f one or more tones. 10 This can vary from chip to chip and is assumed to be measured at the chip energy detectors and provided along with the ordered list of L* largest energy detector out- puts. This side information changes the probabilities {qk} to conditional probabilities which can change from chip to chip. The corresponding max- imum-likelihood metric is referred to as the "collision compensation" metric. It is the same as (2.29) with {qk} replaced by conditional probabil- ities where the condition is on the number of the M chip frequencies with some signal input. Under these assumptions Creighton [116] first examined the bit error probability with diversity alone, which is given by the bound (2.35) where D is given by (2.27) and the energy per chip is related to the energy 10 This is equivalent to knowing how many chip energy detectors had no input tones. Spread-Spectrum Multiple Access with FH/MFSK Waveforms Table 2.1 Maximum number of users-PG = 30 dB. List-of-L* without List-of-L* with Metric Collision Compensation Collision Compensation per bit by mEc = (log,M)Eb. (2.36) Here the energy-per-bit-to-equivalent-noi ratio is (2.37) Tables 2.1 and 2.2 summarize the number of allowable simultaneously trans- mitting radio signals under these conditions. Here L* = 1 corresponds to the hard decision M-ary channel. The fading cases are assumed to be Rayleigh fading, which is independent from chip to chip. As stated throughout this book, when channel interference is unpre- dictable, as with jamming waveforms, optimum detectors and decoding met- rics are not known. The detectors and metrics given here require different amounts of side information regarding the channel. In theory, we could have a perfect system with perfect side information. For example, suppose the receiver knew exactly the intended signal's power level. Then it could dis- tinguish it from all other signals since in practice no two signals will have the same power level at the receiver. Generally, there is a tradeoff between performance, complexi