Asynchronous CDMA systems with random spreading—Part I: Fundamental limits

Spectral efficiency for asynchronous code division multiple access (CDMA) with random spreading is calculated in the large system limit. We allow for arbitrary chip waveforms and frequency-flat fading. Signal to interference and noise ratios (SINRs) for suboptimal receiver structures, such as the linear minimum mean square error (MMSE) detector and various linear multistage detectors are derived. The approach is general and optionally allows even for statistics obtained by under-sampling the received signal. All performance measures are given as a function of the chip waveform and the delay distribution of the users in the large system limit. It turns out that synchronizing users on a chip level impairs performance for all chip waveforms with bandwidth greater than the Nyquist bandwidth, e.g. positive roll-off factors. The benefits of asynchronism stem from the finding that the excess bandwidth of chip waveforms actually spans additional dimensions in signal space, if the users are de-synchronized on the chip-level. The analysis of linear MMSE detectors shows that the limiting interference effects can be decoupled both in the user domain and in the frequency domain such that the concept of spectrum of the effective interference arises. This generalizes and refines Tse and Hanly’s concept of effective interference. In Part II, the analysis is extended to any linear detector that admits a representation as multistage detector an