Asymptotic design and analysis of multistage detectors for asynchronous CDMA systems

In random symbol asynchronous but chip synchronous CDMA systems, the linear MMSE detector suffers from performance degradation compared to its version in synchronous scenarios due to the nite observation window. The performance degradation is known only for a symbol centered in an observation window of length equal to the symbol interval. We propose an algorithm to determine the asymptotic performance of the LMMSE detector for any nite observation window and for any symbol impinging the observed signal. Additionally, a multistage detector that does not suffer from windowing effects and performs as well as the correspondent detector in synchronous systems is presented. In contrast to the synchronous case, in which the full rank LMMSE detector always outperforms the reduced rank linear MMSE detector, we show that, with a sufcient large delay, the proposed multistage detector can even outperform the full rank linear MMSE detector with nite xed observation window. The output signalto- interference and noise ratio (SINR) of the reduced rank detector is shown to be constant for all the symbols.