f3) (0101) (f3,f1) (f2,f2) (f2,f3) (0011) (f3,f2) (fo,f3) (1001) (f3,fo) (f3,f3) (0001) Figure 2.34. Channel for optimum decoder (M = 4, L = 2). The overall system, however, is almost the same as that described by Goodman et al. [117] and discussed in the previous section. The major dif- ference here is that all transmitted signals are decoded simultaneously by regarding all L transmitting radios as a single composite multiple frequency tone transmitting radio. The L separate data sources are viewed as a single L dimensional vector source and the optimum receiver compares all possi- ble sequences of these vector data symbols with the channel output sequence. In this case it looks for the vector sequence of greatest agreement with the channel output sequence. This section examined only the special case where the chip energy detec- tor outputs were quantized to one bit. Generalization to multiple level quan- tization is possible but will require AGC, which is difficult to maintain in a jamming environment. List detectors with various metrics have been stud- ied by Vo [148] for these multiple access systems. In the list detector, side information regarding the L transmitting radio's signal tone energies at the receiving radio can be incorporated in the decision process. The optimum decoder again treats all L data sources as a single L dimensional vector Multiple Access source and compares all possible transmitted vector data sequences with the total channel output sequence. The metric used for making this comparison depends on the kind of detectors used and the available side information. As an example, consider L = 8 identical multiple access transmitters where there are M = 32 orthogonal tone frequencies available. Pure FDMA is achieved when each user is given two tones where we have L = 8 non- overlapping BFSK signals. Assuming the use of coding, Vo [148] has shown that the overall throughput is higher than FDMA when all L = 8 users use all 32 tones (32-FSK) with list detectors and maximum-likelihood metrics. Thi