  Spectral efficiency for asynchronous code division multiple access (CDMA)
with random spreading is calculated in the large system limit allowing for
arbitrary chip waveforms and frequency-flat fading. Signal to interference and
noise ratios (SINRs) for suboptimal receivers, such as the linear minimum mean
square error (MMSE) 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. For example, with the pulse shaping demanded in the UMTS standard,
user synchronization reduces spectral efficiency up to 12% at 10 dB normalized
signal-to-noise ratio. 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 the effective interference spectral density 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 and guidelines for the design of low
complexity multistage detectors with universal weights are provided.
