# Asynchronous CDMA Systems with Random Spreading-Part II: Design Criteria

## TL;DR

This paper explores the design of low-complexity linear multiuser detectors for asynchronous CDMA systems, analyzing their performance and effects of system parameters, with a focus on large-system limits and practical implementation considerations.

## Contribution

It introduces design criteria for multistage linear detectors in asynchronous CDMA, including recursive weight design and performance analysis in large systems.

## Key findings

- Performance of linear detectors is characterized in large-system limits.
- Oversampling improves discrete-time statistics and system performance.
- Design criteria enable low-complexity implementation with performance close to optimal.

## Abstract

Totally asynchronous code-division multiple-access (CDMA) systems are addressed. In Part I, the fundamental limits of asynchronous CDMA systems are analyzed in terms of spectral efficiency and SINR at the output of the optimum linear detector. The focus of Part II is the design of low-complexity implementations of linear multiuser detectors in systems with many users that admit a multistage representation, e.g. reduced rank multistage Wiener filters, polynomial expansion detectors, weighted linear parallel interference cancellers. The effects of excess bandwidth, chip-pulse shaping, and time delay distribution on CDMA with suboptimum linear receiver structures are investigated. Recursive expressions for universal weight design are given. The performance in terms of SINR is derived in the large-system limit and the performance improvement over synchronous systems is quantified. The considerations distinguish between two ways of forming discrete-time statistics: chip-matched filtering and oversampling.