Asynchronous CDMA Systems with Random Spreading-Part I: Fundamental Limits

TL;DR

This paper analyzes the spectral efficiency of asynchronous CDMA systems with random spreading, revealing that asynchronism can improve performance by exploiting additional signal space dimensions, especially with non-Nyquist chip waveforms.

Contribution

It provides a comprehensive large-system analysis of spectral efficiency and SINRs for asynchronous CDMA with arbitrary chip waveforms, including the impact of user synchronization and the development of the effective interference concept.

Findings

Asynchronism can enhance spectral efficiency by utilizing extra signal space dimensions.

Synchronizing users on a chip level can impair performance for wideband chip waveforms.

The effective interference spectral density generalizes previous interference models.

Abstract

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.