nsmitted m chip sequence of the l-th radio is (2.40) This is then sent as an MFSK chip sequence after frequency hopping. 13 After dehopping, the receiver hard quantizes each of the M chip energy detector outputs. That is, at the output of each of the M energy detectors a decision is made as to the presence or absence of a transmitted MFSK chip tone as follows: Any set of chip energy detector outputs (e1,e2, em) is hard quan- hopping schemes where several MFSK chips (tones) are transmitted during each hop, are not effective against partial-band or multitone jammers unless interleaving is also used to create independent channel statistics for each chip. 12 Although there may be many radios, each radio may be transmitting only a small fraction of the time. Superscript(1)For commercial applications frequency hopping may not be used. Spread-Spectrum Multiple Access with FH/MFSK Waveforms tized to (n1, N2, where (2.41) for some decision threshold 8. Naturally, with noise and multipath a deci- sion of a tone being present at a frequency may be made when none has been transmitted (false alarm) as well as a decision of no tone being present when in fact a chip tone was transmitted at the frequency (miss). Each chip time there are M hard quantized bits. The receiver examines the sequence of m such outputs to make decisions as to which symbols were transmitted. The decision rule for the receiver is to choose the data symbol associated with an address pattern as given by (2.40) which has the greatest number of entries or detected tones. For example, suppose m = 5 and the address sequence for the l-th radio is 0,1,2,3,4 (2.42) with M = 8 as the number of possible tones. If X = 6 is the 8-ary data sym- bol, then the transmitted sequence is (see (2.40)) 6,7,0,1,2. (2.43) Suppose the sequence of 5 chip energy detector hard quantized outputs is given by the array The only possible sequences the l-th radio could transmit are Symbol Sequence 0, 1, 2, 3,4 4 1, 2, 3, 4, 5 2, 3, 4, 5, 6 3, 4, 5, 6, 7 4, 5, 6, 7, 0 (2.44) 5, 6, 7, 0,1 