tputs data vector dk at time kT followed by a modulator and an additive white Gaussian noise channel with intersymbol interference. The signal at the receiving radio is a((1) SOURCE DELAY SOURCE DELAY (x(()) SOURCE DELAY Figure 2.14. Equivalent synchronized radios. x(f) y(+) VECTOR INTERSYMBOL DEMODULATOR MODULATOR INTERFERENCE SOURCE Figure 2.15. Intersymbol interference channel model. Multiple Access given by y(t) = x(t) + n (t) (2.15) where n(t) is white Gaussian noise of single-sided spectral density No. Here we introduce receiver noise in the analysis. Now consider the optimum receiver or demodulator. Assume that the receiver has acquired and accurately synchronized estimates of the signal parameters {A1}, {T1}, and {01}. Thus the receiver has complete knowledge of the transmitted radio signals except for the data vector sequence {dk}. The goal of the receiver is to estimate this data vector sequence given the received radio signal {y(t), -00<t<< 00}. The optimum receiver will examine each data vector sequence such as {dk}, which has the corresponding signal (2.16) and determine its likelihood as a transmitted data vector sequence. It uses the maximum-likelihood (ML) criterion based on minimizing [103] (2.17) or maximizing (2.18) Thus, given the received radio signal {y(t),-oo<t<00}, the optimum ML receiver chooses the data vector sequence {₫k} that maximized (2.18). Note that (2.19) where (2.20) Spread-Spectrum Multiple Access with DS/BPSK Waveforms is the matched filter output sampled at time (k + 1)T 1 T1 for the filter matched to the 1-th pseudorandom DS/BPSK waveform. Thus the required (sufficient statistics) received radio signal components are the L matched filter output samples. The energy term (2.21) depends on the cross-correlation properties of the L pseudorandom wave- forms and the particular data vector sequence {dk} being examined (see Verdu [96]). This results in the overall decision rule based on (2.22) where some metric7 and (2.23) is the vector of sampled matched filter outputs. The metric 