportunity to detect that it is being jammed in a specific portion of Wss and take remedial action. Also, to simplify the analysis, we will assume that shifts in the jammed band coincide with carrier hop transitions, SO that the chan- nel is stationary over each hop. Furthermore, we will assume that on a given hop, each M-ary band lies entirely inside or outside W. This last restriction is common to most analytical treatments of partial-band FH jamming and the dual case of pulsed DS jamming. (Since the FH carrier hops in and out of W1, partial-band jamming can be regarded as pulsed jamming with non- uniformly spaced pulses of duration 1/R under the simplifying assumptions made above.) The performance computed based on these assumptions is actually somewhat pessimistic, as Viterbi has noted [6, p. 14]: on a given M-ary symbol transmission, if only part of the M-ary band is jammed, and/or if it is only jammed over part of the symbol band, less noise is inter- cepted by the energy detectors, thereby reducing the probabi