DS-SS code acquisition in a rapid fading environment

In CDMA mobile communication systems, a frequency-spread pilot signal often plays an important role, e.g., for synchronization and for channel impulse response measurement; therefore it usually is given a quite large process gain. However, in a fast fading environment, the received pilot signal level may decrease making synchronization performance deteriorate substantially. In the analysis, modeling the temporal fading function as a lowpass-filtered complex Gaussian process, it is shown that the probability density function (pdf) of the despread signal level follows a Rayleigh distribution whose variance is given by a summation of the discrete-time sampled values of the impulse response of the lowpass filter. The pdf then is used to obtain the mean acquisition time. It is shown that there is no advantage in using a long code when the Doppler frequency is high. The optimum code length is determined as a function of the maximum Doppler frequency. Furthermore, a rapid PN code acquisition scheme expected to be robust under fast fading conditions is proposed. The scheme is based on partial code correlation and a majority decision rule. Partial code correlation is less influenced than full code correlation by a rapid fading and the majority decision rule reduces the misdetection and false alarm probabilities. The optimum parameter values for the proposed scheme are also determined. For a large process gain signal, the partial code length should be optimized for the maximum Doppler frequency.