r each data bit d this code is to simply transmit m bits (3.48) where aj=d;i1,2,...,m. Coded Direct-Sequence Spread Binary Phase-Shift-Keying Thus, each coded bit a is transmitted within Ts = Tblm seconds. As we noted above, as long as m < N, the bandwidth of the direct sequence spread sig- nal is unchanged by the use of this code. The coded DS/BPSK system is sketched in Figure 3.11. Data bit d is encoded into a sequence of m coded bits each identical to d in value. The coded bits are scrambled in time by the interleaver and then BPSK mod- ulated and direct sequence spread by the PN sequence c(t). The transmit- ted DS/BPSK signal is given by (3.24) where s(t) is the ordinary coded BPSK signal. The channel output is again y(t) of (3.28) which after multi- Figure 3.9. Coded and uncoded signals before spreading. Basic Concepts and System Models c(1) ((1) c(f)(((()) Figure 3.10. Coded and uncoded signals after spreading. REPEAT m x (f) INTERLEAVER MODULATOR Ts=To/m TRANSMITTER GENERATOR y (f) DECODER DEINTERLEAVER (.)dt RECEIVER CHANNEL GENERATOR Figure 3.11. Repeat coded DS/BPSK system. Basic Concepts and System Models plication by c(t) becomes r(t) of (3.29). The detector for this signal con- sists of a correlator or matched filter with outputs, after deinterleaving, given by i=1,2,...,m (3.49) where N1,N2, ,Nm are independent zero-mean Gaussian random variables with variance N3(2p). Here again, p is the fraction of time the pulse jammer is on and Z indicates the jammer state where z,={b jammer on during a; transmission (3.50) jammer off during a transmission Pr{Z;=1}=p Pr{Z = 0} = 1 - p. (3.51) 3.5.1 Interleaver and Deinterleaver The purpose of the interleaver and deinterleaver is to scramble the time sequence of the coded symbols before transmission and unscramble the received signals after transmission SO that the impact of the pulse jammer is independent in each of the coded symbols. For ideal interleaving and dein- terleaving this results in Z, Z2, Z3, , Zm becoming independent random variables. In Appendix 3A