Counting solutions for the CDMA multiuser MAP demodulator

TL;DR

This paper analyzes the number of locally minimal solutions in CDMA multiuser MAP demodulation using spin glass theory, revealing how system parameters affect solution complexity and providing insights into computational difficulty.

Contribution

It introduces a novel application of spin glass methods to evaluate the solution landscape of CDMA MAP demodulation, highlighting the impact of system parameters on complexity.

Findings

Number of local minima increases with more users and noise.

Solution complexity exceeds SK model under certain conditions.

Distribution of energies for minima is characterized.

Abstract

We evaluate the average number of locally minimal solutions for maximum-{\it a-posteriori} (MAP) demodulation in code-division multiple-access (CDMA) systems. For this purpose, we use a sophisticated method to investigate the ground state properties for the Sherrington-Kirkpatrick-type (i.e. fully connected) spin glasses established by Tanaka and Edwards in 1980. We derive the number of locally minimal solutions as a function of several parameters which specify the CDMA multiuser MAP demodulator. We also calculate the distribution function of the normalized-energies for the locally minimum states. We find that for a small number of chip intervals (or equivalently a large number of users) and large noise level at the base station, the number of local minimum solutions becomes larger than that of the SK model. This provides us with useful information about the computational complexity of the MAP demodulator.