A unified method for approximating and bounding the average bit error probability for spread-spectrum multiple-access communication systems is presented. Various forms of direct-sequence spreadspectrum modulation are considered including binary phase-shift keying, quadriphase-shift keying, and minimum-shift keying. The analysis of the multiple-access interference makes use of a number of moments sufficent to evaluate the error probability with a high degree of accuracy. A computationally efficient algorithm for computing the moments is also given. The subsequent transformation from the moments to the average bit error probability is carried out by means of Gauss-type numerical integration formulas. It is shown that the same approach can be exploited for evaluating two classes of upper and lower bounds on the bit error rate. Finally, some results and comparisons are reported.

Recently, multiplication-free digital filters have been proposed for different applications to digital radio systems and signal processing. The absence of multiplication is obtained by constraining each coefficient to be sum of powers of two. In this way, multipliers are substituted by shift registers and, if appropriate, some adders. The optimal power-of-two coefficients must be computed through a nonlinear optimization procedure. Until now the problem of adapting the power-of-two coefficients of base band transversal equalizers in the case of time-varying channels had not been considered. In this paper two algorithms are proposed to cope with this problem and are compared from the viewpoint of complexity, accuracy, and convergence speed. As an application example, transmission of a biphase PSK digital radio system over a multipath fading channel is considered.