Analysis of reduced complexity direct-sequence code-division multiple-access systems in doubly spread channels
Thaddeus B. Welch, R.E. Ziemer · 1997
There has been a great deal of recent interest in the use of direct-sequence spread spectrum (DSSS) in combination with multicarrier modulation (MCM). We investigate the performance of one such system transmitting through a Doppler and a doubly spread (Doppler and delay spread) channel. While a system employing a maximal ratio combiner (MRC) provides significant performance improvement, it is also the most complex. The equal gain combiner (EGC) system represents the easiest system to implement; however, it sacrifices performance. In a Doppler spread channel, all systems which do not account for the rapid variations in channel phase will exhibit an irreducible bit error probability (BEP). This phenomenon exists even for the single user case. Systems that employ an MRC or a co-phased equal gain combiner (co-phased EGC) will experience no such effect since they do account for the rapid variations in channel phase. Systems utilizing an MRC, co-phased EGC, or an EGC are analyzed for the single user case and in the presence of multiple access interference (MAI). The effect of an ideal, directional antenna on the spaced-time correlation function and the subsequent improvement in system performance is also analyzed. Finally, we compare selected analytical results with the results from several computer simulations. The computer simulations used M scATLAB M-files to determine the performance of a single user DSSS/MCM system using either a MRC, co-phased EGC, EGC, or average channel gain combiner (ACGC) in a Doppler spread channel. The DSSS/MCM single user system, with the ratio of the energy per bit to the noise power spectral density, $E\sb{b}/N\sb{o}\approx18.5$ dB, can achieve a BEP of $10\sp{-6}$ in a doubly spread channel (maximum Doppler shift - symbol period product, $f\sb{d}T=0.08,$ and a channel delay spread, $\tau\sb{o}=1\mu s),$ while a single carrier DPSK system operating at the same $E\sb{b}/N\sb{o}$ and under the same channel conditions would achieve a BEP of $\approx$0.037. The multi-user system with 50 active users would achieve a BEP of $\approx$0.008 as compared to a BEP of $\approx$0.07 for a single carrier DSSS system with 50 users.