On Optimum Asymptotic Multiuser Efficiency of Randomly Spread CDMA

TL;DR

This paper analyzes the asymptotic multiuser efficiency of randomly spread CDMA systems with BPSK input, considering Gaussian and binary antipodal spreading, and explores conditions under which the system approaches single-user performance at high SNR.

Contribution

It extends previous results by deriving the asymptotic multiuser efficiency for large systems with logarithmic loading factor and connects detection matrices to the coin weighing problem.

Findings

Optimal efficiency approaches single-user performance at high SNR for certain loadings.

Derived lower bounds for binary antipodal spreading efficiency.

Established conditions for random matrices to be detecting matrices in large systems.

Abstract

We extend the result by Tse and Verd\'{u} on the optimum asymptotic multiuser efficiency of randomly spread CDMA with Binary Phase Shift Keying (BPSK) input. Random Gaussian and random binary antipodal spreading are considered. We obtain the optimum asymptotic multiuser efficiency of a $K$-user system with spreading gain $N$ when $K$ and $N\rightarrow\infty$ and the loading factor, $\frac{K}{N}$, grows logarithmically with $K$ under some conditions. It is shown that the optimum detector in a Gaussian randomly spread CDMA system has a performance close to the single user system at high Signal to Noise Ratio (SNR) when $K$ and $N\rightarrow\infty$ and the loading factor, $\frac{K}{N}$, is kept less than $\frac{\log_3K}{2}$. Random binary antipodal matrices are also studied and a lower bound for the optimum asymptotic multiuser efficiency is obtained. Furthermore, we investigate the connection between detecting matrices in the coin weighing problem and optimum asymptotic multiuser efficiency. We obtain a condition such that for any binary input, an $N\times K$ random matrix whose entries are chosen randomly from a finite set, is a detecting matrix as $K$ and $N\rightarrow \infty$.