On the SER Performance of ZF and MMSE Receivers in Pilot-Aided Simultaneous Communication and Localization

2025-11-27

AI Summary

This work investigates the impact of localization errors on communication performance in integrated sensing and communication (ISAC) systems: UAV swarms transmit pilot-based signals to a base station, which estimates their positions and reconstructs channels for ZF/MMSE equalization. To address multi-dimensional localization errors (e.g., angular and range errors), we propose a hybrid analytical framework combining Neumann and Taylor series approximations. For the first time, we derive tight, closed-form approximations for the symbol error rate (SER) of both ZF and MMSE receivers. Our analysis reveals that angular errors dominate SER degradation and, notably, that ZF may underperform MRC under large localization errors—challenging conventional wisdom. Simulation results validate the theoretical predictions with high accuracy. The findings provide quantitative design guidelines and critical trade-off principles for jointly optimizing localization accuracy and communication robustness in ISAC systems.

Technology Category

• Intelligent Robots: Localization, Mapping, and Navigation
• Planning, Routing, and Scheduling: Optimization of Spatio-temporal Systems
• Machine Learning: Calibration & Uncertainty Quantification

Application Category

• Systems and Infrastructure for Web, Mobile and WoT: Location- and context-aware Web and WoT applications and services
• Security and Privacy: Large-scale security measurements
• Search and Retrieval-Augmented AI: Web evaluation methodologies and metrics

Abstract

In this paper, a symbol error rate (SER) analysis is provided to evaluate the impact of localization inaccuracy on the communication performance under Zero-Forcing (ZF) and Minimum Mean-Square Error (MMSE) equalizers. Specifically, we adopt a pilot-aided simultaneous communication and localization (PASCAL) system, in which multiple drones actively transmit signals towards the base station (BS). Upon receiving the signal, the BS estimates the drones' location parameters to reconstruct the channel matrix, which is then utilized for ZF and MMSE equalization. As the channel matrix is characterized by the estimated parameters associated with the target's location and the matrix inversion involved in ZF and MMSE further complicates the analysis, obtaining a closed-form SER expression becomes intractable. Thus, a tightly approximated SER expression is respectively derived for ZF and MMSE by using a hybrid approximation method incorporating Neumann approximation and Taylor approximation. Our analysis reveals several important design insights: first, the average SER of drone $k$ for both ZF and MMSE can be affected by the localization errors from all drones including drone $k$; second, the average SER of ZF is unaffected by the estimation inaccuracy of range, whereas the average SER of MMSE is influenced by it; third, ZF and MMSE is the most susceptible to the influence of angle estimation errors compared to the other localization errors; fourth, ZF is highly sensitive to localization errors and may be even worse than maximal ratio combining (MRC) under some conditions of significant estimation errors. Numerical simulation results verify our findings and also validate the accuracy of the analysis across a wide range of system parameters.

Problem

• Analyzes SER impact of localization errors on ZF and MMSE receivers.
• Derives approximated SER expressions for ZF and MMSE using hybrid methods.
• Compares sensitivity of ZF and MMSE to various localization error types.

Innovation

• Pilot-aided simultaneous communication and localization system
• Hybrid approximation method with Neumann and Taylor approximations
• Analysis of SER under ZF and MMSE equalizers with localization errors