 num- ber of chip time slots in the random time shift interval. Generally, this prob- ability is very small for DS/BPSK signals of interest. The multipoint-to-point SSMA system described here requires radio ter- minals to have more digital signal processing capability in order to simulta- neously receive from several radio transmitters. However, it requires the use of only one key or pseudorandom sequence in a time-varying matched fil- ter. Without collisions the bit error probability for each transmitted data sequence is the same as in the point-to-point system described in the previ- ous section. Here the interference is due to all other simultaneously trans- mitted radio signals, including those using the same key. 2.3.3 Optimum Multipoint-to-Point In this section we present the theoretically optimum multiple access receiver when L radios transmit simultaneously to one radio terminal. Assume each transmitting radio uses a different key for its DS/BPSK waveform and all L radios transmit uncoded data at a rate of one data bit every Tb seconds. As illustrated in Figure 2.3, the distributed multiple access channel has asyn- chronous spatially separate radios transmitting simultaneously to a single destination radio. It was first pointed out by Shnidman [91] that intersymbol interference and crosstalk between multiplexed signals are essentially identical phe- nomena. Kaye and George [92] have worked out this idea by investigat- ing the transmission of multiplexed signals over multiple channel and diversity systems. Savage [93] analyzed such systems using random coding bounds where signal addresses were randomized. Van Etten [94] and Schneider [95] began looking at optimal detector techniques. The optimal multiple access detector for the system presented here was studied by Verdu [96], [97] and is based on earlier work on optimal receivers for chan- nels with intersymbol interferance [98]-[104]. We follow the work of Verdu in this section. During the time interval [kTb, (k + 1)T] each of the L radios will begin tran