smission of its k-th data bit using a DS/BPSK waveform. Since there is no time synchronization among the radios, assume the 1-th radio transmits Spread-Spectrum Multiple Access with DS/BPSK Waveforms a data bit sequence using a continuous sequence of pulses of the form Tb+T,st<(k+1)T+T1 k==...-1,0,1,2, (2.11) Here dk&{-1, 1} is the k-th data bit of the l-th radio. The pseudorandom sequence waveform is given by cit - t1) (see Chapter 1, Volume II). Parameters A, t and O, depend on the propagation conditions of the radio channel as well as the radio transmitter. Figure 2.12 shows a sketch of the k-th pulse sil;; dh) of the l-th radio that transmits the k-th data bit dR. This pulse occupies the time interval [kTb + t1, (k + 1)T + T1]. The actual transmission of this radio is a continuous sequence of such pulses. However, we focus here on the pulse related to the k-th data bit because we are interested in the sum of such pulses from all L radios. This is given by (2.12) which is sketched in Figure 2.13. Here define (2.13) as the k-th data vector consisting of the k-th bits from all L radios. Note that due to the arbitrary delays T1, T2, TL this waveform begins at kT 1 min{T} and ends at (k + 1)T 1 max{T}}, which is confined to the interval [kTb, (k + (k+1)Tb (k+2)Tb Figure 2.12. Single radio pulse. Multiple Access Xk(t;d) Figure 2.13. L radio pulses. The composite signal from all L radios consists of a continuous seuqence of pulses xk(t;dk), denoted x(1)= (2.14) Note that these pulses are spaced T seconds apart, whereas each pulse has length greater than T seconds but less than 2Tb seconds. Transmission of such overlapping pulses is commonly referred to as intersymbol interference. Based on the above discussion now model the set of L asynchronous radios of Figure 2.3 as a set of time synchronous radios followed by arbi- trary delays as shown in Figure 2.14. Mathematically the transmitted sig- nals are the same. Now, however, we have the final equivalent model of Figure 2.15 where we start with a vector source that ou